Theoretical constraints imposed by gradient detection and dispersal on microbial size in astrobiological environments
TTheoretical constraints imposed by gradient detection anddispersal on microbial size in astrobiological environments
Manasvi Lingam ∗ Department of Aerospace, Physics and Space Science, Florida Institute of Technology,Melbourne, FL 32901, USAInstitute for Theory and Computation, Harvard University, Cambridge, MA 02138,USA
Abstract
The capacity to sense gradients efficiently and acquire information about the ambient environ-ment confers many advantages like facilitating movement toward nutrient sources or away fromtoxic chemicals. The amplified dispersal evinced by organisms endowed with motility is possiblybeneficial in related contexts. Hence, the connections between information acquisition, motility,and microbial size are explored from an explicitly astrobiological standpoint. By using prior the-oretical models, the constraints on organism size imposed by gradient detection and motility areelucidated in the form of simple heuristic scaling relations. It is argued that environments suchas alkaline hydrothermal vents, which are distinguished by the presence of steep gradients, mightbe conducive to the existence of “small” microbes (with radii of (cid:38) . µ m) in principle, whenonly the above two factors are considered; other biological functions (e.g., metabolism and geneticexchange) could, however, regulate the lower bound on microbial size and elevate it. The derivedexpressions are potentially applicable to a diverse array of settings, including those entailing sol-vents other than water; for example, the lakes and seas of Titan. The paper concludes with abrief exposition of how this formalism may be of practical and theoretical value to astrobiology. The ability to precisely sense physical and chemical gradients is a ubiquitous feature of the microbialworld, which is not surprising in light of the many desirable outcomes that are documented to resultfrom this ability (Alexandre et al., 2004; Mann and Lazier, 2006; Hu and Tu, 2014; Bi and Sourjik,2018). For instance, the ability to sense gradients in the chemical concentration enables organismsto move either toward or away from these compounds (Phillips et al., 2013, pp. 159-161); see alsoWadhams and Armitage (2004). In the former case, one of the chief advantages is the ability toreach nutrient sources and thereby benefit from enhanced uptake (Lauro et al., 2009; Stocker, 2012;Kirchman, 2018), while other positives include range expansion, biofilm formation and the onset ofsymbiosis (Porter et al., 2011; Cremer et al., 2019; Wong-Ng et al., 2018; Raina et al., 2019).In the latter (i.e., movement away from source), microbes can avoid toxic chemicals by travelling inthe direction with lower concentration, or they can come up ways to mitigate the damage (Kirchman, ∗ Electronic address: [email protected] a r X i v : . [ a s t r o - ph . E P ] F e b Escherichia coli beingone example, exhibits many remarkable features including high sensitivity, flexibility and robustnessvis-`a-vis chemical stimuli (Alon et al., 1999; Bialek and Setayeshgar, 2005; Sourjik and Wingreen,2012; Micali and Endres, 2016; Waite et al., 2018; Figueroa-Morales et al., 2020).Aside from chemotaxis, the likes of phototaxis and thermotaxis – which are reliant on identifyinglight and thermal gradients, respectively – have also been widely investigated in model organisms andvia theoretical modelling (Armitage, 1999; Mori, 1999; J´ekely, 2009; Demir and Salman, 2012; Huand Tu, 2014; Lozano et al., 2016; Wilde and Mullineaux, 2017; Yang et al., 2018). In each of thesemechanisms, the key common point that deserves to be appreciated is: organisms sense information about their environments. While this information can be put to many uses, one of the key aspectsthat we shall focus on herein is targeted locomotion (Webster and Weissburg, 2009)—that is to say,movement along some preferred direction. Thus, if microbes are not efficient at acquiring informationabout their habitats, their capacity for meaningful motility could be stymied, although there arelatent subtleties at play (Celani and Vergassola, 2010; Taktikos et al., 2013). This process of detectinggradients and gaining information is reliant on accurately measuring the “intensity” of the stimulantat multiple points in space or time (Berg and Purcell, 1977; Berg, 1993).As the preceding sentence indicates, there exist two basic modes of sensing, namely, the spatialand the temporal (Dusenbery, 2009). In the former, microbes use the data garnered from receptors atdifferent spatial locations to determine the direction of locomotion. In the latter, measurements fromthe receptors are collected at various moments in time to regulate the direction. The upshot of theprior discussion is that gradient sensitivity is generally expected to play a crucial role in modulatingthe efficacy of motility (Fenchel, 2002). This statement yields a vital corollary: if the organism is toosmall to sense gradients efficiently, this bottleneck would pose difficulties for meaningful locomotion.In other words, the constraints imposed by information specify a minimum cell radius ( R min ) formicrobes that are efficient at gradient sensing and dispersal. Naturally, this does not represent theonly limiting factor, and we will touch upon other controls later in the paper.It is worth highlighting that motility is regarded a viable biosignature candidate for in situ life-detection missions (Nadeau et al., 2016, 2018; Neveu et al., 2018, 2020; Riekeles et al., 2021). Infact, the spatial resolution required to identify motile organisms is lower when compared to theirnon-motile counterparts (Nadeau et al., 2016, pg. 755). The ability to pin down the minimum cellsize, and the cell density of motile lifeforms thence (Lingam and Loeb, 2021b), is valuable thereforefrom the practical goal of gauging and designing suitable instruments for future missions. However,we emphasize that the raison d’ˆetre of this paper is not to solely assess the feasibility of motility assuch. Our major objective is, instead, to unveil the constraints on gradient sensing imposed by size;to put it differently, the chief purpose is to explore how size conditions the efficiency and efficacy oforganisms to acquire information about their environment, which in turn permits them to act in anumber of ways delineated above. It is essential to recognize that this is not the only bottleneck onsize because factors like energy, nutrients, cell structure and physiology also play a role (LaRowe andAmend, 2015; Lever et al., 2015; Kempes et al., 2019; Lopatkin and Collins, 2020). As stated earlier,our goal is to explicate some of the inherent connections between gradient detection and organismdispersal on the one hand and microbial size on the other.For the purposes of this paper, we will adopt the heuristic framework explicated in Dusenbery(1997) due to its comparative simplicity and broad scope. To reiterate, the objective is to developuncomplicated scaling relations that may pave the way toward understanding how the sizes of microbes2n variegated astrobiological environments might be constrained by the capacity to promote dispersalas well as resolve gradients and obtain information about the neighborhood. The importance ofstudying the physical, chemical and biological constraints on size and its attendant evolutionary andecological consequences has a rich history, dating back to at least the pioneering essay by