Calculation of the relative metastabilities of proteins in subcellular compartments of Saccharomyces cerevisiae
CCalculation of the relative metastabilities of proteins in subcellularcompartments of
Saccharomyces cerevisiae
Jeffrey M. Dick
Department of Earth and Planetary ScienceUniversity of CaliforniaBerkeley, CA 94720
Background : The distribution of chemical species in an open system at metastable equilibrium can be expressedas a function of environmental variables which can include temperature, oxidation-reduction potential and others.Calculations of metastable equilibrium for various model systems were used to characterize chemical transformationsamong proteins and groups of proteins found in different compartments of yeast cells.
Results : With increasing oxygen fugacity, the relative metastability fields of model proteins (including iso-forms of glutaredoxin and thioredoxin, and compartmental proteomes) for major subcellular compartments go asmitochondrion, endoplasmic reticulum, cytoplasm, nucleus. Compared with experimental determination of redoxpotential (Eh) in these compartments, the order of the endoplasmic reticulum and nucleus is swapped. In ametastable equilibrium setting at relatively high oxygen fugacity, proteins making up actin are predominant, butthose constituting the microtubule occur with a low chemical activity. Nevertheless, interactions of the micro-tubule with other subcellular compartments are essential in cell development. A reaction sequence involving themicrotubule and spindle pole proteins was predicted by combining the known intercompartmental interactionswith a hypothetical program of oxygen fugacity changes in the local environment. In further calculations, themost-abundant proteins within compartments generally occur in relative abundances that only weakly correspondto a metastable equilibrium distribution. However, physiological populations of proteins that form complexes oftenshow an overall positive or negative correlation with the relative abundances of proteins in metastable assemblages.
Conclusions : This study explored the outlines of a thermodynamic description of chemical transformationsamong interacting proteins in yeast cells. Full correspondence of the model with biochemical and proteomicobservations was not apparent, but the results suggest that these methods can be used to measure the degree ofdeparture of a natural biochemical process or population from a local minimum in Gibbs energy.
Author Summary
Part of a cell’s expenditure of metabolic fuel is directed toward the formation of proteins, including their synthesisand transport to other compartments. Even when it is normalized to the lengths of the proteins, the energyrequired for protein formation is not a constant, but depends on the composition and environment of the protein.If these energy differences are quantified, the relative abundances of model proteins in metastable equilibrium canbe calculated. The compositions of these metastable assemblages depend on local environmental variables such asoxygen fugacity, which is a scale for oxidation-reduction potential in a system. I calculate the oxygen fugacities forequal chemical activities of model proteins in intercompartmental interactions and use the results to obtain modelvalues of oxygen fugacity for subcellular compartments. I show that a environmental gradient of oxygen fugacitycan potentially drive the formation of proteins in a sequential order determined by their chemical compositionsand Gibbs energies. I also show that the relative abundances of proteins within compartments and of those thatform complexes have a dynamic range that can be approximated in some metastable equilibrium assemblages.These results provide theoretical constraints on the natural emergence of spatial and temporal patterns in thedistributions of proteins and imply that work done by maintaining oxidation-reduction gradients can selectivelyalter the degree of formation of proteins and complexes.1 a r X i v : . [ q - b i o . S C ] D ec ntroduction Subcellular compartmentation is a basic feature of eukaryotic life [1, 2, 3, 4]. There exist in eukaryotic cells gradientsbetween subcellular compartments of chemical properties such as pH [5, 6, 7, 8], oxidation-reduction or redox state[9, 10, 11, 12] and chemical activity of water [13, 14, 15, 16]. Furthermore, the proteins required by yeast andother organisms are unevenly localized throughout cells [17, 18, 19, 20, 21, 22, 23]. Even within compartments oramong the proteins that interact to form complexes, the relative abundances or levels of different proteins are notequal [24, 25, 26], and different proteins predominate in the various subcellular populations depending on growthstate of the cell [27, 28], and exposure to environmental stress [29, 30, 31, 32].Much attention has been given to the use of thermodynamics in describing and understanding driving forces inbiological evolution. Energy minimization imparts a direction for spontaneous change of a system, and response of asystem in this direction can at times be tied to an increase in relative fitness [33, 34, 35, 36, 37]. A biological systemthat moves away from minimum energy does not break the laws of thermodynamics but couples its endergonicreactions with the exchange of matter and energy in its surroundings [38, 39, 40, 41]. The thermodynamiccharacteristics of open systems are thus of particular interest to biological evolution [42, 43, 44]; in particular,the interactions of organisms with their environments are important influences on the stable compositions anddistributions of genes or organisms [45, 46, 47, 48].Why are proteins not equally distributed inside cells? Physical separation of key enzymes is thought to beessential in the cytoskeletal network and in regulation of metabolic pathways and other cellular functions [49, 50,51]. The patterns of subcellular structure persist even though populations of proteins turnover through continualdegradation and synthesis in cells [52, 53, 54, 55], and despite the endergonic, or energy-consuming, qualities ofprotein biogenesis [56, 57]. It can be shown that the relative abundances of amino acids in proteins correlateinversely with the metabolic cost of synthesis of the amino acid [58, 59], which is a temperature-dependentfunction [60]. The starting premise of this study, then, is that protein formation reactions are unfavorable todifferent degrees, depending on the environments and compositions of the biomolecules.The application of equilibrium chemical thermodynamics as a way to characterize the relative stabilities ofminerals as a function of temperature, pressure and oxidation-reduction potential [61, 62, 63], or to calculate therelative abundances of coexisting inorganic [64, 65] and/or organic species [41, 66], is well documented in thegeochemical literature. An advantage of performing quantitative chemical thermodynamic calculations for manydifferent model systems is that the equilibrium state serves as a frame of reference for describing both reversibleand irreversible chemical changes. For example, the weathering of igneous rocks is an overall irreversible processbut the sequences of minerals formed can nevertheless be predicted after initial formulation of the relative stabilitylimits of the chemical species involved [67, 68]. One of the motivations for this study is to see whether a similarapproach could be used to describe the sequence of events in irreversible subcellular processes.The thermodynamic calculations reported in this study are based on algorithms for calculating the standardmolal Gibbs energies of ionized proteins [69] and a chemical reaction framework that is used to compute metastableequilibrium relative abundances of proteins [70]. The Supporting Information for this paper includes the softwarepackage (Text S1) and the program script and data files (Text S2) used to carry out these calculations. Thetheoretical approach adopted here is based on the description of a chemical system in terms of intensive variables.These variables are temperature, pressure and the chemical potentials of the system. It is convenient to denote thechemical potentials by the chemical activities or fugacities of basis species, for example the activity of H + (whichdefines pH ) or the fugacity of oxygen. This permits comparison of the parameters of the model with referencesystems described in experimental and other theoretical biochemical studies.A few notes on terminology follow. Formation of a protein refers to the overall process of protein biosynthesisand translocation to a specific compartment.
Activity and species denote, respectively, chemical activity andchemical species, not enzyme activity or biological species. In the present study, activity coefficients are taken tobe unity, so the chemical activities are equivalent to molal concentrations. Below, oxidation-reduction potential and oxygen fugacity are used synonymously, and redox refers specifically to Eh . The oxidation-reduction potentialof a system can be expressed in terms of Eh using an equation given in the Methods. The overall composi-tions of proteins in compartments are referred to here as proteologs (or model proteologs). The interactions ofproteins are processes in which the proteins come into physical contact, for example in transport processes be-tween compartments and in the formation of complexes. If a process results in a change in the composition ofa population of interacting proteins, then a chemical reaction has occurred. Protein-protein interactions do notnecessarily correspond to chemical reactions. However, a population of interacting proteins does chemically react2able 1: Subcellular isoforms of glutaredoxin, thioredoxin and thioredoxin reductase in yeast a . Protein SWISS-PROT Location Length Formula ∆ G ◦ Z Z C GlutaredoxinGLRX1 P25373 Cytoplasm 110 C H N O S -4565 -5.8 -0.182GLRX2 P17695 Mitochondrion 143 C H N O S -5617 0.1 -0.255GLRX3 Q03835 Nucleus 285 C H N O S -12031 -24.5 -0.094GLRX4 P32642 Nucleus 244 C H N O S -10276 -17.8 -0.140GLRX5 Q02784 Mitochondrion 150 C H N O S -5841 -6.1 -0.192ThioredoxinTRX1 P22217 Cytoplasm 102 C H N O S -3969 -3.1 -0.211TRX2 P22803 Cytoplasm 103 C H N O S -4056 -3.1 -0.197TRXB1 P29509 Cytoplasm 318 C H N O S -12330 -4.7 -0.159TRX3 P25372 Mitochondrion 127 C H N O S -4617 4.9 -0.255TRXB2 P38816 Mitochondrion 342 C H N O S -12841 -1.5 -0.145 a. Amino acid compositions of subcellular isoforms of glutaredoxin (GLRX), thioredoxin (TRX) and thioredoxinreductase (TRXB) in
S. cerevisiae were taken from the SWISS-PROT database [71] (accession numbers shownin the table). Chemical formulas of nonionized proteins, and calculated standard molal Gibbs energy of formationfrom the elements ( ∆ G ◦ , in kcal mol − , at 25 ◦ C and 1 bar) and net ionization state ( Z ) at pH = 7 of chargedproteins are listed. Average nominal oxidation state of carbon ( Z C ) was calculated using Eqn. (12).if the turnover rates of the proteins are not all the same or if, through evolution, the genes coding for the proteinsundergo different non-synonymous mutations. Model systems consisting of interacting proteins are useful targetsfor assessing the potential for chemical reactivity, which might occur on evolutionary time scales longer than thephysical interactions.The purpose of this study is to quantify using a metastable equilibrium reference state the responses of popu-lations of model proteins for different subcellular compartments of S. cerevisiae to gradients of oxidation-reductionpotential . There are two major parts to this paper. In the first part, the reactions corresponding to intercompart-mental interactions between isoforms (or homologs) of particular enzymes and between proteologs are quantifiedby calculating the oxygen fugacities for equal chemical activities of the reacting proteins or proteologs in metastableequilibrium. A ranking of relative metastabilities of the proteologs is discussed. Specific known interactions be-tween compartments are considered in order to derive values of the oxygen fugacity within compartments thatbest metastabilize the corresponding proteologs relative to those of other compartments. Equal-activity values ofthe oxygen fugacity in the reactions are used to predict a sequence of formation of model proteologs in responseto a temporal oxidation-reduction gradient.In the second part of this paper, the relative abundances of model proteins in metastable equilibrium arecalculated and compared with measured abundances. The range of protein abundances in a metastable equilibriumpopulation often approaches that seen in experiments over a narrow window of oxygen fugacity. Positive andnegative correlations between the calculated and experimental relative abundances are found in some cases. Localenergy minimization and its opposition in the cellular demands for selectivity in protein formation are discussed aspossible processes leading to the observed patterns.
Results and Discussion
Calculated metastability relations are described below for intercompartmental interactions between the modelhomologs and proteologs, and for intracompartmental interactions among the most abundant proteins in com-partments or the reference model complexes. Experimental comparisons and discussion of their implications areintegrated with these results. 3 elative metastabilities of subcellular homologs of redoxins
The cytoplasmic, nuclear and mitochondrial homologs of glutaredoxin [72, 73, 74] and thioredoxin/thioredoxinreductase [75, 11] in yeast cells represent the first model systems for subcellular environments studied here. Thenames and chemical formulas of these proteins are listed in Table 1, together with some computed properties. Theaverage nominal oxidation state of carbon ( Z C ) is a function of the relative proportions of the elements in thechemical formula (see Methods). These values are provided just to get some initial bearing on the differences incompositions of the proteins. In Table 1 the proteins with the lowest values of Z C are the mitochondrial homologsand those with the highest values of Z C are the nuclear homologs. pH l og f O ( g ) ( a ) pH l og f O ( g ) ( b ) TRX3 (M)pH E h ( v o l t ) ( c ) GLRX2 (M) GLRX1 (C)GLRX3(N) pH E h ( v o l t ) ( d ) T R X ( C ) T R X ( C ) T R X ( M ) T R XB ( C ) log a H2O ( liq ) l og f O ( g ) −10 −8 −6 −4 −2 0−85−80−75−70−65−60 ( e ) GLRX1 (C)GLRX2(M)GLRX3 (N)GLRX5 (M) log a H2O ( liq ) l og f O ( g ) −10 −8 −6 −4 −2 0−85−80−75−70−65−60 ( f ) TRX1 (C) TRX2 (C)TRXB1 (C) TRX3 (M)
Figure 1:
Relative metastabilities of homologs of glutaredoxinand thioredoxin/thioredoxin reductase.
