The Interrelationship between Promoter Strength,Gene Expression,and Growth Rate

In exponentially growing bacteria, expression of heterologous protein impedes cellular growth rates. Quantitative understanding of the relationship between expression and growth rate will advance our ability to forward engineer bacteria, important for metabolic engineering and synthetic biology applications. Recently, a work described a scaling model based on optimal allocation of ribosomes for protein translation. This model quantitatively predicts a linear relationship between microbial growth rate and heterologous protein expression with no free parameters. With the aim of validating this model, we have rigorously quantified the fitness cost of gene expression by using a library of synthetic constitutive promoters to drive expression of two separate proteins (eGFP and amiE) in E. coli in different strains and growth media. In all cases, we demonstrate that the fitness cost is consistent with the previous findings. We expand upon the previous theory by introducing a simple promoter activity model to quantitatively predict how basal promoter strength relates to growth rate and protein expression. We then estimate the amount of protein expression needed to support high flux through a heterologous metabolic pathway and predict the sizable fitness cost associated with enzyme production. This work has broad implications across applied biological sciences because it allows for prediction of the interplay between promoter strength, protein expression, and the resulting cost to microbial growth rates.     

Environmental Statistics and Optimal Regulation

Any organism is embedded in an environment that changes over time. The timescale for and statistics of environmental change, the precision with which the organism can detect its environment, and the costs and benefits of particular protein expression levels all will affect the suitability of different strategies–such as constitutive expression or graded response–for regulating protein levels in response to environmental inputs. We propose a general framework–here specifically applied to the enzymatic regulation of metabolism in response to changing concentrations of a basic nutrient–to predict the optimal regulatory strategy given the statistics of fluctuations in the environment and measurement apparatus, respectively, and the costs associated with enzyme production. We use this framework to address three fundamental questions: (i) when a cell should prefer thresholding to a graded response; (ii) when there is a fitness advantage to implementing a Bayesian decision rule; and (iii) when retaining memory of the past provides a selective advantage. We specifically find that: (i) relative convexity of enzyme expression cost and benefit influences the fitness of thresholding or graded responses; (ii) intermediate levels of measurement uncertainty call for a sophisticated Bayesian decision rule; and (iii) in dynamic contexts, intermediate levels of uncertainty call for retaining memory of the past. Statistical properties of the environment, such as variability and correlation times, set optimal biochemical parameters, such as thresholds and decay rates in signaling pathways. Our framework provides a theoretical basis for interpreting molecular signal processing algorithms and a classification scheme that organizes known regulatory strategies and may help conceptualize heretofore unknown ones.     

The tragedy of the commons in microbial populations: insights from theoretical, comparative and experimental studies

First principles of thermodynamics imply that metabolic pathways are faced with a trade-off between the rate and yield of ATP production. Simple evolutionary models argue that this trade-off generates a fundamental social conflict in microbial populations: average fitness in a population is highest if all individuals exploit common resources efficiently, but individual reproductive rate is maximized by consuming common resources at the highest possible rate, a scenario known as the tragedy of the commons. In this paper, I review studies that have addressed two key questions: What is the evidence that the rate-yield trade-off is an evolutionary constraint on metabolic pathways? And, if so, what determines evolutionary outcome of the conflicts generated by this trade-off? Comparative studies and microbial experiments provide evidence that the rate-yield trade-off is an evolutionary constraint that is driven by thermodynamic constraints that are common to all metabolic pathways and pathway-specific constraints that reflect the evolutionary history of populations. Microbial selection experiments show that the evolutionary consequences of this trade-off depend on both kin selection and biochemical constraints. In well-mixed populations with low relatedness, genotypes with rapid and efficient metabolism can coexist as a result of negative frequency-dependent selection generated by density-dependent biochemical costs of rapid metabolism. Kin selection can promote the maintenance of efficient metabolism in structured populations with high relatedness by ensuring that genotypes with efficient metabolic pathways gain an indirect fitness benefit from their competitive restraint. I conclude by suggesting avenues for future research and by discussing the broader implications of this work for microbial social evolution.     

