Intracellular kinetics of a growing virus: a genetically structured simulation for bacteriophage T7

Lytic/Lysogenic Transition as a Life-History Switch

The transition between lytic and lysogenic life cycles is the most important feature of the life-history of temperate viruses. To explain this transition, an optimal life-history model is offered based a discrete-time formulation of phage/bacteria population dynamics that features infection of bacteria by Poisson sampling of virions from the environment. The time step is the viral latency period. In this model, density-dependent viral absorption onto the bacterial surface produces virus/bacteria coexistence and density dependence in bacterial growth is not needed. The formula for the transition between lytic and lysogenic phases is termed the 'fitness switch'. According to the model, the virus switches from lytic to lysogenic when its population grows faster as prophage than as virions produced by lysis of the infected cells, and conversely for the switch from lysogenic to lytic. A prophage that benefits the bacterium it infects automatically incurs lower fitness upon exiting the bacterial genome, resulting in its becoming locked into the bacterial genome in what is termed here as a 'prophage lock'. The fitness switch qualitatively predicts the ecogeographic rule that environmental enrichment leads to microbialization with a concomitant increase in lysogeny, fluctuating environmental conditions promote virus-mediated horizontal gene transfer, and prophage-containing bacteria can integrate into the microbiome of a eukaryotic host forming a functionally integrated tripartite holobiont. These predictions accord more with the 'Piggyback-the-Winner' hypothesis than with the 'Kill-the-Winner' hypothesis in virus ecology.

Genomic and Biological Profile of a Novel Bacteriophage, Vibrio phage Virtus, Which Improves Survival of Sparus aurata Larvae Challenged with Vibrio harveyi

Due to the emergence of multidrug-resistant bacteria, commonly known as “superbugs”, phage therapy for the control of bacterial diseases rose in popularity. In this context, the use of phages for the management of many important bacterial diseases in the aquaculture environment is auspicious. Vibrio harveyi, a well-known and serious bacterial pathogen, is responsible for many disease outbreaks in aquaculture, resulting in huge economic and production losses. We isolated and fully characterized a novel bacteriophage, Vibrio phage Virtus, infecting V. harveyi strain VH2. Vibrio phage Virtus can infect a wide spectrum of Vibrio spp., including strains of V. harveyi, V. owensii, V. campbellii, V. parahaemolyticus, and V. mediterranei. It has a latent period of 40 min with an unusually high burst size of 3200 PFU/cell. Vibrio phage Virtus has a double-stranded DNA of 82,960 base pairs with 127 predicted open reading frames (ORFs). No virulence, antibiotic resistance, or integrase-encoding genes were detected. In vivo phage therapy trials in gilthead seabream, Sparus aurata, larvae demonstrated that Vibrio phage Virtus was able to significantly improve the survival of larvae for five days at a multiplicity of infection (MOI) of 10, which suggests that it can be an excellent candidate for phage therapy.

Generating dynamic gene expression patterns without the need for regulatory circuits

Synthetic biology has successfully advanced our ability to design and implement complex, time-varying genetic circuits to control the expression of recombinant proteins. However, these circuits typically require the production of regulatory genes whose only purpose is to coordinate expression of other genes. When designing very small genetic constructs, such as viral genomes, we may want to avoid introducing such auxiliary gene products while nevertheless encoding complex expression dynamics. To this end, here we demonstrate that varying only the placement and strengths of promoters, terminators, and RNase cleavage sites in a computational model of a bacteriophage genome is sufficient to achieve solutions to a variety of basic gene expression patterns. We discover these genetic solutions by computationally evolving genomes to reproduce desired gene expression time-course data. Our approach shows that non-trivial patterns can be evolved, including patterns where the relative ordering of genes by abundance changes over time. We find that some patterns are easier to evolve than others, and comparable expression patterns can be achieved via different genetic architectures. Our work opens up a novel avenue to genome engineering via fine-tuning the balance of gene expression and gene degradation rates.

Engineering a Dynamic Controllable Infectivity Switch in Bacteriophage T7

Transcriptional repressors play an important role in regulating phage life cycle. Here, we examine how synthetic transcription repressors can be used in bacteriophage T7 to create a dynamic, controllable infectivity switch. We engineered T7 phage by replacing a large region of the early phage genome with different combinations of ligand-responsive promoters and ribosome binding sites (RBS) designed to control the phage RNA polymerase, gp1. Phages with engineered infectivity switch are fully viable at levels comparable to wildtype T7, when not repressed, indicating the phage can be engineered without loss of fitness. The most effective switch used a TetR-responsive promoter and an attenuated RBS, resulting in a 2-fold increase in latent period and a 10-fold decrease in phage titer when repressed. Phage activity can be further tuned using different inducer concentrations. Our study provides a proof of concept for how a simple synthetic circuit introduced into the phage genome enables user control over phage infectivity.

Patterns of virus growth across the diversity of life

Although viruses in their natural habitats add up to less than 10% of the biomass, they contribute more than 90% of the genome sequences [1]. These viral sequences or 'viromes' encode viruses that populate the Earth's oceans [2, 3] and terrestrial environments [4, 5], where their infections impact life across diverse ecological niches and scales [6, 7], including humans [8-10]. Most viruses have yet to be isolated and cultured [11-13], and surprisingly few efforts have explored what analysis of available data might reveal about their nature. Here, we compiled and analyzed seven decades of one-step growth and other data for viruses from six major families, including their infections of archaeal, bacterial and eukaryotic hosts [14-191]. We found that the use of host cell biomass for virus production was highest for archaea at 10%, followed by bacteria at 1% and eukarya at 0.01%, highlighting the degree to which viruses of archaea and bacteria exploit their host cells. For individual host cells, the yield of virus progeny spanned a relatively narrow range (10-1000 infectious particles per cell) compared with the million-fold difference in size between the smallest and largest cells. Furthermore, healthy and infected host cells were remarkably similar in the time they needed to multiply themselves or their virus progeny. Specifically, the doubling time of healthy cells and the delay time for virus release from infected cells were not only correlated (r = 0.71, p < 10-10, n = 101); they also spanned the same range from tens of minutes to about a week. These results have implications for better understanding the growth, spread and persistence of viruses in complex natural habitats that abound with diverse hosts, including humans and their associated microbes.

