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ORIGINAL ARTICLE

Evolutionary tradeoffs in cellular composition acrossdiverse bacteria

Christopher P Kempes1,2,3, Lawrence Wang2, Jan P Amend4,5, John Doyle2 and Tori Hoehler31The Santa Fe Institute, Santa Fe, NM, USA; 2Control and Dynamical Systems, California Institute ofTechnology, Pasadena, CA, USA; 3NASA Ames Research Center, Moffett Field, CA, USA; 4Department ofEarth Sciences, University of Southern California, Los Angeles, CA, USA and 5Department of BiologicalSciences, University of Southern California, Los Angeles, CA, USA

One of the most important classic and contemporary interests in biology is the connection betweencellular composition and physiological function. Decades of research have allowed us to understandthe detailed relationship between various cellular components and processes for individual species,and have uncovered common functionality across diverse species. However, there still remains theneed for frameworks that can mechanistically predict the tradeoffs between cellular functions andelucidate and interpret average trends across species. Here we provide a comprehensive analysis ofhow cellular composition changes across the diversity of bacteria as connected with physiologicalfunction and metabolism, spanning five orders of magnitude in body size. We present an analysis ofthe trends with cell volume that covers shifts in genomic, protein, cellular envelope, RNA andribosomal content. We show that trends in protein content are more complex than a simpleproportionality with the overall genome size, and that the number of ribosomes is simply explained bycross-species shifts in biosynthesis requirements. Furthermore, we show that the largest andsmallest bacteria are limited by physical space requirements. At the lower end of size, cell volume isdominated by DNA and protein content—the requirement for which predicts a lower limit on cell sizethat is in good agreement with the smallest observed bacteria. At the upper end of bacterial size, wehave identified a point at which the number of ribosomes required for biosynthesis exceeds availablecell volume. Between these limits we are able to discuss systematic and dramatic shifts in cellularcomposition. Much of our analysis is connected with the basic energetics of cells where we show thatthe scaling of metabolic rate is surprisingly superlinear with all cellular components.The ISME Journal (2016) 10, 2145–2157; doi:10.1038/ismej.2016.21; published online 5 April 2016

Introduction

An important question in evolution, ecology andastrobiology is: what fundamental limitations arepresent for the simplest organisms and what limita-tions might have been present when life emergedand started to evolve? It is important to understandhow limitations differ for broad classes of organismsas this informs competitive dynamics and motivatesevolutionary trajectories and transitions. Althoughspeciation is the subtle process of unique evolu-tionary trajectories, it should be noted that thesetrajectories occur within boundaries defined by basicphysical, energetic and chemical limitations. Forexample, scaling laws relating numerous organismfeatures to body size often illustrate a sharedphysical limitation that, on the average, organizes

biological features (e.g., Niklas, 2004; Brown et al.,2004; West and Brown, 2005; DeLong et al., 2010).Recent work has shown that these scaling laws canbe connected with metabolic partitioning to antici-pate the smallest possible bacterium (Kempes et al.,2012). Indeed, in the fields of bioengineering,ecology and evolution, there are a large number ofknown scaling relationships, and mapping the entirespace of physical, energetic and chemical limitationsis a significant task of central consequence forevolution and ecology (Brown et al., 2004).

Here we present an analysis, which we verifyusing compiled data, of the changes in molecular,physiological and structural composition across theentire range of bacterial cell sizes. Specifically, weexamine the total amount of the following compo-nents: DNA, ribosomes, proteins, cell membrane,tRNA and mRNA. For each of these features we oftenfocus on power-law relationships for various organ-ism features, and when two properties ‘scale’ withdifferent exponents, this often implies the onset of alimitation at a given size which may have importantevolutionary consequences. Using this framework

Correspondence: CP Kempes, The Santa Fe Institute, 1399 HydePark Road, Santa Fe, NM 87501, USA.E-mail: [email protected] 17 August 2015; revised 11 January 2016; accepted16 January 2016; published online 5 April 2016

The ISME Journal (2016) 10, 2145–2157© 2016 International Society for Microbial Ecology All rights reserved 1751-7362/16www.nature.com/ismej

http://dx.doi.org/10.1038/ismej.2016.21

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we show that the interconnection between energetic,physical, informational (genomic), chemical andtemporal processes leads to predictions of the upperand lower boundaries of bacterial size and definesthe evolutionary flexibility for bacteria betweenthese two bounds. This perspective, which spans ahuge diversity of species and five orders of magni-tude in cell volume, adds explicit cross-species andsize-based dependencies to the large body of work onthe interconnection between various cellular pro-cesses (e.g., Tempest and Hunter, 1965; Tempestet al., 1965; Simon and Azam, 1989; Bremer et al.,1996; Cayley and Record, 2003; Dethlefsen andSchmidt, 2007; Zaslaver et al., 2009; DeLong et al.,2010; Scott et al., 2010; Goehring and Hyman, 2012;Kempes et al., 2012; Turner et al., 2012; Lloyd, 2013;Burnap, 2015). Furthermore, our work connectsthese cross-species trends to previous considerationsof space limitation for the smallest organisms (Knollet al., 1999) and the recent observations of smallenvironmental bacteria (e.g., Luef et al., 2015).Knowing these connections may help us to inferecological trait tradeoffs, quantify the constraints indesigning organisms or interpret long-standingenvironmental observations such as the Redfieldratio for nutrient proportionalities in the ocean(Geider and La Roche, 2002).

Finally, most of the cellular components analyzedhere should have a deep connection with overallcellular metabolism. In some cases, such as theprocesses determined by growth rate (Kempes et al.,2012), metabolic rate explicitly constrains compo-nent requirements. However, we find that it is moredifficult to determine what cellular features setoverall metabolic rate, which scales superlinearlyfor bacteria in contrast to other classes of organisms(DeLong et al., 2010). In fact, we find that there is noobvious connection between the scaling of any singlecellular feature and the overall metabolic rate,highlighting the continuing mystery of metabolicscaling in bacteria. We also find increasing trends inthe overall efficiency of bacteria defined as themetabolic power per genetic and protein content,which is surprising given previous considerations(Lane and Martin, 2010).