The tragedy of the commons in microbial populations: insights from theoretical, comparative and experimental studies

First principles of thermodynamics imply that metabolic pathways are faced with a trade-off between the rate and yield of ATP production. Simple evolutionary models argue that this trade-off generates a fundamental social conflict in microbial populations: average fitness in a population is highest if all individuals exploit common resources efficiently, but individual reproductive rate is maximized by consuming common resources at the highest possible rate, a scenario known as the tragedy of the commons. In this paper, I review studies that have addressed two key questions: What is the evidence that the rate-yield trade-off is an evolutionary constraint on metabolic pathways? And, if so, what determines evolutionary outcome of the conflicts generated by this trade-off? Comparative studies and microbial experiments provide evidence that the rate-yield trade-off is an evolutionary constraint that is driven by thermodynamic constraints that are common to all metabolic pathways and pathway-specific constraints that reflect the evolutionary history of populations. Microbial selection experiments show that the evolutionary consequences of this trade-off depend on both kin selection and biochemical constraints. In well-mixed populations with low relatedness, genotypes with rapid and efficient metabolism can coexist as a result of negative frequency-dependent selection generated by density-dependent biochemical costs of rapid metabolism. Kin selection can promote the maintenance of efficient metabolism in structured populations with high relatedness by ensuring that genotypes with efficient metabolic pathways gain an indirect fitness benefit from their competitive restraint. I conclude by suggesting avenues for future research and by discussing the broader implications of this work for microbial social evolution.     

Integrating thermodynamic and enzymatic constraints into genome-scale metabolic models

Stoichiometric genome-scale metabolic network models (GEMs) have been widely used to predict metabolic phenotypes. In addition to stoichiometric ratios, other constraints such as enzyme availability and thermodynamic feasibility can also limit the phenotype solution space. Extended GEM models considering either enzymatic or thermodynamic constraints have been shown to improve prediction accuracy. In this paper, we propose a novel method that integrates both enzymatic and thermodynamic constraints in a single Pyomo modeling framework (ETGEMs). We applied this method to construct the EcoETM (E. coli metabolic model with enzymatic and thermodynamic constraints). Using this model, we calculated the optimal pathways for cellular growth and the production of 22 metabolites. When comparing the results with those of iML1515 and models with one of the two constraints, we observed that many thermodynamically unfavorable and/or high enzyme cost pathways were excluded from EcoETM. For example, the synthesis pathway of carbamoyl-phosphate (Cbp) from iML1515 is both thermodynamically unfavorable and enzymatically costly. After introducing the new constraints, the production pathways and yields of several Cbp-derived products (e.g. L-arginine, orotate) calculated using EcoETM were more realistic. The results of this study demonstrate the great application potential of metabolic models with multiple constraints for pathway analysis and phenotype prediction.     

Constitutive versus responsive gene expression strategies for growth in changing environments

Microbes respond to changing environments by adjusting gene expression levels to the demand for the corresponding proteins. Adjusting protein levels is slow, consequently cells may reach the optimal protein level only by a time when the demand changed again. It is therefore not a priori clear whether expression “on demand” is always the optimal strategy. Indeed, many genes are constitutively expressed at intermediate levels, which represents a permanent cost but provides an immediate benefit when the protein is needed. Which are the conditions that select for a responsive or a constitutive expression strategy, what determines the optimal constitutive expression level in a changing environment, and how is the fitness of the two strategies affected by gene expression noise? Based on an established model of the lac- and gal-operon expression dynamics, we study the fitness of a constitutive and a responsive expression strategy in time-varying environments. We find that the optimal constitutive expression level differs from the average demand for the gene product and from the average optimal expression level; depending on the shape of the growth rate function, the optimal expression level either provides intermediate fitness in all environments, or maximizes fitness in only one of them. We find that constitutive expression can provide higher fitness than responsive expression even when regulatory machinery comes at no cost, and we determine the minimal response rate necessary for “expression on demand” to confer a benefit. Environmental and inter-cellular noise favor the responsive strategy while reducing fitness of the constitutive one. Our results show the interplay between the demand-frequency for a gene product, the genetic response rate, and the fitness, and address important questions on the evolution of gene regulation. Some of our predictions agree with recent yeast high throughput data, for others we propose the experiments that are needed to verify them.     

Glycolysis/gluconeogenesis specialization in microbes is driven by biochemical constraints of flux sensing

Central carbon metabolism is highly conserved across microbial species, but can catalyze very different pathways depending on the organism and their ecological niche. Here, we study the dynamic reorganization of central metabolism after switches between the two major opposing pathway configurations of central carbon metabolism, glycolysis, and gluconeogenesis in Escherichia coli, Pseudomonas aeruginosa, and Pseudomonas putida. We combined growth dynamics and dynamic changes in intracellular metabolite levels with a coarse‐grained model that integrates fluxes, regulation, protein synthesis, and growth and uncovered fundamental limitations of the regulatory network: After nutrient shifts, metabolite concentrations collapse to their equilibrium, rendering the cell unable to sense which direction the flux is supposed to flow through the metabolic network. The cell can partially alleviate this by picking a preferred direction of regulation at the expense of increasing lag times in the opposite direction. Moreover, decreasing both lag times simultaneously comes at the cost of reduced growth rate or higher futile cycling between metabolic enzymes. These three trade‐offs can explain why microorganisms specialize for either glycolytic or gluconeogenic substrates and can help elucidate the complex growth patterns exhibited by different microbial species.     

