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SARS-CoV-2 induces delayed type-I/III interferon production, allowing it to escape the early innate immune response. The delay has been attributed to a deficiency in the ability of cells to sense viral replication upon infection, which in turn hampers activation of the antiviral state in bystander cells. Here, we introduce a cellular automaton model to investigate the spatiotemporal spreading of viral infection as a function of virus and host-dependent parameters. The model suggests that the considerable person-to-person heterogeneity in SARS-CoV-2 infections is a consequence of high sensitivity to slight variations in biological parameters near a critical threshold. It further suggests that within-host viral proliferation can be curtailed by the presence of remarkably few cells that are primed for IFN production. Thus, the observed heterogeneity in defense readiness of cells reflects a remarkably cost-efficient strategy for protection.

Superspreading is known to have played an important role in the transmission dynamics of SARS-CoV-2. In this Comment, the authors discuss how knowledge of the extent and cause of superspreading is important for designing appropriate control measures for emerging infectious diseases.

Notch signaling is crucial for pancreatic cell fate choice. With mathematical modeling and experiments, Xu et al. provides new insights into how different Notch ligands and Hes1 oscillation guide the spatial-temporal dynamics of cell differentiation.

Identifying drivers of viral diversity is key to understanding the evolutionary as well as epidemiological dynamics of the COVID-19 pandemic. Using rich viral genomic data sets, we show that periods of steadily rising diversity have been punctuated by sudden, enormous increases followed by similarly abrupt collapses of diversity. We introduce a mechanistic model of saltational evolution with epistasis and demonstrate that these features parsimoniously account for the observed temporal dynamics of inter-genomic diversity. Our results provide support for recent proposals that saltational evolution may be a signature feature of SARS-CoV-2, allowing the pathogen to more readily evolve highly transmissible variants. These findings lend theoretical support to a heightened awareness of biological contexts where increased diversification may occur. They also underline the power of pathogen genomics and other surveillance streams in clarifying the phylodynamics of emerging and endemic infections. In public health terms, our results further underline the importance of equitable distribution of up-to-date vaccines.

Abstract The quantification of spreading heterogeneity in the COVID-19 epidemic is crucial as it affects the choice of efficient mitigating strategies irrespective of whether its origin is biological or social. We present a method to deduce temporal and individual variations in the basic reproduction number directly from epidemic trajectories at a community level. Using epidemic data from the 98 districts in Denmark we estimate an overdispersion factor k for COVID-19 to be about 0.11 (95% confidence interval 0.08–0.18), implying that 10 % of the infected cause between 70 % and 87 % of all infections.

The SARS-CoV-2 ancestral strain has caused pronounced superspreading events, reflecting a disease characterized by overdispersion, where about 10% of infected people cause 80% of infections. New variants of the disease have different person-to-person variability in viral load, suggesting for example that the Alpha (B.1.1.7) variant is more infectious but relatively less prone to superspreading. Meanwhile, non-pharmaceutical mitigation of the pandemic has focused on limiting social contacts (lockdowns, regulations on gatherings) and decreasing transmission risk through mask wearing and social distancing. Using a mathematical model, we show that the competitive advantage of disease variants may heavily depend on the restrictions imposed. In particular, we find that lockdowns exert an evolutionary pressure which favours variants with lower levels of overdispersion. Our results suggest that overdispersion is an evolutionarily unstable trait, with a tendency for more homogeneously spreading variants to eventually dominate.

Phages and bacteria manage to coexist and sustain ecosystems with a high diversity of strains, despite limited resources and heavy predation. This diversity can be explained by the "kill the winner" model where virulent phages predominantly prey on fast-growing bacteria and thereby suppress the competitive exclusion of slower-growing bacteria. Here we computationally investigate the robustness of these systems against invasions, where new phages or bacteria may interact with more than one of the resident strains. The resulting interaction networks were found to self-organize into a network with strongly interacting specialized predator-prey pairs, resembling that of the "kill the winner" model. Furthermore, the "kill the winner" dynamics is enforced with the occasional elimination of even the fastest-growing bacteria strains due to a phage infecting the fast and slow growers. The frequency of slower-growing strains was increased with the introduction of even a few non-diagonal interactions. Hence, phages capable of infecting multiple hosts play significant roles both in the evolution of the ecosystem by eliminating the winner and in supporting diversity by allowing slow growers to coexist with faster growers.