Inhibiting the reproduction of SARS-CoV-2 through perturbations in human lung cell metabolic network

Viruses rely on their host for reproduction. Here, we made use of genomic and structural information to create a biomass function capturing the amino and nucleic acid requirements of SARS-CoV-2. Incorporating this biomass function into a stoichiometric metabolic model of the human lung cell and applying metabolic flux balance analysis, we identified host-based metabolic perturbations inhibiting SARS-CoV-2 reproduction. Our results highlight reactions in the central metabolism, as well as amino acid and nucleotide biosynthesis pathways. By incorporating host cellular maintenance into the model based on available protein expression data from human lung cells, we find that only few of these metabolic perturbations are able to selectively inhibit virus reproduction. Some of the catalysing enzymes of such reactions have demonstrated interactions with existing drugs, which can be used for experimental testing of the presented predictions using gene knockouts and RNA interference techniques. In summary, the developed computational approach offers a platform for rapid, experimentally testable generation of drug predictions against existing and emerging viruses based on their biomass requirements.

Pseudomonas Phage PaBG-A Jumbo Member of an Old Parasite Family

Bacteriophage PaBG is a jumbo Myoviridae phage isolated from water of Lake Baikal. This phage has limited diffusion ability and thermal stability and infects a narrow range of Pseudomonas aeruginosa strains. Therefore, it is hardly suitable for phage therapy applications. However, the analysis of the genome of PaBG presents a number of insights into the evolutionary history of this phage and jumbo phages in general. We suggest that PaBG represents an ancient group distantly related to all known classified families of phages.

Transcript degradation and codon usage regulate gene expression in a lytic phage

Many viral genomes are small, containing only single- or double-digit numbers of genes and relatively few regulatory elements. Yet viruses successfully execute complex regulatory programs as they take over their host cells. Here, we propose that some viruses regulate gene expression via a carefully balanced interplay between transcription, translation, and transcript degradation. As our model system, we employ bacteriophage T7, whose genome of approximately sixty genes is well annotated and for which there is a long history of computational models of gene regulation. We expand upon prior modeling work by implementing a stochastic gene expression simulator that tracks individual transcripts, polymerases, ribosomes, and ribonucleases participating in the transcription, translation, and transcript-degradation processes occurring during a T7 infection. By combining this detailed mechanistic modeling of a phage infection with high-throughput gene expression measurements of several strains of bacteriophage T7, evolved and engineered, we can show that both the dynamic interplay between transcription and transcript degradation, and between these two processes and translation, appear to be critical components of T7 gene regulation. Our results point to targeted degradation as a generic gene regulation strategy that may have evolved in many other viruses. Further, our results suggest that detailed mechanistic modeling may uncover the biological mechanisms at work in both evolved and engineered virus variants.

Pinetree: a step-wise gene expression simulator with codon-specific translation rates

MOTIVATION

Stochastic gene expression simulations often assume steady-state transcript levels, or they model transcription in more detail than translation. Moreover, they lack accessible programing interfaces, which limit their utility.

RESULTS

We present Pinetree, a step-wise gene expression simulator with codon-specific translation rates. Pinetree models both transcription and translation in a stochastic framework with individual polymerase and ribosome-level detail. Written in C++ with a Python front-end, any user familiar with Python can specify a genome and simulate gene expression. Pinetree was designed to be efficient and scale to simulate large plasmids or viral genomes.

AVAILABILITY AND IMPLEMENTATION

Pinetree is available on GitHub (https://github.com/benjaminjack/pinetree) and the Python Package Index (https://pypi.org/project/pinetree/).

Combinatorial Approaches to Viral Attenuation

Live viral vaccines rely on attenuated viruses that can successfully infect their host but have reduced fitness or virulence. Such attenuated viruses were originally developed through trial and error, typically by adaptation of the wild-type virus to novel conditions. That method was haphazard, with no way of controlling the degree of attenuation or the number of attenuating mutations or preventing evolutionary reversion. Synthetic biology now enables rational design and engineering of viral attenuation, but rational design must be informed by biological principles to achieve stable, quantitative attenuation. This work shows that in a model system for viral attenuation, bacteriophage T7, attenuation can be obtained from rational design principles, and multiple different attenuation approaches can be combined for enhanced overall effect.

Attenuated viruses have numerous applications, in particular in the context of live viral vaccines. However, purposefully designing attenuated viruses remains challenging, in particular if the attenuation is meant to be resistant to rapid evolutionary recovery. Here we develop and analyze a new attenuation method, promoter ablation, using an established viral model, bacteriophage T7. Ablation of promoters of the two most highly expressed T7 proteins (scaffold and capsid) led to major reductions in transcript abundance of the affected genes, with the effect of the double knockout approximately additive of the effects of single knockouts. Fitness reduction was moderate and also approximately additive; fitness recovery on extended adaptation was partial and did not restore the promoters. The fitness effect of promoter knockouts combined with a previously tested codon deoptimization of the capsid gene was less than additive, as anticipated from their competing mechanisms of action. In one design, the engineering created an unintended consequence that led to further attenuation, the effect of which was studied and understood in hindsight. Overall, the mechanisms and effects of genome engineering on attenuation behaved in a predictable manner. Therefore, this work suggests that the rational design of viral attenuation methods is becoming feasible.

IMPORTANCE Live viral vaccines rely on attenuated viruses that can successfully infect their host but have reduced fitness or virulence. Such attenuated viruses were originally developed through trial and error, typically by adaptation of the wild-type virus to novel conditions. That method was haphazard, with no way of controlling the degree of attenuation or the number of attenuating mutations or preventing evolutionary reversion. Synthetic biology now enables rational design and engineering of viral attenuation, but rational design must be informed by biological principles to achieve stable, quantitative attenuation. This work shows that in a model system for viral attenuation, bacteriophage T7, attenuation can be obtained from rational design principles, and multiple different attenuation approaches can be combined for enhanced overall effect.

Mathematical Analysis of Viral Replication Dynamics and Antiviral Treatment Strategies: From Basic Models to Age-Based Multi-Scale Modeling

Viral infectious diseases are a global health concern, as is evident by recent outbreaks of the middle east respiratory syndrome, Ebola virus disease, and re-emerging zika, dengue, and chikungunya fevers. Viral epidemics are a socio-economic burden that causes short- and long-term costs for disease diagnosis and treatment as well as a loss in productivity by absenteeism. These outbreaks and their socio-economic costs underline the necessity for a precise analysis of virus-host interactions, which would help to understand disease mechanisms and to develop therapeutic interventions. The combination of quantitative measurements and dynamic mathematical modeling has increased our understanding of the within-host infection dynamics and has led to important insights into viral pathogenesis, transmission, and disease progression. Furthermore, virus-host models helped to identify drug targets, to predict the treatment duration to achieve cure, and to reduce treatment costs. In this article, we review important achievements made by mathematical modeling of viral kinetics on the extracellular, intracellular, and multi-scale level for Human Immunodeficiency Virus, Hepatitis C Virus, Influenza A Virus, Ebola Virus, Dengue Virus, and Zika Virus. Herein, we focus on basic mathematical models on the population scale (so-called target cell-limited models), detailed models regarding the most important steps in the viral life cycle, and the combination of both. For this purpose, we review how mathematical modeling of viral dynamics helped to understand the virus-host interactions and disease progression or clearance. Additionally, we review different types and effects of therapeutic strategies and how mathematical modeling has been used to predict new treatment regimens.

