Phenotype Design Space Provides a Mechanistic Framework Relating Molecular Parameters to Phenotype Diversity Available for Selection.

Two long-standing challenges in theoretical population genetics and evolution are predicting the distribution of phenotype diversity generated by mutation and available for selection, and determining the interaction of mutation, selection and drift to characterize evolutionary equilibria and dynamics. More fundamental for enabling such predictions is the current inability to causally link genotype to phenotype. There are three major mechanistic mappings required for such a linking - genetic sequence to kinetic parameters of the molecular processes, kinetic parameters to biochemical system phenotypes, and biochemical phenotypes to organismal phenotypes. This article introduces a theoretical framework, the Phenotype Design Space (PDS) framework, for addressing these challenges by focusing on the mapping of kinetic parameters to biochemical system phenotypes. It provides a quantitative theory whose key features include (1) a mathematically rigorous definition of phenotype based on biochemical kinetics, (2) enumeration of the full phenotypic repertoire, and (3) functional characterization of each phenotype independent of its context-dependent selection or fitness contributions. This framework is built on Design Space methods that relate system phenotypes to genetically determined parameters and environmentally determined variables. It also has the potential to automate prediction of phenotype-specific mutation rate constants and equilibrium distributions of phenotype diversity in microbial populations undergoing steady-state exponential growth, which provides an ideal reference to which more realistic cases can be compared. Although the framework is quite general and flexible, the details will undoubtedly differ for different functions, organisms and contexts. Here a hypothetical case study involving a small molecular system, a primordial circadian clock, is used to introduce this framework and to illustrate its use in a particular case. The framework is built on fundamental biochemical kinetics. Thus, the foundation is based on linear algebra and reasonable physical assumptions, which provide numerous opportunities for experimental testing and further elaboration to deal with complex multicellular organisms that are currently beyond its scope. The discussion provides a comparison of results from the PDS framework with those from other approaches in theoretical population genetics.

Phenotype-centric modeling for rational metabolic engineering.

Phenotype-centric modeling enables a paradigm shift in the analysis of mechanistic models. It brings the focus to a network's biochemical phenotypes and their relationship with measurable traits (e.g., product yields, system dynamics, signal amplification factors, etc.) and away from computationally intensive simulation-centric modeling. Here, we explore applications of this new modeling strategy in the field of rational metabolic engineering using the amorphadiene biosynthetic network as a case study. This network has previously been studied using a mechanistic model and the simulation-centric strategy, and thus provides an excellent means to compare and contrast results obtained from these two very different strategies. We show that the phenotype-centric strategy, without values for the parameters, not only identifies beneficial intervention strategies obtained with the simulation-centric strategy, but it also provides an understanding of the mechanistic context for the validity of these predictions. Additionally, we propose a set of hypothetical strains with the potential to outperform reported production strains and to enhance the mechanistic understanding of the amorphadiene biosynthetic network. Further, we identify the landscape of possible intervention strategies for the given model. We believe that phenotype-centric modeling can advance the field of rational metabolic engineering by enabling the development of next generation kinetics-based algorithms and methods that do not rely on a priori knowledge of kinetic parameters but allow a structured, global analysis of system design in the parameter space.

TaxisPy: A Python-based software for the quantitative analysis of bacterial chemotaxis.

Several species of bacteria are able to modify their swimming behavior in response to chemical attractants or repellents. Methods for the quantitative analysis of bacterial chemotaxis such as quantitative capillary assays are tedious and time-consuming. Computer-based video analysis of swimming bacteria represents a valuable method to directly assess their chemotactic response. Even though multiple studies have used this approach to elucidate various aspects of bacterial chemotaxis, to date, no computer software for such analyses is freely available. Here, we introduce TaxisPy, a Python-based software for the quantitative analysis of bacterial chemotaxis. The software comes with an intuitive graphical user interface and can be accessed easily through Docker on any operating system. Using a video of freely swimming cells as input, TaxisPy estimates the culture's average tumbling frequency over time. We demonstrate the utility of the software by assessing the effect of different concentrations of the attractant shikimate on the swimming behavior of Pseudomonas putida F1 and by capturing the adaptation process that Escherichia coli undergoes after being exposed to l-aspartate.