Materials and methods

Our overarching goal is to understand how therequirement for each cellular component dependson total cell size so that we can constrain the limitsfacing cells at various scales. We approach theseconstraints from both energetic perspectives andoverall space constraints, the latter of which oftenderives from energetics via the requirements ofcertain rate processes (e.g., growth rates; Kempeset al., 2012). For the space constraints our analysisfocuses on both the scaling of individual compo-nents and the sum total of all cellular components.Thus, it is useful to define the total volume of the

cell, Vc, as

Vc ¼ Vw þ V comp ð1Þwhere Vw is the total volume of water in the celland Vcomp is the volume of cellular componentsdefined as

Vcomp ¼ VDNA þ Vp þ V r þ Venv þ V tRNA þ VmRNA ð2Þwhere VDNA is the total volume of DNA in the cell, Vp

is the protein volume, Vr is the ribosomal volume,Venv is the volume of the cellular envelope, VtRNA isthe volume of tRNA and VmRNA is the total mRNAvolume. One of our main efforts here is to determinethe sizes at which single components or the totalcomponent volume limits cell size, and the combi-nation of the both types of analysis allows us to infertradeoffs across the range of bacteria. Additionally, itis useful within our considerations to definethe volumetric fraction, fd, of the cell that is dryweight as

f d ¼ V comp

V c: ð3Þ

In general, we describe the scaling of a generic cellcomponent (e.g., DNA) as Ci ¼ C0Vbi

c , where βi is theexponent for volume (measured in m3 throughoutthis paper) dependence of the component. It isimportant to note that if βio1 then component Ci

will be a decreasing fraction of total cell volume withincreasing cell size, while βi41 leads to an increas-ing fraction of cell volume. In either case, if βi≠1,then there will be a size at which the componentvolume equals total cell volume, implying a limita-tion because extrapolation beyond this point wouldproduce Ci4Vc, which is impossible. It should alsobe noted that if some of the terms in Vcomp scale withβi≠1 then other terms cannot be simple power laws inorder for the equalities in Equations (1) and (2) tohold. We will see that several aspects of the cell donot follow simple power-law relationships withoverall cell volume. It should be noted, moregenerally, that if any component depends on Vc ina manner that is not a simple proportionality thenthe fractional composition of the cell will changeacross cell sizes, and many nonlinear functions willlead to critical sizes beyond which the volume of acomponent will exceed Vc, a physical impossibilitythat implies a constraint on size.

The basic perspective of physiological scaling issupported by many previous observations of organ-ism features that follow power-law relationships;however, it should be noted that in many of the casesstudied here more complicated relationships arewarranted as illustrated, for example, by previousefforts on growth rates (Kempes et al., 2012).Furthermore, many cellular features are expected tobe connected mechanistically with others (e.g.,growth rates and ribosome content), and Figure 1illustrates these interconnections, along with thecascading dependence of many cellular features ontotal cell volume. We begin with the scaling of

Cellular composition across diverse bacteriaCP Kempes et al

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cellular energetics given the central role that thesewill play in our analysis and the previous demon-strations that energetics can be used to derive otherfeatures such as growth rate (Kempes et al., 2012).

Metabolic ratePrevious work has shown that metabolic rate, B (W),scales with body size according to

B ¼ B0VbBc ð4Þ

where βB≈2 in bacteria (DeLong et al., 2010) (βB≈1.7for an OLS fit) and B0 is a normalization constantwith units W m3Cellð Þ�bB . Although most previousallometric studies focus on mass as the size unit fororganisms, we use cell volume, Vc, here because thisis typically what is directly measured in bacteriaand, as can be inferred from our later findings,conversion to mass units can be complicated as celldensity is not constant with cell size (we later findthat density is greatest for the smallest and largestbacteria with a minimum value of 1.06 × 106 gm−3

for an intermediate cell size of 4.92 × 10− 18 m3; seeSupplementary Figure S5). Furthermore, many pre-vious studies report wet masses, which were theresult of applying a constant density factor tomeasured volumes, so conversion to volumeunits is straightforward: Vc =mw/dc, wheredc = 1.1 × 106 gm− 3 is the previously used cell den-sity assumed to be constant and mw is the calculatedwet mass from previous studies (e.g., West andBrown, 2005; Makarieva et al., 2008; DeLong et al.,2010). It should be noted that this conversion willnot change the scaling exponents found in studiesthat use wet mass provided that these studies used aconstant value for dc.

Growth ratesTo derive growth rates, it has been demonstrated(Kempes et al., 2012) that the metabolic scalingrelationship from the preceding section can becombined with the concept of metabolic partitioningaccording to

B ¼ Emdmdt

þ Bmm ð5Þwhere Bm (W g− 1) is the unit maintenance metabo-lism and Em (J g−1) is the unit cost of biosynthesis.Both of these parameters can be derived from bulkcommunity energetic constants of the yield (e.g.,g cells per mol resource) and maintenance (mols ofresource consumed for survival alone) coefficients,measured, for example, in a chemostat and con-verted to energy units (e.g., J per mol of resource; seeKempes et al., 2012 for a more detailed presenta-tion). The partitioned metabolism in Equation (5) hasbeen used to derive a single-cell growth curve(Kempes et al., 2012), from which it is possible todetermine the generation or division time, td (s), of asingle cell, along with the cross-species populationgrowth rate, μ≡ln(2)/td (s−1), of bacteria following therelationship

