Disentangling the cost of gene expression

Disentangling the fitness cost of gene expression | bioRxiv /* */ /* */ <!-- <!-- /*! * yepnope1.5.4 * (c) WTFPL, GPLv2 */ (function(a,b,c){function d(a){return"[object Function]"==o.call(a)}function e(a){return"string"==typeof a}function f(){}function g(a){return!a||"loaded"==a||"complete"==a||"uninitialized"==a}function h(){var a=p.shift();q=1,a?a.t?m(function(){("c"==a.t?B.injectCss:B.injectJs)(a.s,0,a.a,a.x,a.e,1)},0):(a(),h()):q=0}function i(a,c,d,e,f,i,j){function k(b){if(!o&&g(l.readyState)&&(u.r=o=1,!q&&h(),l.onload=l.onreadystatechange=null,b)){"img"!=a&&m(function(){t.removeChild(l)},50);for(var d in y[c])y[c].hasOwnProperty(d)&&y[c][d].onload()}}var j=j||B.errorTimeout,l=b.createElement(a),o=0,r=0,u={t:d,s:c,e:f,a:i,x:j};1===y[c]&&(r=1,y[c]=[]),"object"==a?l.data=c:(l.src=c,l.type=a),l.width=l.height="0",l.onerror=l.onload=l.onreadystatechange=function(){k.call(this,r)},p.splice(e,0,u),"img"!=a&&(r||2===y[c]?(t.insertBefore(l,s?null:n),m(k,j)):y[c].push(l))}function j(a,b,c,d,f){return q=0,b=b||"j",e(a)?i("c"==b?v:u,a,b,this.i++,c,d,f):(p.splice(this.i++,0,a),1==p.length&&h()),this}function k(){var a=B;return a.loader={load:j,i:0},a}var l=b.documentElement,m=a.setTimeout,n=b.getElementsByTagName("script")[0],o={}.toString,p=[],q=0,r="MozAppearance"in l.style,s=r&&!!b.createRange().compareNode,t=s?l:n.parentNode,l=a.opera&&"[object Opera]"==o.call(a.opera),l=!!b.attachEvent&&!l,u=r?"object":l?"script":"img",v=l?"script":u,w=Array.isArray||function(a){return"[object Array]"==o.call(a)},x=[],y={},z={timeout:function(a,b){return b.length&&(a.timeout=b[0]),a}},A,B;B=function(a){function b(a){var a=a.split("!"),b=x.length,c=a.pop(),d=a.length,c={url:c,origUrl:c,prefixes:a},e,f,g;for(f=0;f<d;f++)g=a[f].split("="),(e=z[g.shift()])&&(c=e(c,g));for(f=0;f<b;f++)c=x[f](c);return c}function g(a,e,f,g,h){var i=b(a),j=i.autoCallback;i.url.split(".").pop().split("?").shift(),i.bypass||(e&&(e=d(e)?e:e[a]||e[g]||e[a.split("/").pop().split("?")[0]]),i.instead?i.instead(a,e,f,g,h):(y[i.url]?i.noexec=!0:y[i.url]=1,f.load(i.url,i.forceCSS||!i.forceJS&&"css"==i.url.split(".").pop().split("?").shift()?"c":c,i.noexec,i.attrs,i.timeout),(d(e)||d(j))&&f.load(function(){k(),e&&e(i.origUrl,h,g),j&&j(i.origUrl,h,g),y[i.url]=2})))}function h(a,b){function c(a,c){if(a){if(e(a))c||(j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}),g(a,j,b,0,h);else if(Object(a)===a)for(n in m=function(){var b=0,c;for(c in a)a.hasOwnProperty(c)&&b++;return b}(),a)a.hasOwnProperty(n)&&(!c&&!--m&&(d(j)?j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}:j[n]=function(a){return function(){var b=[].slice.call(arguments);a&&a.apply(this,b),l()}}(k[n])),g(a[n],j,b,n,h))}else!c&&l()}var h=!!a.test,i=a.load||a.both,j=a.callback||f,k=j,l=a.complete||f,m,n;c(h?a.yep:a.nope,!!i),i&&c(i)}var i,j,l=this.yepnope.loader;if(e(a))g(a,0,l,0);else if(w(a))for(i=0;i (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0];var j=d.createElement(s);var dl=l!='dataLayer'?'&l='+l:'';j.src='//www.googletagmanager.com/gtm.js?id='+i+dl;j.type='text/javascript';j.async=true;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-M677548'); Skip to main content Home About Submit ALERTS / RSS Search for this keyword Advanced Search New Results Disentangling the fitness cost of gene expression View ORCID Profile Yichen Yan , View ORCID Profile Jie Lin doi: https://doi.org/10.1101/2025.06.02.656972 Yichen Yan 1 Peking-Tsinghua Center for Life Sciences, Peking University , Beijing, China Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Yichen Yan Jie Lin 1 Peking-Tsinghua Center for Life Sciences, Peking University , Beijing, China 2 Center for Quantitative Biology, Peking University , Beijing, China 3 School of Physics, Peking University , Beijing, China Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Jie Lin For correspondence: linjie{at}pku.edu.cn Abstract Full Text Info/History Metrics Supplementary material Preview PDF Abstract Gene expression is essential for biological functions but also incurs a fitness cost. Although the fitness cost can be experimentally measured as the relative reduction in growth rate, it remains unclear how the cost quantitatively depends on different limiting factors. In this work, we establish a resource competition model and disentangle the fitness cost into components arising from limiting resources, including ribosomes, RNA polymerases, and transcription factors. Comparing our model predictions with experimental data for Saccharomyces cerevisiae , we demonstrate that ribosome competition dominates the translation cost, and that transcription factor competition dominates the transcription cost. Our model reveals that the fitness costs originate from the processes of transcription and translation, rather than from the products. The model also systematically