Kinetic Modeling of Virus Growth in Cells

When a virus infects a host cell, it hijacks the biosynthetic capacity of the cell to produce virus progeny, a process that may take less than an hour or more than a week. The overall time required for a virus to reproduce depends collectively on the rates of multiple steps in the infection process, including initial binding of the virus particle to the surface of the cell, virus internalization and release of the viral genome within the cell, decoding of the genome to make viral proteins, replication of the genome, assembly of progeny virus particles, and release of these particles into the extracellular environment. For a large number of virus types, much has been learned about the molecular mechanisms and rates of the various steps. However, in only relatively few cases during the last 50 years has an attempt been made-using mathematical modeling-to account for how the different steps contribute to the overall timing and productivity of the infection cycle in a cell. Here we review the initial case studies, which include studies of the one-step growth behavior of viruses that infect bacteria (Qβ, T7, and M13), human immunodeficiency virus, influenza A virus, poliovirus, vesicular stomatitis virus, baculovirus, hepatitis B and C viruses, and herpes simplex virus. Further, we consider how such models enable one to explore how cellular resources are utilized and how antiviral strategies might be designed to resist escape. Finally, we highlight challenges and opportunities at the frontiers of cell-level modeling of virus infections.

Reduced Protein Expression in a Virus Attenuated by Codon Deoptimization

A general means of viral attenuation involves the extensive recoding of synonymous codons in the viral genome. The mechanistic underpinnings of this approach remain unclear, however. Using quantitative proteomics and RNA sequencing, we explore the molecular basis of attenuation in a strain of bacteriophage T7 whose major capsid gene was engineered to carry 182 suboptimal codons. We do not detect transcriptional effects from recoding. Proteomic observations reveal that translation is halved for the recoded major capsid gene, and a more modest reduction applies to several coexpressed downstream genes. We observe no changes in protein abundances of other coexpressed genes that are encoded upstream. Viral burst size, like capsid protein abundance, is also decreased by half. Together, these observations suggest that, in this virus, reduced translation of an essential polycistronic transcript and diminished virion assembly form the molecular basis of attenuation.

Simulation of the M13 life cycle I: Assembly of a genetically-structured deterministic chemical kinetic simulation

To expand the quantitative, systems level understanding and foster the expansion of the biotechnological applications of the filamentous bacteriophage M13, we have unified the accumulated quantitative information on M13 biology into a genetically-structured, experimentally-based computational simulation of the entire phage life cycle. The deterministic chemical kinetic simulation explicitly includes the molecular details of DNA replication, mRNA transcription, protein translation and particle assembly, as well as the competing protein-protein and protein-nucleic acid interactions that control the timing and extent of phage production. The simulation reproduces the holistic behavior of M13, closely matching experimentally reported values of the intracellular levels of phage species and the timing of events in the M13 life cycle. The computational model provides a quantitative description of phage biology, highlights gaps in the present understanding of M13, and offers a framework for exploring alternative mechanisms of regulation in the context of the complete M13 life cycle.

Determining host metabolic limitations on viral replication via integrated modeling and experimental perturbation

Viral replication relies on host metabolic machinery and precursors to produce large numbers of progeny - often very rapidly. A fundamental example is the infection of Escherichia coli by bacteriophage T7. The resource draw imposed by viral replication represents a significant and complex perturbation to the extensive and interconnected network of host metabolic pathways. To better understand this system, we have integrated a set of structured ordinary differential equations quantifying T7 replication and an E. coli flux balance analysis metabolic model. Further, we present here an integrated simulation algorithm enforcing mutual constraint by the models across the entire duration of phage replication. This method enables quantitative dynamic prediction of virion production given only specification of host nutritional environment, and predictions compare favorably to experimental measurements of phage replication in multiple environments. The level of detail of our computational predictions facilitates exploration of the dynamic changes in host metabolic fluxes that result from viral resource consumption, as well as analysis of the limiting processes dictating maximum viral progeny production. For example, although it is commonly assumed that viral infection dynamics are predominantly limited by the amount of protein synthesis machinery in the host, our results suggest that in many cases metabolic limitation is at least as strict. Taken together, these results emphasize the importance of considering viral infections in the context of host metabolism.

Viral infection is a serious problem with relatively few known solutions. Much of the complexity of viral infection is contributed by the host's own resources that the virus commandeers. Viruses lack the machinery and precursors required to replicate, and thus may be considered metabolic products of their host. Our goal is a systems-level understanding of host-viral metabolic interaction via computational tools and quantitative dynamic measurements. Here we present an integrated model of T7 phage viral replication and host E. coli metabolism that predicts phage production changes across media conditions and provides insight into the underlying limiting factors in T7 replication. The model simulations, supported by our experimental measurements, highlight the role of host metabolism in determining the dynamics of viral infection.

Modeling the intracellular dynamics of influenza virus replication to understand the control of viral RNA synthesis

Influenza viruses transcribe and replicate their negative-sense RNA genome inside the nucleus of host cells via three viral RNA species. In the course of an infection, these RNAs show distinct dynamics, suggesting that differential regulation takes place. To investigate this regulation in a systematic way, we developed a mathematical model of influenza virus infection at the level of a single mammalian cell. It accounts for key steps of the viral life cycle, from virus entry to progeny virion release, while focusing in particular on the molecular mechanisms that control viral transcription and replication. We therefore explicitly consider the nuclear export of viral genome copies (vRNPs) and a recent hypothesis proposing that replicative intermediates (cRNA) are stabilized by the viral polymerase complex and the nucleoprotein (NP). Together, both mechanisms allow the model to capture a variety of published data sets at an unprecedented level of detail. Our findings provide theoretical support for an early regulation of replication by cRNA stabilization. However, they also suggest that the matrix protein 1 (M1) controls viral RNA levels in the late phase of infection as part of its role during the nuclear export of viral genome copies. Moreover, simulations show an accumulation of viral proteins and RNA toward the end of infection, indicating that transport processes or budding limits virion release. Thus, our mathematical model provides an ideal platform for a systematic and quantitative evaluation of influenza virus replication and its complex regulation.