Predominance diagramswere generated for homologs of ( a,c , e ) glutaredoxin and of ( b , d , f )thioredoxin/thioredoxin reductase in S. cerevisiae . The letters inparentheses following the labels indicate the subcellular compartmentto which the protein is localized (C – cytoplasm; M – mitochondrion;N – nucleus). Calculations were performed for ionized proteins at 25 ◦ C and 1 bar and for reference activities of basis species noted inthe Methods. Reduction stability limits of H O are shown by dashedlines; the dotted lines in ( c ) and ( d ) correspond to the plot limits of( a ) and ( b ).Because the current objective is to de-scribe the compositions of populations ofproteins in terms of a variable like oxidation-reduction potential, a quantity such as Z C is not sufficient; it has no explicitly deriv-able relation to intensive properties that canbe measured. The forces acting on chem-ical transformations among proteins can,however, be assessed by first writing chem-ical reactions denoting their formation. Anexample of this procedure is given furtherbelow for a specific model system. Thebasic methods that apply there were usedthroughout this study. The standard mo-lal Gibbs energies ( ∆ G ◦ ) and net chargesof ionized proteins at pH = 7 are listed inTable 1 so that the results described belowcan be reproduced at this pH .In Figs. 1a and b the metastableequilibrium predominance limits of ionizedproteins in the glutaredoxin and thiore-doxin/thioredoxin reductase model systemsare shown as a function of the logarithmof oxygen fugacity and pH . Here, the pre-dominant protein in a population is takento be the one with the greatest chemicalactivity. The computation of the relativemetastabilities of the proteins included allfive model proteins in the glutaredoxin sys-tem as candidates, but note regarding Fig.1a that only two of the five proteins appearon the diagram. Those that do not appearare less metastable, or have greater energyrequirements for their formation over therange of conditions represented in Fig. 1athan either of the proteins appearing in thefigure.The equal-activity lines in these pH di-agrams are curved because the ionizationstates of the proteins depend on pH . The observation apparent in Fig. 1a that increasing log f O g ) favorsformation of the cytoplasmic protein homolog relative to its mitochondrial counterpart is also true for the thiore-doxin/thioredoxin reductase system shown in Fig. 1b. In comparing Figs. 1a and b note that in the latterfigure, predominance fields for a greater number of candidate proteins appear, and that the predominance fieldboundary between mitochondrial and cytoplasmic proteins occurs at a lower oxidation-reduction potential. Thedashed lines shown in each diagram of Fig. 1 are reference lines denoting the reduction stability limit of H O ( log f O g ) ≈ − . at 25 ◦ C and 1 bar [76]). 4redominance diagrams as a function of Eh and pH for the glutaredoxin and thioredoxin/thioredoxin reductasesystems are shown in Figs. 1c and d. Like log f O g ) , Eh and pH together are a measure of the oxidation-reductionpotential of the system; the different scales can be converted using Eqn. (11). The trapezoidal areas boundedby dotted lines in Figs. 1c and d show the ranges of Eh and pH corresponding to the log f O g ) - pH diagrams ofFigs. 1a and b. It can be deduced from these diagrams that if the upper log f O g ) limit of Fig. 1a were extendedupward, this diagram would include a portion of the predominance field for the nuclear protein GLRX3.It appears from Figs. 1a-b that increasing increasing log f O g ) at constant pH , or increasing pH at constantoxidation-reduction potential have similar consequences for the relative metastabilities of the cytoplasmic andmitochondrial homologs. In this analysis, however, pH does not appear to be a very descriptive variable; themagnitude of the effect of changing oxygen fugacity over several log units is greater than the effect of changing pH by several units. In further metastability calculations pH was set to 7. Also, because Eh itself is defined interms of pH , the oxidation-reduction potential variable adopted below is log f O g ) , which is more directly relatedto the potential of a thermodynamic component.In Figs. 1e and f the logarithm of activity of water ( log a H O ) appears as a variable. In Fig. 1e it can be seenthat the formation of a nuclear homolog of GLRX is favored relative to the cytoplasmic homologs by decreasingactivity of water and/or increasing oxygen fugacity, and that increasing relative metastabilities of the mitochondrialproteins are consistent with lower oxidation-reduction potentials and to some extent higher activities of water. InFig. 1f it appears that the formation of the thioredoxin reductases relative to thioredoxins in each compartmentis favored by increasing f O g ) , and that for the TRX the relative metastabilities of the mitochondrial proteinsincrease with decreasing f O g ) . Comparison with subcellular redox measurements
Table 2: Nominal electrochemical characteristics of subcellular environ-ments in eukaryotes. Values refer to yeast cells unless noted otherwise.
Environment Eh , volt pH log f O g ) m Extracellular (intestine) − . to − . a g − . to − . Cytoplasm − . to − . b . h − . to − . Nucleus – c . i – c Mitochondrion − . d j − . Endoplasmic reticulum − . to − . e . k − . to − . Vacuole > +0 . f . l > − . a. [77] ( Homo sapiens ). b. The lower and upper values are taken from[78] and [79], respectively. c. The state of the GSSG/GSH couple in thenucleus is thought to be more reduced than in the cytoplasm [4]; see text. d. [10] ( Homo sapiens
HeLa [80] cells). e. [9] ( Mus musculus : mousehybridoma cells [81]). f. Calculated by combining the law of mass actionfor Fe +3 + e − (cid:10) Fe +2 (standard molal Gibbs energies taken from [82])with a Fe +3 = a Fe +2 (see text). g. [83] ( Homo sapiens ). h. [6] (yeast). i. [84] (organism unspecified). j. [7] (HeLa) k. [8]. l. [5]. m. Values of Eh and pH listed here were combined with Eqn. (11) at T = 25 ◦ C, P = 1 bar and a H O = 1 to generate the values of log f O g ) .Let us compare the positions of thepredominance fields in Fig. 1 withmeasured subcellular redox states.The values of Eh derived from theconcentrations of oxidized and re-duced glutathione (GSSG and GSH,respectively) in extra- and subcel-lular environments reported in vari-ous studies [9, 77, 10, 79, 78] wereconverted to corresponding values of log f O g ) using Eqn. (11) in theMethods and are listed in Table 2. Inorder to fill in the table as completelyas possible, it was necessary to con-sider measurements performed on eu-karyotic cells other than those of S.cerevisiae ( e.g. , HeLa [80] and mousehybridoma [81] cells). The values of pH required for conversion of Eh to log f O g ) were also retrieved from theliterature [83, 6, 7]. The computationof log f O g ) from Eh was performedat 25 ◦ C and 1 bar and with log a H O = 0 . No measurements of vacuolar Eh have been reported, but it hasbeen noted that Fe +3 predominates over Fe +2 in this compartment [85]. Hence, a nominal (and relatively veryoxidizing) value of Eh for the vacuole was calculated that corresponds to equal activities of Fe +3 and Fe +2 .The available measurements of redox states in compartments of eukaryotic cells can be summarized as, frommost reducing to most oxidizing, mitochondria - nucleus - cytoplasm - endoplasmic reticulum - extracellular [4].Strong redox gradients within the mitochondrion are essential to its function [86], which is not captured by thesingle values listed in Table 2. Comparison nevertheless with the computational results shown in Fig. 1 indicatesthat a relatively reducing environment does metastably favor the mitochondrial homolog.Measurements of GSH/GSSG concentrations point to a lower redox state in the nucleus than in the cytoplasm,5able 3: Overall protein compositions (proteologs) of compartments in yeast cells a . Location Number Length Formula ∆ G ◦ Z Z C log f O g ) actin 22 469.4 C . H . N . O . S -18500 -5.2 -0.119 -75.0ambiguous 123 821.3 C . H . N . O . S . -32181 -22.4 -0.123 NAbud 57 429.9 C . H . N . O . S . -15314 6.8 -0.171 -75.2bud.neck 11 905.2 C . H . N . O . S . -38092 -16.8 -0.113 -69.2cell.periphery 38 826.1 C . H . N . O . S . -30639 1.8 -0.164 -74.7cytoplasm 746 458.5 C . H . N . O . S . -18106 -3.9 -0.132 -74.6early.Golgi 9 622.9 C . H . N . O . S . -25456 -19.9 -0.193 -75.3endosome 30 457.6 C . H . N . O . S . -18833 -9.4 -0.131 -76.7ER 197 309.7 C . H . N . O S . -10292 9.4 -0.245 -75.5ER.to.Golgi 5 594.9 C . H . N . O . S . -22855 -13.3 -0.127 NAGolgi 14 478.2 C . H . N . O . S . -18229 -3.4 -0.182 -75.3late.Golgi 29 602.4 C . H . N . O . S . -24962 -22.6 -0.141 -75.1lipid.particle 17 502.1 C . H . N . O S . -18691 -4.0 -0.167 -75.0microtubule 10 497.0 C . H . N . O . S . -20024 -3.9 -0.125 -75.0mitochondrion 426 484.9 C . H . N . O . S . -18244 6.8 -0.156 -75.9nuclear.periphery 46 815.6 C . H . N . O . S . -33153 -11.5 -0.159 -75.2nucleolus 60 564.3 C . H . N . O . S . -23928 -10.9 -0.104 -75.0nucleus 453 572.1 C . H . N . O . S . -23525 -2.3 -0.108 -71.5peroxisome 18 422.3 C . H . N . O . S . -16397 -2.0 -0.150 -74.8punctate.composite 61 474.7 C . H . N . O . S . -20313 -22.6 -0.102 NAspindle.pole 30 470.9 C . H . N . O . S . -19820 -6.3 -0.131 -78.8vacuolar.membrane 45 762.2 C . H . N . O . S . -29221 -15.5 -0.153 -75.2vacuole 67 511.7 C . H . N . O . S . -20239 -15.9 -0.125 -70.6 a. Chemical formulas of nonionized proteologs and standard molal Gibbs energy of formation from the elements( ∆ G ◦ , in kcal mol − , at 25 ◦ C and 1 bar) and net ionization state ( Z ) at pH = 7 of ionized proteologs werecalculated using the overall amino acid compositions given in Table S1. Values of the nominal oxidation stateof carbon ( Z C ) were calculated using Eqn. (12). log f O g ) values for compartments were determined from themetastable equilibrium limits of subcellular interactions listed in Table 4.but the chemical thermodynamic predictions show the nuclear proteins favored by relatively oxidizing conditions.Studies using nuclear magnetic resonance (NMR) showing that the hydration state of the nucleus is higher thanthe cytoplasm [16, 13] bring into question the prediction consistent with Fig. 1e that the formation of the nuclearproteins is favored relative to their cytoplasmic counterparts by decreasing activity of water. Also, mitochondrial pH is somewhat higher than that of the cytoplasm [6, 7], but in Figs. 1a and b it appears that the predictedenergetic constraints favor the cytoplasmic proteins at higher pH s. These comparisons indicate that all metastableequilibrium constraints are not preserved in the spatial relationships of the homologous redoxins in the cell. Relative metastabilities of proteologs
The chemical formulas and thermodynamic properties of the model proteologs – hypothetical proteins representingthe overall amino acid compositions of compartments (see Methods) – are listed in Table 3. The predominancediagrams in Fig. 2 depicting the relative metastabilities of the model proteologs as a function of log f O g ) and log a H O were generated in sequential order. The first diagram in this figure corresponds to a system in which all23 proteologs were considered. Subsequent diagrams in Fig. 2 were generated by eliminating from considerationsome or all of the proteologs represented by predominance fields in the immediately preceding diagram. It canbe seen in Fig. 2a that consideration of 23 proteologs resulted in predicted predominance fields for six proteinsover the ranges of log f O g ) and log a H O shown in the diagram. Subsequent diagrams in the sequence representproteologs with lower predicted relative metastabilities, i.e., higher energy requirements for formation relative toproteologs appearing earlier in the sequence.There is a large difference between the relatively oxidized conditions of the endoplasmic reticulum reportedin the literature (see Table 2) and the theoretically relatively reduced environment of the ER proteolog shown in6ig. 2a. Also note the average nominal carbon oxidation state of the ER proteolog, which is the lowest of any inTable 3. A possible interpretation of these observations is that there is significant chemical heterogeneity withinthis compartment and a relatively high energy demand for the formation of these proteins in the oxidizing spaces.Nevertheless, the juxtaposition in the ER of very reduced proteins and high redox potential does permit a possibleadvantage: If the redox potential of the compartment were much lower, the proteins constituting the endoplasmicreticulum would become more favorable to produce than any other proteins (see below) ultimately localized toother compartments that are initially produced there. Perhaps in this way a high redox state could signal theproduction of cytoplasmic and secreted proteins and a drop in redox state the production of biosynthetic enzymes,i.e. the reproduction of the ER itself. log a H2O ( liq ) l og f O ( g ) −5 −4 −3 −2 −1 0−80−78−76−74−72−70−68−66 ERlipid.particle peroxisomeactin ( a )
23 locations early.Golgi log a H2O ( liq ) l og f O ( g ) −5 −4 −3 −2 −1 0−80−78−76−74−72−70−68−66 Golgibudpunctate.compositenucleolus ( b )
18 locations vacuolar.membranelog a H2O ( liq ) l og f O ( g ) −5 −4 −3 −2 −1 0−80−78−76−74−72−70−68−66 cell.peripherycytoplasmER.to.Golginucleus ( c )
13 locations late.Golgi log a H2O ( liq ) l og f O ( g ) −5 −4 −3 −2 −1 0−80−78−76−74−72−70−68−66 vacuolemitochondrion ( d ) ambiguouslog a H2O ( liq ) l og f O ( g ) −5 −4 −3 −2 −1 0−80−78−76−74−72−70−68−66 endosomebud.neckmicrotubule ( e ) nuclear.periphery log a H2O ( liq ) l og f O ( g ) −5 −4 −3 −2 −1 0−80−78−76−74−72−70−68−66 spindle.polemicrotubule ( f ) Figure 2:
Relative metastabilities of proteologs of compartments.
Predomi-nance diagrams were generated as a function of log f O g ) and log a H O at 25 ◦ Cand 1 bar for the proteologs listed in Table 3. The diagram in ( a ) represents 23model proteologs; diagrams in panels ( b )–( f ) represent successively fewer modelproteologs.The proteologs appearingin successive diagrams in Fig.2 are characterized by increas-ingly higher predicted energyrequirements for their for-mation. Hence, the nu-clear, cytoplasmic and mito-chondrial proteologs appear-ing in Fig. 2c-d are rela-tively less metastable com-pared to those of actin, earlyGolgi and ER appearing inFig. 2a. It is noteworthythat the proteologs represent-ing the two cytoskeletal sys-tems in yeast cells, actin andmicrotubule, appear at oppo-site ends of the energy spec-trum. This prediction maybe consistent with the ob-servation that actin in dif-ferent forms appears to bepresent at most stages ofthe cell cycle [87], but thatthe microtubule cytoskeletongrows during anaphase (i.e.,the stage of the cell cyclecharacterized by physical sep-aration of the chromosomes;[88]) and is degraded duringother stages of the cell cycle[87, 88].The order of appearanceof phases throughout a reac-tion sequence is determinedby the relative stabilities ofthe phases [63]. Examplesof the application of this no-tion in inorganic systems arethe reaction series of meta-morphic minerals, paragenetic sequences of mineralization [89], Ostwald ripening [90], and weathering reactionpaths [91]. Can the relative metastabilities of proteins provide information about their order of appearance in thecell cycle?The outcome of the mitotic cycle in S. cerevisiae is the growth of a new cell in the form of a bud [88]. Notall structures in the bud form simultaneously. Instead, it has been observed that [92] “the endoplasmic reticulum,7able 4: Major intercompartmental protein interactions in yeast a . Interaction ∆ n O log f O g ) Interaction ∆ n O log f O g ) actin – bud vacuole – bud actin –bud.neck 0.078 -83.4 vacuole – cell.periphery actin – cell.periphery vacuole – cytoplasm actin – endosome vacuole – endosome actin – vacuolar.membrane vacuole – late.Golgi actin – mitochondrion actin -0.023 -88.7 actin –microtubule 0.124 -78.3 nucleus –microtubule 0.101 -75.9microtubule– bud nucleus – spindle.pole microtubule – bud.neck -0.045 -69.4 nucleus – bud cell.periphery nucleus –bud.neck 0.056 -81.3microtubule– cytoplasm -0.037 -83.3 nucleus – cytoplasm spindle.pole nucleolus -0.034 -78.7 spindle.pole – cytoplasm -0.075 -78.7 nuclear.periphery – bud.neck -0.080 -69.3spindle.pole– nuclear.periphery -0.004 -119.1 nuclear.periphery– cytoplasm -0.072 -76.5 ER – cell.periphery -0.460 -74.7 nuclear.periphery – nucleus -0.136 -74.2 ER – cytoplasm -0.557 -74.7 nuclear.periphery – nucleolus -0.169 -75.1 ER – early.Golgi -0.345 -75.4 peroxisome –cell.periphery 0.062 -78.7 ER –nuclear.periphery -0.485 -74.4 peroxisome –cytoplasm -0.034 -67.2 ER – peroxisome -0.522 -75.2 peroxisome – lipid.particle Golgi –endosome -0.199 -74.3 peroxisome –mitochondrion 0.040 -82.6
Golgi – vacuole -0.285 -74.2 mitochondrion– cell.periphery Golgi – late.Golgi -0.213 -75.2 mitochondrion – cytoplasm -0.074 -75.4Golgi– early.Golgi -0.030 -84.4 mitochondrion – nucleus -0.138 -73.7 a. Interactions between proteins in different subcellular locations in
S. cerevisiae were identified in the literature.The calculated reaction coefficients on O g ) and the metastable equilibrium value of log f O g ) were calculatedfor each reaction between model proteologs. Names of locations shown in bold indicate that the model value of log f O g ) for this compartment (Table 3) lies in the metastability range for the proteolog in the particular reaction.Golgi, mitochondria, and vacuoles all begin to populate the bud well before anaphase and that their segregationinto the bud does not require microtubules”. The results in Fig. 2 indicate that the proteolog for bud is ofcomparable metastability relative to that of Golgi but it less metastable than the proteolog of ER. In the absenceof energy input, it follows that there would be a chemical driving force to form the ER proteins at the expenseof any of the bud that may be present. The appearance in the bud of the less-metastable mitochondrial proteinssuggests that there is a source of energy to the bud that is nevertheless not sufficient to drive the formation ofthe proteins in the microtubule. The formation of these proteins may not be possible until the products of themitochondrial reactions and other energy-rich metabolites have accumulated in the cell. Intercompartmental protein interactions
The diagrams in Fig. 2 show the predominant metastability interactions between proteologs for different subcel-lular compartments. However, many subcellular interactions may in fact be meta-metastable with respect to Fig.2. For example, interactions occur between proteins in the cytoplasm and nucleus [93], but the proteologs forthese compartments do not share a reaction boundary in Fig. 2c. Below, known intercompartmental interactionsare combined with the oxygen fugacity requirements for (meta-)metastable equilibrium of the proteologs to char-acterize compartmental oxidation-reduction potentials. These are used in the next section to explore a possibledevelopmental reaction path.To assess the biochemical evidence for specific interactions between proteins in different compartments in yeastcells, a series of review papers was surveyed [87, 94, 95, 93, 96, 97]. Statements implying interaction betweenproteins in different compartments were identified by scanning for action words including interact, are at, align, endat, organize, embed, move, associate, found, locate, extend, bisect, move, migrate, enter, attach, translocate, carry,sort, composed of, line, dock and fuse, recycle, transport, pinch, proceed, reach, degrade in, deliver, colocalize,8 og f O ( g ) −78−76−74−72 actin microtubule spindle.p ER Golgi vacuole nucleus nuclear.p peroxisomemitochondrion microtubule budspindle.p cytoplasm nuclear.pperoxisome endosomevacuole budcell.pendosomelate.G microtubulespindle.pbudcytoplasmnucleolus cytoplasmnucleus cell.p cell.pcytoplasmnucleus actincell.p cytoplasmearly.Gendosome ER Golgilate.G lipid.pmitochondrion nuclear.pnucleolusnucleus peroxisomespindle.pvacuolar.m Figure 3:
Logarithms of oxygen fugacity for equal chemical activities of proteologs in intercompartmentalinteractions . Metastable equilibrium values of log f O g ) were obtained for the model reactions listed in Table 4.Reactions are grouped by a common proteolog, listed along the bottom of the plot. Reactions that were used toderive model values of oxygen fugacity of compartments listed in Table 3 are denoted by arrows and bold linesand labels. The position of the reaction labels denotes the direction of the reaction that favors formation of thecorresponding proteolog. The actin–bud and ER–cell periphery interactions were omitted from this plot to aid inclarity of labeling; they overlap with actin–vacuolar membrane and ER–cytoplasm, respectively.contain, associate, separate, protrude, penetrate, cooperate, crosstalk, anchor, reside, continuous with, shuttle,oxidize, essential to, convey, arrange, import, and transcribe. The source statements are listed in Text S3 andsimplified pairwise representations of the interactions are summarized in Table 4. Of 190 possible combinationsbetween any two of the 20 subcellular compartments (this count excludes the ambiguous location and ER to Golgiand punctate composite, which did not appear in the literature survey), 46 interactions were identified throughthis survey.Chemical reactions corresponding to each of the interactions listed in Table 4 were written between residueequivalents of the proteologs, with the reactant proteolog being the one on the left-hand side of the interaction andthe product proteolog the one on the right-hand side. The reactions are listed in Table S2. Corresponding valuesof ∆ n O g ) (reaction coefficient on O g ) ) are listed in Table 4 together with the values of log f O g ) where thecalculated chemical activities of the two proteologs in each reaction are equal. Note that there are some reactionswhere the absolute value of ∆ n O g ) is substantially smaller than the others; these include spindle pole–nuclearperiphery, Golgi–early Golgi and nucleus–actin. Because of the small value of ∆ n O g ) in these reactions, the valuesof log f O g ) for equal activities of these proteins tend to be more extreme than for other reactions. Note that thesign of ∆ n O g ) denotes the thermodynamically favored direction of the reaction as log f O g ) is changed from itsequal-activity value; for example, at log f O g ) = − . , the proteologs of actin and bud metastably coexist withequal chemical activities, but at higher values that of actin predominates in metastable equilibrium.The interactions listed in Table 4 were used to generate model values of the oxygen fugacity in each compart-ment that are listed in Table 3. The criterion used for this analysis was that the oxygen fugacity in a compartmentshould in as many cases as possible favor the formation of its proteolog relative to those of interacting compart-ments. For example, consider the proteolog for endosome, which occurs in three interactions listed in Table 4.9he endosomal proteolog is favored to form relative to that of actin by log f O g ) < − . and relative to that ofvacuole by log f O g ) < − . . In contrast, the endosomal proteolog is favored to form relative to the proteologof Golgi by log f O g ) > − . . A single value of log f O g ) can satisfy at most two of these constraints; themodel value for endosome is taken to be just below the limit for its interaction with actin, or log f O g ) = − . (Table 3). Because this value favors formation of the endosomal proteolog relative to those of actin and vacuole,the proteolog of endosome is listed in bold font in these interactions in Table 4, but is shown in normal font inthe interaction with the Golgi proteolog. Similar reasoning was used to derive oxygen fugacities for the othersubcellular compartments listed in Table 3, except for microtubule.The outcome of the above analysis is summarized in Fig. 2, where the values of log f O g ) for interactions thatfall between − and − are plotted. The interactions are grouped by a common interacting proteolog so thatdifferences between them can be more easily visualized. To avoid clutter, the reaction labels are generally restrictedto the name of a single proteolog to indicate the direction of log f O g ) change that favors its formation in thereaction. Model interactions that were used to constrain the limits of oxygen fugacities for one compartment (suchas the actin–endosome interaction noted above) or two compartments (such as Golgi–late Golgi) are identifiedwith one or two arrows, respectively, and the names of the corresponding proteologs are shown in bold font.If the model compartmental values of log f O g ) all favored formation of the corresponding proteologs relative totheir interacting partners, the name of every proteolog would appear in bold font in Table 4. This is only the case,however, for some proteologs such as that of actin, where log f O g ) − favors formation of this proteolog relativeto any of its interacting partners. At the same oxygen fugacity, it can be shown that the proteolog for microtubuleis unmetastable with respect to any of its interacting partners except for bud neck. Notably, the proteolog formicrotubule only becomes relatively metastable at high oxygen fugacities (w.r.t. bud, cell periphery and spindlepole) or at low oxygen fugacities (w.r.t. actin, cytoplasm and nucleus). Hence, the value of log f O g ) − takenhere for the microtubule compartment is different from all the others, in that this represents conditions where theformation of its proteolog is more unfavorable than that of any of its interacting partners. Sequential formation driven by oxygen fugacity gradients
We have already seen theoretical evidence that the microtubule is a relatively unmetastable assemblage of proteinsin the cell. It is known in spite of this that the microtubule as well as the spindle pole are essential in cellulardivision [87]. Can the metastable equilibrium relationships reveal anything about the origins of the interactionsof the microtubule and spindle pole in this process? The following thought experiment explores why the irre-versible formation of proteologs might follow a sequence that is related to metastable equilibrium thermodynamicrelationships.To start, consider a permeable sac consisting of the cytoplasmic proteolog, which we will expose to a chang-ing oxidation-reduction environment. The oxidation-reduction program will begin at log f O g ) = − , drop to log f O g ) = − . , increase to log f O g ) = − and return to log f O g ) = − . At any point along this programthe only reactions we will consider are those involving the proteologs of microtubule or spindle pole. Let us assumein addition that none of these reactions proceeds to completion, and that any reaction may only proceed while log f O g ) is near the equal-activity value for the reaction. Keeping in mind that no mechanism for the reactionsis implied here, it may still be worthwhile to note that others have observed near-equilibrium concentrations ofsubstrates in a subset of enzymatically catalyzed reactions [98, 99].At log f O g ) = − , no reaction occurs because the conditions coincide with the metastability field of thecytoplasmic proteolog relative to either microtubule or spindle pole. As soon as the log f O g ) decreases below − . , some of the spindle pole proteolog may form irreversibly at the expense of the cytoplasmic proteolog. Below log f O g ) = − . , the microtubular proteolog can begin to form at the expense of the cytoplasmic proteolog.At log f O g ) = − . both of these reactions may favorably proceed, and we begin now to increase log f O g ) .As we pass log f O g ) = − . , then log f O g ) = − . going in the positive direction, some of the proteolog ofmicrotubule, then spindle pole can react irreversibly to form the cytoplasmic proteolog. These are the opposite ofthe first two irreversible reactions.As long as the current and following reactions do not proceed to completion, there will be a population ofthe microtubule and spindle pole proteologs available to react. Above log f O g ) = − . , where the formation ofthe cytoplasmic proteolog becomes favored relative to spindle pole (see above), the proteolog of actin may alsofavorably form at the expense of that of microtubule. The nuclear proteolog can form above log f O g ) = − . at the expense of the microtubular proteolog, and above log f O g ) = − . at the expense of the spindle pole10able 5: Hypothetical oxygen fugacity cycle and sequence of reactions of proteologs. log f O g ) Reaction log f O g ) Reaction-75.0