connects the fitness cost to genetic and environmental properties, making quantitative predictions consistent with various experimental observations. Our work establishes a systematic framework for gene expression cost, guiding synthetic biology to optimize genetic design. INTRODUCTION Gene expression is one of the most fundamental cellular processes, where genes are transcribed into mRNAs, and mRNAs are translated into proteins critical for a cell’s viability. However, gene expression also imposes a fitness cost: expression of unnecessary proteins burdens the cell, slowing its growth rate [ 1 – 7 ]. The fitness cost is typically quantified by the relative reduction in growth rate [ 8 ]. Despite its fundamental importance in the evolution of gene expression, the sources of the fitness cost are not well understood. One potential source is the energy or metabolic cost of gene expression, which arises from the consumption of metabolites, e.g., ATP, nucleotides, and amino acids [ 5 , 9 , 10 ]. Nevertheless, the energy cost fails to explain the fitness cost, as producing mRNA imposes a fitness cost comparable to that of producing proteins [ 8 ], even though mRNA synthesis consumes far less ATP than protein synthesis [ 5 , 9 ]. In addition, because the relationship between numerous biochemical processes and cell growth is complex, predicting fitness cost based on metabolic consumption is challenging. Prior theories largely attribute the fitness cost to dilution effects, where overexpressed proteins dilute the concentrations of key biomolecules, such as ribosomes and RNA polymerases (RNAPs), leading to a lower growth rate [ 4 , 11 ]. However, the dilution theory cannot relate the cost to a specific process during gene expression, or to particular properties of the studied gene, which are crucial for synthetic biology. Moreover, the dilution theory disagrees with the experimental observations showing that the gene expression cost is generated by the processes of transcription and translation, rather than by the products; particularly, the fitness cost is independent of the degradation rate of the overexpressed protein [ 8 , 12 ]. Furthermore, it remains unclear how the fitness cost can be decomposed into a sum of transcription and translation costs [ 8 , 13 ]. In this work, we calculate the fitness cost based on a resource competition scenario. In the simplest scenario, we assume that genes compete for RNA polymerases for transcription and mRNAs compete for ribosomes for translation. We successfully disentangle the fitness cost into two components generated from the competition for RNAPs and ribosomes. The ribosome cost turns out to be the relative fraction of ribosomes used by the exogenous mRNA, and the RNAP cost is the relative fraction of RNAPs used by the exogenous gene multiplied by the fraction of free ribosomes. Remarkably, our predicted cost due to ribosome competition agrees quantitatively with experimental data for S. cerevisiae [ 8 ]. Surprisingly, the measured cost generated by transcription is much higher than the RNAP cost. We next extend our model to include transcription factors (TFs) and show that the cost generated by competition for TFs dominates the transcription cost, and the predicted TF cost aligns with experiments. Our model quantitatively explains why the fitness cost of mRNA production can be comparable to that of protein production despite significantly lower energy expenditure. We also explicitly account for dilution effects and reveal that their net contribution is negligible; therefore, gene expression costs primarily stem from the transcription and translation processes, which offers an alternative to the prevailing assumption that fitness costs arise from the dilution effects of protein products. Our model also quantitatively connects the fitness cost to genetic and environmental properties, showing robust predictive power across diverse biological contexts. From an application perspective, our work establishes a systematic framework for the fitness cost of gene expression, providing design guidelines for synthetic biology and facilitating genetic circuit optimization. RESULTS Resource competition model of gene expression We introduce a gene expression model at the genomewide level, in which genes compete for RNA polymerase (RNAP) to transcribe mRNAs, and mRNAs compete for ribosomes to translate proteins ( Figure 1 ) [ 14 , 15 ]. In eukaryotes, “RNAP” in this work refers to RNA polymerase II, which transcribes mRNAs. We consider the fitness cost of an exogenous gene, denoted by “ex”. To simplify without affecting the main results, we treat all the endogenous genes as an ensemble of “average” genes so that they have the same binding affinity to RNAP and their mRNAs have the same binding affinity to the ribosome. The exogenous gene can have