ON EXPLORING EFFECTS OF MOLECULAR NOISE IN A SIMPLE VIRAL INFECTION MODEL

Intrinsic and extrinsic noises are all believed to be important in the development and function of many living organisms. In this study, we investigate the sources of the intrinsic noise and the influence of the extrinsic noise on an intracellular viral infection system. The contribution of the intrinsic noise from each reaction is measured by means of a special form of stochastic differential equations (SDEs), chemical Langevin equation. The intrinsic noise of the system is a linear sum of the noise in each of the reactions. The intrinsic noise mainly arises from the degradation of mRNA and the transcription processes. We then study the effects of extrinsic noise by the means of a general form of SDE. It is found that the noise of the viral components grows logarithmically with the increasing noise intensities. The system is most susceptible to the noise in the virus assembly process. A high level of noise in this process can even inhibit the growth of the viruses. This study also demonstrates the utility of SDEs in analyzing genetic regulatory networks perturbed by either inherent or parametric stochasticity.

Dynamics of alternative modes of RNA replication for positive-sense RNA viruses

We propose and study nonlinear mathematical models describing the intracellular time dynamics of viral RNA accumulation for positive-sense single-stranded RNA viruses. Our models consider different replication modes ranging between two extremes represented by the geometric replication (GR) and the linear stamping machine replication (SMR). We first analyse a model that quantitatively reproduced experimental data for the accumulation dynamics of both polarities of turnip mosaic potyvirus RNAs. We identify a non-degenerate transcritical bifurcation governing the extinction of both strands depending on three key parameters: the mode of replication (α), the replication rate (r) and the degradation rate (δ) of viral strands. Our results indicate that the bifurcation associated with α generically takes place when the replication mode is closer to the SMR, thus suggesting that GR may provide viral strands with an increased robustness against degradation. This transcritical bifurcation, which is responsible for the switching from an active to an absorbing regime, suggests a smooth (i.e. second-order), absorbing-state phase transition. Finally, we also analyse a simplified model that only incorporates asymmetry in replication tied to differential replication modes.

The virus as metabolic engineer

Recent genome-wide screens of host genetic requirements for viral infection have reemphasized the critical role of host metabolism in enabling the production of viral particles. In this review, we highlight the metabolic aspects of viral infection found in these studies, and focus on the opportunities these requirements present for metabolic engineers. In particular, the objectives and approaches that metabolic engineers use are readily comparable to the behaviors exhibited by viruses during infection. As a result, metabolic engineers have a unique perspective that could lead to novel and effective methods to combat viral infection.

Optimal viral strategies for bypassing RNA silencing

The RNA silencing pathway constitutes a defence mechanism highly conserved in eukaryotes, especially in plants, where the underlying working principle relies on the repressive action triggered by the intracellular presence of double-stranded RNAs. This immune system performs a post-transcriptional suppression of aberrant mRNAs or viral RNAs by small interfering RNAs (siRNAs) that are directed towards their target in a sequence-specific manner. However, viruses have evolved strategies to escape from silencing surveillance while promoting their own replication. Several viruses encode suppressor proteins that interact with different elements of the RNA silencing pathway and block it. The different suppressors are not phylogenetically nor structurally related and also differ in their mechanism of action. Here, we adopt a model-driven forward-engineering approach to understand the evolution of suppressor proteins and, in particular, why viral suppressors preferentially target some components of the silencing pathway. We analysed three strategies characterized by different design principles: replication in the absence of a suppressor, suppressors targeting the first protein component of the pathway and suppressors targeting the siRNAs. Our results shed light on the question of whether a virus must opt for devoting more time into transcription or into translation and on which would be the optimal step of the silencing pathway to be targeted by suppressors. In addition, we discussed the evolutionary implications of such designing principles.

Replication mode and landscape topology differentially affect RNA virus mutational load and robustness

Regardless of genome polarity, intermediaries of complementary sense must be synthesized and used as templates for the production of new genomic strands. Depending on whether these new genomic strands become themselves templates for producing extra antigenomic ones, thus giving rise to geometric growth, or only the firstly synthesized antigenomic strands can be used to this end, thus following Luria's stamping machine model, the abundances and distributions of mutant genomes will be different. Here we propose mathematical and bit string models that allow distinguishing between stamping machine and geometric replication. We have observed that, regardless the topology of the fitness landscape, the critical mutation rate at which the master sequence disappears increases as the mechanism of replication switches from purely geometric to stamping machine. We also found that, for a wide range of mutation rates, large-effect mutations do not accumulate regardless the scheme of replication. However, mild mutations accumulate more in the geometric model. Furthermore, at high mutation rates, geometric growth leads to a population collapse for intermediate values of mutational effects at which the stamping machine still produces master genomes. We observed that the critical mutation rate was weakly dependent on the strength of antagonistic epistasis but strongly dependent on synergistic epistasis. In conclusion, we have shown that RNA viruses may increase their robustness against the accumulation of deleterious mutations by replicating as stamping machines and that the magnitude of this benefit depends on the topology of the fitness landscape assumed.

Computational fitness landscape for all gene-order permutations of an RNA virus

How does the growth of a virus depend on the linear arrangement of genes in its genome? Answering this question may enhance our basic understanding of virus evolution and advance applications of viruses as live attenuated vaccines, gene-therapy vectors, or anti-tumor therapeutics. We used a mathematical model for vesicular stomatitis virus (VSV), a prototype RNA virus that encodes five genes (N-P-M-G-L), to simulate the intracellular growth of all 120 possible gene-order variants. Simulated yields of virus infection varied by 6,000-fold and were found to be most sensitive to gene-order permutations that increased levels of the L gene transcript or reduced levels of the N gene transcript, the lowest and highest expressed genes of the wild-type virus, respectively. Effects of gene order on virus growth also depended upon the host-cell environment, reflecting different resources for protein synthesis and different cell susceptibilities to infection. Moreover, by computationally deleting intergenic attenuations, which define a key mechanism of transcriptional regulation in VSV, the variation in growth associated with the 120 gene-order variants was drastically narrowed from 6,000- to 20-fold, and many variants produced higher progeny yields than wild-type. These results suggest that regulation by intergenic attenuation preceded or co-evolved with the fixation of the wild type gene order in the evolution of VSV. In summary, our models have begun to reveal how gene functions, gene regulation, and genomic organization of viruses interact with their host environments to define processes of viral growth and evolution.