Mechanistic Modeling of Biochemical Systems without A Priori Parameter Values Using the Design Space Toolbox v.3.0.

Mechanistic models of biochemical systems provide a rigorous description of biological phenomena. They are indispensable for making predictions and elucidating biological design principles. To date, mathematical analysis and characterization of these models encounter a bottleneck consisting of large numbers of unknown parameter values. Here, we introduce the Design Space Toolbox v.3.0 (DST3), a software implementation of the Design Space formalism enabling mechanistic modeling without requiring previous knowledge of parameter values. This is achieved by using a phenotype-centric modeling approach, in which the system is first decomposed into a series of biochemical phenotypes. Parameter values realizing phenotypes of interest are subsequently predicted. DST3 represents the most generally applicable implementation of the Design Space formalism and offers unique advantages over earlier versions. By expanding the Design Space formalism and streamlining its distribution, DST3 represents a valuable tool for elucidating biological design principles and designing novel synthetic circuits.

Molecular Mechanisms Driving Switch Behavior in Xylem Cell Differentiation.

Plant xylem cells conduct water and mineral nutrients. Although most plant cells are totipotent, xylem cells are unusual and undergo terminal differentiation. Many genes regulating this process are well characterized, including the Vascular-related NAC Domain 7 (VND7), MYB46, and MYB83 transcription factors, which are proposed to act in interconnected feedforward loops (FFLs). Less is known regarding the molecular mechanisms underlying the terminal transition to xylem cell differentiation. Here, we generate whole-root and single-cell data, which demonstrate that VND7 initiates sharp switching of root cells to xylem cell identity. Based on these data, we identified 4 candidate VND7 downstream target genes capable of generating this switch. Although MYB46 responds to VND7 induction, it is not among these targets. This system provides an important model to study the emergent properties that may give rise to totipotency relative to terminal differentiation and reveals xylem cell subtypes.

Phenotype-centric modeling for elucidation of biological design principles.

A recently developed 'phenotype-centric' modeling strategy combines four innovations with the potential to advance our understanding of complex biological systems: (1) a rigorous mathematical definition of biochemical phenotypes, (2) a method for enumerating the phenotypic repertoire based on the biomolecular network architecture, (3) an integrated suite of computational algorithms for the efficient prediction of parameter values and analysis of the phenotypic repertoire, and (4) a user-focused environment for navigating the resulting space of phenotypes and identifying biologically relevant features and system design principles. These innovations will facilitate deterministic and stochastic simulations that require parameter values, will accelerate both hypothesis discrimination in systems biology and the design cycle in synthetic biology. Here we first review the fundamental definition of biochemical phenotype that enables this new modeling strategy and give an overview of the strategy using a simple system from phage λ to provide an example of a global design principle. Second, we illustrate this approach in more detail with an application to a common network architecture involving positive and negative feedback. We report system design principles related to the global tolerances of this system's phenotypes. Finally, we apply the phenotype-centric strategy to a logic network and compare the results with those obtained from a Boolean approach. Mechanistic and Boolean models have well-documented complementary advantages and disadvantages. Mechanistic models have the advantage of being biologically realistic; however, they also are limited by the large number of kinetic parameters whose values are largely unknown. Boolean models have the advantage of being parameter free; however, they also are limited by the absence of well-known physical and chemical constraints. We show that the phenotype-centric modeling strategy combines advantages of both.

Rapid Discrimination Among Putative Mechanistic Models of Biochemical Systems.

An overarching goal in molecular biology is to gain an understanding of the mechanistic basis underlying biochemical systems. Success is critical if we are to predict effectively the outcome of drug treatments and the development of abnormal phenotypes. However, data from most experimental studies is typically noisy and sparse. This allows multiple potential mechanisms to account for experimental observations, and often devising experiments to test each is not feasible. Here, we introduce a novel strategy that discriminates among putative models based on their repertoire of qualitatively distinct phenotypes, without relying on knowledge of specific values for rate constants and binding constants. As an illustration, we apply this strategy to two synthetic gene circuits exhibiting anomalous behaviors. Our results show that the conventional models, based on their well-characterized components, cannot account for the experimental observations. We examine a total of 40 alternative hypotheses and show that only 5 have the potential to reproduce the experimental data, and one can do so with biologically relevant parameter values.