different binding affinities from the “average” ones. One should note that our results are equally valid for an overexpressed endogenous gene, and one only needs to treat the additional copy of the endogenous gene as the “exogenous” gene. Download figure Open in new tab FIG. 1. Schematic of the resource competition model. The exogenous gene and the endogenous genes compete for the limiting RNAP and ribosomes. RNAP can be actively transcribing endogenous genes, actively transcribing the exogenous gene, or inactive. Their numbers sum to a fixed total RNAP copy number. Endogenous genes (blue) and the exogenous gene compete for RNAP, where g and g ex are their copy numbers, and P n and P n,ex are their probabilities for promoters to be bound by an RNAP, respectively. Similarly, endogenous mRNAs (blue) and the exogenous mRNAs (red) compete for ribosomes, where m and m ex are their copy numbers, and P r and P r,ex are probabilities for their RBSs to be bound by a ribosome, respectively. At the transcription level, RNAP can be in three states ( Figure 1 ): actively transcribing endogenous genes, actively transcribing the exogenous gene, and inactive (i.e., free or bound to non-coding regions). Without the exogenous gene, the conservation of the total RNAP copy number can be written as Here, g is the genome size, i.e., the total copy number of endogenous genes; Λ n is the gene capacity of RNAP, i.e., the maximum number of RNAP on a single gene copy, including initiating and elongating RNAP; P n is the probability of an endogenous promoter bound by an RNAP, which we model as a Michaelis-Menten (MM) function of the concentration of free RNAP [ 16 – 18 ] (Methods A); N n is the total number of RNAP; and f n is the fraction of inactive RNAP molecules which can be either free or bound to non-coding regions. The introduction of the exogenous gene leads to the changes in P n and f n : Δ P n and Δ f n , which can be found by Here, N n,ex is the number of RNAP working on the exogenous gene. In this work, we mainly consider a simplified scenario in which the resource pool is fixed (e.g., Δ N n = 0), and we later show that this is a good approximation because the effects of changes in the resource copy number and the cell volume are largely canceled out. Eq. (2) states that the resource competition from the exogenous gene leads to a reduction in both the inactive RNAP fraction and the probability of endogenous promoters bound by an RNAP. The equilibrium of production and degradation sets the total endogenous mRNA copy number: Here, is the mRNA production rate per gene, where is the transcription initiation rate for an RNAP-bound promoter (number of initiations per unit time), and τ is the mRNA lifetime. Without the exogenous gene, a similar conservation equation applies to ribosomes: Here, m is the copy number of endogenous mRNA; Λ r is the mRNA capacity of ribosomes (i.e., the maximum number of ribosomes on a single mRNA copy); P r is the probability for the ribosome-binding-site (RBS) of endogenous mRNA to be bound by a ribosome, which we model as an MM function of the free ribosome concentration [ 15 , 19 , 20 ] (Methods A); N r is the total number of ribosomes; f r is the fraction of free ribosomes that are not actively involved in translation. The introduction of the exogenous gene leads to changes in m, P r , and f r : Δ m , Δ P r , and Δ f r , which can be found by where N r,ex is the number of ribosomes working on the exogenous mRNA produced by the exogenous gene. We note that the change in the endogenous mRNA copy number originates from a lower mRNA production rate due to the reduced P n after introducing the exogenous gene (Eqs. ( 2 - 3 )). The time derivative of endogenous protein mass M is set by production and degradation: where a is the mass of the “average” endogenous protein, and d is the average protein degradation rate. Here, is the protein production rate per mRNA, where is the translation initiation rate for a ribosome-bound RBS. Because the growth rates of all extensive variables are the same in the exponential steady state, we calculate the growth rate using the endogenous protein mass as Decomposing the fitness cost of gene expression We introduce the fitness cost defined as the relative reduction in the growth rate due to the expression of the exogenous gene, assuming the exogenous gene generates no benefit: Intriguingly, the resource competition model predicts that the fitness cost of gene expression can be explicitly disentangled into a cost due to RNAP competition (RNAP cost) and a cost due to ribosome competition (ribosome cost) ( Figure 2 ; derivation details in Methods A): Download figure Open in new tab FIG. 2. The RNAP and ribosome costs of gene expression. The fitness cost can be disentangled into a ribosome cost and an RNAP cost. The ribosome cost equals