Abstract Epidemics are regularly associated with reports of superspreading: single individuals infecting many others. How do we determine if such events are due to people inherently being biological superspreaders or simply due to random chance? We present an analytically solvable model for airborne diseases which reveal the spreading statistics of epidemics in socio-spatial heterogeneous spaces and provide a baseline to which data may be compared. In contrast to classical SIR models, we explicitly model social events where airborne pathogen transmission allows a single individual to infect many simultaneously, a key feature that generates distinctive output statistics. We find that diseases that have a short duration of high infectiousness can give extreme statistics such as 20% infecting more than 80%, depending on the socio-spatial heterogeneity. Quantifying this by a distribution over sizes of social gatherings, tracking data of social proximity for university students suggest that this can be a approximated by a power law. Finally, we study mitigation efforts applied to our model. We find that the effect of banning large gatherings works equally well for diseases with any duration of infectiousness, but depends strongly on socio-spatial heterogeneity.

Summary: Transcription factors can exert opposite effects depending on the chromosomal context. The fission yeast transcription factor Atf1 both activates numerous genes in response to stresses and mediates heterochromatic gene silencing in the mating-type region. Investigating this context dependency, we report here that the establishment of silent heterochromatin in the mating-type region occurs at a reduced rate in the absence of Atf1 binding. Quantitative modeling accounts for the observed establishment profiles by a combinatorial recruitment of histone-modifying enzymes: locally by Atf1 at two binding sites and over the whole region by dynamically appearing heterochromatic nucleosomes, a source of which is the RNAi-dependent cenH element. In the absence of Atf1 binding, the synergy is lost, resulting in a slow rate of heterochromatin formation. The system shows how DNA-binding proteins can influence local nucleosome states and thereby potentiate long-range positive feedback on histone-modification reactions to enable heterochromatin formation over large regions in a context-dependent manner.

The rapid succession of new variants of SARS-CoV-2 emphasizes the need to understand the factors driving pathogen evolution. Here, we investigate a possible tradeoff between the rate of progression of a disease and its reproductive number. Using an SEIR framework, we show that in the exponential growth phase of an epidemic, there is an optimal disease duration that balances the advantage of a fast disease progression with that of causing many secondary infections. This result offers one possible explanation for the ever shorter generation times of novel variants of SARS-CoV-2, as it progressed from the original strain to the Alpha, Delta, and, from late 2021 onwards, to several Omicron variant subtypes. In the endemic state, the optimum disappears and longer disease duration becomes advantageous for the pathogen. However, selection pressures depend on context: mitigation strategies such as quarantine of infected individuals may slow down the evolution towards longer-lasting, more infectious variants. This work then suggests that, in the future, the trend towards shorter generation times may reverse, and SARS-CoV-2 may instead evolve towards longer-lasting variants.

The West African Ebola (2014-2016) epidemic caused an estimated 11.310 deaths and massive social and economic disruption. The epidemic was comprised of many local outbreaks of varying sizes. However, often local outbreaks recede before the arrival of international aid or susceptible depletion. We modeled Ebola virus transmission under the effect of behavior changes acting as a local inhibitor. A spatial model is used to simulate Ebola epidemics. Our findings suggest that behavior changes can explain why local Ebola outbreaks recede before substantial international aid was mobilized during the 2014-2016 epidemic.

Polycomb and Trithorax group proteins regulate silent and active gene expression states, but also allow poised states in pluripotent cells. Here the authors present a mathematical model that integrates data on Polycomb/ Trithorax biochemistry into a single coherent framework which predicts that poised chromatin is not bivalent as previously proposed, but is bistable, meaning that the system switches frequently between stable active and silent states.