Begin -74.3 spindle.pole → microtubule-78.7 cytoplasm → spindle.pole -69.4 microtubule → bud.neck-83.3 cytoplasm → microtubule -69.0 Maximum point -83.5
Minimum point -69.2 microtubule → cell.periphery-83.3 microtubule → cytoplasm -69.4 bud.neck → microtubule-78.7 spindle.pole → cytoplasm -72.3 microtubule → bud-78.7 microtubule → actin -74.3 microtubule → spindle.pole-75.9 microtubule → nucleus -75.0 End -75.5 spindle.pole → nucleusproteolog. We now momentarily pass through our starting point, log f O g ) = − . So far, the proteologsfrom spindle pole, microtubule, actin and nucleus, in that order, may have formed as a result of irreversiblereactions of the original cytoplasmic proteolog. Also, the proteologs of microtubule and spindle pole may havebeen subsequently partially degraded after their possible formation.Now, as log f O g ) is increased above − . , the proteolog of spindle pole becomes unmetastable relative to thatof microtubule. Above log f O g ) = − . , the proteolog of bud neck may be formed irreversibly at the expenseof that of microtubule. At our maximum log f O g ) = − this reaction can continue, but as we drop below log f O g ) = − . it may be joined by formation of the proteolog of cell periphery. Below log f O g ) = − . any proteolog of bud neck that may have formed becomes unmetastable relative to that of microtubule. Below log f O g ) = − . any proteolog of microtubule that remains may degrade in favor of formation of the proteolog ofbud. Finally, as we drop past log f O g ) = − . and return to our starting point of log f O g ) = − the proteologof spindle pole once again becomes relatively metastable instead of microtubule. In summary, at log f O g ) > − the potential arises for formation of proteologs of the microtubule, bud neck, cell periphery, bud and spindle pole,as well as for retrograde reactions that may destroy the proteolog of microtubule.It is important to emphasize the qualified nature of these predictions; all we know from thermodynamics isthat any of these reactions could have progressed in the direction of a local Gibbs energy minimum. Whetherand to what extent they actually move forward is a consequence of the reaction mechanism. The purpose ofthis analysis is not to suggest any mechanism but to ask whether work performed by control of log f O g ) mayenergize such a mechanism. The enzymatic properties of the proteins themselves are probably essential in anyactual mechanism. It is encouraging to observe that at and below the starting log f O g ) = − the proteologof endoplasmic reticulum is favored to form relative to the cytoplasmic proteolog. Hence under these conditionsthere exists a potential for production of biosynthetic enzymes.The results of this thought experiment are summarized in Table 5. The range of theoretical values of f O g ) required for the chemical transformations among the proteologs is between − . and − , which in terms ofredox potential at 25 ◦ C, 1 bar, pH = 7 and log a H O = 0 correspond to Eh = − . V and
Eh = − . V,respectively (Eqn. 11). The former value is just below the stability limit for water ( log f O = − . ) but theredox state of the NADPH/NADP + pool in rat liver mitochondria might approach this value ( Eh = − . V[86]). The latter value is consistent with the state of human cells during differentiation (
Eh = − . V), whichis about . V higher than proliferating cells [100].Oscillations in the redox state of yeast cells are coupled to many metabolic changes including protein tran-scription and turnover [101]. Reductive and oxidative phases in the metabolic cycle of yeast have been identified,with DNA replication occurring during the former and cell cycle initiation occurring at an advanced stage of thelatter [102]. Oxidative stress was shown to hasten HeLa cells into anaphase by overcoming the normal spindlecheckpoint mechanism [103]. Although the results shown in Table 5 do not directly address the synthesis of DNA,they do show that there is a potential for the formation of the nuclear proteolog during a relatively reducing partof the hypothetical f O g ) cycle. In the oxidizing part of this cycle, above log f O g ) = − . , the metastability ofthe proteolog for spindle pole is decreased, and at the highest oxidation-reduction potentials a favorable chemicalpotential field exists for metastable formation of the proteolog for bud neck. Hence, the notion that “a fundamen-tal redox attractor underpins ... core cellular processes” [104] is in principle supported by the changing relativemetastabilities of the proteologs as a function of oxidation-reduction potential.11 og f O2 ( g ) l og a −80 −78 −76 −74 −72 −70 −68 −66−5.0−4.5−4.0−3.5−3.0 ( a ) actinearly.GolgiERvacuolar.membranecell.periphery nucleolusGolgilipid.particle punctate.compositeperoxisome ER.to.Golgibud vacuoleambiguouslate.Golgicytoplasm nucleusnuclear.peripherymitochondrionendosomespindle.pole bud.neckmicrotubulelog f O2 ( g ) l og a −80 −79 −78 −77 −76 −75 −74 −73−4.5−4.0−3.5−3.0 ( b ) Y D L 1 9 5 W Y HR C Y L R W Y N L049 C Y P
L 0 8 5 W YDL195WYHR098CYLR208WYNL049CYPL085W log f O2 ( g ) l og a −80 −78 −76 −74 −72 −70 −68 −66−5.0−4.5−4.0−3.5−3.0 ( a ) actinearly.GolgiERvacuolar.membranecell.periphery nucleolusGolgilipid.particle punctate.compositeperoxisome ER.to.Golgibud vacuoleambiguouslate.Golgicytoplasm nucleusnuclear.peripherymitochondrionendosomespindle.pole bud.neckmicrotubulelog f O2 ( g ) l og a −80 −79 −78 −77 −76 −75 −74 −73−4.5−4.0−3.5−3.0 ( b ) Y D L 1 9 5 W Y HR C Y L R W Y N L049 C Y P
L 0 8 5 W YDL195WYHR098CYLR208WYNL049CYPL085W
Figure 4:
Metastable equilibrium abundances of model proteologs and proteins as a function of oxygenfugacity.
Chemical speciation diagrams were generated as a function of log f O g ) at 25 ◦ C and 1 bar and withtotal activity of protein residues equal to unity for ( a ) the proteologs shown in Table 1 and ( b ) the five proteinslocalized to ER to Golgi whose experimental abundances were reported in [105]. The rightmost dotted line in( b ) indicates conditions where the calculated abundance ranking of the proteins is identical to that found in theexperiments, and the leftmost dotted line where the calculated logarithms of activities have a lower overall deviationfrom experimental ones, which are indicated by the points. This value of log f O g ) ( − ) was used to constructthe corresponding diagram in Fig. 5. Calculation of relative abundances of proteins
Above, the interactions between homologs (enzyme isoforms) in subcellular compartments and proteologs repre-senting overall protein compositions in subcellular compartments were used to derive oxygen fugacity limits formetastable reaction of proteins in different compartments. In the second part of this study, attention is focusedon the relative abundances and intracompartmental interactions of proteins.The logarithms of activities of proteologs consistent with metastable equilibrium among all 23 model proteologsare plotted in Fig. 4a as a function of log f O g ) . This diagram was generated based on metastable equilibriumamong the residues of the proteins [70] in the same manner as described in detail below for a smaller set of proteins(those appearing in Fig. 4b). The purpose of Fig. 4a is to recapitulate the relationships shown in Fig. 2. Note thatthe same proteins predominate at the extremes of oxygen fugacity represented in 4a and in Fig. 1a (reducing – ER;oxidizing – actin) and that the proteolog of microtubule appears with low relative abundance. More importantly,perhaps, there is a minimum in the range of calculated activities of the proteologs around log f O g ) = − ;changing oxidation-reduction potential alters not only the identity of the predominant protein in a metastablyinteracting population but also the relative abundances of all the others. There is probably not a single value of log f O g ) where the calculated relative abundances of the proteologs shown in Fig. 2 reflect the composition ofthe cell. Let us therefore look more closely at the relative abundances of proteins within compartments.In Fig. 4b the relative abundances of the five model proteins localized exclusively to ER to Golgi are shownas a function of log f O g ) . A worked-out example of the calculations leading to this figure, which method alsounderlies the generation of the other figures shown here, is presented in the following paragraphs.The model proteins for ER to Golgi, in order of decreasing abundance in the cell reported by [105], areYLR208W, YHR098C, YDL195W, YNL049C and YPL085W. (For simplicity, the proteins are identified here bythe names of the open reading frames (ORF).) The formula of the uncharged form of the first protein, YLR208W,is C H N O S , and its amino acid sequence length is 297 residues. The standard molal Gibbs energyof formation from the elements ( ∆ G ◦ ) of this protein at 25 ◦ C and 1 bar calculated using group additivity[69] is − kcal mol − . At this temperature and pressure and at pH = 7 , group additivity can also beused [69] to calculate the charge of the protein ( − . ) and the standard molal Gibbs energy of formationfrom the elements of the charged protein ( − kcal mol − ). The formula of the protein in this ionizationstate is C H . N O S − . . Dividing by the length of the protein, we find that the formulaand standard molal Gibbs energy of formation from the elements of the residue equivalent of YLR208W are C . H . N . O . S − . . and − . kcal mol − , respectively.12he formation from basis species of the residue equivalent of YLR208W is consistent with . aq ) + 1 . O + 1 . aq ) + 0 . S ( aq ) (cid:10) C . H . N . O . S − . . + 5 . g ) + 0 . + . (1)Similar reasoning can be applied to write the formation reaction of the residue equivalent of YHR098C as . aq ) + 1 . O + 1 . aq ) + 0 . S ( aq ) (cid:10) C . H . N . O . S − . . + 5 . g ) + 0 . + . (2)The double arrows signify that a priori one does not know the sign of the chemical affinity of either of thesereactions.At 929 residues, YHR098C is over 3 times as long as YLR208W, but in the formation reactions from the basisspecies of the residue equivalents of the two proteins, the coefficients on the basis species are similar. The differencebetween the coefficients of the same basis species in the reactions signifies the response (owing to moderation, i.e.LeChatelier’s principle [106]) of the metastable equilibrium assemblage to changes in the corresponding chemicalactivity or fugacity. For example, because ν CO , < ν CO , , ν NH , < ν NH , and ν O , < ν O , , increasing a CO aq ) , a NH aq ) or f O g ) at constant T , P and chemical activities of the other basis species shifts the metastableequilibrium in favor of YLR208W at the expense of YHR098C. Here, ν i denotes the reaction coefficient of the i th basis species or protein, which is negative for reactants and positive for products as written. Conversely,because ν H O , > ν H O , , ν H S , > ν H S , and ν H + , > ν H + , increasing a H O , a H S ( aq ) or a H + (decreasing pH )at constant T , P and chemical activities of the other basis species shifts the metastable equilibrium in favor ofYHR098C at the expense of YLR208W. The magnitude of the effect is proportional to the size of the differencebetween the coefficients of the basis species in the reactions, and it can be quantified for a specific model systemusing the following calculations.To assess the relative abundances of the proteins in metastable equilibrium, we proceed by calculating thechemical affinities of each of the formation reactions. The chemical affinity ( A ) is calculated by combining theequilibrium constant ( K ) with the reaction activity product ( Q ) according to [107] A / . RT = log ( K/Q ) = log (cid:18) − ∆ G ◦ r / . RT (cid:81) a ν i i (cid:19) , (3)where 2.303 is the natural logarithm of 10, R stands for the gas constant, T is temperature in degrees Kelvin, ∆ G ◦ r is the standard molal Gibbs energy of the reaction, and a i and ν i represent the chemical activity and reactioncoefficient of the i th basis species or species of interest (i.e., residue equivalent of the protein) in the reaction. Letus calculate ∆ G ◦ r (in kcal mol − ) of Reaction 1 by writing ∆ G ◦ = 1 × − .