Haldane(1926). While this topic has been commonly explored at the level of macroscopic organisms (Went,1968; Denny, 1993; Blanckenhorn, 2000; Angilletta, 2009; Ginzberg et al., 2015), size constraints atthe microscopic level have also been investigated (Morowitz, 1967; Koch, 1996; Knoll et al., 1999;Andersen et al., 2016; Cockell, 2018).There are certain aspects, however, whereby our treatment diverges from that of Dusenbery (1997).First, one of the principal purposes of the aforementioned publication is to estimate the signal-to-noiseratio (S/N), the metric used for measuring the efficacy of gradient detection, as a function of the cellsize. Here, we tackle the converse problem, in which we employ the condition S / N = 1 to deduce thecorresponding R min . Second, we modify some of the fiducial values employed in Dusenbery (1997) inlight of current developments; the pertinent references are cited when we deviate from the canonicalestimates. Third, and most importantly, we frame our analysis in an astrobiological context byfocusing on domains and worlds that are perceived as promising from this standpoint.The outline of the paper is as follows. We begin by presenting the salient equations and modelparameters in Section 2. We explore the predictions of this framework for two distinct environmentsin Section 3 – to wit, submarine hydrothermal vents on Earth (and elsewhere), and generic lakes andseas of Titan. Finally, we conclude with a summary of our findings along with a brief exposition oftheir practical and theoretical implications in Section 4. Given that our analysis mirrors that of Dusenbery (1997), we begin with a brief summary of thecaveats and simplifications involved in constructing the heuristic model for surface and subsurfacehabitats. For starters, the organisms are taken to have spherical symmetry; changing the shape toellipsoidal or cylindrical is anticipated to yield noteworthy benefits but also incur concomitant costs,as elucidated in Kiørboe (2008, pp. 31-32) and Schuech et al. (2019). Second, the power per unitvolume accessible by an organism for swimming is held roughly constant (cf. Makarieva et al., 2008;DeLong et al., 2010). Third, the effect of noise (the S/N to be more precise) is taken to directly impactthe capability of organisms to obtain information about stimuli and it is consequently pressed intoservice as a proxy. Fourth, the temporal duration over which an organism can undertake rectilinearmotion or ascertain the direction of stimuli is governed by rotational Brownian motion.Fifth, the scaling relations expounded herein are applicable at low Reynolds number (Purcell,1977; Lauga, 2016). Turbulence can lead to sizable quantitative changes, such as through the effectsof turbulent diffusion (Weissburg, 2000; Okubo and Levin, 2001). Sixth, the methodology is aproposonly for single microbes and is therefore not applicable to collective behavior, which is characterized bymuch richer dynamics (Brenner et al., 1998; Vicsek and Zafeiris, 2012; Hakim and Silberzan, 2017; Fuet al., 2018). When microbes form consortia, which is particularly pertinent in harsh environmentalconditions, it might be feasible for these aggregates to perform gradient sensing beyond the limits ofsingle-cell chemotaxis analyzed herein (Varennes et al., 2016; Camley, 2018). Lastly, it is assumed thatthe gradients in question are maintained continuously (with spatiotemporal variations) by virtue ofgeological activity and are consequently not dissipated by metabolism and other biological processes.Certain environments on Earth (e.g., submarine hydrothermal vents) are known to sustain long-livedchemical and thermal gradients (Russell et al., 2014; Meadows et al., 2020).In spite of these limitations, we note that the results have proven to be fairly accurate for prokary-3tes (e.g., Martens et al., 2015; Kirchman, 2018; Beeby et al., 2020); similar considerations could applyto eukaryotes in differentiating between motile and non-motile species (Wan and J´ekely, 2021).
The first point to note is that motility, by definition, can facilitate faster dispersal. In the absence ofmotility, the behavior of microbes can be described by the classical diffusion coefficient D , whereasits inclusion leads to an “effective” diffusion coefficient D M (Berg, 1993). The ratio of these twodiffusion coefficients is ζ ≡ D M /D . We can solve for R min by demanding that this ratio must exceedthe minimum threshold of ζ = 1 in order for dispersal to start becoming effective. By implementingthis procedure, we end up with R min ≈ . µ m (cid:18) UU ⊕ (cid:19) − / (cid:18) ηη ⊕ (cid:19) − / (cid:18) TT ⊕ (cid:19) / , (1)where the subscript ‘ ⊕ ’ hereafter is taken to signify representative values on Earth, chosen based onDusenbery (1997, Table 1) and other sources, with the explicit proviso understanding that Earth-based organisms and habitats display a substantial degree of heterogeneity. In the above equation, η denotes the dynamic viscosity of the environment and U embodies the speed of swimming relativeto the organism’s size. The reason behind introducing U (units of s − ) has to do with the empiricallinear scaling discerned between the speeds and sizes of organisms (Bonner, 2006, Figure 34), which issupported by theoretical arguments (Vogel, 2008; Dusenbery, 2009; Meyer-Vernet and Rospars, 2016).We have adopted T ⊕ = 293 K (20 ◦ C), η ⊕ = 10 − N s m − , and U ⊕ = 10 s − ; note that the latterparameter is close to the median value for swimming microbes (Meyer-Vernet and Rospars, 2016) andto Escherichia coli in particular (Milo and Phillips, 2016, pg. 270). With that said, some species of
Archaea evince fast swimming speeds that are more than one order of magnitude higher than
E. coli (Herzog and Wirth, 2012). Our understanding of archaeal motility remains incomplete despite theavailable data (Albers and Jarrell, 2018), partly due to the variety of propulsion methods accessiblein theory (Bechinger et al., 2016).Next, we turn our attention to the various constraints imposed by garnering information fromgradients in stimuli via spatial and temporal methods. The rest of the formulae are derived by takingthe corresponding equations from Dusenbery (1997, Table 2) for the signal-to-noise ratio (S/N), anddeploying the criterion S / N = 1 to solve for R min . The first example from this category are chemicalgradients. For the spatial mode, the relevant scaling is given by R min ≈ . µ m (cid:18) D c D ⊕ (cid:19) − / (cid:18) CC ⊕ (cid:19) − / (cid:18) L c L c ⊕ (cid:19) / (cid:18) ηη ⊕ (cid:19) − / (cid:18) TT ⊕ (cid:19) / (2)whereas the equivalent expression for the temporal mode is R min ≈ . µ m (cid:18) UU ⊕ (cid:19) − / (cid:18) D c D ⊕ (cid:19) − / (cid:18) CC ⊕ (cid:19) − / (cid:18) L c L c, ⊕ (cid:19) / (cid:18) ηη ⊕ (cid:19) − / (cid:18) TT ⊕ (cid:19) / , (3)where C represents the average concentration of the appropriate chemical in the environment, D c denotes the diffusion coefficient corresponding to that chemical in the given solvent, and L c ≈C ( d C /dz ) − embodies the characteristic length scale associated with the chemical gradient. Thefiducial values chosen are D ⊕ = 10 − m s − , L c, ⊕ = 10 − m, and C ⊕ ≈ µ M; note that thelatter is commensurate with the concentrations of nutrients and other chemicals observed in marineenvironments (Sarmiento and Gruber, 2006; Schlesinger and Bernhardt, 2013).4n the same vein, we tackle the second category—to wit, thermal gradients. For the spatial modeof obtaining information, the minimum cell size is R min ≈ . µ m (cid:18) κκ ⊕ (cid:19) − / (cid:18) HH ⊕ (cid:19) / (cid:18) L t L t, ⊕ (cid:19) / (cid:18) ηη ⊕ (cid:19) − / (cid:18) TT ⊕ (cid:19) / , (4)while this quantity under the temporal mode is estimated to be R min ≈ . µ m (cid:18) UU ⊕ (cid:19) − / (cid:18) κκ ⊕ (cid:19) − / (cid:18) HH ⊕ (cid:19) / (cid:18) L t L t, ⊕ (cid:19) / (cid:18) ηη ⊕ (cid:19) − / (cid:18) TT ⊕ (cid:19) / , (5)where κ constitutes the thermal conductivity of the organism and the ambient solvent, H representsthe volumetric heat capacity of this system, and L t ≈ T ( dT /dz ) − encapsulates the characteristiclength scale linked with the thermal gradient. The normalization factors for these parameters are κ ⊕ = 0 . − K − , H ⊕ = 4 . × J K − m − , and L t, ⊕ = 10 m; the last relation follows fromthe above definition of L t along with an average thermal gradient of 30 K/km and temperature of 288K for Earth (Chiasson, 2016, pg. 65).The third, and last, category of interest is gradients in photon flux (i.e., intensity). As before, onecan determine the minimum cell sizes for the spatial and temporal pathways. After simplification,they are respectively given by R min ≈ . µ m (cid:18) δδ ⊕ (cid:19) − / (cid:18) ΦΦ ⊕ (cid:19) − / (cid:18) L (cid:96) L (cid:96), ⊕ (cid:19) / (cid:18) ηη ⊕ (cid:19) − / (cid:18) TT ⊕ (cid:19) / , (6) R min ≈ . µ m (cid:18) UU ⊕ (cid:19) − / (cid:18) δδ ⊕ (cid:19) − / (cid:18) ΦΦ ⊕ (cid:19) − / (cid:18) L (cid:96) L (cid:96), ⊕ (cid:19) / (cid:18) ηη ⊕ (cid:19) − / (cid:18) TT ⊕ (cid:19) / , (7)where δ quantifies the fraction of photons that are absorbed by a single layer composed of pho-toreceptors (taken to be rhodopsins), Φ is the flux of photons in a suitable wavelength range, and L (cid:96), ⊕ ≈ Φ ( d Φ /dz ) − represents the characteristic length scale associated with light gradients. Thefiducial value of δ ⊕ = 3 × − is constructed from the absorption coefficient of photoreceptors (War-rant and Nilsson, 1998, Table 1) and the thickness of an individual rhodopsin molecule (Hargrave,2001). As the longest dimension of rhodopsin is ∼ . (cid:38) . µ m; the exact numberof such molecules will depend on the undetermined packing fraction. We choose the normalizationΦ ⊕ = 10 photons m − s − , as it corresponds to the maximal flux of 400-700 nm photons incident onthe Earth’s surface. Lastly, to maintain consistency with Dusenbery (1997, Table 1), we have chosen L (cid:96), ⊕ = 10 − m.Apart from the spatial and temporal modes of information sensing, microbes are also capable ofdetecting the orientation of the light source, i.e., discerning the direction in which light is propagating.This requirement is, however, feasible only when the radiation passing across the organism is subjectto substantial attenuation. The minimum cell size required in order to determine the positioning ofthe light source is expressible as R min ≈ . µ m (cid:18) δδ ⊕ (cid:19) − / (cid:18) ΦΦ ⊕ (cid:19) − / (cid:18) KK ⊕ (cid:19) − / (cid:18) ηη ⊕ (cid:19) − / (cid:18) TT ⊕ (cid:19) / , (8)where K denotes the attenuation coefficient for photoreceptors, and the nominal value of K ⊕ = 10 m − is taken from Warrant and Nilsson (1998, Table 1). .1 0.5 1 5 100.0010.10010100010 Cell radius ( μ m ) S i gn a l - t o - no i se r a t i o Figure 1: The signal-to-noise ratio (S/N) as a function of the cell size R (in µ m) for Earth-analogs.The curves reflect the various ambient gradients and attendant pathways for perceiving them. Red,green and blue are used to demarcate chemical, thermal and light gradients, respectively. The dottedand dashed lines (for all colours) indicate the spatial and temporal means for identifying gradients.The solid blue line represents the S/N for detecting the direction of the light source via gradientsensing. All results were obtained by combining (9) with (2)-(8).6or the sake of completeness, the consolidated expression for the signal-to-noise ratio for arbitrarycell radius R is furnished below: S / N = (cid:18) RR min (cid:19) β , (9)where the values of R min are β are dependent on the type and modality of gradient detection. • Chemical gradients: for the spatial mode, R min is calculated using (2) and β = 3, whereas forthe temporal mode R min is determined by (3) and β = 6. • Thermal gradients: for the spatial mode, R min is computed from (4) and β = 13 /
4, whereas forthe temporal mode R min is estimated using (5) and β = 25 / • Light gradients: for the spatial mode, R min is evaluated via (6) and β = 7 /
2, whereas for thetemporal mode R min is ascertained using (7) and β = 13 /
2. When it comes to sensing thedirection of the light source, R min is set by (8) and β = 7 / R would result in a significant gain in the signal-to-noise ratio. To illustrate our point, let us choose R ≈ R min , which translates to S / N ≈ R in Figure 1,where the expressions for R min in (9) were held fixed at their normalization factors in (2)-(8). In allmodels, we see that S/N grows rapidly with the size, along expected lines.Finally, as we had remarked at the beginning of Section 2.1, larger cell size permits effectivedispersal. The latter is measured in terms of ζ , the ratio of the two motile and non-motile diffusioncoefficients, and obeys the relationship: ζ = (cid:18) RR min (cid:19) , (10)where R min is given by (1). If we adopt R ≈ R min , as we did in the preceding paragraph, we obtain ζ ≈ Our final results for the minimal cell size are exemplified by (1)-(8). It is instructive to define R min ,which is the global minimum of these equations, namely, it refers to the R min that is smaller than all theother expressions; it goes without saying, the exact form of R min will vary based on the parameters ofthe system under consideration. The mathematical significance of R min can be understood as follows.If R < R min , it would imply that the organism is incapable of efficient dispersal and gradient sensing.Hence, at least insofar as these issues are concerned, R min would comprise a viable lower bound forthe radius of microbes.At this stage, it is helpful to carry out a meticulous scrutiny of the parameters involved in ourformulae prior to applying them to specific astrobiological settings. The first group is composed ofvariables that are chiefly dictated by the nature of the environment(s), which includes the solvent(s).The likes of η , H , κ , and T are straightforward examples, since they can be predicted from basicproperties, e.g., solvent, temperature and pressure. On a more subtle level, Φ, D c , C , and the gradientlength scales (collectively denoted by L ) also fall under this umbrella. It is harder to quantify themprecisely, but one could at least draw upon either physical principles or analogues on Earth (see Section3) to estimate them. For instance, calculating the photon flux (Φ) in underwater environments is quitestraightforward if the depth, temperature and solvent are provided (Lingam and Loeb, 2020a).7he second group is composed of δ and K , both of which are intimately connected to the molec-ular properties of photoreceptors. It is certainly conceivable that extraterrestrial life may use macro-molecules other than rhodopsins. Yet, the ubiquity and diversity of rhodopsins warrants furtherexplication. Rhodopsins are widespread in photoreceptors in plants, animals and unicellular eukary-otes (Foster et al., 1984; Hegemann, 2008; M¨oglich et al., 2010). Looking beyond eukaryotes, theso-called microbial rhodopsins are known to play myriad roles in phototaxis, intracellular signallingand harvesting electromagnetic energy (Gordeliy et al., 2002; Ernst