Summary: How do flat sheets of cells form gut and neural tubes? Across systems, several mechanisms are at play: cells wedge, form actomyosin cables, or intercalate. As a result, the cell sheet bends, and the tube elongates. It is unclear to what extent each mechanism can drive tube formation on its own. To address this question, we computationally probe if one mechanism, either cell wedging or intercalation, may suffice for the entire sheet-to-tube transition. Using a physical model with epithelial cells represented by polarized point particles, we show that either cell intercalation or wedging alone can be sufficient and that each can both bend the sheet and extend the tube. When working in parallel, the two mechanisms increase the robustness of the tube formation. The successful simulations of the key features in Drosophila salivary gland budding, sea urchin gastrulation, and mammalian neurulation support the generality of our results. : Developmental Biology; Experimental Models in Systems Biology Subject Areas: Developmental Biology, Experimental Models in Systems Biology

ABSTRACT The competition between bacteria often involves both nutrients and phage predators and may give rise to abrupt regime shifts between the alternative stable states characterized by different species compositions. While such transitions have been previously studied in the context of competition for nutrients, the case of phage-induced bistability between competing bacterial species has not been considered yet. Here we demonstrate a possibility of regime shifts in well-mixed phage-bacterium ecosystems. In one of the bistable states, the fast-growing bacteria competitively exclude the slow-growing ones by depleting their common nutrient. Conversely, in the second state, the slow-growing bacteria with a large burst size generate such a large phage population that the other species cannot survive. This type of bistability can be realized as the competition between a strain of bacteria protected from phage by abortive infection and another strain with partial resistance to phage. It is often desirable to reliably control the state of microbial ecosystems, yet bistability significantly complicates this task. We discuss successes and limitations of one control strategy in which one adds short pulses to populations of individual species. Our study proposes a new type of phage therapy, where introduction of the phage is supplemented by the addition of a partially resistant host bacteria. IMPORTANCE Phage-microbe communities play an important role in human health as well as natural and industrial environments. Here we show that these communities can assume several alternative species compositions separated by abrupt regime shifts. Our model predicts these regime shifts in the competition between bacterial strains protected by two different phage defense mechanisms: abortive infection/CRISPR and partial resistance. The history dependence caused by regime shifts greatly complicates the task of manipulation and control of a community. We propose and study a successful control strategy via short population pulses aimed at inducing the desired regime shifts. In particular, we predict that a fast-growing pathogen could be eliminated by a combination of its phage and a slower-growing susceptible host.

Chromosomes contain large heterochromatin domains. Here, the authors measure the kinetics of heterochromatin formation in fission yeast and show both global and local feedbacks by nucleosome-bound enzymes are important for formation and stability of the large heterochromatin domains.

The unexpected early cessation of the recent West Africa Ebola outbreak demonstrated shortcomings of popular forecasting approaches and has not been fully understood yet. A popular hypothesis is that public health interventions mitigated the spread, such as ETUs and safe burials. We investigate whether risk heterogeneity within the population could serve as an alternative explanation. We introduce a model for spread in heterogeneous host population that is particularly well suited for early predictions due to its simplicity and ease of application. Furthermore, we explore the conditions under which the observed epidemic trajectory can be explained without taking into account the effect of public health interventions. While the obtained fits closely match the total case count time series, closer inspection of sub-population results made us conclude that risk heterogeneity is unlikely to fully explain the early cessation of Ebola; other factors such as behavioral changes and other interventions likely played a major role. More accurate predictions in a future scenario require models that allow for early sub-exponential growth, as well as access to additional data on patient occupation (risk level) and location, to allow identify local phenomena that influence spreading behavior.