633 + 5 . × . × − . × − . − . × − . − . × − . − . × − . . . (4)In Eqn. (4) the values of ∆ G ◦ of O g ) and H + are both zero, which are consistent with the standard stateconventions for gases and the hydrogen ion convention used in solution chemistry. The values of ∆ G ◦ of theother basis species are taken from the literature [108, 109, 110]. The value of log K consistent with Eqn. (4) is − . .We now calculate the activity product of the reaction using log Q = 1 × . × − . . × − − . × − − . × − . × − − . × − − . . (5)The values of a i used to write Eqn. (5) are the reference values listed in the Methods for a CO aq ) , a H O , a NH aq ) , a H S ( aq ) and a H + . The value of f O g ) used in Eqn. (5) ( log f O g ) = − . ) is also a reference value that, it will13e shown, characterizes a metastable equilibrium distribution of proteins that is rank-identical to the measuredrelative abundances of the proteins. Finally, the value of a of the residue equivalent of the protein in Eqn. (5) isset to a reference value of unity ( log a = 0 ). If we are only concerned with the relative abundances of the proteinsin metastable equilibrium, the actual value used here does not matter so long as it is the same in the analogouscalculations for the other proteins.Combining Eqns. (3)–(5) yields A / . RT = − . (this is a non-dimensional number). Following thesame procedure for the other four proteins (YHR098C, YDL195W, YNL049C and YPL085W) results in A / . RT equal to − . , − . , − . and − . , respectively. Now let us turn to the relative abundances of theproteins in metastable equilibrium, which we compute using a Boltzmann distribution for the relative abundancesof the residue equivalents: a i a t = e A i /RT (cid:80) ni =1 e A i /RT , (6)where a t denotes the total activity of residue equivalents in the system and n stands for the number of proteinsin the system. Note regarding the left-hand side of Eqn. (6) that because we are taking activity coefficients ofunity, the ratio a i /a t is equal to the ratio of concentrations, or proportionally numbers, of residue equivalentsin the system. There is not a negative sign in front of A /RT in the exponents Eqn. (6) because the chemicalaffinity is the negative of Gibbs energy change of the reaction. Note in addition that the values of A / . RT given above must be multiplied by ln 10 = 2 . before being substituted in Eqn. (6). By taking a t = 1 , we cancombine Eqn. (6) with A /RT of each of the formation reactions to calculate chemical activities of the residueequivalents of the proteins equal to . , . , . , . and . , respectively. The lengths ofthe proteins are , , , and , so the corresponding logarithms of activities of the proteins aree.g. log (0 . / − . for YLR208W, and − . , − . , − . and − . for the remaining proteins,respectively.If one now iterates calculation of the chemical affinities of the residue formation reactions using the calculatedmetastable equilibrium logarithms of activities of the residue equivalents (instead of the starting reference valueof log a = 0 ), the resulting chemical affinities for each formation reaction will be all equal and generally non-zero.This property of metastable equilibrium was used in [70] to describe specific application of a method using asystem of linear equations for finding the metastable equilibrium state without explicitly writing Eqn. (6).The results of the calculation described above correspond to the dotted line at log f O g ) = − . in Fig.4b. At this oxygen fugacity, the ranks of abundance of the model proteins in metastable equilibrium are identicalto the ranks of experimental abundances. The figure was generated in whole by carrying out this procedure fordifferent reference values of log f O g ) . It can be seen in Fig. 4a that there is a narrow range on either side of log f O g ) = − . (ca. ± . ) where the relative abundances of the proteins in metastable equilibrium occur inthe same rank order. Beyond these limits, changing f O g ) drives the composition of the metastable equilibriumassemblage to other states that do not overlap as closely with the experimental rankings. The experimentalabundances of the proteins reported by [105] are 21400, 12200, 1840, 1720 and 358, respectively, in relative units.These abundances were scaled to the same total activity of residues (unity) used in the calculations to generatethe experimental relative abundances plotted at the dashed line in Fig. 4b at log f O g ) = − . Under theseconditions, the metastable equilibrium abundances of the proteins do not occur in exactly the same rank order asthe experimental ones, but there is a greater overall correspondence with the experimental relative abundances. Relative abundances of proteins within compartments
The procedure outlined above for calculating the relative abundances of model proteins in ER to Golgi was repeatedfor each of the other compartments identified in [22]. Up to 50 experimentally most abundant proteins were chosento model each of the compartments. The relative abundances of the proteins were calculated at 0.5 log unitincrements from log f O g ) = − to − . . Scatterplots of the experimental vs. calculated relative abundancesfor each set of proteins are shown in Figure S1. These comparisons were visually assessed to regress values of log f O g ) , listed in Table 6, that yield the best fit between calculated and experimental relative abundances. Theresulting calculated relative abundances are listed together with the experimental ones in Table S3; the best-fitscatterplots for each set of model proteins are shown in Fig. 5The retrieval of optimal values of log f O g ) was aided by also calculating the root mean square deviation(RMSD) of logarithms of activities using Eqn. (13) and the Spearman rank correlation coefficient ( ρ ; Eqn. 14)between experimental and calculated logarithms of activities. The dotted lines in Fig. 5 were drawn at one RMSD14able 6: Oxygen fugacities, deviations and correlation coefficients in comparisons of intracompartmental proteininteractions a . Most abundant proteins Model complexesLocation n log f O g ) RMSD ρ Complex n log f O g ) RMSD ρ actin 22 -75.5 0.61 0.19 1 5 -80.0 0.35 0.90ambiguous 50 -74.5 0.90 0.16 2 7 -78.0 0.58 0.57bud 50 -74.5 0.85 0.02 3 5 -75.0 0.25 0.80bud.neck 11 -75.5 0.73 0.02 4 6 -75.0 0.80 0.71cell.periphery 38 -74.5 0.63 0.42 5 4 -74.5 0.29 0.80cytoplasm 50 -77.0 1.20 0.16 6 7 -80.0 0.20 0.96early.Golgi 9 -74.0 0.72 0.45 7 4 -75.5 0.21 0.80endosome 30 -75.5 0.98 0.04 8 4 -73.5 0.60 -1.00ER 49 -76.0 0.94 0.09 9 3 -77.0 0.16 -1.00ER.to.Golgi 5 -78.0 0.40 0.40 10 4 -76.5 0.82 -0.80Golgi 14 -75.5 0.80 0.08 11 10 -74.5 0.76 -0.28late.Golgi 29 -74.5 0.61 0.18 12 5 -76.5 1.74 -0.30lipid.particle 17 -78.0 0.92 0.23 13 12 -74.5 0.97 0.01microtubule 10 -75.0 0.61 0.36 14 7 -73.0 1.05 -0.93mitochondrion 50 -76.0 0.49 0.43 15 17 -74.0 0.49 -0.14nuclear.periphery 46 -76.0 0.62 0.32 16 23 -76.0 0.43 0.53nucleolus 50 -75.5 0.79 -0.18 17 6 -74.0 0.57 0.66nucleus 50 -75.0 0.80 -0.02 18 5 -79.0 0.25 0.90peroxisome 18 -75.5 0.55 0.56 19 8 -76.0 0.39 0.91punctate.composite 49 -74.0 0.78 0.19 20 15 -74.5 0.59 0.66spindle.pole 30 -76.0 1.07 -0.13 21 5 -80.0 1.06 0.60vacuolar.membrane 45 -76.5 1.07 0.36 22 15 -78.5 1.14 0.14vacuole 50 -74.5 1.49 -0.02 23 9 -78.0 0.93 0.32 a. Values of log f O g ) in each location were regressed by comparing calculated and experimental logarithms ofactivities of the most abundant proteins in different subcellular locations and of selected complexes for each location(Figure S1). n denotes the number of model proteins used in the calculations. RMSD values were calculated usingEqn. (13), and ρ denotes the Spearman rank correlation coefficient, calculated using Eqn. (14).on either side of the one-to-one correspondence, denoted by the solid lines in this figure. The RMSD values wereused to identify outliers that are identified in Fig. 5 by letters and open symbols and that are listed in Table 7. Toaid in distinguishing the points, they were assigned colors on a red-blue scale that denotes the average nominaloxidation state of carbon of the protein (Eqn. 12).There is a considerable degree of scatter apparent in many of the plots shown in Fig. 5, so a low significanceis attached with the log f O g ) values regressed from these comparisons. In specific cases such as late Golgi andnuclear periphery a lower overall deviation is apparent and there is a visual indication of a positive correlationbetween the calculated and experimental relative abundances. Because they were regressed from individual noisydata, the values of log f O g ) listed in Table 6 are probably not as representative of subcellular oxidation-reductionconditions as those listed in Table 3, which have the additional benefit of being partly based on known subcellularinteractions (see above).The comparisons depicted in Fig. 5 and in Figure S1 are important because they reveal that the range of proteinabundance observed in cells is accessible in a metastable equilibrium assemblage at some values of log f O g ) . Forexample, the range of experimental abundances of the model proteins in actin covers about . orders of magnitude,while the calculated abundances vary over about . orders of magnitude. Extreme values of log f O g ) tend toweaken this correspondence (Figure S1). The lowest degree of correspondence occurs for the cytoplasmic proteins,where ∼ orders of magnitude separate the predicted relative abundances of the top most abundant proteins,which in the experiments have a dynamic range spanning about . orders of magnitude. The great degree ofscatter apparent in many of the comparisons in Fig. 5a is troublesome. The scatter could be partly a consequenceof including in the comparisons model proteins that do not actually interact with each other, despite their highrelative abundances. To address this concern, a more selective approach was adopted below that takes account offewer numbers of proteins that interact through the formation of complexes.15 alculated log a e x pe r i m en t a l l og a −5.0 −4.5 −4.0 −3.5−5.0−4.5−4.0−3.5 fe gba dc h actin calculated log a e x pe r i m en t a l l og a −6.0 −5.0 −4.0 −3.0−5.5−5.0−4.5−4.0−3.5 jkd ic he mf ob l nga ambiguous calculated log a e x pe r i m en t a l l og a −6.0 −5.0 −4.0 −3.0−5.5−5.0−4.5−4.0−3.5−3.0 b lhea g i mkjcd of n bud calculated log a e x pe r i m en t a l l og a −5.0 −4.5 −4.0 −3.5 −3.0 −2.5−5.0−4.5−4.0−3.5 cab d bud.neck calculated log a e x pe r i m en t a l l og a −6.0 −5.0 −4.0 −3.0−6.0−5.5−5.0−4.5−4.0−3.5 da efg hb j kc i cell.periphery calculated log a e x pe r i m en t a l l og a −8 −7 −6 −5 −4 −3−4.6−4.4−4.2−4.0−3.8−3.6 bc f h kd ge ia lj cytoplasm calculated log a e x pe r i m en t a l l og a −4.5 −4.0 −3.5 −3.0 −2.5−4.5−4.0−3.5 b ca early.Golgi calculated log a e x pe r i m en t a l l og a −5.5 −4.5 −3.5 −2.5−5.0−4.5−4.0−3.5 a ihfedcb g endosome calculated log a e x pe r i m en t a l l og a −6 −5 −4 −3−5.0−4.5−4.0−3.5−3.0 nleb oijd mkc hgfa ER calculated log a e x pe r i m en t a l l og a −4.6 −4.2 −3.8 −3.4−4.5−4.0−3.5−3.0 a ER.to.Golgi calculated log a e x pe r i m en t a l l og a −5.0 −4.5 −4.0 −3.5−5.5−5.0−4.5−4.0−3.5 a cb Golgi calculated log a e x pe r i m en t a l l og a −5.0 −4.5 −4.0 −3.5 −3.0−5.5−5.0−4.5−4.0−3.5 ica g mfb lkje hd late.Golgi calculated log a e x pe r i m en t a l l og a −5.5 −4.5 −3.5 −2.5−5.5−5.0−4.5−4.0−3.5 ab c lipid.particle calculated log a e x pe r i m en t a l l og a −5.0 −4.5 −4.0 −3.5−4.5−4.0−3.5−3.0 a b dc microtubule calculated log a e x pe r i m en t a l l og a −5.5−5.0−4.5−4.0−3.5−3.0−4.8−4.6−4.4−4.2−4.0−3.8−3.6 c nf lida h kgb e mj mitochondrion calculated log a e x pe r i m en t a l l og a −6.0−5.5−5.0−4.5−4.0−3.5−6.0−5.5−5.0−4.5−4.0 da f hg ib kc je nuclear.periphery calculated log a e x pe r i m en t a l l og a −6.5 −5.5 −4.5 −3.5−5.0−4.5−4.0 hkd gfa b mje nc i l nucleolus calculated log a e x pe r i m en t a l l og a −5.5 −5.0 −4.5 −4.0 −3.5−5.0−4.5−4.0−3.5 hea id kjgfbc l nucleus calculated log a e x pe r i m en t a l l og a −5.0 −4.5 −4.0 −3.5 −3.0−4.8−4.6−4.4−4.2−4.0−3.8−3.6−3.4 ed fbca peroxisome calculated log a e x pe r i m en t a l l og a −6.0 −5.0 −4.0 −3.0−5.5−5.0−4.5−4.0−3.5 a j kigb ec hd f punctate.composite calculated log a e x pe r i m en t a l l og a −6.0 −5.0 −4.0 −3.0−4.8−4.6−4.4−4.2−4.0−3.8−3.6 m nd fhc g oia lke jb spindle.pole calculated log a e x pe r i m en t a l l og a −7 −6 −5 −4 −3−6.5−6.0−5.5−5.0−4.5−4.0−3.5 lf gc id ke jh noma pb vacuolar.membrane calculated log a e x pe r i m en t a l l og a −7 −6 −5 −4 −3 −2−5.0−4.5−4.0−3.5 rice jdb spkola qhfg nm vacuole Figure 5:
Comparison of experimental and calculated logarithms of activities of proteins in compartments .Red and blue colors denote, respectively, low and high average nominal carbon oxidation states ( Z C ) of the protein.Dotted lines are positioned at one RMSD above and below one-to-one correspondence, which is denoted by thesolid lines. Outlying points are labeled with letters that are keyed to the proteins in Table 7. The values of log f O g ) used in the calculations are listed in Table 6. 16able 7: Outliers in Fig. 5 a . ID ORF ID ORF ID ORF ID ORF ID ORF ID ORFactin cell.periphery endosome microtubule nucleolus spindle.polea YLR206W a YDR034W-B a YBR131W a YBL031W a YKR092C a YLR457Cb YIL095W b YLL010C b YOR132W b YBL063W b YLL011W b YPL255Wc YNR035C c YOR153W c YNR006W c YPL209C c YNL299W c YJR053Wd YMR092C d YBR043C d YMR171C d YMR198W d YGR159C d YDR356We YGR080W e YDR038C e YLR240W e YMR014W e YOR373Wf YCR088W f YDR039C f YLR073C mitochondrion f YJR063W f YGL061Cg YIL062C g YDR040C g YGR206W a YIL125W g YGR271C-A g YKL089Wh YOR367W h YHR146W h YKR035W-A b YNL063W h YCR086W h YIL144Wi YPR156C i YJR044C c YCL009C i YNR004W i YLR381Wambiguous j YLR413W d YHR051W j YLR367W j YPL233Wa YGL021W k YOR094W ER e YOR108W k YDR156W k YOL069Wb YLR454W a YLR390W-A f YDR232W l YOR310C l YMR117Cc YHR115C cytoplasm b YEL002C g YMR083W m YLR221C m YDR016Cd YER070W a YNL255C c YML012W h YKL040C n YNL113W n YDR201We YIL065C b YBL027W d YJR131W i YFL018C o YKR083Cf YJR011C c YBR084C-A e YDR221W j YPL078C nucleusg YPR139C d YER131W f YOR254C k YKL085W a YBR010W vacuolar.membraneh YHR129C e YML026C g YNL258C l YDR298C b YNL251C a YPL180Wi YHR025W f YDL082W h YML013W m YOR142W c YNR053C b YMR160Wj YAR028W g YGL031C i YHR007C n YDL067C d YDR432W c YDL185Wk YBR256C h YDR012W j YHR042W e YBR009C d YGL006Wl YMR202W i YMR205C k YKL154W nuclear.periphery f YNL030W e YLR447Cm YJL034W j YPR035W l YDL128W a YDL088C g YLR153C f YBR127Cn YMR214W k YDR382W m YKL096W-A b YGR202C h YBL002W g YBR207Wo YJR085C l YOL039W n YBR106W c YKR095W i YDR190C h YML121Wo YEL027W d YAR002W j YIL021W i YDR486Cbud early.Golgi e YPR174C k YDR513W j YML018Ca YDR309C a YGL223C ER.to.Golgi f YER105C l YPL028W k YGR163Wb YBL085W b YBL102W a YNL049C g YGL092W l YBR077Cc YNL278W c YDR100W h YFR002W punctate.composite m YOR332Wd YNR049C Golgi i YGL247W a YAR009C n YOL092We YDR166C lipid.particle a YDR245W j YLR450W b YGL200C o YOL129Wf YPL032C a YCL005W b YNL041C k YHR133C c YJL186W p YHR039C-Ag YER149C b YML008C c YLR268W d YNL243Wh YDR033W c YMR148W peroxisome e YGR086C vacuolei YGR191W late.Golgi a YMR204C f YOL044W a YNL326Cj YMR295C a YDR407C b YKL197C g YER071C b YER123Wk YLR414C b YJL044C c YLR324W h YNL173C c YBR205Wl YBR054W c YDR170C d YGL037C i YDR357C d YER001Wm YLL028W d YBL010C e YDL022W j YBR052C e YDL211Cn YPR124W e YMR218C f YGL153W k YDR032C f YOR099Wo YOR304C-A f YGL083W g YPL019Cg YDR472W h YOL088Cbud.neck h YPL259C i YBR199Wa YJR092W i YBR254C j YDR483Wb YPL116W j YLR330W k YIL005Wc YHR023W k YKR068C l YLR300Wd YPR188C l YKL135C m YPR159Wm YEL048C n YPL163Co YJR161Cp YHR215Wq YNL336Wr YBR187Ws YGR105W a. Proteins are listed whose calculated logarithm of activity differs from experimental values by more than theroot mean square deviation shown in Table 6.