the fraction of ribosomes used by the exogenous mRNA ( N r,ex /N r ). The RNAP cost equals the fraction of RNAPs used by the exogenous gene ( N n,ex /N n ) multiplied by the free ribosome fraction. β m,ex , β p,ex , 1 /τ ex , γ ex are the rates of mRNA production, protein production, mRNA degradation, and protein decay for the corresponding molecule of the exogenous gene, respectively. Here, N n,ex and N r,ex are the copy numbers of RNAP and ribosomes working on the exogenous gene and mRNA, respectively. The above equation shows that the cost of expressing the exogenous gene is determined by the number of RNAPs and ribosomes it consumes. Interestingly, the RNAP cost is damped by a downstream factor f r , the fraction of free ribosomes in the total ribosome pool: the upstream RNAP cost only becomes apparent when ribosome availability downstream is not limiting. We can also express the fitness cost as a function of the produced mRNA and protein copy number of the exogenous gene (Methods A): where are the RNAP cost per mRNA and the ribosome cost per protein, respectively. Here, T tx,ex is the total duration for an RNAP to transcribe the exogenous gene, including the duration in the initiation state. T tl,ex is the total duration for a ribosome to translate the corresponding mRNA, including the duration in the initiation state. τ ex is the lifetime of the exogenous mRNA, and γ ex = µ + d ex is the decay rate of the exogenous protein, which is the sum of the growth rate and the degradation rate d ex . Eq. (10) suggests that cells can lower the gene expression cost by using fewer mRNA copies to produce a given amount of proteins, in agreement with experiments [ 21 , 22 ]. Limiting transcription factors dominate transcription cost in S. cerevisiae Having established that the fitness cost can be decomposed into a linear combination of RNAP cost and ribo-some cost, we analyze experimental data and compare them with our model. Kafri et al. integrated exogenous mCherry genes into S. cerevisiae and measured the relative reduction in growth rate due to exogenous gene expression [ 8 ]. To compare with their experiments, we estimate the cost coefficients using the resource competition model with the relevant parameters of S. cerevisiae . Interestingly, the predicted ribosome cost is very close to the measured translation cost ( Table I ), meaning that ribosome competition is the dominant source of translation cost, consistent with previous findings [ 19 , 42 , 43 ]. View this table: View inline View popup Download powerpoint TABLE I. Comparisons between the costs estimated from the experimental data and the resource competition model for an mCherry gene in S. cerevisiae . Here, we analyze the data of TDH3 promoter in the standard culture from Ref. [ 8 ]. In this table, all variables correspond to one exogenous gene copy ( g ex = 1) for simplicity. Numerical values are rounded to one significant figure, considering the uncertainties in experiments and estimations. Details of the experimental values are in Methods B. Details of the theoretical estimations are as follows: (1) To estimate ( Eqs. [9 - 11 ]), we take the following parameters: the protein decay rate γ ex ≈ µ = 0.4/h [ 8 ], the ribosome copy number N r = 3 ×10 5 [ 23 , 24 ], and the mCherry protein copy number for each gene copy p ex = 1.5 ×10 6 (Methods B). The protein decay rate is dominated by growth rate ( γ ex ≈ µ ) because degradation is much slower compared to cell growth [ 25 – 27 ]. The duration for a ribosome to translate an mCherry mRNA is estimated as , where L tl,ex is the length of the exogenous mCherry protein in amino acids [ 28 ], and v tl,ex is the translation elongation speed of the ribosome [ 29 , 30 ]. (2) To estimate ( Eqs. [9 - 11 ]), we take the following parameters: the fraction of free ribosomes f r = 0.3 [ 31 ], the copy number of RNAP N n = 3 × 10 4 [ 32 ], the mRNA lifetime τ ex = 15 min [ 33 – 35 ], and the mCherry mRNA copy number for each gene copy m ex = 6 × 10 2 (Methods B). The duration for an RNAP to transcribe an mCherry gene is estimated as , where L tx,ex is the length of the exogenous gene transcribed in nucleotides [ 8 ], and v tx,ex is the transcription elongation speed of RNAP [ 36 – 38 ]. In both (1) and (2), we neglect the duration of initiation, which is typically much shorter than the duration of elongation. (3) An mCherry gene driven by the TDH3 promoter accounts for 3.4% of the total protein number, 200 times more than the contribution of an average gene, which we estimate as 1 /g with g = 6000 [ 39 , 40 ]. Assuming the primary difference comes from the promoter strength, we take β m,ex /β m = 200. Since the actual fraction of free transcription factors is unknown, we take f t = 0.5, which does not affect the order of magnitude. We use Eq. (13) to estimate c g , which is equal to