Dosage, deletions and dominance: simple models of the evolution of gene expression

Dominance of the wild-type allele over spontaneous null mutations, such as deletions, can be explained in terms of the effects of changes in enzyme dose on the flux of metabolic pathways. If ever increasing levels of enzyme activity have ever decreasing effects on the flux of the biochemical pathway, then halving of dosage will always have a lesser effect on flux than half the effect of complete removal of gene activity. Furthermore, if gene expression rates are high, then halving of dose can have a negligible effect on flux and dominance will be strong. Given that strong dominance appears to be common, this leaves open the issue of why enzyme activity levels are so high that a halving of expression rates is of minimal effect. Why produce so much surplus enzyme? One explanation, suggested by Haldane, is that selection favoured high expression levels as a defence against mutation. We model this scenario formally and show that protection from mutation is an extremely weak force determining expression levels. The selective coefficients are only of the order of the mutation rate. However, if we suppose a linear mapping of flux with fitness and a monotonic cost to increased gene expression, it follows simply that here exists an optimal level of gene expression. By contrast to the mutational model, doubling of gene expression rates when the system is distant from the optimum is associated with extremely high selective coefficients (orders of magnitude higher than the mutation rate). When the cost of gene expression is slight the optimal rate of expression is such that strong dominance will follow.     

Relationship between fitness and heterogeneity in exponentially growing microbial populations

Despite major environmental and genetic differences, microbial metabolic networks are known to generate consistent physiological outcomes across vastly different organisms. This remarkable robustness suggests that, at least in bacteria, metabolic activity may be guided by universal principles. The constrained optimization of evolutionarily motivated objective functions, such as the growth rate, has emerged as the key theoretical assumption for the study of bacterial metabolism. While conceptually and practically useful in many situations, the idea that certain functions are optimized is hard to validate in data. Moreover, it is not always clear how optimality can be reconciled with the high degree of single-cell variability observed in experiments within microbial populations. To shed light on these issues, we develop an inverse modeling framework that connects the fitness of a population of cells (represented by the mean single-cell growth rate) to the underlying metabolic variability through the maximum entropy inference of the distribution of metabolic phenotypes from data. While no clear objective function emerges, we find that, as the medium gets richer, the fitness and inferred variability for Escherichia coli populations follow and slowly approach the theoretically optimal bound defined by minimal reduction of variability at given fitness. These results suggest that bacterial metabolism may be crucially shaped by a population-level trade-off between growth and heterogeneity.     

Adaptive laboratory evolution of microbial co‐cultures for improved metabolite secretion

Adaptive laboratory evolution has proven highly effective for obtaining microorganisms with enhanced capabilities. Yet, this method is inherently restricted to the traits that are positively linked to cell fitness, such as nutrient utilization. Here, we introduce coevolution of obligatory mutualistic communities for improving secretion of fitness‐costly metabolites through natural selection. In this strategy, metabolic cross‐feeding connects secretion of the target metabolite, despite its cost to the secretor, to the survival and proliferation of the entire community. We thus co‐evolved wild‐type lactic acid bacteria and engineered auxotrophic Saccharomyces cerevisiae in a synthetic growth medium leading to bacterial isolates with enhanced secretion of two B‐group vitamins, viz., riboflavin and folate. The increased production was specific to the targeted vitamin, and evident also in milk, a more complex nutrient environment that naturally contains vitamins. Genomic, proteomic and metabolomic analyses of the evolved lactic acid bacteria, in combination with flux balance analysis, showed altered metabolic regulation towards increased supply of the vitamin precursors. Together, our findings demonstrate how microbial metabolism adapts to mutualistic lifestyle through enhanced metabolite exchange.     

The population genetics of alleles affecting enzyme activity.

It is possible to predict the population genetics of allozymes by assuming that fitness is proportional to flux through a biochemical pathway. The model presented here extends previous work by incorporating two additional features of biological realism. Firstly, that more than one biochemical route may exist between any two metabolites. The major routes have been identified as the classical biochemical pathways but in the event of a mutation blocking a major route, minor routes become significant. These minor routes are named "bypass fluxes" and have profound effects on the population genetics of allozymes. Secondly, recent work has suggested that a metabolic cost is associated with enzyme synthesis; this will constitute an additional selective pressure on alleles which affect the amount of enzyme synthesized. The model generates a fitness curve which predicts the fitness associated with any level of enzyme activity. It can utilize data on null or near-null, structural or regulatory, mutations in the presence or absence of bypass fluxes. When data from natural populations of Drosophila are investigated, it is concluded that selection pressures acting on enzyme variants may be much higher than previously thought.     