Relative abundances of proteins in complexes
The correspondence between the calculated and experimental relative abundances of the five model proteins in ERto Golgi raises the question of what characteristics of the proteins might be responsible for this result. Searchingthe functional annotations of these proteins reveals that they are part of the COPII coat complex [111]. Theinclusion of the COPII complex above was largely unintentional, as the procedure there was to look at the mostabundant proteins in given compartments. Nevertheless, the results for that model system suggested that focusingon specific complexes in other compartments could yield interesting results. Because the interactions of proteinsto form complexes is essential in cellular structure and regulating functions of enzymes [51], factors that affect therelative abundances of the complexing proteins may be fundamental to the control of metabolic processes.The model complexes used in this study are identified in Table 8. Each complex was nominally associated witha subcellular compartment based on the names and descriptions of the complexes available in the literature. Someexceptions are the cyclin-dependent protein kinase complex, the proteins of which are largely cytoplasmic andnuclear [22], but here is placed in the slot for the ambiguous location because no definitely ambiguously localizedcomplexes could be identified. For a similar reason, the proteins listed in Table 8 under punctate composite arenot part of a named complex but were chosen because they are localized to early Golgi in addition to the punctate17able 8: Model proteins in complexes a . Name ORF Name ORF Name ORF Name ORF1. actin: Arp2/3 complex (423) 9. ER: signal recognition 14. microtubule: DASH 20. punctate.composite: proteins([112]; complex (52) complex [113] localized here and early.Golgi[114]) Sec65 YML105C NA Dam1 YGR113W X Arl1 YBR164C dArc15 YIL062C b Srp14 YDL092W Duo1 * YGL061C a Apm3 YBR288CArc18 YLR370C Srp54 YPR088C X Dad1 * YDR016C Bug1 YDL099WArc19 YKL013C Spp68 * YPL243W a Dad2 * YKR083C b Arf1 YDL192WArc35 YNR035C a Srp72 YPL210C b Spc19 * YDR201W Luv1 YDR027C aArc40 YBR234C NA 10. ER.to.Golgi: coatomer Spc34 * YKR037C NA Tvp23 YDR084CArp2 * YDL029W COPII complex (340) Ask1 * YKL052C Dop1 YDR141C aArp3 YJR065C X Sec13 YLR208W a Dad3 * YBR233W-A Kei1 YDR367W2. ambiguous: cyclin-dependent Sec16 YPL085W Dad4 * YDR320C-A Vrg4 YGL225Wprotein kinase complex (343) Sec23 YPR181C X Hsk3 YKL138C-A X Apl6 YGR261CCdc28 * YBR160W b Sfb2 YNL049C 16. nuclear.periphery: nuclear Aps3 YJL024C cCks1 * YBR135W a Sec24 YIL109C NA pore complex [24] Vps53 YJL029C NACln2 * YPL256C Grh1 * YDR517W Nup60 YAR002W Tvp38 YKR088CCys4 * YGR155W 11. Golgi: Golgi transport Nup170 YBL079W Ssp120 YLR250WSic1 * YLR079W complex (293) Asm4 YDL088C a NA YMR010WClb3 * YDL155W Cog1 * YGL223C Nup84 YDL116W NA YMR253C NACln1 * YMR199W Cog2 YGR120C b Gle1 YDL207W Kex2 YNL238W NA3. bud: actin-associated motor Cog3 YER157W Nup42 YDR192C X Mon2 YNL297Cprotein complex 2 (49) Cog4 * YPR105C Nup157 YER105C c 21. spindle.pole: spindle-pole[115] Cog5 YNL051W c Gle2 YER107C body complex (219) [116]Myo2 YAL029C Cog6 YNL041C Nic96 YFR002W g Pfk1 * YGR240C aShe4 * YKL130C b Cog7 YGL005C Nup145 YGL092W Spc72 YAL047CMlc1 YBR130C Cog8 * YML071C Seh1 YGL100W X Spc97 YHR172WMyo1 YGL106W X Iml1 * YJR138W Nup49 YGL172W j Spc98 YNL126WCmd1 * YKL007W Nrp1 * YDL167C a Nup57 YGR119C Tub4 YLR212C bMyo5 * YIL034C a 12. late.Golgi: retrograde Nup159 YIL115C 22. vacuolar.membrane: VO4. bud.neck: septin complex (333) protein complex (114) Nup192 YJL039C vacuolar ATPase complex (14)[117] [118] Nsp1 YJL041W i Emi2 * YDR516CBud4 YJR092W a Kar2 * YJL034W c Nup82 YJL061W f Vma6 YLR447CCdc10 YCR002C c Vps52 * YDR484W Nup85 YJR042W Vph2 * YKL119C aCdc11 YJR076C Vps53 * YJL029C NA Nup120 YKL057C X Bni1 * YNL271C bCdc12 YHR107C Vps54 * YDR027C a Nup100 YKL068W h Drs2 * YAL026CCdc3 YLR314C X Vps51 * YKR020W b Nup133 YKR082W Gaa1 * YLR088W NAShs1 YDL225W b Scj1 * YMR214W Pom34 YLR018C NA Lys9 * YNR050CMdh1 * YKL085W 13. lipid.particle: sterol Ndc1 YML031W Nop6 * YDL213C c5. cell.periphery: exocyst biosynthesis enzymes Nup188 YML103C e Pdc1 * YLR044Ccomplex (120) [119] Nup116 * YMR047C NA Pgi1 * YBR196CExo84 YBR102C NA Erg9 * YHR190W Pom152 YMR129W b Vac8 YEL013WSec10 YLR166C Erg1 * YGR175C Nup53 YMR153W Vma10 YHR039C-A dSec3 YER008C b Erg7 YHR072W c Nup1 YOR098C d Vma2 YBR127CSec5 YDR166C a Erg11 * YHR007C Cdc31 YOR257W X Vma7 YGR020CSec6 YIL068C Erg24 * YNL280C 17. nucleolus: small subunit Vph1 YOR270CSec8 YPR055W NA Erg25 * YGR060W processome (70) Vtc4 YJL012C X6. cytoplasm: translation Erg26 * YGL001C [120] Yor1 * YGR281Winitiation factor eIF3 (45) Erg27 YLR100W NA Utp8 YGR128C Yra1 * YDR381W NAFun12 YAL035W Erg6 YML008C d Nan1 YPL126W b 23. vacuole: vacuolar proteasesHcr1 YLR192C c Erg2 * YMR202W Utp10 YJL109C a and other canonical proteinsNip1 YMR309C a Erg3 * YLR056W a Utp15 YMR093W [12]Prt1 YOR361C Erg5 * YMR015C Utp4 YDR324C Ape1 * YKL103C bRli1 YDR091C Erg4 * YGL012W b Utp9 YHR196W Ape3 * YBR286WRpg1 YBR079C 15. mitochondrion: mitochondrial 18. nucleus: RNA Lap3 * YNL239WTif34 YMR146C X ribosome small subunit (9) polymerase I (30) Pep4 YPL154C NATif35 YDR429C NA Ehd3 YDR036C f Rpa49 * YNL248C NA Prb1 * YEL060CTif5 YPR041W b Mrp13 YGR084C a Rpa12 * YJR063W Prb1 YMR297W7. early.Golgi: SNARE complex Mrp17 YKL003C NA Rpa190 * YOR341W Ams1 * YGL156W a(113) [121] Mrp21 YBL090W h RPApa3 * YOR340C Ath1 YPR026W XDsl1 * YNL258C a Mrp4 YHL004W Rpc40 YPR110C a Pho8 YDR481CSec39 * YLR440C Mrp51 YPL118W Rpa135 * YPR010C Vtc4 YJL012C XTip20 * YGL145W Mrps16 YPL013C NA Rpb5 YBR154C X Ypt7 * YML001W cUfe1 * YOR075W NA Mrps17 YMR188C c 19. peroxisome: integral to Npc2 YDL046W dUse1 * YGL098W Mrps18 YNL306W peroxisomal membrane NA YHR202W NAPep12 YOR036W X Mrps28 YDR337W e (GO:0005779)Ykt6 YKL196C X Mrps5 YBR251W d Ant1 YPR128C8. endosome: ESCRT I & II Mrps8 YMR158W X Inp2 * YMR163Ccomplexes ([122]; Mrps9 YBR146W X Pex12 YMR026C[123]) Pet123 YOR158W g Pex15 * YOL044WVps23 YCL008C X Rsm10 YDR041W b Pex22 * YAL055W bVps28 * YPL065W Rsm19 YNR037C X Pex3 YDR329CVps37 YLR119W X Rsm22 YKL155C Pex30 YLR324W cMvb12 YGR206W a Rsm23 YGL129C Pex31 * YGR004W aVps22 * YPL002C b Rsm27 YGR215W NA Pex32 * YBR168W NAVps36 * YLR417W Rsm7 YJR113C Pxa1 YPL147W XVps25 YJR102C X Mrp1 YDR347W Pxa2 YKL188C XRsm25 YIL093CNam9 YNL137C a. Numbers in parentheses refer to the ID of the complex, if available, from http://yeast-complexes.embl.de [124]. Compositions and localizations of complexes were also taken from references listed in square brackets.Symbols: “*” the protein was not localized in the compartment [22]; “X” or “NA” not tagged or no abundance[105]; “a”, ”b”, etc. refer to outliers in Fig. 7. 18omposite characterization [22]. Other exceptions are the vacuolar model proteins (proteases and other canonicalvacuolar proteins [12]), enzymes of the ergosterol biosynthetic pathway, some of which are associated with thelipid particle [119], and proteins integral to the peroxisomal membrane, which were identified using the GeneOntology (GO) annotations in the SGD [111]. Where they could be found, the ID numbers of the complexes ina yeast complex database [124] are listed in parentheses in Table 8, as are literature references that describe thecomposition and/or localization of the complexes. If any of the proteins in the complexes do not localize [22]to the compartment shown in Table 8 they are marked with an asterisk; those proteins that were not presentin the YeastGFP database or that are lacking an abundance count therein [105] are marked with “X” and “NA”,respectively.The calculated metastable equilibrium logarithms of activities of the proteins in each complex are shown asa function of log f O g ) in Fig. 6. The calculated logarithms of activities of the proteins were compared withexperimental ones by constructing scatterplots at . unit intervals from log f O g ) = − to − . , whichare shown in Figure S1. As above, visual assessment of fit was the first resort to obtain values of log f O g ) that maximize the correspondence with experimental relative abundances, but the RMSD and Spearman rankcorrelation coefficient were also considered in these comparisons. Because of the small sample size in many ofthe comparisons, the sign of the correlation coefficient is as useful as its magnitude in assessing the results. Theresulting calculated relative abundances are listed together with the experimental ones in Table S4.The number of model proteins in each of the complexes is less than the number of most abundant proteins ineach compartment considered in the preceding section, so the visible decrease in scatter is expected. Some of themodel complexes represented in Fig. 7 exhibit an apparent positive correlation between calculated and experimentallogarithms of activities; these include translation initiation factor eIF3, nuclear pore complex and proteins integralto peroxisomal membrane. An inverse correlation between calculated and experimental logarithms of activities isapparent for proteins in the ESCRT I & II complexes, signal recognition complex, and DASH complex. A few of theother complexes (Golgi transport complex, sterol biosynthesis enzymes) exhibit very little overall correspondencebetween calculated and experimental logarithms of activities.The results in Fig. 7 permit an interpretation of the relative energetic requirements for formation of differentgroups of interacting proteins. Take for example complex 14, which is the DASH complex that associates withthe microtubule. An inverse correlation between the experimental and calculated relative abundances is apparentfor this complex in Fig. 7. The RMSD between calculated and experimental logarithms of activities of proteins is . , which is among the highest listed in Table 6. Note from Eqn. (3) that a ∼ log unit change in the chemicalactivity of a chemical species corresponds to a Gibbs energy difference equal to . RT . An average differenceof ∼ between calculated and experimental logarithms of activity indicates that the formation of the proteinsrequires . RT = 1364 cal mol − per protein beyond what would be needed if the proteins formed in metastableequilibrium relative abundances. On the other hand, the formation in specific oxidation-reduction conditions ofproteins making up translation initiation factor eIF3 and other assemblages where cellular abundances positivelycorrelate with and span the same range as the metastable equilibrium distribution can proceed close to a localminimum energy required for protein formation.Because of their relatively high energy demands, proteins in complexes such as the DASH complex and thespindle pole body are likely to be more dynamic in the cell. Although a positive rank correlation coefficientfor the latter complex is reported in Table 6, at a higher oxygen fugacity ( log f O g ) = − ) a strong inversecorrelation obtains between experimental abundances and calculated metastable equilibrium relative abundancesof the proteins in this complex (Figure S1). The finding made elsewhere of