et al., 2014). Recent studies in-dicate that microbial rhodopsins constitute the dominant source of light harvesting in Earth’s oceans(G´omez-Consarnau et al., 2019). Despite their multifarious functions, rhodopsins across taxa sharemany core structural features in common (Birge, 1990; Bryant and Frigaard, 2006). It has been con-jectured that rhodopsins might have been widespread on the young Earth and exoplanets (DasSarmaand Schwieterman, 2018). In view of these details, it does not seem unreasonable to utilize fiducialvalues derived from Earth as proxies for δ and K .The remaining parameter, which is also the one subject to the most ambiguity, is U . The reason isthat U is dictated by physiology and not by the properties of the medium or individual macromoleculesas in the former two categories. A careful inspection of Milo and Phillips (2016, pg. 270) and Bechingeret al. (2016, Table 1) reveals that U deviates from our choice of U ⊕ by roughly an order of magnitudeonly for certain microbes. Due to the relatively weak dependence of R min on U – as evident from(1), (3), (5) and (7) – our results are likely to change by a factor of (cid:46)
2. However, these resultspertain solely to Earth-based organisms, which leads us to the question: what about extraterrestrialorganisms? Although there is admittedly no clear answer, it has been conjectured by Meyer-Vernetand Rospars (2016, Section 4.4) that the magnitude of U has a strong mechanistic basis and is thereforeconstrained to a somewhat narrow interval. Before we tackle a couple of specific environments, a few general trends are discernible from Section2.1, which are adumbrated below.1. R min decreases when the swimming velocity measured in units of body size is increased.2. In all of the formulae, R min is proportional to ( T /η ) γ , where γ > R min displays monotonically increasing behaviour with respect to the gradient length scales ( L ).To put it differently, sharper gradients (i.e., smaller values of L ) are predicted to bring about areduction in R min .4. Broadly speaking, R min decreases monotonically with many environmental parameters such as D c , C , κ and Φ, although exceptions can and do exist. For such variables, increasing theirmagnitude would result in lowered R min and vice-versa.5. If U is held fixed, we perceive that R min evinces a stronger algebraic dependence on the appro-priate parameters for the spatial mode as opposed to the temporal mode.Even though it is tempting to dismiss the above points because they are qualitative, there are severalimportant trends and consequences that emerge from them. We will illustrate this aspect with onenotable example by focusing on point R min can decrease significantly, and so could R min . A microbe with smaller cell8ize, but equipped with similar gradient detection capabilities, would entail a lower metabolic cost ceteris paribus , as per current allometric models and empirical data (Brown et al., 2004; DeLonget al., 2010). Moreover, theoretical models indicate that the total energetic costs incurred for pro-tein and nucleic acid repair are reduced for smaller cells because they are posited to have a lowerinventory of biomolecules (Kempes et al., 2017, Figures 2 and 3). Last, if we make the ostensiblyreasonable assumption that the first living organisms were on the smaller side, this premise suggeststhat environments with sharp gradients might have been conducive to the origin of life in this regard.It is intriguing, therefore, that both past and recent research has emphasized thermodynamic dis-equilibria as a sine qua non for abiogenesis (Schr¨odinger, 1944; Prigogine and Nicolis, 1971; Russellet al., 1994; Fry, 2000; Smith and Morowitz, 2016; Barge et al., 2017; Branscomb et al., 2017; Lingamand Loeb, 2019b; Spitzer, 2021), and several geological settings have been proposed as viable candi-dates (Westall et al., 2018; Sleep, 2018; Kitadai and Maruyama, 2018; Camprub´ı et al., 2019; Meadowset al., 2020; Altair et al., 2020). We will explore one of the leading contenders – to wit, submarinealkaline hydrothermal vents – from this standpoint in more detail shortly hereafter. Geothermalfields in subaerial locations (e.g., hot springs), which have a long history in origins-of-life research(Harvey, 1924), exhibit marked gradients in inorganic substances, temperature and redox chemistry(Brock and Brock, 1968; Swingley et al., 2012; Mulkidjanian et al., 2012; Deamer et al., 2019; DesMarais and Walter, 2019; Damer and Deamer, 2020; Boyer et al., 2020). Beaches represent anothercrucial environment that have been relatively underappreciated in origins-of-life research, despite thepresence of strong gradients in salinity, temperature and light intensity (Lathe, 2004; Bywater andConde-Frieboesk Kilian, 2005; St¨ueken et al., 2013; Lingam and Loeb, 2018a). In the event that lifeemerged in one (or more) of these domains, it is conceivable that the concomitant existence of steepgradients may have permitted (proto)cells to efficiently acquire information via chemotaxis, phototaxisor thermotaxis among other avenues.It is worth taking a brief detour at this juncture, and highlighting that the aforementioned variantsof taxis are by no means the only ones that abound on Earth. Magnetotactic bacteria are capableof magnetotaxis, whereby these bacteria orient themselves along Earth’s magnetic field (Blakemore,1975; Bazylinski and Frankel, 2004; Sch¨uler, 2007; Lef`evre and Bazylinski, 2013). Magnetotacticmicrobes are not tackled in this study for two principal reasons: (i) important questions pertaining totheir evolution, ecological distribution, physiology and mechanistic basis are not yet unambiguouslysettled (Erglis et al., 2007; Faivre and Schuler, 2008; Lef`evre and Bazylinski, 2013; Uebe and Sch¨uler,2016); and (ii) not all worlds possess strong magnetic fields (Christensen, 2010; de Pater and Lissauer,2015); the likes of Titan, Venus and Mars are either weakly magnetized or unmagnetized (Stevenson,2010; Brain et al., 2016; Horner et al., 2020) and the same might hold true for tidally locked terrestrialexoplanets around M-dwarfs (Dong et al., 2017, 2018; McIntyre et al., 2019). In spite of these caveats,further research along these lines is clearly warranted.With this essential qualitative discussion out of the way, we will now outline how our formalismcan be harnessed to arrive at quantitative predictions by concentrating on two representative localesof relevance to astrobiology. Submarine hydrothermal vents have been recognized as promising sites for abiogenesis ever sincethe 1980s at the minimum (Corliss et al., 1981; Baross and Hoffman, 1985), with alkaline (low-temperature) hydrothermal vents (AHVs) garnering the lion’s share of attention. Reviews and analysesof this rapidly developing field were expounded in Russell et al. (1994); Russell and Hall (1997); Martinet al. (2008); Russell et al. (2014); Sojo et al. (2016); Weiss et al. (2018); Cartwright and Russell (2019);Russell and Ponce (2020), whereas dissenting viewpoints and critiques of the underlying principles have9een laid out in Bada (2004); Cleaves et al. (2009); Orgel (2008); Jackson (2016); Sutherland (2017);Deamer and Damer (2017). In recent experiments, the availability of mineral and metal catalystshas been shown to facilitate the emerge of protometabolic networks under roughly hydrothermalconditions, with close connections to the reverse tricarboxylic acid cycle and the Wood–Ljungdahlpathway (Kitadai et al., 2019; Preiner et al., 2020; Muchowska et al., 