m ¼ Bm=Emð Þ 1� bBð Þln e½ �ln 1� Bm=B0ð ÞðVcdcÞ1�bB

1�e1�bB Bm=B0ð ÞðVcdcÞ1�bB

h i ð6Þ

where eE2 is the ratio of the size of the cell atdivision compared with its initial size. Our effortshere largely concern the physiological requirementsof a single cell, and thus most of our derivations(e.g., Supplementary Equations (S6)–(S47)) relyfundamentally on the division time td; however,the final results appear as functions of ln(2)/td and soit is convenient to report equations in terms of μ.It should also be noted that we have presented thisequation with the previous conversion (Kempeset al., 2012) between cell volume and wetmass explicitly stated, where dc (g m− 3) is the celldensity. The relationship for μ in Equation (6)demonstrates an asymptotic behavior for thesmallest bacteria that limits the smallest possiblecells (Kempes et al., 2012) and approximates thepower law

mEm0VbB�1c ð7Þ

for larger cell volumes (see SupplementaryInformation) showing that growth rate increasesrapidly as bacteria become larger. It should be notedthat in this framework Vc is the only true variablewhile all of the other parameters are, on average,expected to be constants, which has been supportedby data (Kempes et al., 2012). However, it should benoted that the model could incorporate futurediscoveries of unknown dependencies of any of theconstants; for example, Bm could have a complexresponse under extreme energy limitation, which is aregime that has not yet been well characterized. Theoverall growth rate, as represented by μ, defines the

Cellular Volume(Vc)

GenomicContent(VDNA)

CellularEnvelope

(Venv)

GrowthRate(µ)

ProteinContent

(Vp)

RibosomeContent

(Vr)

mRNAContent(VmRNA)

tRNAContent(VtRNA)

Figure 1 A schematic showing the proposed dependencies ofvarious cellular features on cell volume where several of theserelationships are connected to cell volume through several layersof dependencies. It should be noted that many of these features areintimately connected with cellular metabolism and energetics andthat these connections have not been drawn in this figure. Forexample, previous work has shown that the growth rate, μ, isconnected to the total cell size via the scaling of total metabolismand the energetics of basic maintenance requirements (Kempeset al., 2012).


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dominant rate processes of the cell, and we will latershow that this connection is central to determiningthe number of ribosomes, tRNA and mRNA.

Given the strong dependence of growth rate on cellsize, we should furthermore expect significant shiftsin macromolecular content for bacteria of differentvolumes. This is consistent with previous workshowing that the growth rate of bacteria is stronglyconnected with the relative abundance of variousmacromolecular components, most notably ribo-somes, RNA and proteins (e.g., Bremer et al., 1996;Zaslaver et al., 2009; Scott et al., 2010; Burnap,2015).

Genome sizeIt is interesting then to consider how the genomiccomplexity of bacteria changes in comparison withthe patterns in metabolic and growth rates. Asbacteria are becoming larger how rapidly is theirgenome increasing? Previous efforts have shown thatgenome size has a strong scaling with cell size inbacteria (Shuter et al., 1983; West and Brown, 2005;DeLong et al., 2010) and here we consider

VDNA ¼ D0VbDc ð8Þ

where we later determine D0 and βD from a compila-tion of data and previous compilations.

Protein scalingThe genomic scaling law is expected to be a powerfultool for understanding basic constraints on bacteriabecause it should influence many other features ofthe cell. For example, the total volume of proteinscan be related to genome length by knowing howmany proteins are produced per gene:

Vp ¼ npvpL

lpð9Þ

where vp (m3) is the volume of an average protein, lp(bp) is the average length, in nucleotides, of a proteinencoding gene and np (copies cell− 1) is the averagecopy number of a protein, and

L ¼ VDNA

vNð10Þ

is the length of the genome given the average volumeof a nucleotide vN (m3) (see Supporting Informationand Supplementary Figure S1) which allows us towrite the volume-dependent form:

Vp ¼ npvpD0VbDc

lpvNð11Þ

In Equation (11), vp, lp and np could each scale withcell volume. This relationship for protein volumespecifies the explicit relationship with protein copynumber and the scaling of genome size with cellvolume, however, for simplicity in presenting results

we consider and report the analogous scaling

Vp ¼ P0Vbpc ð12Þ

which can be easily connected with Equation (11).

Model of ribosome requirementWe derive the ribosome requirement by consideringhow many ribosomes are required to replicate allribosomes and proteins within a division cycle whilealso replacing proteins and ribosomes that have beendegraded. This perspective is complicated by the factthat as ribosomes and proteins are dynamicallyproduced they contribute, respectively, to the bio-synthetic capacity or biosynthetic requirements of acell. This leads to a conceptually simple, butalgebraically complicated derivation, which wepresent in the Supplementary Information, with thesimple final ribosome requirement that

N rZlpNp

fm þ 1� �

rrm � lr

Zm þ 1� � ð13Þ

where lr is the average length of a ribosome in basepairs, Nr is the number or ribosomes in the cell, rr(bp s− 1) is the maximum base pair processing rate ofthe ribosome which is assumed to be constant acrossboth taxa and cell size, η (s− 1) and ϕ (s− 1) are specificdegradation rates for ribosomes and proteins, respec-tively, and Np is the total number of proteins givenby

Np ¼ Vp

vp¼ npD0VbD

c

lpvNð14Þ

which depends on overall cell volume. The totalnumber of proteins could also be found usingEquation (12) as Np ¼ P0V

bpc =vp when P0 and βp are

known. In Equation (13) it is important to note that μis a function determined solely by overall cell sizegiven that the other parameters in Equation (6) areexpected to be pure constants. In the SupplementaryInformation we present Nr with the dependence onVc, via μ and Np, explicitly stated (SupplementaryEquations (S46) and (S47)). Our relationship for thenumber of ribosomes can be converted to the totalvolume of required ribosomes in the cell:

V r ¼ v rN r ð15Þwhere v r is the average volume of a ribosome (seeSupplementary Information for the explicit depen-dence on Vc).