Although many viruses are linked to diseases that adversely impact the health of their human, animal, and plant hosts, viruses could help promote wellness and treat disease if their “good traits” could be harnessed. Potentially useful virus traits include their abilities to stimulate a robust immune response, target specific tissues for the delivery of foreign genes, and destroy tumors. The exploitation of such traits in the engineering of virus-based vaccines, gene therapies and anti-cancer strategies is limited in part by our inability to control how viruses grow. Generally, viruses that grow poorly will be more desirable for vaccine applications, whereas viruses that grow and spread rapidly will be useful for destroying tumors. Further, gene therapies will rely on controlling the extent to which a therapeutic gene is delivered and expressed. Robust methods for controlling virus growth have yet to be discovered. However, for some viruses, such as vesicular stomatitis virus (VSV), growth can be very sensitive to the specific linear order of its five genes. Our current work is significant in combining experiments and computational models to identify which virus genes and genome positions most sensitively impact VSV growth, providing a foundation for its applications in human health.

Implications of decoupling the intracellular and extracellular levels in multi-level models of virus growth

Virus infections are characterized by two distinct levels of detail: the intracellular level describing how viruses hijack the host machinery to replicate, and the extracellular level describing how populations of virus and host cells interact. Deterministic, population balance models for viral infections permit incorporation of both the intracellular and extracellular levels of information. In this work, we identify assumptions that lead to exact, selective decoupling of the interaction between the intracellular and extracellular levels, effectively permitting solution of first the intracellular level, and subsequently the extracellular level. This decoupling leads to (1) intracellular and extracellular models of viral infections that have been previously reported and (2) a significant reduction in the computational expense required to solve the model. However, the decoupling restricts the behaviors that can be modeled. Simulation of a previously reported multi-level model demonstrates this decomposition when the intracellular level of description consists of numerous reaction events. Additionally, examples demonstrate that viruses can persist even when the intracellular level of description cannot sustain a steady-state production of virus (i.e., has only a trivial equilibrium). We expect the combination of this modeling framework with experimental data to result in a quantitative, systems-level understanding of viral infections and cellular antiviral strategies that will facilitate controlling both these infections and antiviral strategies.

Modeling the fitness consequences of a cyanophage-encoded photosynthesis gene

Background

Phages infecting marine picocyanobacteria often carry a psbA gene, which encodes a homolog to the photosynthetic reaction center protein, D1. Host encoded D1 decays during phage infection in the light. Phage encoded D1 may help to maintain photosynthesis during the lytic cycle, which in turn could bolster the production of deoxynucleoside triphosphates (dNTPs) for phage genome replication.

Methodology / Principal Findings

To explore the consequences to a phage of encoding and expressing psbA, we derive a simple model of infection for a cyanophage/host pair — cyanophage P-SSP7 and Prochlorococcus MED4— for which pertinent laboratory data are available. We first use the model to describe phage genome replication and the kinetics of psbA expression by host and phage. We then examine the contribution of phage psbA expression to phage genome replication under constant low irradiance (25 µE m⁻² s⁻¹). We predict that while phage psbA expression could lead to an increase in the number of phage genomes produced during a lytic cycle of between 2.5 and 4.5% (depending on parameter values), this advantage can be nearly negated by the cost of psbA in elongating the phage genome. Under higher irradiance conditions that promote D1 degradation, however, phage psbA confers a greater advantage to phage genome replication.

Conclusions / Significance

These analyses illustrate how psbA may benefit phage in the dynamic ocean surface mixed layer.

A virtual look at Epstein-Barr virus infection: simulation mechanism

Epstein-Barr virus (EBV) is an important human pathogen that establishes a life-long persistent infection and for which no precise animal model exists. In this paper, we describe in detail an agent-based model and computer simulation of EBV infection. Agents representing EBV and sets of B and T lymphocytes move and interact on a three-dimensional grid approximating Waldeyer's ring, together with abstract compartments for lymph and blood. The simulation allows us to explore the development and resolution of virtual infections in a manner not possible in actual human experiments. Specifically, we identify parameters capable of inducing clearance, persistent infection, or death.

TABASCO: A single molecule, base-pair resolved gene expression simulator

Background

Experimental studies of gene expression have identified some of the individual molecular components and elementary reactions that comprise and control cellular behavior. Given our current understanding of gene expression, and the goals of biotechnology research, both scientists and engineers would benefit from detailed simulators that can explicitly compute genome-wide expression levels as a function of individual molecular events, including the activities and interactions of molecules on DNA at single base pair resolution. However, for practical reasons including computational tractability, available simulators have not been able to represent genome-scale models of gene expression at this level of detail.

Results

Here we develop a simulator, TABASCO , which enables the precise representation of individual molecules and events in gene expression for genome-scale systems. We use a single molecule computational engine to track individual molecules interacting with and along nucleic acid polymers at single base resolution. Tabasco uses logical rules to automatically update and delimit the set of species and reactions that comprise a system during simulation, thereby avoiding the need for a priori specification of all possible combinations of molecules and reaction events. We confirm that single molecule, base-pair resolved simulation using TABASCO (Tabasco) can accurately compute gene expression dynamics and, moving beyond previous simulators, provide for the direct representation of intermolecular events such as polymerase collisions and promoter occlusion. We demonstrate the computational capacity of Tabasco by simulating the entirety of gene expression during bacteriophage T7 infection; for reference, the 39,937 base pair T7 genome encodes 56 genes that are transcribed by two types of RNA polymerases active across 22 promoters.

Conclusion

Tabasco enables genome-scale simulation of transcription and translation at individual molecule and single base-pair resolution. By directly representing the position and activity of individual molecules on DNA, Tabasco can directly test the effects of detailed molecular processes on system-wide gene expression. Tabasco would also be useful for studying the complex regulatory mechanisms controlling eukaryotic gene expression. The computational engine underlying Tabasco could also be adapted to represent other types of processive systems in which individual reaction events are organized across a single spatial dimension (e.g., polysaccharide synthesis).

Deviant effects in molecular reaction pathways

In biological networks, any manifestations of behaviors substantially 'deviant' from the predictions of continuous-deterministic classical chemical kinetics (CCK) are typically ascribed to systems with complex dynamics and/or a small number of molecules. Here we show that in certain cases such restrictions are not obligatory for CCK to be largely incorrect. By systematically identifying properties that may cause significant divergences between CCK and the more accurate discrete-stochastic chemical master equation (CME) system descriptions, we comprehensively characterize potential CCK failure patterns in biological settings, including consequences of the assertion that CCK is closer to the 'mode' rather than the 'average' of stochastic reaction dynamics, as generally perceived. We demonstrate that mechanisms underlying such nonclassical effects can be very simple, are common in cellular networks and result in often unintuitive system behaviors. This highlights the importance of deviant effects in biotechnologically or biomedically relevant applications, and suggests some approaches to diagnosing them in situ.