2020; Hudson et al., 2020). From adifferent perspective, the synthesis of prebiotic monomers (e.g., amino acids) and their oligomerizationhas been documented in AHV-like laboratory conditions (Burcar et al., 2015; Harrison and Lane, 2018;Barge et al., 2019). Lastly, both theoretical modelling and laboratory experiments have revealed thathydrothermal pores are propitious to the synthesis and efficient accumulation of prebiotic compounds,and could initiate their oligomerization in turn (Baaske et al., 2007; Kreysing et al., 2015; Nietheret al., 2016; Salditt et al., 2020).Several reasons can be identified in favor of our decision to focus on AHVs. First, as explainedin the preceding paragraph, there are compelling (although not definitive) grounds to contend thatthey may represent the sites where the origin of life occurred on Earth. Second, AHVs are viewedas promising candidates for enabling abiogenesis on icy worlds in our Solar system such as Europaand Enceladus (Vance et al., 2007; Russell et al., 2014). Last, and perhaps most importantly, theexistence of ongoing hydrothermal processes has been indirectly confirmed on Enceladus by analyzingthe data from its plume collected by the Cassini spacecraft (Waite et al., 2017; Postberg et al., 2018)and there is broad evidence for past hydrothermal activity on Mars (Osinski et al., 2013; Westall et al.,2015; Michalski et al., 2018; Farley et al., 2020). On a related note, Triton exhibits clear signatures ofgeysers (Soderblom et al., 1990; Hand et al., 2020), and two independent lines of evidence suggest thatEuropa has plumes and perhaps hydrothermal activity (Sparks et al., 2017; Jia et al., 2018). Hence,when viewed collectively, there are robust reasons to apply the model to hydrothermal vents.The dynamic environment of AHVs is distinguished by the manifestation of steep gradients inchemical compounds, temperature, pH, and redox chemistry inter alia (Russell and Martin, 2004;St¨ueken et al., 2013; Cartwright and Russell, 2019; Meadows et al., 2020; Barge et al., 2020a). Wecaution, however, that this very spatial and temporal dynamism makes it challenging to identifyaverage values for the gradient length scales. Bearing this caveat in mind, we remark that the presenceof strong gradients ensures that point R min would involve L in one of its three forms. Next,provided that U does not diverge significantly from U ⊕ , we invoke point R min is given by one of either (2), (4) or (6).Let us begin by scrutinizing the last equation of this trio. Field studies have established thatbacteria from the family Chlorobiaceae are capable of photosynthesis at hydrothermal vents (Beattyet al., 2005; Raven and Donnelly, 2013; Bj¨orn, 2015). Furthermore, both empirical evidence andbiophysical considerations indicate that photosynthesis at photon fluxes ∼ ⊕ is feasible (Raven et al., 2000; Beatty et al., 2005; Manske et al., 2005). In fact, Nisbetet al. (1995); Nisbet and Fowler (1996) hypothesized that photosynthesis evolved in organisms dwellingnear hydrothermal vents as a means of initially detecting infrared radiation via thermotaxis. Thus,there are no compelling a priori reasons for ruling out the prospects for phototaxis near hydrothermalvents, all the more so given that non-thermal radiation at these locations dominates its thermalcounterpart by more than an order of magnitude in select wavelength bands (Van Dover et al., 1996;White et al., 2000). However, upon carefully inspecting (6), we notice that R min ∝ Φ − / . Given thatΦ is many orders of magnitude smaller than Φ ⊕ (White et al., 2002), it follows that R min in (6) mayincrease by nearly an order of magnitude unless the light gradients are unusually large. Hence, wewill direct our attention toward (2) and (4) instead.The remaining step is to motivate characteristic values for the parameters in the formulae. We10egin by adopting T = 323 K (50 ◦ C), which is lower than the temperature of hydrothermal fluids inAHVs by a few tens of K (Sojo et al., 2016). This temperature has been employed in hydrothermalpore experiments (Mast et al., 2013), and higher temperatures could lead to the swift degradation ofbiomolecules. At this temperature and selecting a pressure of ∼
25 MPa, we use Schmelzer et al. (2005,Table 1) to obtain η ≈ . η ⊕ . Next, we adopt κ ≈ κ ⊕ based on Caldwell (1974), in conjunctionwith H ≈ H ⊕ . On-site investigations suggest that the thermal gradients function over length scalesof ∼ . L t ≈ R min ≈
30 nm.Turning our attention to chemotaxis (chemical gradients), the average concentration C is stronglydependent on the compounds under consideration. For instance, there is tentative (albeit equivocal)evidence for the abiotic synthesis of amino acids at nanomolar concentrations in the oceanic lithosphere(M´enez et al., 2018). If we turn our gaze to simpler molecules, however, the concentrations are muchhigher. To begin with, we choose CO as the chemical of interest, due to its prevalence in oceansand the crucial fact that it constitutes the cornerstone of carbon fixation pathways (autotrophy) onEarth (Berg, 2011; Fuchs, 2011; Ward and Shih, 2019). RuBisCO, the primary enzyme in carbonfixation, has a characteristic radius of ∼ . (cid:38)
100 nm (cf. Raven, 1994). The dynamicenvironments emblematic of AHVs induce extensive fluctuations in the CO abundance, which rangesbetween ∼ . µ M to (cid:38) in Earth’s oceans today is ∼ µ M (Gornitz, 2009, pg. 125). At the lower end of the spectrum (i.e., when the abundance ofbioavailable CO is (cid:46) µ M), it is conceivable that CO may function as the limiting resource, whichis bolstered by the analyses of the Lost City hydrothermal field (Lang and Brazelton, 2020).We shall opt for an intermediate value of C ≈ µ M, while the diffusion coefficient is chosen to be D c ≈ . D ⊕ (Cadogan et al., 2014, Table 2). Lastly, experiments in microfluidic reactors have shownthat pH gradients are generated over length scales of ∼ − m (M¨oller et al., 2017; Sojo et al., 2019;Barge et al., 2020b; Hudson et al., 2020), and we adopt this estimate for L c although it is probablyon the optimistic side if AHVs are viewed in toto . By substituting the preceding choices into (2), weobtain R min ≈
130 nm. In contrast, if we consider dissolved inorganic carbon (DIC) as our chemical ofinterest and adopt a fiducial estimate of ∼ R min ≈
55 nm after invoking (2).nstead of working with CO as the chemical compound of relevance, it is feasible to repeat theanalysis for a different species. The preceding emphasis on CO was a direct consequence of focusing oncarbon fixation (autotrophy), but it is necessary to tackle other chemical substances that are relevantfor heterotrophs as well. One natural candidate that springs to mind is phosphorus, specificallyin the form of phosphates, because it constitutes the ultimate limiting nutrient for the past andcurrent Earth (Tyrrell, 1999; Laakso and Schrag, 2018; Hao et al., 2020), and potentially worlds withexclusively (sub)surface oceans (Wordsworth and Pierrehumbert, 2013; Lingam and Loeb, 2018b,2019a,c; Olson et al., 2020). A noteworthy aspect of phosphate is that it represents a vital nutrientfor both heterotrophs and autotrophs (Kirchman, 1994). When it comes to dissolved phosphate, We point out that our ensuing results are only weakly dependent on the temperature, and are thus accurate fortemperature changes of <
10% (measured in K). If one excludes these “sweet spots”, however, it is credible that L c may increase by an order of magnitude or moreeven in the neighbourhood of AHVs.