An alternative perspective, commensurate withour considerations of the other cellular components,is that the number of ribosomes follows a simplescaling with cell volume:

V r ¼ R0VbRc ð16Þ

and we also test this possibility when analyzingtrends in the quantity of ribosomes.


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Trends in other RNAIn relationship to the number of ribosomes we mustalso consider the requirements for tRNA and mRNA.The minimum number of tRNA and mRNA in thecell should be equal to the number of ribosomes sothat every ribosome is engaged in protein synthesisand the cell is maximizing the biosynthetic rate.However, this does not consider the time scalesrequired for mRNA and tRNA to find and ‘react’ withthe ribosome. Another reasonable assumption is thatthere is some local concentration of tRNA andmRNA which allows the ribosome to operate at itsmaximum capacity. If this concentration is heldconstant, then the total number of tRNA and mRNAin the cell should be proportional to the number ofribosomes, as should the total volume of each ofthese components. Thus, we have

V tRNA ¼ v tRNAntRNAN r ð17Þwhere v tRNA is the average volume of a tRNA, andntRNA is the average number of tRNA per ribosome,and

VmRNA ¼ vmRNAnmRNAN r ð18Þwhere vmRNA is the average volume of an mRNA andnmRNA is the average number of mRNA per ribosome.It should be noted that Equations (17) and (18) bothdepend on cell volume because Nr is a function of Vc,and the explicit form is included in theSupplementary Information. Our estimates for thenumber of mRNA per ribosome are in fact close toone, implying that most ribosomes are engaged inprotein synthesis (nmRNA ¼ 1:09, see SupplementaryInformation).

Cellular envelopeCompleting our analysis of cellular composition weconsider the volume of the cellular envelope whichwe can approximate, considering a spherical cell, as

V env ¼ V c � 43p

3V c

4p

� �1=3

� renv

" #3 !1� pp

� �ð19Þ

where renv (m3) is the effective thickness of thecellular envelope and pp is the average percentage ofthe envelope that is occupied by proteins (we findthat this is roughly equal to 0.15, see SupplementaryInformation). It should be noted that renv will varydepending on whether the cell is Gram negative orpositive.

Predicting limiting behaviorA key aspect of our scaling analysis is that scalingexponents that deviate from 1 imply that there is adistinct bounding size at which a given componentwill equal and then exceed the total cell volume.This represents an inferred lower bound for βo1 andan upper bound for β41. For example, the

relationship for genome volume (Equation (8)) givesthe size of a cell that is entirely filled by DNA,VDNA =Vc, as

V�DNA ¼ D1= 1�bDð Þ

0 ð20Þand, from Equation (12), the volume at whichproteins are predicted to entirely fill the cell wouldbe given by

V�P ¼ P

1= 1�bpð Þ0 ð21Þ

Similarly, a major prediction of the ribosomerequirements (Equation (13)) is the appearance oftwo asymptotes at both the small and large end ofbacterial sizes. The small-end asymptote is charac-terized by the previous observation that the divisionrate will become zero for a cell volume of roughly1.45 × 10− 20 m3 (Kempes et al., 2012). The large-endasymptote is characterized by the point at which thetime to divide is not sufficient to replicate just theribosomes, and in the context of Equation (13) this isthe point when the denominator is less than or equalto zero leading to

mr rr � Zlrlr

ð22Þ

which we term the ‘ribosome catastrophe’.Beyond these single component limits we also

consider the limitation faced by the combination ofall overall cellular components given in Equation (2).Here it should be noted that some of the subcompo-nents follow power laws, others do not (e.g., RNAcomponents), and the overall relationship, whichrepresents a sum, has a more complicated nonlinearform than a simple power law. However, it is stillpossible to solve for the point at which Vtot =Vc,where it should be noted that the errors associatedwith each scaling may become amplified at thelargest and smallest scales. In plotting the relation-ships, either predicted or fit, for single componentsand the total component volume we extrapolate thefits to regions where these volumes would exceedthe total cell volume. This is physically impossible,but we make these extrapolations to show the scaleof the challenge faced at certain sizes in terms ofcomponent requirements.

Results and discussion

Basic scaling relationships and component trendsFigure 2a gives our own compilation (whichincludes data from Shuter et al., 1983; West andBrown, 2005; DeLong et al., 2010) of genome size,VDNA, showing that the scaling follows Equation (8)with D0 = 3.0 × 10− 17 (m3 DNA m3Cellð Þ�bD) andβD = 0.21 ± 0.03 (see Supplementary Information forthe 95% confidence intervals on all reported normal-izations constants such as D0). As previously noted(DeLong et al., 2010), this scaling shows that genomesize is increasing much less steeply than metabolic


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rate, which is perhaps surprising, although it is notclear how the number of genes should explicitlydetermine overall metabolism. For example, perhapsmetabolic rate should be related instead to thenumber of copies of certain pathway genes or tothe concentration of specific proteins in the cell(Burnap, 2015).

Our analysis, which includes data compiled inTempest and Hunter (1965), Tempest et al. (1965),Simon and Azam (1989), Dethlefsen and Schmidt(2007), Milo (2013) and Valgepea et al. (2013), showsthat the scaling for the volume of protein comparedwith that of overall cell volume is also less thanlinear, with P0 = 3.42 × 10− 7 (m3Protein m3Cellð Þ�bp ),and βp = 0.70 ± 0.06 (Figure 2b). Considering theobserved scaling for protein volume and DNAvolume in the context of Equation (11), we calculatethat npvp

lpscales like V0:49

c . It is likely that vp and lp are

roughly constant across cells (e.g., the average genelength has been found to be approximately invariantacross all bacteria (Xu et al., 2006)) and, therefore,this result implies that the average copy number of

proteins is likely increasing as cells become larger.Thus, not only are the number of unique proteinsincreasing for larger cells and genomes but thenumber of times that each protein is copied is alsoincreasing.