Control of Streptococcus pyogenes virulence: modeling of the CovR/S signal transduction system

The CovR/S system in Streptococcus pyogenes (Group A Streptococcus, or GAS), a two-component signal transduction/transcription regulation system, controls the expression of major virulence factors. The presence of a negative feedback loop distinguishes the CovR/S system from the majority of bacterial two-component systems. We developed a deterministic model of the CovR/S system consisting of eight delay differential equations. Computational experiments showed that the system possessed a unique stable steady state. The dynamical behavior of the system showed a tendency for oscillations becoming more pronounced for longer but still biochemically realistic delays resulting from reductions in the rates of translation elongation. We have devised an efficient procedure for computing the system's steady state. Further, we have shown that the signal-response curves are hyperbolic for the default parameter values. However, in experiments with randomized parameters we demonstrated that sigmoidality of signal-response curves, implying a response threshold, is not only possible, but seems to be rather typical for CovR/S-like systems even when binding of the CovR response regulator protein to a promoter is non-cooperative. We used sensitivity analysis to simplify the model in order to make it analytically tractable. The existence and uniqueness of the steady state and hyperbolicity of signal-response curves for the majority of the variables was proved for the simplified model. Also, we found that provided CovS was active, the system was insensitive to changes in the concentration of any other phosphoryl donor such as acetyl phosphate.

Biological network design strategies: discovery through dynamic optimization

An important challenge in systems biology is the inherent complexity of biological network models, which complicates the task of relating network structure to function and of understanding the conceptual design principles by which a given network operates. Here we investigate an approach to analyze the relationship between a network structure and its function using the framework of optimization. A common feature found in a variety of biochemical networks involves the opposition of a pair of enzymatic chemical modification reactions such as phosphorylation-dephosphorylation or methylation-demethylation. The modification pair frequently adjusts biochemical properties of its target, such as activating and deactivating function. We applied optimization methodology to study a reversible modification network unit commonly found in signal transduction systems, and we explored the use of this methodology to discover design principles. The results demonstrate that different sets of rate constants used to parameterize the same network topology represent different compromises made in the resulting network operating characteristics. Moreover, the same topology can be used to encode different strategies for achieving performance goals. The ability to adopt multiple strategies may lead to significantly improved performance across a range of conditions through rate modulation or evolutionary processes. The optimization framework explored here is a practical approach to support the discovery of design principles in biological networks.

Model-based design of growth-attenuated viruses

Live-virus vaccines activate both humoral and cell-mediated immunity, require only a single boosting, and generally provide longer immune protection than killed or subunit vaccines. However, growth of live-virus vaccines must be attenuated to minimize their potential pathogenic effects, and mechanisms of attenuation by conventional serial-transfer viral adaptation are not well-understood. New methods of attenuation based on rational engineering of viral genomes may offer a potentially greater control if one can link defined genetic modifications to changes in virus growth. To begin to establish such links between genotype and growth phenotype, we developed a computer model for the intracellular growth of vesicular stomatitis virus (VSV), a well-studied, nonsegmented, negative-stranded RNA virus. Our model incorporated established regulatory mechanisms of VSV while integrating key wild-type infection steps: hijacking of host resources, transcription, translation, and replication, followed by assembly and release of progeny VSV particles. Generalization of the wild-type model to allow for genome rearrangements matched the experimentally observed attenuation ranking for recombinant VSV strains that altered the genome position of their nucleocapsid gene. Finally, our simulations captured previously reported experimental results showing how altering the positions of other VSV genes has the potential to attenuate the VSV growth while overexpressing the immunogenic VSV surface glycoprotein. Such models will facilitate the engineering of new live-virus vaccines by linking genomic manipulations to controlled changes in virus gene-expression and growth.

Refactoring bacteriophage T7

Natural biological systems are selected by evolution to continue to exist and evolve. Evolution likely gives rise to complicated systems that are difficult to understand and manipulate. Here, we redesign the genome of a natural biological system, bacteriophage T7, in order to specify an engineered surrogate that, if viable, would be easier to study and extend. Our initial design goals were to physically separate and enable unique manipulation of primary genetic elements. Implicit in our design are the hypotheses that overlapping genetic elements are, in aggregate, nonessential for T7 viability and that our models for the functions encoded by elements are sufficient. To test our initial design, we replaced the left 11 515 base pairs (bp) of the 39 937 bp wild-type genome with 12 179 bp of engineered DNA. The resulting chimeric genome encodes a viable bacteriophage that appears to maintain key features of the original while being simpler to model and easier to manipulate. The viability of our initial design suggests that the genomes encoding natural biological systems can be systematically redesigned and built anew in service of scientific understanding or human intention.

Mathematical model of influenza A virus production in large-scale microcarrier culture

A mathematical model that describes the replication of influenza A virus in animal cells in large-scale microcarrier culture is presented. The virus is produced in a two-step process, which begins with the growth of adherent Madin-Darby canine kidney (MDCK) cells. After several washing steps serum-free virus maintenance medium is added, and the cells are infected with equine influenza virus (A/Equi 2 (H3N8), Newmarket 1/93). A time-delayed model is considered that has three state variables: the number of uninfected cells, infected cells, and free virus particles. It is assumed that uninfected cells adsorb the virus added at the time of infection. The infection rate is proportional to the number of uninfected cells and free virions. Depending on multiplicity of infection (MOI), not necessarily all cells are infected by this first step leading to the production of free virions. Newly produced viruses can infect the remaining uninfected cells in a chain reaction. To follow the time course of virus replication, infected cells were stained with fluorescent antibodies. Quantitation of influenza viruses by a hemagglutination assay (HA) enabled the estimation of the total number of new virions produced, which is relevant for the production of inactivated influenza vaccines. It takes about 4-6 h before visibly infected cells can be identified on the microcarriers followed by a strong increase in HA titers after 15-16 h in the medium. Maximum virus yield Vmax was about 1x10(10) virions/mL (2.4 log HA units/100 microL), which corresponds to a burst size ratio of about 18,755 virus particles produced per cell. The model tracks the time course of uninfected and infected cells as well as virus production. It suggests that small variations (<10%) in initial values and specific rates do not have a significant influence on Vmax. The main parameters relevant for the optimization of virus antigen yields are specific virus replication rate and specific cell death rate due to infection. Simulation studies indicate that a mathematical model that neglects the delay between virus infection and the release of new virions gives similar results with respect to overall virus dynamics compared with a time delayed model.