11e adopt
C ≈ µ M as per measurements in the vicinity of hydrothermal zones on Earth (Wheatet al., 1996; Paytan and McLaughlin, 2007). The diffusion coefficient for phosphate is taken to be D c ≈ . D ⊕ (Krom and Berner, 1980; Cheng et al., 2014). By repeating the calculation using (2) inconjunction with the prior data, we end up with R min ≈ . µ m.In light of the results until this stage, we infer that R min (cid:46) . µ m is theoretically feasible in thegeneral proximity of AHVs; recall that R min is the minimum of all values spanned by R min . However,this statement should not be misconstrued as implying that microbes with radii (cid:46) . µ m wouldexist in actuality. This limit has been derived via the application of a simple “high-level” mechanisticmodel that does not take into account the accompanying constraints imposed by the intricate molecularmachinery associated with cells. For instance, cellular components such as receptor molecules (e.g.,rhodopsins) are necessary for gradient sensing, whereas motility could enforce stringent requirementsfor motor molecules and ATP synthesis. Mechanical action based on the sensed information wouldcall for protein and messenger RNA synthesis (entailing RNA polymerases in turn), which militatesagainst a cell radius of (cid:46)
100 nm. Moreover, in the case of autotrophs, the necessity of large enzymes– such as RuBisCO, which was briefly introduced and analyzed a few paragraphs earlier – imposes anadditional bottleneck on the minimal cell size. This issue is, however, likely to be less significant forheterotrophs because they ought not depend on these macromolecules.There are several other factors that may collectively restrict the minimum radius of living organ-isms to ∼
100 nm. In a classic study, Morowitz (1967, pg. 52) calculated that a radius of (cid:38)
50 nmis necessary for a minimal self-replicating unit on the basis of the desired genetic and metabolic com-plexity. Subsequent evidence from uncultured bacteria as well as additional theoretical constraints –imposed by cell wall, genome size, and nutrient uptake efficiency – suggests that lifeforms must havea minimum radius of ∼
70 nm (Koch, 1996; Maniloff et al., 1997; Velimirov, 2001; Raven et al., 2013;Luef et al., 2015; Andersen et al., 2016). Lastly, the full panoply of evolutionary processes involvingthe (ex)change of genetic material, such as harboring prophage (which influences the rate of lateralgene transfer), might be rendered untenable when the cell radius is (cid:46)
100 nm.It is instructive to compare the above threshold radius of ∼
100 nm against a few of the smallestmicrobes that have been unearthed to date. For starters, the lower limits for picoplankton are knownto approach this threshold (Li et al., 1983; Schmidt et al., 1991; Jones, 1993). For instance, membersof the ubiquitous free-living SAR11 bacterial clade can attain an effective radius of ∼ Mycoplasma genitalium ischaracterized by a radius of 150 nm (Svenstrup et al., 2003) and certain species from the phylum
Nanoarchaeota , such as the recently discovered symbiont
Nanopusillus acidilobi (Wurch et al., 2016),attain cell radii of (cid:38)
50 nm. But, it is essential to appreciate that some of these specific examples areeither parasites or symbionts and not free-living microbes. Hence, by the same token, if the smallestorganisms capable of effective gradient sensing and dispersal are parasites on larger lifeforms (whichis not the case tout court ), discerning the latter would prove to be an easier task for life-detectionmissions. It goes without saying that the limits for viruses, which are, however, not living entities sensu stricto , are much smaller: the porcine circovirus and cowpea mosaic virus have radii of ∼ R min , a number of variablesintimately linked to the ambient environment (e.g., gradient length scales) came into play. Hence,in case other domains evince physico-chemical properties similar to AHVs, mutatis mutandis , it isplausible that the above results are broadly applicable to them. Geothermal fields might representpromising candidates in this respect, because they possess some attributes in common with AHVs As a sidenote, the composition of a minimal protocell is much more pared down relative to current microbes (Or´oand Lazcano, 1984; Dyson, 1999), indicating that smaller sizes are conceivable for these entities.
Titan is one of the most intriguing and compelling astrobiological targets in our Solar system (Sagan,1994; McKay, 2014; Nimmo and Pappalardo, 2016; Schulze-Makuch and Irwin, 2018; Cockell, 2020).Our understanding of this moon – such as its methane cycle, atmospheric composition, sand dunesand transport, lakes and seas – has advanced by leaps and bounds, primarily by virtue of the Cassini-Huygens mission (Brown et al., 2010; Hayes, 2016; H¨orst, 2017; Lorenz, 2019). One of the chief reasonsas to why Titan is considered an exciting target stems from the possibility that it may harbour “weirdlife”, sensu being based on hydrocarbon solvents (Benner et al., 2004; McKay and Smith, 2005;Stevenson et al., 2015; McKay, 2016; Sandstr¨om and Rahm, 2020; Carrer et al., 2020); see also Saganet al. (1992); Schulze-Makuch and Grinspoon (2005); Raulin et al. (2012); Irwin and Schulze-Makuch(2020). Moreover, Titan-like objects endowed with seas of methane or ethane might be among themost common type of habitable worlds (Bains, 2004; Gilliam and McKay, 2011; Ballesteros et al., 2019;Lingam and Loeb, 2020b), which increases the significance of Titan and its analogs in the context ofgauging the frequency of life in the Universe (Lunine, 2009).Due to Titan’s immanent potentiality for hosting life in non-polar solvents, we are free to take thisopportunity to examine how the properties of the solvent influence R min , i.e., in what ways does thesolvent alone influence the capacity for putative organisms to garner information and thereby takepart in directed movement. Hence, we will proceed to modify only the solvent-related parameters liketemperature, viscosity and heat conductivity, while leaving the other variables unaltered. We select T ≈
90 K and an atmospheric pressure of roughly 1 . R min in its diverse forms. For the scenario investigatedherein, we have η ≈ . η ⊕ , and substituting these numbers into (1) yields R min ≈ . µ m (cid:18) UU ⊕ (cid:19) − / . (11)Next, we consider the prospects for chemotaxis; the respective expressions for the spatial and temporalmodes can be simplified to obtain R min ≈ . µ m (cid:18) D c D CH (cid:19) − / (cid:18) CC ⊕ (cid:19) − / (cid:18) L c L c ⊕ (cid:19) / , (12) R min ≈ . µ m (cid:18) UU ⊕ (cid:19) − / (cid:18) D c D CH (cid:19) − / (cid:18) CC ⊕ (cid:19) − / (cid:18) L c L c, ⊕ (cid:19) / , (13) D c in terms of D CH ≈ D ⊕ = 5 × − m s − , which approxi-mates the self-diffusivity of methane (Van Loef, 1978; Harris and Trappeniers, 1980). Moving on tothermal gradients, the spatial and temporal paths toward sensing information respectively impose theconstraints: R min ≈ . µ m (cid:18) L t L t, T (cid:19) / , (14) R min ≈ . µ m (cid:18) UU ⊕ (cid:19) − / (cid:18) L t L t, T (cid:19) / , (15)where we have made use of κ ≈ κ ⊕ / and H ≈ . H ⊕ (Youn-glove, 1974, Figure 4). We have normalized L t in terms of L t, T ≈ . L t, ⊕ , where L t, T is the typicalgradient at the surface of Titan; this normalization is chosen to make the results Titan-centric. It iscalculated by using the definition of L t from Section 2.1, the value of T adopted earlier, and the scal-ing dT /dz ∝ ( R P ) . , with R P representing the