The departure of protein scaling from genomescaling gives an example of a cellular feature that isnot simply predicted by a proportionality withoverall genome size (e.g., the surprising scaling ofVp∝L3.33 given βp/βD ≈ 3.33). Given that total proteincontent is expected to play a strong role indetermining the number of ribosomes (Equation(13)) and the overall RNA content of the cell, weshould also expect these features to have a compli-cated connection with the genomic complexity of abacterium.

We predict the relationship between the totalvolume of ribosomes and overall cell volume fromEquations (13)–(15) using the asymptotic form of μ(see Supplementary Information for explicit forms)and measured values for the degradation rates f andη. This prediction should represent a true lowerbound, and in Figure 2c this curve (dashed line)

Figure 2 The cell-volume-dependent scaling of total (a) genome volume, (b) protein volume, (c) ribosome volume and (d) cellularenvelope volume. In each plot compiled data are given as red points along with predictions or model fits in red and the 95% confidenceintervals as shaded regions around each curve. The green curves represent the total cell volume (one-to-one line) for reference, and thevolume of the smallest observed cell is noted by the black dashed line (Seybert et al., 2006; Luef et al., 2015). In (c) the black curve is a best-fit power law, the red curve is the prediction from Equations (13)–(15) and the dashed line represents a pure prediction for the lowerbound on the number of ribosomes given measured values for degradation rates and our previous model of μ. For (d) the volumes of thecellular envelope are given for an average Gram-negative and -positive bacterium along with the volume of a single membrane. Please seethe Supplementary Information for a summary of the data compilations.


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tracks, but is consistently smaller than the observedvolume of ribosomes from our cross-species compi-lation of published data, which includes Bremeret al. (1996), Fegatella et al. (1998), Seybert et al.(2006) and Luef et al. (2015). We also find arelationship for the number of ribosomesusing a best fit of the degradation rates with thepower-law approximation of μ (see SupplementaryInformation), which accurately captures the cross-species trends in ribosome volume in Figure 2c. Wefind that this fitted prediction, which relies on only asingle free parameter, has a very similar goodness offit to a simple power law, where we find that the bestfit to Equation (16) is given by R0 = 1.54 ×10− 7

(m3Ribosomes m3Cellð Þ�bR ) and βR = 0.73 ± 0.15. Itshould be noted that the best fit of our full model forribosome composition makes predictions for rangesof cell size where we do not have data to test themodel. Some of our later conclusions and inferencesrely on these predictions, and thus provide a set oftestable and open hypotheses, such as the number ofribosomes found at larger bacterial sizes or the exactsize at which the ‘ribosome catastrophe’ occurs.

Shifts in cellular composition and the smallest bacteriaOur analysis now provides the size dependence forthe major cellular components across the domain ofbacteria. This includes the prediction for the volumeof the envelope considering three cases: only a singlemembrane (organisms without a cell wall) and theeffective thickness for Gram-negative or -positivebacteria (Figure 2d), and predictions for tRNA andmRNA given the volume of ribosomes.

Of critical interest is how the relative cellularcomposition changes across species of diverse sizeand what tradeoffs and limitations we might be ableto infer from these shifts. Figure 3a shows all of thecross-species trends for various cellular componentscompared with the overall cell volume. The com-piled trends show that the composition of the cellgreatly shifts across the range of bacterial body sizes.The smallest cell volumes are dominated by DNAand, to a lesser extent, cell membrane and protein,while the largest bacteria are composed of mostlyribosomes, tRNA and mRNA. These changes incomposition are accompanied by shifts in the dryfraction of cells, as discussed later, and the overall

Figure 3 (a) The volume-dependent scaling of each of the major cellular components for bacteria. (b) The total cell volume comparedwith the volume of all cellular components as a function of cell size. (c) The fraction of total cell volume that is occupied by the essentialcomponents. It should be noted that in each of these plots we have extrapolated curves to regions that are not physically possible (such asthe dry fraction exceeding 1) in order to illustrate crossings that represent limiting sizes, and to show the increasing challenges faced bybacteria beyond these critical values.


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cell density (see Supplementary Figure S5 andrelated discussion).

These trends also predict at what scale certaincomponents would become limiting. For example,the relationship for genome volume gives the mass ofa cell that is entirely filled by DNA as

V�DNA¼ 1:14±0:30 ´ 10�21m3 ð23Þ

which is expectedly smaller than the smallestobserved organism by a factor of approximatelythree (Table 1). This result shows that for thesmallest cells there is not much room beyond thebasic requirements for the genome. Similarly, thevolume at which proteins are predicted to entirelyfill the cell would be given by

V�P¼ 3:38±4:72 ´ 10�22m3 ð24Þ

which is about an order of magnitude smaller thanthe smallest cell. The cellular envelope volume thatcompletely fills the cell can be found using Equation(19) given values for the envelope thickness. Fora Gram-negative bacterium, the envelope would fullyoccupy the cell at a size of 7.44 × 10− 22 m3, for aGram-positive, at a size of 2.91 × 10− 23 m3, and for asingle membrane (organisms lacking a cell wall), at asize of 1.01 × 10− 25 m3. These results show that forthe smallest cells the envelope represents a signifi-cant portion of the overall volume. In order to reducethe required envelope volume, the smallest cells areexpected to minimize surface area by becomingincreasingly spherical, which agrees well with themostly spherical cell shapes reported by Luef et al.(2015), and are expected to reduce envelope thick-ness or layers, consistent with Mycoplasma that lacka cell wall.