some inverse relationships betweenrelative abundance of proteins and corresponding mRNA levels was also interpreted as evidence for additionaleffort on the part of the cell [125]. An inverse relationship that opposes equilibrium may be favored in evolutionbecause of the strategic advantage of incorporating otherwise costly (rare) amino acids that increase enzymaticdiversity [126]. The present results show that specific examples of inverse relationships in the relative abundances ofproteins can be identified using a metastable equilibrium reference state that is conditioned by oxidation-reductionconditions. Chemical selectivity in the dynamic formation in the cell of high-energy proteins could lead to transientformation of complexes that function only under certain conditions. In contrast, complexing proteins that interactclose to metastable equilibrium are more likely to be constitutively formed.19 og f O2 ( g ) l og a −82 −80 −78 −76 −74 −72 −70−5.0−4.5−4.0−3.5−3.0−2.5−2.0 YDL029WYIL062CYKL013CYLR370CYNR035C complex 1 log f O2 ( g ) l og a −82 −80 −78 −76 −74 −72 −70−5.0−4.5−4.0−3.5−3.0−2.5−2.0 YBR135WYBR160WYDL155WYGR155WYLR079WYMR199WYPL256C complex 2 log f O2 ( g ) l og a −82 −80 −78 −76 −74 −72 −70−5.0−4.5−4.0−3.5−3.0−2.5−2.0 YAL029CYBR130CYIL034CYKL007WYKL130C complex 3 log f O2 ( g ) l og a −82 −80 −78 −76 −74 −72 −70−5.0−4.5−4.0−3.5−3.0−2.5−2.0 YCR002CYDL225WYHR107CYJR076CYJR092W YKL085W complex 4 log f O2 ( g ) l og a −82 −80 −78 −76 −74 −72 −70−5.0−4.5−4.0−3.5−3.0−2.5−2.0 YDR166CYER008CYIL068CYLR166C complex 5 log f O2 ( g ) l og a −82 −80 −78 −76 −74 −72 −70−5.0−4.5−4.0−3.5−3.0−2.5−2.0 YAL035WYBR079CYDR091C YLR192CYMR309CYOR361CYPR041W complex 6 log f O2 ( g ) l og a −82 −80 −78 −76 −74 −72 −70−5.0−4.5−4.0−3.5−3.0−2.5−2.0 YGL098WYGL145WYLR440CYNL258C complex 7 log f O2 ( g ) l og a −82 −80 −78 −76 −74 −72 −70−5.0−4.5−4.0−3.5−3.0−2.5−2.0 YLR417WYPL002C YPL065WYGR206W complex 8 log f O2 ( g ) l og a −82 −80 −78 −76 −74 −72 −70−5.0−4.5−4.0−3.5−3.0−2.5−2.0 YDL092WYPL210CYPL243W complex 9 log f O2 ( g ) l og a −82 −80 −78 −76 −74 −72 −70−5.0−4.5−4.0−3.5−3.0−2.5−2.0 YDR517WYLR208WYNL049C YPL085W complex 10 log f O2 ( g ) l og a −82 −80 −78 −76 −74 −72 −70−5.0−4.5−4.0−3.5−3.0−2.5−2.0 YDL167CYER157W YGL005CYGL223CYGR120CYJR138WYML071CYNL041C YNL051WYPR105C complex 11 log f O2 ( g ) l og a −82 −80 −78 −76 −74 −72 −70−5.0−4.5−4.0−3.5−3.0−2.5−2.0 YDR027CYDR484W YJL034WYKR020W YMR214W complex 12 log f O2 ( g ) l og a −82 −80 −78 −76 −74 −72 −70−5.0−4.5−4.0−3.5−3.0−2.5−2.0 YGL001CYGL012WYGR060W YGR175CYHR007CYHR072WYHR190WYLR056W YML008CYMR015CYMR202WYNL280C complex 13 log f O2 ( g ) l og a −82 −80 −78 −76 −74 −72 −70−5.0−4.5−4.0−3.5−3.0−2.5−2.0 YBR233W−AYDR016CYDR201WYDR320C−AYGL061CYKR083CYKL052C complex 14 log f O2 ( g ) l og a −82 −80 −78 −76 −74 −72 −70−5.0−4.5−4.0−3.5−3.0−2.5−2.0 YBL090WYBR251WYDR036CYDR041W YDR337WYDR347WYGL129CYGR084C YHL004WYIL093CYJR113CYKL155CYMR188CYNL137CYNL306WYOR158WYPL118W complex 15 log f O2 ( g ) l og a −82 −80 −78 −76 −74 −72 −70−5.0−4.5−4.0−3.5−3.0−2.5−2.0 YAR002WYBL079WYDL088CYDL116WYDL207WYER105CYER107CYFR002WYGL092WYGL172WYGR119CYIL115CYJL039C YJL041WYJL061WYJR042W YKL068WYKR082WYML031WYML103CYMR129WYMR153WYOR098C complex 16 log f O2 ( g ) l og a −82 −80 −78 −76 −74 −72 −70−5.0−4.5−4.0−3.5−3.0−2.5−2.0 YDR324CYGR128CYHR196WYJL109C YMR093WYPL126W complex 17 log f O2 ( g ) l og a −82 −80 −78 −76 −74 −72 −70−5.0−4.5−4.0−3.5−3.0−2.5−2.0 YJR063WYOR340CYOR341WYPR010CYPR110C complex 18 log f O2 ( g ) l og a −82 −80 −78 −76 −74 −72 −70−5.0−4.5−4.0−3.5−3.0−2.5−2.0 YAL055WYDR329CYGR004W YLR324WYMR026CYOL044WYPR128CYMR163C complex 19 log f O2 ( g ) l og a −82 −80 −78 −76 −74 −72 −70−5.0−4.5−4.0−3.5−3.0−2.5−2.0 YBR164CYBR288CYDL099WYDL192WYDR027CYDR084CYDR141CYDR367WYGL225WYGR261CYJL024CYKR088CYLR250WYNL297CYMR010W complex 20 log f O2 ( g ) l og a −82 −80 −78 −76 −74 −72 −70−5.0−4.5−4.0−3.5−3.0−2.5−2.0 YAL047CYGR240CYHR172W YLR212CYNL126W complex 21 log f O2 ( g ) l og a −82 −80 −78 −76 −74 −72 −70−5.0−4.5−4.0−3.5−3.0−2.5−2.0 YAL026C YBR127CYBR196CYDL213CYDR516CYEL013WYGR020CYGR281WYKL119C YLR044CYLR447C YNL271CYNR050CYOR270CYHR039C−A complex 22 log f O2 ( g ) l og a −82 −80 −78 −76 −74 −72 −70−5.0−4.5−4.0−3.5−3.0−2.5−2.0 YBR286WYDL046W YDR481CYEL060CYGL156W YKL103CYML001WYMR297WYNL239W complex 23 Figure 6:
Calculated logarithms of activities of model proteins in complexes . The numbered complexes areidentified in Table 8. Metastable equilibrium activities of proteins in the complexes were calculated as a functionof log f O g ) for total activity of residues set to unity. Dotted red lines denote values of log f O g ) (listed in Table6) and calculated relative abundances that were used in making Fig. 7.20 alculated log a e x pe r i m en t a l l og a −3.6 −3.4 −3.2 −3.0 −2.8 −2.6−3.6−3.4−3.2−3.0−2.8 ba complex 1 calculated log a e x pe r i m en t a l l og a −5.0 −4.5 −4.0 −3.5 −3.0−5.0−4.5−4.0−3.5−3.0 a b complex 2 calculated log a e x pe r i m en t a l l og a −3.6 −3.4 −3.2 −3.0 −2.8−3.8−3.6−3.4−3.2 a b complex 3 calculated log a e x pe r i m en t a l l og a −4.5 −4.0 −3.5 −3.0 −2.5−4.4−4.2−4.0−3.8−3.6−3.4−3.2−3.0 bca complex 4 calculated log a e x pe r i m en t a l l og a −4.2 −4.0 −3.8 −3.6 −3.4 −3.2−4.2−4.0−3.8−3.6−3.4 a complex 5 calculated log a e x pe r i m en t a l l og a −4.0 −3.8 −3.6 −3.4 −3.2−4.4−4.2−4.0−3.8−3.6−3.4 ca b complex 6 calculated log a e x pe r i m en t a l l og a −3.6 −3.4 −3.2 −3.0−3.8−3.6−3.4−3.2−3.0 a complex 7 calculated log a e x pe r i m en t a l l og a −3.6−3.4−3.2−3.0−2.8−2.6−3.3−3.2−3.1−3.0−2.9−2.8 ba complex 8 calculated log a e x pe r i m en t a l l og a −3.20 −3.16 −3.12 −3.08−3.30−3.25−3.20−3.15−3.10−3.05 ba complex 9 calculated log a e x pe r i m en t a l l og a −4.0 −3.8 −3.6 −3.4 −3.2−4.5−4.0−3.5−3.0 a complex 10 calculated log a e x pe r i m en t a l l og a −4.5 −4.0 −3.5 −3.0−4.8−4.6−4.4−4.2−4.0−3.8−3.6−3.4 a b complex 11 calculated log a e x pe r i m en t a l l og a −4.5 −4.0 −3.5 −3.0−6.0−5.5−5.0−4.5−4.0−3.5−3.0 ba complex 12 calculated log a e x pe r i m en t a l l og a −5.0 −4.5 −4.0 −3.5 −3.0−5.0−4.5−4.0−3.5 b ca d complex 13 calculated log a e x pe r i m en t a l l og a −4.5 −4.0 −3.5 −3.0 −2.5−3.6−3.4−3.2−3.0−2.8 a b complex 14 calculated log a e x pe r i m en t a l l og a −4.2 −4.0 −3.8 −3.6 −3.4−4.6−4.4−4.2−4.0−3.8−3.6−3.4−3.2 c fb ea d g complex 15 calculated log a e x pe r i m en t a l l og a −5.5 −5.0 −4.5 −4.0 −3.5−5.5−5.0−4.5−4.0 ba ec d f g complex 16 calculated log a e x pe r i m en t a l l og a −4.2−4.0−3.8−3.6−3.4−3.2−5.0−4.5−4.0−3.5 a complex 17 calculated log a e x pe r i m en t a l l og a −3.8 −3.6 −3.4 −3.2 −3.0−4.0−3.9−3.8−3.7−3.6−3.5−3.4−3.3 a complex 18 calculated log a e x pe r i m en t a l l og a −4.5 −4.0 −3.5 −3.0−4.2−4.0−3.8−3.6−3.4−3.2−3.0 a b c complex 19 calculated log a e x pe r i m en t a l l og a −5.0 −4.5 −4.0 −3.5 −3.0−4.5−4.0−3.5 eba c d complex 20 calculated log a e x pe r i m en t a l l og a −5.0 −4.5 −4.0 −3.5−6.0−5.5−5.0−4.5−4.0−3.5−3.0 a b complex 21 calculated log a e x pe r i m en t a l l og a −6 −5 −4 −3−6.0−5.5−5.0−4.5−4.0−3.5 ba c complex 22 calculated log a e x pe r i m en t a l l og a −5.0−4.5−4.0−3.5−3.0−2.5−5.0−4.5−4.0−3.5 ca b complex 23 Figure 7:
Comparison of experimental and calculated logarithms of activities of interacting proteins .Symbols are as in Fig. 5; the model proteins and the outliers are listed in Table 8.21 oncluding Remarks
This study was concerned with thermodynamic selectivity of protein formation primarily as a function of onevariable: oxidation-reduction potential represented by the logarithm of the fugacity of oxygen ( log f O g ) ). In reality,many variables are changing in cells, including the hydration state, pH , activity of CO and H S , temperatureand pressure. These all factor into the Gibbs energy changes accompanying the overall chemical transformationbetween proteins. Except for oxygen fugacity, the other variables were held constant in most of the calculationsreported here. It is tempting to explore the effects of these variables on the compositions of metastable equilibriumassemblages. Incorporation into the framework of protein folding reactions and a non-ideality contribution, orexcess Gibbs energy, that would encompass the effects of electrostatic interactions and macromolecular crowdingis another target for expanding the scope of the thermodynamic characterizations.The model results reported above were chosen in order to test specific predictions made using the hypothesisthat the selection for or against metastable equilibrium has measurable consequences in organisms. The findingscan be summarized as:1. The oxidation-reduction potential ( log f O g ) ) limits of relative metastabilities of redoxin isoforms overlapwith measured Eh (redox potential) in the cytoplasm and mitochondrion but not the nucleus.2. The model proteologs represent the overall amino acid compositions of proteins in different compartments.At relatively low oxidation-reduction potential, proteologs in order of decreasing relative metastability arethose of ER, Golgi, cell periphery, mitochondrion, nuclear periphery and spindle pole. At higher oxidation-reduction potential, proteologs in order of decreasing relative metastability are those of actin, nucleolus,nucleus, vacuole, bud neck and microtubule. At intermediate oxygen fugacities, proteologs of lipid particle,peroxisome and early Golgi are relatively metastable compared to those of cytoplasm, vacuolar membraneand late Golgi.3. In a chemically reacting system starting with the cytoplasmic proteolog where all interactions include theproteologs of microtubule or spindle pole, environmental shifts in log f O g ) going from − to − . to − to − can drive the sequential formation of proteologs of spindle pole, microtubule, cytoplasm, actin,nucleus, cell periphery, bud neck and bud.4. Oxidation-reduction potentials within − < log f O g ) < − give rise to metastable equilibrium popu-lations of most abundant model proteins within compartments in which the range of protein abundancebecomes closest to that seen in reported measurements. Substantial scatter is evident in the comparisons,but a moderate overall positive rank correlation was observed.5. Closer fits between calculated and experimental relative abundances were obtained within − < log f O g ) < − by considering fewer numbers of model proteins that interact in complex formation. Strong positivecorrelations were found for, among others, cytoplasmic translation initiation factor eIF3 and nuclear porecomplex; negative correlations were found for the microtubule-associated DASH complex and the endosomalESCRT I & II complexes.This study contributes to understanding the products of evolution by quantifying the extent of departure frommetastable equilibrium in populations of interacting proteins. The observed positive correlations are consistentwith a trend of some populations of interacting proteins to be imprinted with the consequences of local energyminimization in chemical reactions. These results and observations also support the notion that changing oxidation-reduction potential can selectively promote or hold back the reactions leading to formation of complexing proteinsin relative abundances seen in the cell. Combining proteomic data with metastable equilibrium calculations istherefore a promising avenue for predicting complexes that form in specific oxidation-reduction conditions thatvary temporally and spatially in biochemical systems. Methods
