Timothy C. Elston

Stochasticity in gene expression: from theories to phenotypes

Genetically identical cells exposed to the same environmental conditions can show significant variation in molecular content and marked differences in phenotypic characteristics. This variability is linked to stochasticity in gene expression, which is generally viewed as having detrimental effects on cellular function with potential implications for disease. However, stochasticity in gene expression can also be advantageous. It can provide the flexibility needed by cells to adapt to fluctuating environments or respond to sudden stresses, and a mechanism by which population heterogeneity can be established during cellular differentiation and development.

Stochasticity in Transcriptional Regulation: Origins, Consequences and Mathematical Representations

Transcriptional regulation is an inherently noisy process. The origins of this stochastic behavior can be traced to the random transitions among the discrete chemical states of operators that control the transcription rate and to finite number fluctuations in the biochemical reactions for the synthesis and degradation of transcripts. We develop stochastic models to which these random reactions are intrinsic and a series of simpler models derived explicitly from the first as approximations in different parameter regimes. This innate stochasticity can have both a quantitative and qualitative impact on the behavior of gene-regulatory networks. We introduce a natural generalization of deterministic bifurcations for classification of stochastic systems and show that simple noisy genetic switches have rich bifurcation structures; among them, bifurcations driven solely by changing the rate of operator fluctuations even as the underlying deterministic system remains unchanged. We find stochastic bistability where the deterministic equations predict monostability and vice-versa. We derive and solve equations for the mean waiting times for spontaneous transitions between quasistable states in these switches.

Energy transduction in ATP synthase

Mitochondria, bacteria and chloroplasts use the free energy stored in transmembrane ion gradients to manufacture ATP by the action of ATP synthase. This enzyme consists of two principal domains. The asymmetric membrane-spanning Fo portion contains the proton channel, and the soluble F1 portion contains three catalytic sites which cooperate in the synthetic reactions. The flow of protons through Fo is thought to generate a torque which is transmitted to F1 by an asymmetric shaft, the coiled-coil γ-subunit. This acts as a rotating ‘cam’ within F1, sequentially releasing ATPs from the three active sites. The free-energy difference across the inner membrane of mitochondria and bacteria is sufficient to produce three ATPs per twelve protons passing through the motor. It has been suggested that this protonmotive force biases the rotors diffusion so that Fo constitutes a rotary motor turning the γ shaft. Here we show that biased diffusion, augmented by electrostatic forces, does indeed generate sufficient torque to account for ATP production. Moreover, the motors reversibility — supplying torque from ATP hydrolysis in F1 converts the motor into an efficient proton pump — can also be explained by our model.

A bottom-up approach to gene regulation.

The ability to construct synthetic gene networks enables experimental investigations of deliberately simplified systems that can be compared to qualitative and quantitative models. If simple, well-characterized modules can be coupled together into more complex networks with behaviour that can be predicted from that of the individual components, we may begin to build an understanding of cellular regulatory processes from the ‘bottom up’. Here we have engineered a promoter to allow simultaneous repression and activation of gene expression in Escherichia coli. We studied its behaviour in synthetic gene networks under increasingly complex conditions: unregulated, repressed, activated, and simultaneously repressed and activated. We develop a stochastic model that quantitatively captures the means and distributions of the expression from the engineered promoter of this modular system, and show that the model can be extended and used to accurately predict the in vivo behaviour of the network when it is expanded to include positive feedback. The model also reveals the counterintuitive prediction that noise in protein expression levels can increase upon arrest of cell growth and division, which we confirm experimentally. This work shows that the properties of regulatory subsystems can be used to predict the behaviour of larger, more complex regulatory networks, and that this bottom-up approach can provide insights into gene regulation.

Β2-Adrenergic Receptor Signaling and Desensitization Elucidated by Quantitative Modeling of Real Time cAMP Dynamics

G protein-coupled receptor signaling is dynamically regulated by multiple feedback mechanisms, which rapidly attenuate signals elicited by ligand stimulation, causing desensitization. The individual contributions of these mechanisms, however, are poorly understood. Here, we use an improved fluorescent biosensor for cAMP to measure second messenger dynamics stimulated by endogenous β2-adrenergic receptor (β2AR) in living cells. β2AR stimulation with isoproterenol results in a transient pulse of cAMP, reaching a maximal concentration of ∼10 μm and persisting for less than 5 min. We investigated the contributions of cAMP-dependent kinase, G protein-coupled receptor kinases, and β-arrestin to the regulation of β2AR signal kinetics by using small molecule inhibitors, small interfering RNAs, and mouse embryonic fibroblasts. We found that the cAMP response is restricted in duration by two distinct mechanisms in HEK-293 cells: G protein-coupled receptor kinase (GRK6)-mediated receptor phosphorylation leading to β-arrestin mediated receptor inactivation and cAMP-dependent kinase-mediated induction of cAMP metabolism by phosphodiesterases. A mathematical model of β2AR signal kinetics, fit to these data, revealed that direct receptor inactivation by cAMP-dependent kinase is insignificant but that GRK6/β-arrestin-mediated inactivation is rapid and profound, occurring with a half-time of 70 s. This quantitative system analysis represents an important advance toward quantifying mechanisms contributing to the physiological regulation of receptor signaling.