The above analysis is useful for understandingwhich individual components become limiting at thesmallest cell sizes. More generally, we can under-stand the overall space constraints of the cell at the

small end of life by considering the total volumefrom Equation (2). This summed component volumewill equal the total cellular volume for a size of1.02 × 10− 20 m3 for a Gram-positive bacterium, whichis comparable to the previous energetic prediction(Kempes et al., 2012; Figure 3b) and larger than thesmallest observed and hypothesized cells by roughlya factor of two (Knoll et al., 1999; Seybert et al., 2006;Luef et al., 2015). Considering only a single mem-brane would give a minimal size of 4.10 ×10− 21 m3,which closely matches measurements for the smal-lest bacteria (Table 1). Considerations of the spacefor the smallest cells is a topic that has been deeplyconsidered in the past and previous estimates agreewith our prediction for a lower bound, where it wasestimated that the minimum size required for a cellof modern biochemical complexity should fall in therange of 4.19×10−21–1.41×10−20 m3 (Knoll et al., 1999).Furthermore, this result, and our space constraintestimate from Vcomp=Vtot, also compare well with thelimit anticipated from energetic considerations (Kempeset al., 2012), thus highlighting that multiple constraintsare likely limiting the possibility of becoming smaller atthe smallest scale of life.

Our result shows that the average cross-speciestrends converge to predict the smallest cell at theappropriate size range while still being an accuratepredictor of cellular composition as cells moveorders of magnitude away from this lower bound(Figures 2 and 3). This is remarkable because ouranalysis shows that average trends in cellularcomposition across the diversity of bacteria areconsistent with the scale of the lower limits of life.However, these predictions also highlight necessarytradeoffs for the smallest cells, where the totalvolume requirements accurately predict theobserved minimum size only for a reduced cellularenvelope of a single membrane. This may not bebiologically feasible and thus other compositional

Table 1 Comparisons of estimates and measurements for the smallest bacterium

Minimum size estimate Type of estimate

Space limitations from this studyFor a Gram-positive bacterium 1.02×10− 20 m3 Cross-species prediction and theoryFor bacterium with a minimal membrane 4.10×10− 21 m3

Previous measurements and estimatesGround water microbes (Luef et al., 2015) 4.00×10−21 to 1.3 × 10− 20 m3 MeasuredMycoplasma pneumoniae (Seybert et al., 2006) 3.00×10−21 to 2.4 × 10− 19 m3 MeasuredEnergetic/growth limitations (Kempes et al., 2012) 1.45×10− 20 m3 Cross-species prediction and theoryNRC basic metabolism and components (Knoll et al., 1999) 4.19×10− 21 m3 Calculation of average biochemical

properties

Size at which individual components would fill the entire cell volumeGenome scaling 1.14×10− 21 m3 (8.66×10−22,

1.46×10−21)a

Protein scaling 3.38×10− 22 m3 (6.90×10−23,6.75×10− 22)

Cross-species prediction and theory

Single membrane scaling 1.01×10− 25 m3

Ribosome scaling 3.99×10− 26 m3 (2.03×10−28,1.17×10− 23)

aThe bracketed values, ( , ), denote the 95% confidence interval.


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tradeoffs may be required for the smallest cells. Forexample, the genome size for Mycoplasma genita-lium is 5.8 × 105 bp (Moya et al., 2009), which isabout half the size of the prediction from the averagetrend for a bacterium of this volume. Similarly, at thesmallest sizes, it is possible that cells could evolve tohave lower copy number of proteins per gene, orhave smaller average protein sizes—all to accom-modate cell volume constraints.

Our own previous cross-species considerations(Kempes et al., 2012) predict a smallest bacteriumthat compares well with the mean cell size of Luefet al. (2015) and Seybert et al. (2006) but is about fourto five times larger than the smallest cells from thesestudies (Table 1). This difference highlights that thesmallest organisms may deviate from average ener-getic properties, such as unit maintenance costs, inaddition to compositional shifts, though some ofthese deviations would require a cellular biochem-istry that differs from modern examples. For exam-ple, previous estimates for possible primitive cellswould lead to a size of 3.59 ×10−24 m3 (Knoll et al.,1999), which is not much bigger than the size atwhich the cell volume is entirely filled by a singlemembrane (1.01 × 10− 25 m3).

Although the data presented here are for thedomain of bacteria, we may find similar constraintsin archaea. For example, the smallest observedarchaea are roughly comparable to the smallestbacteria in volume (≈3.41× 10− 20 m3; Huber et al.,2002; Comolli et al., 2009) and have similar genomesizes (0.5 megabases (Huber et al., 2002)) andribosome counts (≈92; Comolli et al., 2009) atthis size.

RNA limitations and the largest bacteriaFor the largest bacteria, the dominant cell compo-nents are determined by the increasing need forprocesses related to transcription and translation tomatch increasing growth rates. As discussed earlier,this eventually leads to a ‘ribosome catastrophe’,where a finite size would require an infinite numberof ribosomes, tRNA and mRNA. The limits antici-pated in our model for the volume of ribosomes canbe seen in the prediction curve of Figure 2c, wherethe entire cell volume would be filled by ribosomes,the ‘ribosome catastrophe’, at a size of1.39 ±0.03 × 10− 15m3. This is in contrast to thesmallest bacteria, where the need for ribosomes,tRNA and mRNA are predicted to diminish based onthe decreasing growth rates. Previous predictionspredict that growth rate goes to zero at a size of1.45 ×10− 20 m3 (Kempes et al., 2012).