Correlation between in vivo and in vitro metabolic measurements. Maximum capacity for urea synthesis.

Estimations of enzyme activity in vivo have been or can often only be done at unphysiological conditions. A main biochemical goal is to correlate in vivo and in vitro measurements. A possible approach to this problem is presented based on forcing metabolic activity in vivo to the maximum for a certain metabolic sequence. Since the urea synthesis system, including maximal rates of enzyme activities, is well known, we have compared in vitro maximum rates for the individual enzymes of urea synthesis with in vivo rates as judged by urea levels in blood of rats given large amounts of protein. The excellent agreement found between the calculated maximum activities from in vitro measurements to the time needed to metabolize a protein overload is presented and comments made on its significance and on the importance of maintaining protein intake at moderate levels, for the capacity of the urea system is limited. Since the intake of large quantities of protein increases the urea level in blood and in other tissues and since high urea levels are somewhat deleterious "per se" and particularly due to equilibrium with cyanate, ingestion of excessive amounts of protein is at best expensive and possibly hazardous.     

Shifts in growth strategies reflect tradeoffs in cellular economics

The growth rate‐dependent regulation of cell size, ribosomal content, and metabolic efficiency follows a common pattern in unicellular organisms: with increasing growth rates, cell size and ribosomal content increase and a shift to energetically inefficient metabolism takes place. The latter two phenomena are also observed in fast growing tumour cells and cell lines. These patterns suggest a fundamental principle of design. In biology such designs can often be understood as the result of the optimization of fitness. Here we show that in basic models of self‐replicating systems these patterns are the consequence of maximizing the growth rate. Whereas most models of cellular growth consider a part of physiology, for instance only metabolism, the approach presented here integrates several subsystems to a complete self‐replicating system. Such models can yield fundamentally different optimal strategies. In particular, it is shown how the shift in metabolic efficiency originates from a tradeoff between investments in enzyme synthesis and metabolic yields for alternative catabolic pathways. The models elucidate how the optimization of growth by natural selection shapes growth strategies.     

The cost of enzyme synthesis in the genetics of energy balance and physiological performance

The study of metabolism has traditionally focused upon factors that influence metabolic rate, at levels of both the metabolic pathway and the whole organism. This paper focuses on the cost, and thereby the efficiency, of metabolic processes. The genotype-dependent cost of enzyme turnover is proposed as a biochemical genetic mechanism for relating genetic variation at single genes to phenotypic variation in quantitative traits of energy metabolism. Decreased costs of maintenance metabolism can accompany artificial selection for increased production (e.g. growth, reproduction, etc.) and lower maintenance is correlated with multiple locus heterozygosity in outbred populations. In both cases, high production has been associated with lower rates of protein turnover. Several factors influence the ATP-equivalent cost of enzyme turnover. These factors are used to calculate the cost of turnover for a single enzyme. This cost can conservatively constitute up to several percent of the total daily mass-specific energy demands of maintenance metabolism. Genetic variants of an enzyme can differ in the cost of turnover. These differences can constitute the basis for metabolic changes associated with artificial selection for production and the metabolic differences that are associated with individual levels of heterozygosity. The metabolic and evolutionary significance of genotype-dependent turnover costs is a function of individual energy balance. The strength of selection against increases in cost will be an inverse function of individual energy balance and is therefore influenced by both environmental and genetic factors.     

Fitness and stability of obligate cross-feeding interactions that emerge upon gene loss in bacteria

Cross-feeding interactions, in which bacterial cells exchange costly metabolites to the benefit of both interacting partners, are very common in the microbial world. However, it generally remains unclear what maintains this type of interaction in the presence of non-cooperating types. We investigate this problem using synthetic cross-feeding interactions: by simply deleting two metabolic genes from the genome of Escherichia coli, we generated genotypes that require amino acids to grow and release other amino acids into the environment. Surprisingly, in a vast majority of cases, cocultures of two cross-feeding strains showed an increased Darwinian fitness (that is, rate of growth) relative to prototrophic wild type cells—even in direct competition. This unexpected growth advantage was due to a division of metabolic labour: the fitness cost of overproducing amino acids was less than the benefit of not having to produce others when they were provided by their partner. Moreover, frequency-dependent selection maintained cross-feeding consortia and limited exploitation by non-cooperating competitors. Together, our synthetic study approach reveals ecological principles that can help explain the widespread occurrence of obligate metabolic cross-feeding interactions in nature.     