Design Space Toolbox V2: Automated Software Enabling a Novel Phenotype-Centric Modeling Strategy for Natural and Synthetic Biological Systems.

Mathematical models of biochemical systems provide a means to elucidate the link between the genotype, environment, and phenotype. A subclass of mathematical models, known as mechanistic models, quantitatively describe the complex non-linear mechanisms that capture the intricate interactions between biochemical components. However, the study of mechanistic models is challenging because most are analytically intractable and involve large numbers of system parameters. Conventional methods to analyze them rely on local analyses about a nominal parameter set and they do not reveal the vast majority of potential phenotypes possible for a given system design. We have recently developed a new modeling approach that does not require estimated values for the parameters initially and inverts the typical steps of the conventional modeling strategy. Instead, this approach relies on architectural features of the model to identify the phenotypic repertoire and then predict values for the parameters that yield specific instances of the system that realize desired phenotypic characteristics. Here, we present a collection of software tools, the Design Space Toolbox V2 based on the System Design Space method, that automates (1) enumeration of the repertoire of model phenotypes, (2) prediction of values for the parameters for any model phenotype, and (3) analysis of model phenotypes through analytical and numerical methods. The result is an enabling technology that facilitates this radically new, phenotype-centric, modeling approach. We illustrate the power of these new tools by applying them to a synthetic gene circuit that can exhibit multi-stability. We then predict values for the system parameters such that the design exhibits 2, 3, and 4 stable steady states. In one example, inspection of the basins of attraction reveals that the circuit can count between three stable states by transient stimulation through one of two input channels: a positive channel that increases the count, and a negative channel that decreases the count. This example shows the power of these new automated methods to rapidly identify behaviors of interest and efficiently predict parameter values for their realization. These tools may be applied to understand complex natural circuitry and to aid in the rational design of synthetic circuits.

Unrelated toxin-antitoxin systems cooperate to induce persistence.

Persisters are drug-tolerant bacteria that account for the majority of bacterial infections. They are not mutants, rather, they are slow-growing cells in an otherwise normally growing population. It is known that the frequency of persisters in a population is correlated with the number of toxin-antitoxin systems in the organism. Our previous work provided a mechanistic link between the two by showing how multiple toxin-antitoxin systems, which are present in nearly all bacteria, can cooperate to induce bistable toxin concentrations that result in a heterogeneous population of slow- and fast-growing cells. As such, the slow-growing persisters are a bet-hedging subpopulation maintained under normal conditions. For technical reasons, the model assumed that the kinetic parameters of the various toxin-antitoxin systems in the cell are identical, but experimental data indicate that they differ, sometimes dramatically. Thus, a critical question remains: whether toxin-antitoxin systems from the diverse families, often found together in a cell, with significantly different kinetics, can cooperate in a similar manner. Here, we characterize the interaction of toxin-antitoxin systems from many families that are unrelated and kinetically diverse, and identify the essential determinant for their cooperation. The generic architecture of toxin-antitoxin systems provides the potential for bistability, and our results show that even when they do not exhibit bistability alone, unrelated systems can be coupled by the growth rate to create a strongly bistable, hysteretic switch between normal (fast-growing) and persistent (slow-growing) states. Different combinations of kinetic parameters can produce similar toxic switching thresholds, and the proximity of the thresholds is the primary determinant of bistability. Stochastic fluctuations can spontaneously switch all of the toxin-antitoxin systems in a cell at once. The spontaneous switch creates a heterogeneous population of growing and non-growing cells, typical of persisters, that exist under normal conditions, rather than only as an induced response. The frequency of persisters in the population can be tuned for a particular environmental niche by mixing and matching unrelated systems via mutation, horizontal gene transfer and selection.

Design principles of a conditional futile cycle exploited for regulation.