radius of the world (e.g., Lingam and Loeb, 2020b).Finally, we turn our attention to the trio of equations associated with phototaxis. The formulae forthe spatial and temporal pathways are respectively given by R min ≈ . µ m (cid:18) δδ ⊕ (cid:19) − / (cid:18) ΦΦ T (cid:19) − / (cid:18) L (cid:96) L (cid:96), ⊕ (cid:19) / , (16) R min ≈ . µ m (cid:18) UU ⊕ (cid:19) − / (cid:18) δδ ⊕ (cid:19) − / (cid:18) ΦΦ T (cid:19) − / (cid:18) L (cid:96) L (cid:96), ⊕ (cid:19) / , (17)where we have normalized Φ in terms of Φ T ≈ . ⊕ , the maximal photon flux at Titan’s surface forthe same reasons as those underlying L t, T in the previous paragraph. To keep our derivation simple,we have used the inverse square law for the photon flux to determine Φ T relative to Φ ⊕ . Lastly, weare left with the analogue of (8), which duly yields R min ≈ . µ m (cid:18) δδ ⊕ (cid:19) − / (cid:18) ΦΦ T (cid:19) − / (cid:18) KK ⊕ (cid:19) − / . (18)To recapitulate, (11)-(18) embody the constraints on cell size for Titan and Titan-like worlds,which feature methane as the dominant component of the solvent. By inspecting these equations, wesee that, ceteris paribus , the smallest magnitude is attained by (12). By definition, therefore, we have R min ≈ . µ m, which is nearly identical to Earth’s value of R min ≈ . µ m (Dusenbery, 1997,Table 2). Thus, at first glimpse, it would appear as though the constraints on cell size on Titan arevery close to that on Earth inasmuch as gradient sensing and dispersal is concerned. We caution,however, that these estimates for R min are applicable to relatively gentle gradients. In contrast, aswe have seen in Section 3.1, R min can potentially become lower than the smallest microbes on Earthin settings with prominent chemical or thermal gradients; under similar conditions, these conclusionsmay apply to Titan as well.For the sake of completeness, the signal-to-noise ratio has been plotted as a function of the cellradius in Figure 2 for Titan-analogs. In generating this figure, we have made use of (9) and substitutedthe fiducial estimates for the expressions for R min derived in (12)-(18). In line with our expectations,we notice that S/N is strongly dependent on R and becomes much larger than unity when R exceedsa few µ m, demonstrating that bigger lifeforms are ostensibly advantageous from this perspective,provided that all the other salient factors are held fixed. .1 0.5 1 5 100.0010.10010100010 Cell radius ( μ m ) S i gn a l - t o - no i se r a t i o Figure 2: The signal-to-noise ratio (S/N) as a function of the cell size R (in µ m) for Titan-analogs.The curves reflect the various ambient gradients and attendant pathways for perceiving them. Red,green and blue are used to demarcate chemical, thermal and light gradients, respectively. The dottedand dashed lines (for all colours) indicate the spatial and temporal means for identifying gradients.The solid blue line represents the S/N for detecting the direction of the light source via gradientsensing. All results were obtained by combining (9) with (12)-(18).15here are some general inferences that can be drawn at this juncture. If we compare (1)-(8) andFigure 1 on the one hand with (11)-(18) and Figure 2 on the other, we notice that the two sets arenearly of the same magnitude when the various gradient length scales (e.g., L c and L t ) are held fixed.Note that the former set is applicable to Earth as well as other worlds with water as the solvent (e.g.,Europa and Enceladus), while the latter pertains to Titan and Titan-like worlds involving methaneas the solvent. The similarity is unexpected because these two classes are markedly different in termsof not only their solvents but also other characteristics such as photon flux and temperature.From a mathematical standpoint, the reason that the two groups yield closely matched results isbecause the equations for R min exhibit a fairly weak dependence on the environmental parameters; toput it differently, there is no single variable that distinctly stands out. The corollary of this statementis that the scalings for R min possess a certain degree of universality, provided that the gradient lengthscales are held invariant. Thus, if we compare R min for generic lakes and seas on Titan with those onEarth, the two will be close to each other in terms of their magnitudes. In contrast, if hydrothermalvents on Earth (or Enceladus and Europa) with their accompanying steep gradients are juxtaposedagainst the lakes and seas of Titan, the former will typically engender a lower value than the latter.To put it more simply, the first scenario is akin to comparing “apples with apples”, whereas the secondis analogous to comparing “apples with oranges.”The goal of this section was to demonstrate that the formalism might be suitably modified totackle worlds with solvents other than water by taking Titan as our case study. Although we shall notdelve into this subject further, another intriguing milieu that could merit theoretical analysis in thesame vein is the lower and middle cloud decks of Venus, which are known to host liquid sulfuric acidwith traces of liquid water (Schulze-Makuch and Irwin, 2018). This layer of the Venusian atmospherehas been long regarded as a promising astrobiological target for multiple reasons (Morowitz andSagan, 1967; Schulze-Makuch et al., 2004; Grinspoon and Bullock, 2007; Limaye et al., 2018; Greaveset al., 2020; Seager et al., 2021; Lingam and Loeb, 2020c), but any putative lifeforms are likely toface substantive challenges in this region such as the extremely low water activity, regulation of theosmotic pressure, and high acidity (Cockell, 1999; Cockell et al., 2021).From a more “exotic” standpoint, the formalism could be employed to study size constraints incrystalline and amorphous ices. There is growing awareness that glacial and sea ices harbor a diverserange of extremophiles (Boetius et al., 2015; Martin and McMinn, 2018). There are, however, severalchallenges that confront putative microbes in these environments insofar as our analysis is concerned.First, the sizes of veins and pores are a few millimeters at the maximum (Martin and McMinn, 2018,pg. 2), but at lower temperatures, the typical dimensions are much reduced and may become (cid:46) µ m for subsurface ocean worlds in the outer Solar system (Price, 2007, pg. 218); this is expected toobstruct motility over extended intervals.Second, in order for high concentrations of chemicals to exist in the ice – which would be partlyresponsible for lowering R min on the basis of (2) and (3) – they must be incorporated in some fashionfrom the external environment. However, the diffusion through ice is many orders of magnitude smallerrelative to water (Mispelaer et al., 2013; Cuppen et al., 2017), which can impede the accumulationof reactants and nutrients to significant concentrations. Lastly, a number of the parameters inherentin (1)-(8) are poorly constrained in (extra)terrestrial ices, thereby rendering quantitative analysesdifficult to undertake. On account of these reasons, we have not attempted to derive explicit estimatesfor R min in the realm of saline and freshwater ices.16 Conclusion