C TF given g ex = 1. Other parameters are taken as f n = 0.9 [ 41 ] and f r = 0.3 [ 31 ]. We remark that the inactive RNAP fraction f n includes both free RNAPs and RNAPs that are associated with non-coding regions. (4) The translation cost C tl (theory) is equal to the ribosome cost C ribo . (5) The transcription cost C tx (theory) is the sum of the RNAP cost and the TF cost: C tx = C RNAP + C TF . The ratio of the RNAP cost to the ribosome cost is about 1/50 ( Table I ), comparable to the transcription-translation cost ratio estimated by the ATP consumption rate [ 5 , 9 ], suggesting that the cellular resources for transcription and translation are coordinated with their energy expenditures. However, the experimentally measured transcription cost is on the same order of magnitude as the translation cost, much higher than the RNAP cost ( Table I ), which cannot be accounted for by either ATP consumption or RNAP competition. These results suggest that other limiting factors must exist at the transcription level besides RNAP. Experiments have shown that protein-burdened cells resemble mutants lacking transcription coactivators, including Mediator, SAGA, and SWI-SNF, both transcriptionally and phenotypically [ 44 ]. These results suggest that transcription-initiation-associated proteins may also be limiting factors for transcription. Therefore, we extend our model to include the resource competition for transcription-initiation-associated proteins, including general transcription factors, mediators, and chromatin remodeling proteins [ 45 – 47 ]. For simplicity, we combine all these proteins into a coarse-grained type of TF, and the transcription initiation requires the binding of TFs near the promoter ( Figure 3a ). Therefore, the mRNA production rate also depends on the TF concentration: where P t is the TF binding probability, which we model as a MM function of the free TF concentration (Methods C). Notably, the fitness cost can be explicitly decomposed as (Methods C) Download figure Open in new tab FIG. 3. The extended model incorporating the TF cost. (a) Competition for the limiting TFs generates an additional component of transcription cost. (b) The fitness cost in S. cerevisiae can be decomposed into a TF cost, an RNAP cost, and a ribosome cost, proportional to the gene copy number, mRNA copy number, and protein copy number of the exogenous gene, respectively. The arrow widths approximately represent their relative contributions to the total fitness cost ( Table I ). The transcription cost now consists of two components generated by competition for TF and RNAP: C tx = C TF + C RNAP ( Figure 3b ). Here, N t,ex is the copy number of TF working on the exogenous gene, and N t is the total copy number of TF. One should note that the TF cost is damped by the two downstream factors f n and f r . We introduce the TF cost per gene as c g = Λ t,ex P t,ex f n f r /N t where Λ t,ex is the maximum TF number recruited by one copy of the exogenous gene and P t,ex is the corresponding TF binding probability. The TF cost shows that introducing an exogenous gene into the genome alone already imposes a cost due to TF competition, even without downstream mRNA production. Because it is difficult to estimate N t,ex and N t directly, we take an indirect approach assuming that the TF binding limits the mRNA production rates, that is, the ratio between the mRNA production rates of the exogenous gene and other genes can be approximated by the corresponding ratio of the copy numbers of TFs working on each promoter, β m,ex /β m ≈ ( N t,ex /g ex ) / ( N t (1 − f t ) /g ) where f t is the fraction of free TFs. Given this approximation, we estimate c g in Eq. (12) as Intriguingly, the estimated TF cost is close to the measured transcription cost ( Table I ), meaning that the TF cost dominates the total transcription cost. To summarize, our theory decomposes the total fitness cost into different components. In particular, the translation cost is dominated by competition for ribosomes, and the transcription cost is dominated by competition for TF ( Figure 3b ). Effects of gene constructs and growth conditions We rewrite Eq. (12) as where β m,ex is the mRNA production rate per copy of the exogenous gene and β p,ex is the protein production rate per copy of the exogenous mRNA. Eq. (14) predicts that the cost per gene copy positively correlates with the mRNA production rate β m,ex . We compare our predictions with experimental data for S. cerevisiae [ 8 ], where the control is the wild-type mCherry gene driven by the TDH3 promoter in standard culture (SC). In agreement with our predictions, the construct with the promoter PGK1, which is weaker than TDH3, has a lower cost in SC ( Figure 4a ). Eq. (14) also predicts that if the produced mRNA has a shorter lifetime τ ex , the cost per gene copy should