In this report, we characterize the design principles of futile cycling in providing rapid adaptation by regulatory proteins that act as environmental sensors. In contrast to the energetically wasteful futile cycles that are avoided in metabolic pathways, here we describe a conditional futile cycle exploited for a regulatory benefit. The FNR (fumarate and nitrate reduction) cycle in Escherichia coli operates under two regimes - a strictly futile cycle in the presence of O2 and as a pathway under anoxic conditions. The computational results presented here use FNR as a model system and provide evidence that cycling of this transcription factor and its labile sensory cofactor between active and inactive states affords rapid signaling and adaptation. We modify a previously developed mechanistic model to examine a family of FNR models each with different cycling speeds but mathematically constrained to be otherwise equivalent, and we identify a trade-off between energy expenditure and response time that can be tuned by evolution to optimize cycling rate of the FNR system for a particular ecological context. Simulations mimicking experiments with proposed double mutant strains offer suggestions for experimentally testing our predictions and identifying potential fitness effects. Our approach provides a computational framework for analyzing other conditional futile cycles, which when placed in their larger biological context may be found to confer advantages to the organism.

Elucidating the genotype-phenotype map by automatic enumeration and analysis of the phenotypic repertoire.

BACKGROUND: The gap between genotype and phenotype is filled by complex biochemical systems most of which are poorly understood. Because these systems are complex, it is widely appreciated that quantitative understanding can only be achieved with the aid of mathematical models. However, formulating models and measuring or estimating their numerous rate constants and binding constants is daunting. Here we present a strategy for automating difficult aspects of the process. METHODS: The strategy, based on a system design space methodology, is applied to a class of 16 designs for a synthetic gene oscillator that includes seven designs previously formulated on the basis of experimentally measured and estimated parameters. RESULTS: Our strategy provides four important innovations by automating: (1) enumeration of the repertoire of qualitatively distinct phenotypes for a system; (2) generation of parameter values for any particular phenotype; (3) simultaneous realization of parameter values for several phenotypes to aid visualization of transitions from one phenotype to another, in critical cases from functional to dysfunctional; and (4) identification of ensembles of phenotypes whose expression can be phased to achieve a specific sequence of functions for rationally engineering synthetic constructs. Our strategy, applied to the 16 designs, reproduced previous results and identified two additional designs capable of sustained oscillations that were previously missed. CONCLUSIONS: Starting with a system's relatively fixed aspects, its architectural features, our method enables automated analysis of nonlinear biochemical systems from a global perspective, without first specifying parameter values. The examples presented demonstrate the efficiency and power of this automated strategy.

Evolution of a genome-encoded bias in amino acid biosynthetic pathways is a potential indicator of amino acid dynamics in the environment.

Overcoming the stress of starvation is one of an organism's most challenging phenotypic responses. Those organisms that frequently survive the challenge, by virtue of their fitness, will have evolved genomes that are shaped by their specific environments. Understanding this genotype-environment-phenotype relationship at a deep level will require quantitative predictive models of the complex molecular systems that link these aspects of an organism's existence. Here, we treat one of the most fundamental molecular systems, protein synthesis, and the amino acid biosynthetic pathways involved in the stringent response to starvation. These systems face an inherent logical dilemma: Building an amino acid biosynthetic pathway to synthesize its product-the cognate amino acid of the pathway-may require that very amino acid when it is no longer available. To study this potential "catch-22," we have created a generic model of amino acid biosynthesis in response to sudden starvation. Our mathematical analysis and computational results indicate that there are two distinctly different outcomes: Partial recovery to a new steady state, or full system failure. Moreover, the cell's fate is dictated by the cognate bias, the number of cognate amino acids in the corresponding biosynthetic pathway relative to the average number of that amino acid in the proteome. We test these implications by analyzing the proteomes of over 1,800 sequenced microbes, which reveals statistically significant evidence of low cognate bias, a genetic trait that would avoid the biosynthetic quandary. Furthermore, these results suggest that the pattern of cognate bias, which is readily derived by genome sequencing, may provide evolutionary clues to an organism's natural environment.

Strategy revealing phenotypic differences among synthetic oscillator designs.