Resource-allocation constraint governs structure and function of microbial communities in metabolic modeling

Predictive modeling tools for assessing microbial communities are important for realizing transformative capabilities of microbiomes in agriculture, ecology, and medicine. Constraint-based community-scale metabolic modeling is unique in its potential for making mechanistic predictions regarding both the structure and function of microbial communities. However, accessing this potential requires an understanding of key physicochemical constraints, which are typically considered on a per-species basis. What is needed is a means of incorporating global constraints relevant to microbial ecology into community models. Resource-allocation constraint, which describes how limited resources should be distributed to different cellular processes, sets limits on the efficiency of metabolic and ecological processes. In this study, we investigate the implications of resource-allocation constraints in community-scale metabolic modeling through a simple mechanism-agnostic implementation of resource-allocation constraints directly at the flux level. By systematically performing single-, two-, and multi-species growth simulations, we show that resource-allocation constraints are indispensable for predicting the structure and function of microbial communities. Our findings call for a scalable workflow for implementing a mechanistic version of resource-allocation constraints to ultimately harness the full potential of community-scale metabolic modeling tools.     

Bioreactor performance: a more scientific approach for practice

In practice, the performance of a biochemical conversion process, i.e. the bioreactor performance, is essentially determined by the benefit/cost ratio. The benefit is generally defined in terms of the amount of the desired product produced and its market price. Cost reduction is the major objective in biochemical engineering. There are two essential engineering approaches to minimizing the cost of creating a particular product in an existing plant. One is to find a control path or operational procedure that optimally uses the dynamics of the process and copes with the many constraints restricting production. The other is to remove or lower the constraints by constructive improvements of the equipment and/or the microorganisms. This paper focuses on the first approach, dealing with optimization of the operational procedure and the measures by which one can ensure that the process adheres to the predetermined path. In practice, feedforward control is the predominant control mode applied. However, as it is frequently inadequate for optimal performance, feedback control may also be employed. Relevant aspects of such performance optimization are discussed.     

Costs and limits of phenotypic plasticity: Tests with predator-induced morphology and life history in a freshwater snail

Potential constraints on the evolution of phenotypic plasticity were tested using data from a previous study on predator-induced morphology and life history in the freshwater snail Physa heterostropha. The benefit of plasticity can be reduced if facultative development is associated with energetic costs, developmental instability, or an impaired developmental range. I examined plasticity in two traits for 29 families of P. heterostropha to see if it was associated with growth rate or fecundity, within-family phenotypic variance, or the potential to produce extreme phenotypes. Support was found for only one of the potential constraints. There was a strong negative selection gradient for growth rate associated with plasticity in shell shape (β = ?0.3, P < 0.0001). This result was attributed to a genetic correlation between morphological plasticity and an antipredator behavior that restricts feeding. Thus, reduced growth associated with morphological plasticity may have had unmeasured fitness benefits. The growth reduction, therefore, is equivocal as a cost of plasticity. Using different fitness components (e.g., survival, fecundity, growth) to seek constraints on plasticity will yield different results in selection gradient analyses. Procedural and conceptual issues related to tests for costs and limits of plasticity are discussed, such as whether constraints on plasticity will be evolutionarily ephemeral and difficult to detect in nature.     

Heterogeneous Timing of Gene Induction as a Regulation Strategy

In response to environmental changes, cells often adapt by up-regulating genes to synthesize proteins that generate a benefit in the new environment. Several such cases of gene induction have been reported where the timing was heterogeneous, with some cells responding early and others responding late, although the microbial population was genetically homogeneous and the environment was well mixed. Here, we explore under which conditions heterogeneous timing of gene induction could be advantageous for the population as a whole. We base our study on a mathematical model that accounts for the cost of protein synthesis in terms of resources, which cells must provide immediately, whereas the associated benefit accumulates only slowly over the protein lifetime. Due to this delayed benefit, gene induction can be a risky investment, if resources are scarce and the environment fluctuates rapidly and unpredictably. Unprofitable gene induction then depletes the remaining limiting resource needed for maintenance of cell viability. We show that whenever gene induction is associated with a transient risk but beneficial in the long run, the stochastic timing of gene induction maximizes the reproductive success of a population. In particular, in an environment of stochastic periods of famine and feast, an optimum emerges from a trade-off between short-term growth, favoring rapid and homogeneous responses, and long-term survival, favoring a broadly heterogeneous response. Our analysis suggests that the optimal variability of induction times is just as large as the time required for the amortization of the initial investment into protein synthesis.