also be smaller, and this prediction agrees with the lower cost of the DAmP mutant of mCherry mRNA [ 8 ], whose lifetime is about 1/10 of the control ( Figure 4a ). Since the protein degradation rate does not enter Eq. (14) , we also predict that the cost per gene copy is independent of protein stability, as validated by the experiments showing that the protein variant (CLN2) with a much higher degradation rate has a cost per gene copy similar to that of the control ( Figure 4a ). Download figure Open in new tab FIG. 4. The fitness cost of S. cerevisiae for different gene constructs and growth conditions. (a) The experimentally measured fitness cost per gene copy number ( g ex ). We use the wild-type mCherry gene under the TDH3 promoter in standard culture (SC) as the control. PGK1 is a weaker promoter compared to TDH3. The DAmP construct produces an unstable mRNA with a shorter lifetime. The CLN2 construct produces a protein with a high degradation rate (note that in the experiments of Ref. [ 8 ], the CLN2 construct in fact produced GFP, which is practically identical to mCherry regarding fitness cost). Low N represents a nitrogen-limited medium, where the amount of transcriptional resources is measured to be higher than SC [ 31 ]. YPEG medium lacks fermentable carbon sources, while YPD is a rich medium with a complete nutrient supply. (b) The experimentally measured fitness cost per proteome fraction. (c) The fold change (FC) of the cost per gene copy and per proteome fraction compared to the control (TDH3, SC). We also calculate the cost per proteome fraction generated by the exogenous gene (Supplementary Information Section B), a metric often used in experiments for both S. cerevisiae and E. coli (Table S3): where M tot is the total protein mass, ϕ ex is the proteome fraction of the exogenous proteins. Interestingly, our model predicts that the PGK1 construct with a lower β m,ex , the DAmP construct with a shorter τ ex , and the CLN2 construct with a higher protein degradation rate γ ex than TDH3, should all have a higher cost per proteome fraction than TDH3. All these predictions agree with experiments ( Figure 4b ). When altering growth conditions, the cost per gene copy and the cost per proteome fraction change differently. In the low N condition where cells are richer in transcriptional resources [ 31 ], we expect a smaller c g (the TF cost per gene copy, Eq. (12) ) and a larger N n (the total number of RNAP), corresponding to a lower cost both per gene copy and per proteome fraction. This is in agreement with the experimental data for the control and the same construct in the low N condition ( Figure 4a-b ). For the nutrient-poor medium YPEG, the transcription and translation elongation speeds are presumably slower, leading to a longer T tx,ex and T tl,ex . Therefore, we predict that the cost per gene copy and per proteome fraction should both be higher for TDH3 in YPEG than the control, i.e., TDH3 in SC. In contrast, for the rich medium YPD, we expect a shorter T tx,ex and T tl,ex , and the cost per gene copy and per proteome fraction should both be lower for TDH3 in YPD than SC ( Figure 4a-b ). We also calculate the fold change (FC) of different gene constructs and conditions compared to the control, which clearly illustrates that the cost per gene copy and the cost per proteome fraction move in opposite directions for different gene constructs but move in the same direction when the medium changes ( Figure 4c ). Cost generated by the products is negligible So far, we have considered a fixed resource pool with constant resource copy numbers and cell volume, which can be a good approximation when the exogenous protein is quickly degraded. For non-degradable proteins, the cell volume can increase upon expression of an exogenous gene [ 4 , 8 , 48 ], which may dilute key factors such as ribosomes and RNAP. On the other hand, cells also make more endogenous proteins to compensate for the dilution effects [ 8 ]. We extend our model to a more general scenario where the resource copy numbers (i.e., RNAP number N n and ribosome number N r ) and cell volume change due to the expression of the exogenous gene, which may generate an additional fitness cost. We refer to this additional fitness cost as the cost of the products ( C ′ , as opposed to the cost in the processes of transcription and translation), which is found to be (Supplementary Information Section C): Here, , the ribosome proteome fraction in the endogenous proteins, different from ϕ r = N r a r /M tot , the ribosome proteome fraction in the total proteome. ϕ tx is the proteome fraction encoding transcriptional proteins (e.g., RNAP and transcription factors). η nc = V n /V c is the volume ratio of nucleus to cytoplasm (N/C ratio). , Δ ϕ tx , and Δ η nc in Eq. (16) represent the active/passive regulation of