Considerable progress has been made in identifying and characterizing the component parts of genetic oscillators, which play central roles in all organisms. Nonlinear interaction among components is sufficiently complex that mathematical models are required to elucidate their elusive integrated behavior. Although natural and synthetic oscillators exhibit common architectures, there are numerous differences that are poorly understood. Utilizing synthetic biology to uncover basic principles of simpler circuits is a way to advance understanding of natural circadian clocks and rhythms. Following this strategy, we address the following questions: What are the implications of different architectures and molecular modes of transcriptional control for the phenotypic repertoire of genetic oscillators? Are there designs that are more realizable or robust? We compare synthetic oscillators involving one of three architectures and various combinations of the two modes of transcriptional control using a methodology that provides three innovations: a rigorous definition of phenotype, a procedure for deconstructing complex systems into qualitatively distinct phenotypes, and a graphical representation for illuminating the relationship between genotype, environment, and the qualitatively distinct phenotypes of a system. These methods provide a global perspective on the behavioral repertoire, facilitate comparisons of alternatives, and assist the rational design of synthetic gene circuitry. In particular, the results of their application here reveal distinctive phenotypes for several designs that have been studied experimentally as well as a best design among the alternatives that has yet to be constructed and tested.

Relative amino acid composition signatures of organisms and environments.

BACKGROUND: Identifying organism-environment interactions at the molecular level is crucial to understanding how organisms adapt to and change the chemical and molecular landscape of their habitats. In this work we investigated whether relative amino acid compositions could be used as a molecular signature of an environment and whether such a signature could also be observed at the level of the cellular amino acid composition of the microorganisms that inhabit that environment. METHODOLOGIES/PRINCIPAL FINDINGS: To address these questions we collected and analyzed environmental amino acid determinations from the literature, and estimated from complete genomic sequences the global relative amino acid abundances of organisms that are cognate to the different types of environment. Environmental relative amino acid abundances clustered into broad groups (ocean waters, host-associated environments, grass land environments, sandy soils and sediments, and forest soils), indicating the presence of amino acid signatures specific for each environment. These signatures correlate to those found in organisms. Nevertheless, relative amino acid abundance of organisms was more influenced by GC content than habitat or phylogeny. CONCLUSIONS: Our results suggest that relative amino acid composition can be used as a signature of an environment. In addition, we observed that the relative amino acid composition of organisms is not highly determined by environment, reinforcing previous studies that find GC content to be the major factor correlating to amino acid composition in living organisms.

Phenotypic deconstruction of gene circuitry.

It remains a challenge to obtain a global perspective on the behavioral repertoire of complex nonlinear gene circuits. In this paper, we describe a method for deconstructing complex systems into nonlinear sub-systems, based on mathematically defined phenotypes, which are then represented within a system design space that allows the repertoire of qualitatively distinct phenotypes of the complex system to be identified, enumerated, and analyzed. This method efficiently characterizes large regions of system design space and quickly generates alternative hypotheses for experimental testing. We describe the motivation and strategy in general terms, illustrate its use with a detailed example involving a two-gene circuit with a rich repertoire of dynamic behavior, and discuss experimental means of navigating the system design space.

Molecular mechanisms of multiple toxin-antitoxin systems are coordinated to govern the persister phenotype.

Toxin-antitoxin systems are ubiquitous and have been implicated in persistence, the multidrug tolerance of bacteria, biofilms, and, by extension, most chronic infections. However, their purpose, apparent redundancy, and coordination remain topics of debate. Our model relates molecular mechanisms to population dynamics for a large class of toxin-antitoxin systems and suggests answers to several of the open questions. The generic architecture of toxin-antitoxin systems provides the potential for bistability, and even when the systems do not exhibit bistability alone, they can be coupled to create a strongly bistable, hysteretic switch between normal and toxic states. Stochastic fluctuations can spontaneously switch the system to the toxic state, creating a heterogeneous population of growing and nongrowing cells, or persisters, that exist under normal conditions, rather than as an induced response. Multiple toxin-antitoxin systems can be cooperatively marshaled for greater effect, with the dilution determined by growth rate serving as the coordinating signal. The model predicts and elucidates experimental results that show a characteristic correlation between persister frequency and the number of toxin-antitoxin systems.

Transcription factors in Escherichia coli prefer the holo conformation.