Energy-efficient growth of phage Q Beta in Escherichia coli

The role of natural selection in the optimal design of organisms is controversial. Optimal forms, functions, or behaviors of organisms have long been claimed without knowledge of how genotype contributes to phenotype, delineation of design constraints, or reference to alternative designs. Moreover, arguments for optimal designs have been often based on models that were difficult, if not impossible, to test. Here, we begin to address these issues by developing and probing a kinetic model for the intracellular growth of bacteriophage Q beta in Escherichia coli. The model accounts for the energetic costs of all template-dependent polymerization reactions, in ATP equivalents, including RNA-dependent RNA elongation by the phage replicase and synthesis of all phage proteins by the translation machinery of the E. coli host cell. We found that translation dominated phage growth, requiring 85% of the total energy expenditure. Only 10% of the total energy was applied to activities other than the direct synthesis of progeny phage components, reflecting primarily the cost of making the negative-strand RNA template that is needed for replication of phage genomic RNA. Further, we defined an energy efficiency of phage growth and showed its direct relationship to the yield of phage progeny. Finally, we performed a sensitivity analysis and found that the growth of wild-type phage was optimized for progeny yield or energy efficiency, suggesting that phage Q beta has evolved to optimally utilize the finite resources of its host cells.

2004 ASM Conference on the New Phage Biology: the 'Phage Summit'

In August, more than 350 conferees from 24 countries attended the ASM Conference on the New Phage Biology, in Key Biscayne, Florida. This meeting, also called the Phage Summit, was the first major international gathering in decades devoted exclusively to phage biology. What emerged from the 5 days of the Summit was a clear perspective on the explosive resurgence of interest in all aspects of bacteriophage biology. The classic phage systems like lambda and T4, reinvigorated by structural biology, bioinformatics and new molecular and cell biology tools, remain model systems of unequalled power and facility for studying fundamental biological issues. In addition, the New Phage Biology is also populated by basic and applied scientists focused on ecology, evolution, nanotechnology, bacterial pathogenesis and phage-based immunologics, therapeutics and diagnostics, resulting in a heightened interest in bacteriophages per se, rather than as a model system. Besides constituting another landmark in the long history of a field begun by d'Herelle and Twort during the early 20th century, the Summit provided a unique venue for establishment of new interactive networks for collaborative efforts between scientists of many different backgrounds, interests and expertise.

Structured model of influenza virus replication in MDCK cells

Intracellular events that take place during influenza virus replication in animal cells are well understood qualitatively. However, to better understand the complex interaction of the virus with its host cell and to quantitatively analyze the use of cellular resources for virion formation or the overall dynamic for the entire infection cycle, a mathematical model for influenza virus replication has to be formulated. Here, we present a structured model for the single-cell reproductive cycle of influenza A virus in animal cells that accounts for the individual steps of the process such as attachment, internalization, genome replication and translation, and progeny virion assembly. The model describes an average cell surrounded by a small quantity of medium and infected by a low number of virus particles. The model allows estimation of the cellular resources consumed by virus replication. Simulation results show that the number of cellular surface receptors and endosomes, as well as other resources, such as the number of free nucleotides or amino acids, is not significantly influenced by influenza virus propagation. A factor that limits the growth rate of progeny viruses and their release is the total amount of matrix proteins (M1) in the nucleus while other newly synthesized viral proteins (e.g., nucleoprotein NP) and viral RNAs accumulate. During budding, synthesis of vRNPs (viral ribonucleoprotein complexes) represents another limiting factor. Based on this model it is also possible to analyze effects of parameter changes on the dynamics of virus replication, to identify possible targets for molecular engineering, or to develop strategies for improving yields in vaccine production processes. Furthermore, a better insight into the interactions of viruses and host cells might help to improve our understanding of virus-related diseases and to develop therapies.

Forces during bacteriophage DNA packaging and ejection

The conjunction of insights from structural biology, solution biochemistry, genetics, and single-molecule biophysics has provided a renewed impetus for the construction of quantitative models of biological processes. One area that has been a beneficiary of these experimental techniques is the study of viruses. In this article we describe how the insights obtained from such experiments can be utilized to construct physical models of processes in the viral life cycle. We focus on dsDNA bacteriophages and show that the bending elasticity of DNA and its electrostatics in solution can be combined to determine the forces experienced during packaging and ejection of the viral genome. Furthermore, we quantitatively analyze the effect of fluid viscosity and capsid expansion on the forces experienced during packaging. Finally, we present a model for DNA ejection from bacteriophages based on the hypothesis that the energy stored in the tightly packed genome within the capsid leads to its forceful ejection. The predictions of our model can be tested through experiments in vitro where DNA ejection is inhibited by the application of external osmotic pressure.

Genome function--a virus-world view

By studying viruses one may begin to understand how static genomes can define dynamic processes of development. This talk will describe some of the approaches we are taking, using computer simulations and laboratory experiments, to account for the many molecular-level processes and interactions that occur when a common bacterium, E. coli, is infected by one of its viruses, phage T7. We accounted for processes of phage genome entry, transcription, translation, and DNA replication, including protein-DNA and protein-protein regulatory interactions, and we predicted the dynamics of phage progeny formation. The simulations have enabled us to identify limiting host-cell resources in phage growth, discover novel anti-viral strategies, and suggest frameworks for mining data from global mRNA and protein studies.

A nonlinear discrete dynamical model for transcriptional regulation: construction and properties

Transcriptional regulation is a fundamental mechanism of living cells, which allows them to determine their actions and properties, by selectively choosing which proteins to express and by dynamically controlling the amounts of those proteins. In this article, we revisit the problem of mathematically modeling transcriptional regulation. First, we adopt a biologically motivated continuous model for gene transcription and mRNA translation, based on first-order rate equations, coupled with a set of nonlinear equations that model cis-regulation. Then, we view the processes of transcription and translation as being discrete, which, together with the need to use computational techniques for large-scale analysis and simulation, motivates us to model transcriptional regulation by means of a nonlinear discrete dynamical system. Classical arguments from chemical kinetics allow us to specify the nonlinearities underlying cis-regulation and to include both activators and repressors as well as the notion of regulatory modules in our formulation. We show that the steady-state behavior of the proposed discrete dynamical system is identical to that of the continuous model. We discuss several aspects of our model, related to homeostatic and epigenetic regulation as well as to Boolean networks, and elaborate on their significance. Simulations of transcriptional regulation of a hypothetical metabolic pathway illustrate several properties of our model, and demonstrate that a nonlinear discrete dynamical system may be effectively used to model transcriptional regulation in a biologically relevant way.