Expanding from the number of ribosomes to thetotal RNA content, the prediction from Equation (18)compares well with measurements for mRNA inEscherichia coli and Mycoplasma pneumoniae (seeSupplementary Information for the value of theconstants in Equations (17) and (18)). For E. coli,previous measurements give a range of 1380

(Neidhardt et al., 1996) to ≈10 000 mRNA per cell(see compilation in the Supplementary Informationof Lu et al., 2007), compared with our estimate of2540 to 12 257 using a cell volume between roughly0.7 and 6 μm3 (Dethlefsen and Schmidt, 2007; Milo,2013), and dividing Equation (18) by v tRNA. For M.pneumoniae, the mRNA quantities are two orders ofmagnitude lower than E. coli at around 10 per cell(Maier et al., 2011), which is similar to the lowerbound of our estimate of 68-1159 given the consider-able range in observed cell size of 0.005–0.24 μm3

(Seybert et al., 2006).Similarly, the number of tRNA per cell in E. coli

has been observed to range between 52 000 and375 000 (Jakubowski and Goldman, 1984; Neidhardtet al., 1996; Mackie, 2013), where we would predicta range of 23 561 to 113 707 based on the range ofcell volumes used above. For M. pneumoniae,observations give 190 tRNA per cell (Maier et al.,2011), which is similar to our prediction of 631 to10 755. It should be noted that in both cases weoverestimate the number of tRNA and mRNA inMycoplasma which is likely due to the considerablespace constraints faced by these minimal organisms,as discussed earlier.

Parallel to our analysis of the smallest cells, thetotal component volume also sets an upper bound onsize, where Vcomp =Vtot at a size of 1.19 ×10−15 m3.This limit is dominated by the ‘ribosome cata-strophe’, where the cell will require more ribosomesthan can fit in its volume in order for biosynthesis tokeep up with increasing growth rate. It should benoted that this predicted upper bound is four ordersof magnitude smaller than the largest observedbacterium of ≈4.19× 10− 12 m3 (Schulz et al., 1999).However, this giant sulfur bacterium (Thiomargaritanamibiensis) is dominated by vacuoles used fornutrient storage, which does not represent themetabolic active or relevant volume considered inour model of the required components (Schulz et al.,1999). If we remove the vacuole volume (approxi-mately 98% of the total cell volume; Schulz et al.,1999) then we are left with a size of 1.05 ×10− 14 m3,which is only an order of magnitude larger than ourpredicted upper bound. It is interesting to considerwhat tradeoffs these cells have made to avoid the‘ribosome catastrophe’, and one possibility is that theenvironment regulates growth at a slower rate thancell size would dictate.

Similar to our biosynthetic limit, previous workhas shown that there is a linear increase in thefraction of promoter activity devoted to ribosomeswith increasing growth rate (Zaslaver et al., 2009). Ifthe observed trend is extrapolated, then at a growthrate of 2.9 divisions per hour all promoter activitywould be devoted to ribosomes, which is notfeasible, and this would correspond to a cell volumeof 2.1 × 10− 17 m3. This predicted upper bound issmaller than our space limitation and highlights themultiple constraints that could be faced for thelargest bacteria. Both of these upper bounds on cell


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volume correspond to the rough size at which thereis an observed transition to eukaryotic life, alongwith corresponding and dramatic shifts in growthand metabolic rates (DeLong et al., 2010; Kempeset al., 2012). Thus, this major transition may in partbe motivated by the challenges related to biosynth-esis and ribosome requirements.

Free volumeIn between this lower and upper limit, changes incomposition can be most easily understood byconsidering the total physical space required foressential components compared with the remainingvolume. Considering the average composition trendsthat we have discussed thus far, the fraction of thecell that is dry weight (Equation (3)) is 1 for thesmallest bacteria and decreases quickly for largercells until reaching a minimum around 0.13 at a sizeof 2.83 × 10− 17 m3, before increasing again towardsthe largest cell (Figure 3c). From this relationship wecan see that bacteria of intermediate size have themost free volume, and the maximum of this volumeoccurs around the size of many well-studied speciessuch as E. coli.

This free volume, which is an inferred and testableprediction from our model, has important evolu-tionary and ecological consequences because itimplies that there is a range of cell sizes that mayhave the most flexibility due to the lack of physicalspace constraints. This flexibility could manifest asan increase in the copies of specific proteins instressful conditions, greater ability to buffer wasteproducts or plasticity in increasing the number ofribosomes for faster growth, among many otherpossible benefits. This is in sharp contrast to thesmallest cells that barely have enough space for basicbiochemical requirements. An important avenue offuture research is to examine whether and howindividual taxa allocate ‘free volume’ differently tovarious components or functions, and whether suchallocation can be understood as an adaptation tospecific niches or conditions.

However, it is also important to consider, as part ofthis ‘free volume’, the volume of water necessary forcellular reactions and internal transport. For exam-ple, if all of the free volume were dedicated to water,and given the size of E. coli, we would predict that67–76% of the cell is filled with water, in goodagreement with previous estimates of 70%(Neidhardt et al., 1996). This comparison impliesthat all of the free volume could reasonably beoccupied by water, and that evolutionary flexibilityat these cell sizes could depend on the degree towhich the water content is constrained. Our predic-tions suggest that the smallest and largest cells havelower water content, which is consistent withprevious efforts that describe a cytoplasm with highmolecular packing densities (e.g., von Hippel andBerg, 1989; Cayley and Record, 2003; Golding andCox, 2006; Burnap, 2015). Similarly, these changes

in water content may alter processes related to thesolvent capacity or diffusive, sub-diffusive or activetransport in the cell (e.g., von Hippel and Berg, 1989;Cayley and Record, 2003; Errington, 2003; Goldingand Cox, 2006; Burnap, 2015), and it is of potentialfuture interest to understand whether there arespecific and calculable requirements for watercontent in cells of different size in connection withcellular composition. Furthermore, these resultsimply that the application of a constant dry weightratio to diverse species may often be inaccurate.