The transcriptional regulatory network of Escherichia coli K-12 is among the best studied gene networks of any living cell. Transcription factors bind to DNA either with their effector bound (holo conformation), or as a free protein (apo conformation) regulating transcription initiation. By using RegulonDB, the functional conformations (holo or apo) of transcription factors, and their mode of regulation (activator, repressor, or dual) were exhaustively analyzed. We report a striking discovery in the architecture of the regulatory network, finding a strong under-representation of the apo conformation (without allosteric metabolite) of transcription factors when binding to their DNA sites to activate transcription. This observation is supported at the level of individual regulatory interactions on promoters, even if we exclude the promoters regulated by global transcription factors, where three-quarters of the known promoters are regulated by a transcription factor in holo conformation. This genome-scale analysis enables us to ask what are the implications of these observations for the physiology and for our understanding of the ecology of E. coli. We discuss these ideas within the framework of the demand theory of gene regulation.

A bistable hysteretic switch in an activator-repressor regulated restriction-modification system.

Restriction-modification (RM) systems are extremely widespread among bacteria and archaea, and are often specified by mobile genetic elements. In type II RM systems, where the restriction endonuclease (REase) and protective DNA methyltransferase (MTase) are separate proteins, a major regulatory challenge is delaying expression of the REase relative to the MTase after RM genes enter a new host cell. Basic understanding of this regulation is available for few RM systems, and detailed understanding for none. The PvuII RM system is one of a large subset in which the central regulatory role is played by an activator-repressor protein (called C, for controller). REase expression depends upon activation by C, whereas expression of the MTase does not. Thus delay of REase expression depends on the rate of C-protein accumulation. This is a nonlinear process, as C also activates transcription of its own gene. Mathematical modeling of the PvuII system led to the unexpected predictions of responsiveness to a factor not previously studied in RM system control--gene copy number--and of a hysteretic response. In this study, those predictions have been confirmed experimentally. The results may apply to many other C-regulated RM systems, and help explain their ability to spread so widely.

Regulatory design governing progression of population growth phases in bacteria.

It has long been noted that batch cultures inoculated with resting bacteria exhibit a progression of growth phases traditionally labeled lag, exponential, pre-stationary and stationary. However, a detailed molecular description of the mechanisms controlling the transitions between these phases is lacking. A core circuit, formed by a subset of regulatory interactions involving five global transcription factors (FIS, HNS, IHF, RpoS and GadX), has been identified by correlating information from the well- established transcriptional regulatory network of Escherichia coli and genome-wide expression data from cultures in these different growth phases. We propose a functional role for this circuit in controlling progression through these phases. Two alternative hypotheses for controlling the transition between the growth phases are first, a continuous graded adjustment to changing environmental conditions, and second, a discontinuous hysteretic switch at critical thresholds between growth phases. We formulate a simple mathematical model of the core circuit, consisting of differential equations based on the power-law formalism, and show by mathematical and computer-assisted analysis that there are critical conditions among the parameters of the model that can lead to hysteretic switch behavior, which--if validated experimentally--would suggest that the transitions between different growth phases might be analogous to cellular differentiation. Based on these provocative results, we propose experiments to test the alternative hypotheses.

Design of the lac gene circuit revisited.

The lactose (lac) operon of Escherichia coli serves as the paradigm for gene regulation, not only for bacteria, but also for all biological systems from simple phage to humans. The details of the systems may differ, but the key conceptual framework remains, and the original system continues to reveal deeper insights with continued experimental and theoretical study. Nearly as long lasting in impact as the pivotal work of Jacob and Monod is the classic experiment of Novick and Weiner in which they demonstrated all-or-none gene expression in response to an artificial inducer. These results are often cited in claims that normal gene expression is in fact a discontinuous bistable phenomenon. In this paper, I review several levels of analysis of the lac system and introduce another perspective based on the construction of the system design space. These represent variations on a theme, based on a simply stated design principle, that captures the key qualitative features of the system in a largely mechanism-independent fashion. Moreover, this principle can be readily interpreted in terms of specific mechanisms to make predictions regarding monostable vs. bistable behavior. The regions of design space representing bifurcations are compared with the corresponding regions identified through bifurcation analysis. I present evidence based on biological considerations as well as modeling and analysis to suggest that induction of the lac system in its natural setting is a monostable continuously graded phenomenon. Nevertheless, it must be acknowledged that the lac stability question remains unsettled, and it undoubtedly will remain so until there are definitive experimental results.