A cisternal maturation mechanism can explain the asymmetry of the Golgi stack

Morphological data suggest that Golgi cisternae form at the cis‐face of the stack and then progressively mature into trans‐cisternae. However, other studies indicate that COPI vesicles transport material between Golgi cisternae. These two observations can be reconciled by assuming that cisternae carry secretory cargo through the stack in the anterograde direction, while COPI vesicles transport Golgi enzymes in the retrograde direction. This model provides a mechanism for cisternal maturation. If Golgi enzymes compete with one another for packaging into COPI vesicles, we can account for the asymmetric distribution of enzymes across the stack.

Biochemical Network Stochastic Simulator (BioNetS): software for stochastic modeling of biochemical networks

BackgroundIntrinsic fluctuations due to the stochastic nature of biochemical reactions can have large effects on the response of biochemical networks. This is particularly true for pathways that involve transcriptional regulation, where generally there are two copies of each gene and the number of messenger RNA (mRNA) molecules can be small. Therefore, there is a need for computational tools for developing and investigating stochastic models of biochemical networks.ResultsWe have developed the software package Biochemical Network Stochastic Simulator (BioNetS) for efficientlyand accurately simulating stochastic models of biochemical networks. BioNetS has a graphical user interface that allows models to be entered in a straightforward manner, and allows the user to specify the type of random variable (discrete or continuous) for each chemical species in the network. The discrete variables are simulated using an efficient implementation of the Gillespie algorithm. For the continuous random variables, BioNetS constructs and numerically solvesthe appropriate chemical Langevin equations. The software package has been developed to scale efficiently with network size, thereby allowing large systems to be studied. BioNetS runs as a BioSpice agent and can be downloaded from http://www.biospice.org. BioNetS also can be run as a stand alone package. All the required files are accessible from http://x.amath.unc.edu/BioNetS.ConclusionsWe have developed BioNetS to be a reliable tool for studying the stochastic dynamics of large biochemical networks. Important features of BioNetS are its ability to handle hybrid models that consist of both continuous and discrete random variables and its ability to model cell growth and division. We have verified the accuracy and efficiency of the numerical methods by considering several test systems.

Regulation of Cell Signaling Dynamics by the Protein Kinase-Scaffold Ste5

Cell differentiation requires the ability to detect and respond appropriately to a variety of extracellular signals. Here we investigate a differentiation switch induced by changes in the concentration of a single stimulus. Yeast cells exposed to high doses of mating pheromone undergo cell division arrest. Cells at intermediate doses become elongated and divide in the direction of a pheromone gradient (chemotropic growth). Either of the pheromone-responsive MAP kinases, Fus3 and Kss1, promotes cell elongation, but only Fus3 promotes chemotropic growth. Whereas Kss1 is activated rapidly and with a graded dose-response profile, Fus3 is activated slowly and exhibits a steeper dose-response relationship (ultrasensitivity). Fus3 activity requires the scaffold protein Ste5; when binding to Ste5 is abrogated, Fus3 behaves like Kss1, and the cells no longer respond to a gradient or mate efficiently with distant partners. We propose that scaffold proteins serve to modulate the temporal and dose-response behavior of the MAP kinase.

A Systems-Biology Analysis of Feedback Inhibition in the Sho1 Osmotic-Stress-Response Pathway

BACKGROUND A common property of signal transduction systems is that they rapidly lose their ability to respond to a given stimulus. For instance in yeast, the mitogen-activated protein (MAP) kinase Hog1 is activated and inactivated within minutes, even when the osmotic-stress stimulus is sustained. RESULTS Here, we used a combination of experimental and computational analyses to investigate the dynamic behavior of Hog1 activation in vivo. Computational modeling suggested that a negative-feedback loop operates early in the pathway and leads to rapid attenuation of Hog1 signaling. Experimental analysis revealed that the membrane-bound osmosensor Sho1 is phosphorylated by Hog1 and that phosphorylation occurs on Ser-166. Moreover, Sho1 exists in a homo-oligomeric complex, and phosphorylation by Hog1 promotes a transition from the oligomeric to monomeric state. A phosphorylation-site mutation (Sho1(S166E)) diminishes the formation of Sho1-oligomers, dampens activation of the Hog1 kinase, and impairs growth in high-salt or sorbitol conditions. CONCLUSIONS These findings reveal a novel phosphorylation-dependent feedback loop leading to diminished cellular responses to an osmotic-stress stimulus.

Force Generation in RNA Polymerase

RNA polymerase (RNAP) is a processive molecular motor capable of generating forces of 25-30 pN, far in excess of any other known ATPase. This force derives from the hydrolysis free energy of nucleotides as they are incorporated into the growing RNA chain. The velocity of procession is limited by the rate of pyrophosphate release. Here we demonstrate how nucleotide triphosphate binding free energy can rectify the diffusion of RNAP, and show that this is sufficient to account for the quantitative features of the measured load-velocity curve. Predictions are made for the effect of changing pyrophosphate and nucleotide concentrations and for the statistical behavior of the system.