Energetic limitations and complexitiesPrevious studies have highlighted that prokaryoteshave a superlinear scaling between metabolic rateand body size. This observation has been success-fully used to derive cross-species trends in growthrates and a limit where growth rate should go to zeroin bacteria (Kempes et al., 2012). However, thesuperlinear scaling of metabolism is still not funda-mentally understood and here we are surprised tofind that every cellular feature scales sublinearlywith overall cell volume. This implies that metabo-lism is not a simple proportionality of any onecellular feature. Figure 4b gives the scaling of thetotal metabolic rate as a function of the volume ofeach cellular component where it can be seen that allof the scalings are superlinear. Taken together theseobservations suggest that metabolic rate is a compli-cated emergent property of some measure of increas-ing cellular complexity. In particular, the scaling ofmetabolic rate with genome size stands out with anexponent close to 8, and it may be the case thatmetabolism is a complicated function of the growingcomplexity of the metabolic network which addscapacity quickly with the addition of novel proteins(DeLong et al., 2010). Metabolism also goes upsteeply (exponents close to 2.4) with the totalenvelope volume and total number of proteins whichalso makes sense given that the membrane surfacearea controls ATP synthesis (Lane and Martin, 2010)and the number of proteins are the actual compo-nents of the metabolic network. The scaling ofproteins scales closely to a power-law approximationof the growth rate equation (6) (an exponent of 0.65compared with 0.70). Since growth rate is set by theoverall scaling of metabolic rate (Kempes et al.,2012), it is possible that the protein concentrationcould be the dominant factor controlling bothmetabolic rate and growth rate, albeit not via anydirect proportionality. Yet the explicit connectionbetween any of these components to the scaling ofmetabolic rate remains unclear.

Furthermore, these scalings also highlight theunexpected result that cellular efficiency, definedas the metabolic power per unit of component (Laneand Martin, 2010), is increasing for every cellularcomponent. It has previously been pointed out thatthe plasma membrane serves as the only region forATP synthesis in bacteria, and since this surface area


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scales sublinearly with volume it will be outpaced byanything that is proportional to volume (Lane andMartin, 2010). Previous analyses have thus suggestedthat bacteria are becoming less efficient on a per-protein or per-gene level (Lane and Martin, 2010).However, the surprising superlinear scaling of meta-bolic rate and the sublinear scaling of both genomesize and protein content lead to an increasingefficiency for both components. Figure 4a gives thepower per gene as a function of cell size showing thatit is increasing superlinearly across bacteria. Thisscaling agrees with the average values from Lane andMartin (2010) for mid-range bacteria and as bacteriagrow larger the values approach the reportedeukaryotic average (Lane and Martin, 2010) at theupper range of bacteria. If bacteria were able to grow

larger they would be expected to continue toincrease the power per gene and overtake theeukaryotes. Thus, it would seem that bacteria arenot limited by an energetic efficiency challenge butrather by an energetic surplus that demands everfaster rates of biosynthesis and eventually leads to aspace limitation via the packing of ribosomes asdiscussed earlier. It may be that the evolutionarytransition to eukaryotes was motivated by biosyn-thetic and space constraints resulting from a fastmetabolism rather than to increased metaboliccapacity. In fact, eukaryotes have a metabolism thatscales with cell size following a smaller exponentthan bacteria (DeLong et al., 2010). These results arecounterintuitive and bring up deep questions aboutthe explicit connection between membrane areasand metabolic rate: if mitochondria evolved toincrease the ATP synthesis area and provide anadvantage over bacteria (Lane and Martin, 2010),then how and why can metabolic rate scale super-linearly in bacteria when the surface area is growingsublinearly with body size?

Concluding remarks

In general, we find that cellular components followstrong trends, often power laws, with overall cellsize. From the perspective of size limitations of cells,these cross-species trends, along with previous work(Knoll et al., 1999; Kempes et al., 2012), show that,on average, the smallest cells face challenges relatedto growth rate, energetic constraints and the physicalspace required to contain basic components. Ourwork here demonstrates how various cellular com-ponents are connected with one another and pro-vides a foundation for understanding tradeoffs inphysiology as related to cell size. Moving forward itis important to connect this work with detailedperspectives of how cell size and compositionrespond to environmental conditions and stress(e.g., Chien et al., 2012).

Furthermore, while we can predict many cross-species trends, such as the number of ribosomes orthe growth rate (Kempes et al., 2012), several basicscaling relationships remain unexplained in bacteriasuch as the scaling of genome size and the overallmetabolic rate (West and Brown, 2005; DeLong et al.,2010). These relationships imply surprising conse-quences for the cell such as the increasing power pergene or protein as cells become larger based on thesuperlinear scaling of metabolism compared with thesublinear scaling of all other cellular components. Totruly understand the full set of limitations thatconstrain the smallest cells and define speciestradeoffs, we will need to continue to mechanisti-cally underpin these observed cross-species trends.In doing so, we may be able to gain further insightinto key evolutionary bifurcations, adaptation tovarious niches and better understand the require-ments for originating and sustaining simple life.

Figure 4 (a) The estimated scaling of metabolic rate per gene as afunction of overall cell volume calculated from the scaling ofgenome size here and the data from DeLong et al. (2010). Previousaverage values from Lane and Martin (2010) for prokaryotes andeukaryotes are both shown. It can be seen that the previousprokaryote average value agrees with the scaling for the middlerange of bacteria, and that bacterial values are close to the eukaryoticaverage value for the largest bacteria. Surprisingly, bacteria areincreasing the metabolic rate per gene with a scaling exponent of1.49. (b) Scaling of the total cellular metabolism as a function of thetotal volume of each cellular component. It can be seen that all ofthese relationships scale with an exponent greater than 1 (linearscaling is indicated by the gray dashed line), implying thatmetabolism is not a simple proportionality of any single cellularcomponent. This suggests that the way in which cellular compo-nents are combining to produce superlinear scaling in cells is acomplicated and emergent phenomena. Most notably, metabolic ratescales with total genome volume with an astonishing power of ≈ 8.


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Conflict of Interest

The authors declare no conflict of interest.

AcknowledgementsCPK acknowledges the support of the ‘Life Underground’NASA Astrobiology Institute (NNA13AA92A) and theGordon and Betty Moore Foundation.

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