The Engineering of Gene Regulatory Networks

The rapid accumulation of genetic information and advancement of experimental techniques have opened a new frontier in biomedical engineering. With the availability of well-characterized components from natural gene networks, the stage has been set for the engineering of artificial gene regulatory networks with sophisticated computational and functional capabilities. In these efforts, the ability to construct, analyze, and interpret qualitative and quantitative models is becoming increasingly important. In this review, we consider the current state of gene network engineering from a combined experimental and modeling perspective. We discuss how networks with increased complexity are being constructed from simple modular components and how quantitative deterministic and stochastic modeling of these modules may provide the foundation for accurate in silico representations of gene regulatory network function in vivo.

Genetic "code": representations and dynamical models of genetic components and networks

Dynamical modeling of biological systems is becoming increasingly widespread as people attempt to grasp biological phenomena in their full complexity and make sense of an accelerating stream of experimental data. We review a number of recent modeling studies that focus on systems specifically involving gene expression and regulation. These systems include bacterial metabolic operons and phase-variable piliation, bacteriophages T7 and lambda, and interacting networks of eukaryotic developmental genes. A wide range of conceptual and mathematical representations of genetic components and phenomena appears in these works. We discuss these representations in depth and give an overview of the tools currently available for creating and exploring dynamical models. We argue that for modeling to realize its full potential as a mainstream biological research technique the tools must become more general and flexible, and formal, standardized representations of biological knowledge and data must be developed.

Stochastic vs. deterministic modeling of intracellular viral kinetics

Within its host cell, a complex coupling of transcription, translation, genome replication, assembly, and virus release processes determines the growth rate of a virus. Mathematical models that account for these processes can provide insights into the understanding as to how the overall growth cycle depends on its constituent reactions. Deterministic models based on ordinary differential equations can capture essential relationships among virus constituents. However, an infection may be initiated by a single virus particle that delivers its genome, a single molecule of DNA or RNA, to its host cell. Under such conditions, a stochastic model that allows for inherent fluctuations in the levels of viral constituents may yield qualitatively different behavior. To compare modeling approaches, we developed a simple model of the intracellular kinetics of a generic virus, which could be implemented deterministically or stochastically. The model accounted for reactions that synthesized and depleted viral nucleic acids and structural proteins. Linear stability analysis of the deterministic model showed the existence of two nodes, one stable and one unstable. Individual stochastic simulation runs could access and remain at the unstable node. In addition, deterministic and averaged stochastic simulations yielded different transient kinetics and different steady-state levels of viral components, particularly for low multiplicities of infection (MOI), where few virus particles initiate the infection. Furthermore, a bimodal population distribution of viral components was observed for low MOI stochastic simulations. The existence of a low-level infected subpopulation of cells, which could act as a viral reservoir, suggested a potential mechanism of viral persistence.

Effects of Escherichia coli physiology on growth of phage T7 in vivo and in silico

Phage development depends not only upon phage functions but also on the physiological state of the host, characterized by levels and activities of host cellular functions. We established Escherichia coli at different physiological states by continuous culture under different dilution rates and then measured its production of phage T7 during a single cycle of infection. We found that the intracellular eclipse time decreased and the rise rate increased as the growth rate of the host increased. To develop mechanistic insight, we extended a computer simulation for the growth of phage T7 to account for the physiology of its host. Literature data were used to establish mathematical correlations between host resources and the host growth rate; host resources included the amount of genomic DNA, pool sizes and elongation rates of RNA polymerases and ribosomes, pool sizes of amino acids and nucleoside triphosphates, and the cell volume. The in silico (simulated) dependence of the phage intracellular rise rate on the host growth rate gave quantitatively good agreement with our in vivo results, increasing fivefold for a 2.4-fold increase in host doublings per hour, and the simulated dependence of eclipse time on growth rate agreed qualitatively, deviating by a fixed delay. When the simulation was used to numerically uncouple host resources from the host growth rate, phage growth was found to be most sensitive to the host translation machinery, specifically, the level and elongation rate of the ribosomes. Finally, the simulation was used to follow how bottlenecks to phage growth shift in response to variations in host or phage functions.

Dependence of epistasis on environment and mutation severity as revealed by in silico mutagenesis of phage t7

Understanding how interactions among deleterious mutations affect fitness may shed light on a variety of fundamental biological phenomena, including the evolution of sex, the buffering of genetic variations, and the topography of fitness landscapes. It remains an open question under what conditions and to what extent such interactions may be synergistic or antagonistic. To address this question, we employed a computer model for the intracellular growth of bacteriophage T7. We created in silico 90,000 mutants of phage T7, each carrying from 1 to 30 mutations, and evaluated the fitness of each by simulating its growth cycle. The simulations sought to account for the severity of single deleterious mutations on T7 growth, as well as the effect of the resource environment on our fitness measures. We found that mildly deleterious mutations interacted synergistically in poor-resource environments but antagonistically in rich-resource environments. However, severely deleterious mutations always interacted antagonistically, irrespective of environment. These results suggest that synergistic epistasis may be difficult to experimentally distinguish from nonepistasis because its effects appear to be most pronounced when the effects of mutations on fitness are most challenging to measure. Our approach demonstrates how computer simulations of developmental processes can be used to quantitatively study genetic interactions at the population level.

Control motifs for intracellular regulatory networks

A number of technological innovations are yielding unprecedented data on the networks of biochemical, genetic, and biophysical reactions that underlie cellular behavior and failure. These networks are composed of hundreds to thousands of chemical species and structures, interacting via nonlinear and possibly stochastic physical processes. A central goal of modern biology is to optimally use the data on these networks to understand how their design leads to the observed cellular behaviors and failures. Ultimately, this knowledge should enable cellular engineers to redesign cellular processes to meet industrial needs (such as optimal natural product synthesis), aid in choosing the most effective targets for pharmaceuticals, and tailor treatment for individual genotypes. The size and complexity of these networks and the inevitable lack of complete data, however, makes reaching these goals extremely difficult. If it proves possible to modularize these networks into functional subnetworks, then these smaller networks may be amenable to direct analysis and might serve as regulatory motifs. These motifs, recurring elements of control, may help to deduce the structure and function of partially known networks and form the basis for fulfilling the goals described above. A number of approaches to identifying and analyzing control motifs in intracellular networks are reviewed.