translation and transcription resources, and the N/C ratio. Notably, Eq. (16) illustrates that increasing translation and transcription resources can relieve the cost, but the rise of the nucleus-to-cytoplasm volume ratio aggravates the cost. Intriguingly, experimental data from S. cerevisiae show that although ϕ r is diluted by the exogenous proteins produced, stays almost invariant ( Figure 5 ). Furthermore, the proteome fraction encoding transcriptional proteins is also approximately constant [ 31 ], which implies that the volume expansion is compensated for by making more transcriptional proteins. We expect that the N/C ratio is also approximately constant if the protein products of the exogenous gene are evenly distributed in the cell [ 49 ]. Therefore, according to Eq. (16) , the fitness cost generated by the product is insignificant compared to the overall fitness cost, consistent with previous experimental observations in E. coli [ 12 ] and S. cerevisiae [ 8 ]. Here, we point out that this negligible cost of the products applies to unnecessary proteins without any specific function or toxicity when overexpressed. For proteins that can change the nutrient uptake (e.g., LacY [ 50 ]) or are toxic due to misfolding [ 51 – 53 ], the products naturally generate a considerable fitness cost, which should be isolated as a protein-specific cost. Download figure Open in new tab FIG. 5. The ribosomal proteome fraction in the total proteome ( ϕ r ) and the ribosomal proteome fraction in the endogenous proteome . With the expression of mCherry proteins in S. cerevisiae, ϕ r decreases, whereas stays almost constant. The dashed lines show the linear fits to the data points, with the numbers indicating the slopes. Data are taken from Ref. [ 31 ], and the results under the two experimental conditions show consistency. DISCUSSION Many experiments have measured the growth rate reduction to quantify the fitness cost of gene expression [ 1 , 2 , 4 , 8 ]. It has been widely presumed that the cost arises from both transcription and translation [ 8 , 10 , 13 ]. However, the mechanism behind this hypothesis remains poorly understood. In this work, we use a simple resource competition model and disentangle the fitness cost into different components generated by TF, RNAP, and ribosome competition. In particular, we show that the ribosome cost dominates the translation cost, and the transcription cost in S. cerevisiae is dominated by the TF cost. We remark that the coarse-grained TF in our model may correspond to the general transcription factors, which help to position RNAP correctly at the promoters, aid in separating the two strands of DNA, and release RNAP from the promoters to start elongation, including TFIIB, TFIID, etc. These proteins are needed at nearly all promoters used by RNA polymerase II [ 46 , 47 ]. Other crucial proteins may also be candidates for the limiting factors, including mediators [ 45 ], transcription activators, and chromatin remodeling proteins [ 47 ]. Our framework provides valuable guidance on designing gene circuits to minimize interference with the host cells [ 54 , 55 ]. We also discuss the differences between our model and previous ones regarding the fitness cost [ 4 , 10 , 11 , 13 ] in Supplementary Information Section A and Table S1-S2. We propose more systematic experiments in the future to obtain a deeper understanding of the fitness cost of gene expression. First, measurements of the simultaneous changes in the cell volume, ribosome copy number, RNAP copy number, etc., upon gene overexpression will be invaluable for us to understand how cells adapt to limited resources for gene expression. Second, more accurate and high-throughput measurements of fitness cost are required to enable quantitative modeling with more mechanistic insights. METHODS A. Derivation of the fitness cost The probability of an endogenous promoter bound by an RNAP is Here, [ n ] f = N n f n α n /V n is the concentration of free RNAP in the nucleus; α n is the fraction of free RNAP in the inactive RNAP pool, which we set as a constant, as it is determined by molecular binding affinities (e.g., non-specific binding affinity); V n is the nuclear volume; and K n is the corresponding dissociation constant of the endogenous genes [ 16 – 18 ]. Differentiating Eq. (17) leads to Combining the above equation with Eq. (2) , we find that In deriving Eq. (19) , we have used the approximation N n,ex ≪ N n , which holds in biological scenarios where a single gene copy occupies a small fraction of total RNAPs. The probability for the ribosome-binding-site of endogenous mRNA to be bound by a ribosome is Here, [ r ] f = N r f r /V c is the concentration of free ribo-somes in the cytoplasm, V c is the cytoplasmic volume, and K r is the corresponding dissociation constant of endogenous mRNAs [ 14 , 15 ]. Similarly, differentiating Eq. (20) and combining it with Eqs. (2 , 3 , 5 ) lead to where N r,ex is the number of ribosomes on the exogenous mRNA. Differentiating Eq. (7) , we get where γ = µ + d is the protein decay rate of the average endogenous protein, the sum of the growth rate and the average protein degradation rate. Given the definition of cost ( Eq. (8) ), and combining Eqs. (19) and (21 - 22 ), we get Here, we introduce s n and s r as the sensitivity factors In the limit P n →0, transcription activity is rare, and s n reaches its maximum value 1, meaning that transcription initiation is sensitive to changes in the RNAP resources. On the contrary, in the limit P n → 1, cells have plenty of RNAPs and s n = 0, meaning that transcription is RNAP-saturated. A similar discussion applies to s r . We also introduce the downstream factor which represents the dampening effects of downstream processes on the RNAP cost: a small fraction of free ribosomes f r dampens the RNAP cost. In typical biological scenarios applied to microorganisms, Eq. (23) is simplified to Eq. (9) under the following conditions: 1. γ ≈ µ because endogenous protein degradation is negligible compared to the growth rate [ 25 – 27 ]; 2. P n is significantly lower than one such that s n ≈ 1; 3. P r is significantly lower than one such that s r ≈ 1 and θ r ≈ f r . We remark that the conditions P n ≪1 and P r ≪1 are only the properties of the “average” endogenous gene, which is typically weakly expressed [ 13 , 18 , 20 , 56 ]. At steady state, the mRNA degradation rate equals the number of transcription initiation events per unit time, leading to where τ ex is the exogenous mRNA lifetime, and T tx,ex is the time for an RNAP to transcribe the exogenous gene. Similarly, from the equilibrium between the number of proteins diluted and degraded per unit time and the translation initiation events per unit time, we have where γ ex = µ + d ex is the protein decay rate of the exogenous gene. Replacing the N n,ex and N r,ex in Eq. (9) by Eqs. (26 - 27 ), we finally get Eq. (10) . B. Estimating the transcription and translation cost per gene/mRNA/protein from experiments in S. cerevisiae The fitness costs of two gene constructs expressing mCherry proteins were measured, denoted as “wt” and “DAmP”, respectively [ 8 ]. Both constructs were driven by the TDH3 promoter. However, DAmP lacks a terminator, which leads to a shorter mRNA lifetime ( τ DAmP ) than the wt mRNA lifetime ( τ wt ), and further leads to a lower copy number of mRNA and a lower copy number of protein. Assuming all other parameters are unaffected, we have m DAmP /m wt = p DAmP /p wt = τ DAmP /τ wt . Both Eq. (10) and Eq. (14) show that the transcription costs of the two constructs are the same, but the translation costs differ by a factor of τ DAmP /τ wt . Therefore, we have the following linear equations: where C wt and C DAmP are experimentally measured fitness cost per gene copy of the wt and the DAmP construct, respectively. Here, C tx and C tl refer to the transcription and translation costs of the wt construct, respectively. Solving the simultaneous linear equations with C wt /g ex = 1.50 ×10 − 2 , C DAmP /g ex = 7.0 ×10 − 3 , and τ DAmP /τ wt = 0.1, we get C tl /g ex = 8.9× 10 − 3 and C tx /g ex = 6.1 ×10 − 3 . Here, C wt /g ex and C DAmP /g ex are obtained from the linear fitting of the experimental data [ 8 ]. Each gene copy contributes about 1.7% to the proteome for the TDH3 construct in the standard culture [ 8 ], which corresponds to a protein copy number of p ex /g ex = 1.7% M/a ex = 1.5 ×10 6 with M = 4.0 ×10 − 12 g [ 57 , 58 ] and a ex = 27 kDa [ 59 ]. Assuming that the protein production rate per mRNA of the exogenous gene is the same as that of the average endogenous genes ( β p,ex = 1 ×10 3 /h [ 60 ]), we estimate m ex /g ex = γ ex p ex /β p,ex g ex = 6 ×10 2 with γ ex = 0.4/h [ 8 ]. C. The fitness cost due to transcription factors To include the effects of TFs, we write the conservation equation for transcription factors in the absence of the exogenous gene: Here, Λ t is the maximum number of TF on an endogenous promoter, and P t is the probability for an endogenous promoter to be bound by TF, which is TFconcentration dependent: , with K t the coarse-grained dissociation constant. The copy number of RNAPs on each gene is Λ n P t P n , and the endogenous mRNA production rate is . Similar results apply to the exogenous gene. By including the exogenous gene, and following the same method of derivation as in Methods A, we find the fitness cost as Here, N t,ex is the number of TF on the promoter for the exogenous gene. The sensitivity factor of TF is and the downstream factor is Notably, the total fitness cost can be precisely decomposed into the contributions of each limiting resource. 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