The ability of organisms to sense and act upon encountering physical and chemical gradients is ofconsiderable importance. The capacity to garner such information efficiently would, inter alia , permitlifeforms to adapt and coexist with their environment, and undertake locomotion in a directed fashion.Close connections exist between information retrieval and motility on the one hand and cell size onthe other, since organisms below a certain size would become inefficient at undertaking the former.By drawing upon results derived by Dusenbery (1997, 2009), we recast them into formulae for theminimal cell size ( R min ) that are more amenable to astrobiological analyses; we reiterate that theseresults should be viewed as heuristic criteria because they are not necessary and sufficient conditions.After deriving these expressions, we applied the framework to a couple of settings.The first was submarine alkaline hydrothermal vents (AHVs) on Earth and other worlds wherethey appear to exist (e.g., Enceladus). What we inferred is that, inasmuch as information acquisitionvia gradient sensing is concerned, AHVs are theoretically capable of harboring organisms with radii of (cid:38) . µ m. It is worth reiterating that constraints from other biological functions (e.g., metabolism andreplication) could come into play and thereby elevate R min above the values predicted in this work;some of the relevant caveats and additional factors in this context are delineated in Section 3.1. Tooffer one specific example from the section, autotrophs may require large enzymes for carbon fixation(e.g., RuBisCO) that accordingly elevate the magnitude of R min , whereas this is anticipated to beless significant for heterotrophs. Our analysis does not imply, however, that such sub- µ m microbesoriginated in these environments or that they would necessarily manifest this size. Nonetheless, ourresults indicate that information-centric arguments taken in isolation are insufficient to rule out theexistence of organisms with these dimensions in the neighbourhood of AHVs.One might, in fact, contemplate whether the steep gradients at AHVs, which facilitate the reductionin R min , were accordingly amenable to the evolution of sub- µ m microbes in AHV habitats. Lastly,if the parameters we have adopted in the relevant formulae are roughly characteristic of AHVs onicy moons and planets in the outer Solar system like Enceladus and perhaps Europa (Nimmo andPappalardo, 2016; Hand et al., 2020; Jebbar et al., 2020; Taubner et al., 2020), it is conceivable thatthose worlds could also support similar organisms. We caution that small microbes with radii (cid:38) . µ m delineated in the above paragraph might prove to be parasitic, in which case it is easier to searchfor their larger hosts when conducting life-detection experiments. However, on the basis of the simplemechanistic model developed herein, it is not possible to predict a priori whether the smallest microbeswith effective gradient sensing and dispersal abilities will always turn out to be obligate parasites orwhether they may end up being symbionts or free-living cells. Further empirical research, allied totheoretical modeling, is needed to resolve this issue and come up with optimal search strategies inhunting for microorganisms on other worlds.In the second instance, we chose to tackle Titan, largely because of its unique potential for hostingexotic life in non-aqueous solvents. By taking the properties of the new solvent (methane) intoaccount as well as the astrophysical attributes of Titan (e.g., its size and location), we computed theconstraints on the cell size and thereby deduced R min . We found that, when all other traits suchas the microenvironment and organismal physiology are held fixed, R min is virtually identical to itsequivalent on Earth.In mathematical terms, this result was along expected lines because the variousformulae for the microbial size exhibit a fairly weak dependence on the relevant physicochemicalvariables, thereby engendering some degree of universality, provided that the gradient length scalesare held fixed. Hence, taken at face value, this result implies that organisms on Titan with thecapacity to sense gradients efficiently may perhaps possess a similar lower bound on their size despitethe dissimilarities between this world and present-day Earth.Our work has a number of practical implications in the search for extraterrestrial life via in situ R min and might therefore haveaided in the early evolution of life. Thus, the search for biomarkers may benefit from prioritizingenvironments where such gradients exist today or were prevalent in the past; the Gusev crater onMars with its opaline silica deposits reminiscent of hot springs on Earth is an intriguing example(Ruff and Farmer, 2016; McMahon et al., 2018; Ruff et al., 2020). On the other hand, organismsdwelling in relatively homogeneous environments could require higher R min if they are to be effectiveat gradient sensing because of the joint requirements enforced by (2)-(9).The detection of larger organisms is probably more feasible, as is their likelihood of undergoingfossilisation and possibly being unearthed by field studies. In either event, our framework offers asimple heuristic for predicting what are the smallest organisms with gradient sensing and motilityin a given domain, and this tool can be gainfully employed in the selection and design of appositeinstrumentation. The latter subject is being vigorously pursued vis-`a-vis Mars, Venus, and the sub-surface ocean worlds of the Solar system (Ball et al., 2007; Hays et al., 2017; Vago et al., 2017; Chanet al., 2019; Williford et al., 2018; Stamenkovi´c et al., 2019; Dachwald et al., 2020; Taubner et al.,2020; Carrier et al., 2020; Hein et al., 2020). It is not implausible, therefore, that the discovery ofextraterrestrial life might progress a posse ad esse in the coming decades.Naturally, theoretical consequences of some import emerge from this study as well. As noted above,a reduction in R min might prove amenable to the evolution of “minimalistic” lifeforms. Furthermore,due to the lowered constraints on information sensing and motility set by size in this case, the transitionto more complex organisms may have encountered fewer hurdles. There are reasons to suppose thatchemotaxis and movement are intertwined with the prospects for initiating symbiotic interactionsand the emergence of complex spatio-temporal aggregates (Budrene and Berg, 1995; Harshey, 2003;Wadhams and Armitage, 2004; Kearns, 2010; Porter et al., 2011; Raina et al., 2019).Among these critical steps, the advent of multicellularity stands out because it is distinguishedby sophisticated intercellular signalling, coordination and specialization (Shapiro, 1998; Grosberg andStrathmann, 2007; Lyons and Kolter, 2015), each of which presumably entailed significant “motion”in both the physical and informational realms (Ben-Jacob et al., 2000; Kearns, 2010; Zhang et al.,2012; Alexandre, 2015). It is tempting to speculate that environments that are more conducive toinformation flow of the type analysed herein would have relatively higher likelihoods for the evolutionof simple and complex multicellularity and the profound ecological and evolutionary changes thataccompany these transitions (Smith and Szathm´ary, 1995; Knoll, 2015; Lingam and Loeb, 2021a);needless to say, this conjecture remains unproven. Acknowledgments
The author is grateful to Michael Russell, Chris McKay, and Charles Cockell for the valuable commentsand references pertaining to certain facets of this work. The insightful and constructive feedbackprovided by the reviewers is also duly acknowledged. This research was supported by the FloridaInstitute of Technology and the resources provided by the Harvard Library system were of much useduring the course of undertaking this study.
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