The essential steps in the calculations reported here are 1) defining standard states, 2) identifying model proteins forsystems of interest, 3) assessing the relative abundances of model proteins in metastable equilibrium, 4) visualizingthe results of the calculations on speciation or predominance diagrams and 5) comparing the computational resultswith experimental biochemical and proteomic data. 22 tandard states and chemical activities
The activity of a species is fundamentally related to the chemical potential of the species by µ = µ ◦ + RT ln a , (7)where R and T represent, respectively, the gas constant and the temperature, µ and µ ◦ stand for the chemicalpotential and standard chemical potential, respectively, and a denotes activity. No provision for activity coefficientsof proteins or other species was used in this study; under this approximation, the activity of an aqueous species isequal to its concentration (molality).The standard state for aqueous species including proteins specifies unit activity of the aqueous species inhypothetical one molal solution referenced to infinite dilution. The standard molal Gibbs energies of the proteinswere calculated with the CHNOSZ software package [70] using group additivity properties and parameters takenfrom [69]. Proteologs: overall compositions of proteins in compartments
The overall amino acid compositions of proteins in 23 subcellular locations in
S. cerevisiae were calculated bycombining localization [22] and abundance [105] data for proteins measured in the YeastGFP project with aminoacid compositions of proteins downloaded from the
Saccharomyces
Genome Database (SGD) [111]. Of 4155ORF names listed in the YeastGFP dataset, all but 12 are present in SGD (the missing ones are YAR044W,YBR100W, YDR474C, YFL006W, YFR024C, YGL046W, YGR272C, YJL012C-A, YJL017W, YJL018W, YJL021Cand YPR090W).To generate proteologs that are most representative of each compartment, proteins that were annotated in theYeastGFP study as being localized to more than one compartment were excluded from this analysis (except for bud;see below), as were those for which no abundance was reported. The names of the open reading frames (ORFs) cor-responding to the proteins in the YeastGFP data set were matched against the SGD’s protein_properties.tab file downloaded on 2008-08-04. This search yielded a number of model proteins for each compartment, rangingfrom 5 (ER to Golgi) to 746 (cytoplasm); see Table 3. The names of the compartments used throughout the tablesand figures in this paper correspond to the notation used in the YeastGFP data files (where spaces are replacedwith a period).It was found that no proteins with reported abundances and localized to the bud were exclusive to thatcompartment, hence all of the proteins localized there (which also have localizations in other compartments) weretaken as models for the bud proteolog. The amino acid composition of the proteolog for each compartmentwas calculated by taking the sum of the compositions of each model protein for a compartment in proportionto its fractional abundance in the total model protein population of the compartment. The resulting aminoacid compositions are listed in Table S1. The corresponding chemical formulas of the nonionized proteologs andthe calculated standard molal Gibbs energies of formation from the elements at 25 ◦ C and 1 bar of the ionizedproteologs are shown in Table 3.
Metastability calculations
Diagrams showing the predominant proteins and the relative abundances of proteins in metastable equilibrium weregenerated using the CHNOSZ software package [70]. These calculations take account of formation reactions ofthe proteins written for their residue equivalents [70]. This approach is demonstrated in the Results for a specificmodel system.The basis species, or perfectly mobile components of an open system [61], appearing in the formation reactionsstudied here are CO aq ) , H O , NH aq ) , O g ) , H S ( aq ) and H + . The reference activities used for the basisspecies were − , , − , − and − , respectively, for CO aq ) , H O , NH aq ) , H S ( aq ) and H + . Inthe case of diagrams showing Eh as a variable, the aqueous electron ( e − ) was substituted for O g ) in the basisspecies. Reference values for a e − or f O g ) are not listed here because one or the other is used as an independentvariable in each of the calculations described above. 23 onversion between scales of oxidation-reduction potential Conversion between the log f O g ) and Eh scales of oxidation-reduction potential can be made by first writing thehalf-cell reaction for the dissociation of H O as H O (cid:10)
12 O g ) + 2H + + 2 e − . (8)Taking pH = − log a H + and pe = − log a e − , the logarithmic analog of the law of mass action for Reaction 8 canbe written as log K = 12 log f O g ) − − − log a H O , (9)where log K stands for the logarithm of the equilibrium constant of Reaction 8 as a function of temperature andpressure. Eh is related to pe by [127] pe = F . RT Eh , (10)where F and R denote the Faraday constant and the gas constant, respectively. Combining Eqns. (9) and (10)yields the following expression for Eh as a function of log f O g ) and other variables: Eh = 2 . RTF (cid:18)
12 log f O g ) − − log a H O − log K (cid:19) . (11)At 25 ◦ C and 1 bar, F/ . RT = 16 . volt − and log K = − . ; for pH = 7 and log a H O = 0 , a value of Eh = 0
V corresponds to log f O g ) = − . Eqn. (11) permits the conversion between Eh and log f O g ) as wellat other temperatures, pH s, and activities of H O . Average nominal oxidation state of carbon
Let us write the chemical formula of a species of interest as C n C H n H N n N O n O S Zn S , where Z denotes the net charge.The average nominal oxidation state of carbon ( Z C ) of this species is given by Z C = Z − n H + 2 ( n O + n S ) + 3 n N n C . (12)Eqn. (12) is consistent with the electronegativity rules described in [128] and is compatible with the equationfor average oxidation number of carbon used in [129]. For example, Eqn. (12) can be used to calculate theaverage nominal oxidation states of carbon in CO and CH , which are +4 and − , respectively. Note thatthe proportions of oxygen and other covalently-bonded heteroatoms contribute to the value of Z C of a proteinor other molecule, but that proton ionization does not alter the nominal carbon oxidation state, because of theopposite contributions from Z and n H in Eqn. (12). In the 4143 proteins identified in the YeastGFP subcellularlocalization study and found in the Saccharomyces
Genome Database, the minimum and maximum of Z C are − . and . , respectively. Of the proteins in this dataset, six have Z C < − . (YDR193W, YDR276C,YEL017C-A, YJL097W, YML007C-A, YMR292W) and six have Z C > . (YCL028W, YHR053C, YHR055C,YKR092C, YMR173W, YPL223C). The points in the scatterplots in this paper (Figs. 5 and 7 and Figure S1) arecolored on a continuous red-blue scale according to the value of Z C of the proteins, where maximum red occursat Z C = − . and maximum blue occurs at Z C = 0 . . Comparison with experimental relative abundances
In comparison, experimental abundances of proteins in each model system were scaled so that the total chemicalactivity of residues was equal to unity.The root mean square deviation between calculated and experimental logarithms of activities was calculatedusing 24
MSD = (cid:115) (cid:80) ni =1 ( X calc ,i − X expt ,i ) n , (13)where X calc ,i and X expt ,i denote the calculated and experimental logarithms of activities and n stands for thenumber of proteins.xThe Spearman rank correlation coefficient ( ρ ) was calculated using ρ = 1 − dn ( n − , (14)where d = (cid:80) ni =1 ( x calc ,i − x expt ,i ) and x calc ,i and x expt ,i stand for the ranks of the corresponding logarithms ofactivities. Supporting Information
Figure S1: Comparisons of relative abundances of proteins (PDF)
Scatterplots of experimental vs. calculated abundance ranking and logarithm of activity of most abundant proteinsand selected complexes in subcellular compartments are shown as a function of oxygen fugacity.
Table S1: Amino acid compositions of model proteologs (CSV)
Overall amino acid compositions of proteins in subcellular locations of
S. cerevisiae were calculated from YeastGFPlocalization [22] and abundance [105] data downloaded from http://yeastgfp.ucsd.edu/ combined with proteincompositions downloaded from the
Saccharomyces
Genome Database ( ). Theamino acid compositions of the proteologs were used to calculate the properties listed in Table 3.
Table S2: Intercompartmental protein reactions (TXT)
This table lists chemical reactions between residue equivalents of proteologs for interacting compartments. Thecharges of the proteologs were calculated at 25 ◦ C, 1 bar and pH = 7 . Table S3: Abundance data for model proteins in compartments (CSV)
For the up to 50 most abundant model proteins in each compartment are listed the ORF name, sequence length,average nominal oxidation state of carbon (Eqn. 12), computed standard molal Gibbs energy at 25 ◦ C and 1 barof the ionized protein and charge at pH = 7 and calculated and experimental logarithm of activity.
Table S4: Abundance data for protein complexes (CSV)
For the model complexes in each compartment (see Table 8) are listed the same properties as in Table S3.
Text S1: CHNOSZ software package (GZ)
This is the complete package (source code, documentation and data files) for the CHNOSZ program, which wasused together with the program script (below) to perform the calculations in this study. The package is designed tobe used with the R software environment . Additional information about CHNOSZis available in [70] and at . 25 ext S2: Program script and data files for generating figures (GZ)
This program script and supporting files were used to generate the figures shown above. It includes the script itself(plot.R), protein compositions (generated from the protein properties.tab file downloaded from the
Saccharomyces
Genome Database), calculated standard molal thermodynamic properties of the proteins (to speed up calculations),YeastGFP protein localization and abundance data [22, 105], and a .csv version of Table 6. To generate the figures,the contents of the zip file should all be placed into the R working directory before loading CHNOSZ. Then readin the script with source(’plot.R’) . More details on the operation are provided at the top of the script file.
Text S3: Interactions between subcellular compartments in yeast (PDF)
This file lists statements from [87, 94, 95, 93, 96, 97] used to identify the interactions between proteins in differentcompartments of
Saccharomyces cerevisiae that are listed in Table 4.
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