Despite continual renewal and damages, a multicellular organism is able to maintain its complex morphology. How is this stability compatible with the complexity and diversity of living forms? Looking for answers at protein level may be limiting as diverging protein sequences can result in similar morphologies. Inspired by the progressive role of apical-basal and planar cell polarity in development, we propose that stability, complexity, and diversity are emergent properties in populations of proliferating polarized cells. We support our hypothesis by a theoretical approach, developed to effectively capture both types of polar cell adhesions. When applied to specific cases of development – gastrulation and the origins of folds and tubes – our theoretical tool suggests experimentally testable predictions pointing to the strength of polar adhesion, restricted directions of cell polarities, and the rate of cell proliferation to be major determinants of morphological diversity and stability.

The mammalian pancreas is a branched organ that does not exhibit stereotypic branching patterns, similarly to most other glands. Inside branches, it contains a network of ducts that undergo a transition from unconnected microlumen to a mesh of interconnected ducts and finally to a treelike structure. This ductal remodeling is poorly understood, both on a microscopic and macroscopic level. In this article, we quantify the network properties at different developmental stages. We find that the pancreatic network exhibits stereotypic traits at each stage and that the network properties change with time toward the most economical and optimized delivery of exocrine products into the duodenum. Using in silico modeling, we show how steps of pancreatic network development can be deconstructed into two simple rules likely to be conserved for many other glands. The early stage of the network is explained by noisy, redundant duct connection as new microlumens form. The later transition is attributed to pruning of the network based on the flux of fluid running through the pancreatic network into the duodenum.

Near promoters, both nucleosomes and CpG sites form characteristic spatial patterns. Previously, nucleosome depleted regions were observed upstream of transcription start sites and nucleosome occupancy was reported to correlate both with CpG density and the level of CpG methylation. Several studies imply a causal link where CpG methylation might induce nucleosome formation, whereas others argue the opposite, i.e., that nucleosome occupancy might influence CpG methylation. Correlations are indeed evident between nucleosomes, CpG density and CpG methylation—at least near promoter sites. It is however less established whether there is an immediate causal relation between nucleosome occupancy and the presence of CpG sites—or if nucleosome occupancy could be influenced by other factors. In this work, we test for such causality in human genomes by analyzing the three quantities both near and away from promoter sites. For data from the human genome we compare promoter regions with given CpG densities with genomic regions without promoters but of similar CpG densities. We find the observed correlation between nucleosome occupancy and CpG density, respectively CpG methylation, to be specific to promoter regions. In other regions along the genome nucleosome occupancy is statistically independent of the positioning of CpGs or their methylation levels. Anti-correlation between CpG density and methylation level is however similarly strong in both regions. On promoters, nucleosome occupancy is more strongly affected by the level of gene expression than CpG density or CpG methylation—calling into question any direct causal relation between nucleosome occupancy and CpG organization. Rather, our results suggest that for organisms with cytosine methylation nucleosome occupancy might be primarily linked to gene expression, with no strong impact on methylation.

Early mammalian development is both highly regulative and self-organizing. It involves the interplay of cell position, predetermined gene regulatory networks, and environmental interactions to generate the physical arrangement of the blastocyst with precise timing. However, this process occurs in the absence of maternal information and in the presence of transcriptional stochasticity. How does the preimplantation embryo ensure robust, reproducible development in this context? It utilizes a versatile toolbox that includes complex intracellular networks coupled to cell-cell communication, segregation by differential adhesion, and apoptosis. Here, we ask whether a minimal set of developmental rules based on this toolbox is sufficient for successful blastocyst development, and to what extent these rules can explain mutant and experimental phenotypes. We implemented experimentally reported mechanisms for polarity, cell-cell signaling, adhesion, and apoptosis as a set of developmental rules in an agent-based in silico model of physically interacting cells. We find that this model quantitatively reproduces specific mutant phenotypes and provides an explanation for the emergence of heterogeneity without requiring any initial transcriptional variation. It also suggests that a fixed time point for the cells' competence of fibroblast growth factor (FGF)/extracellular signal-regulated kinase (ERK) sets an embryonic clock that enables certain scaling phenomena, a concept that we evaluate quantitatively by manipulating embryos in vitro. Based on these observations, we conclude that the minimal set of rules enables the embryo to experiment with stochastic gene expression and could provide the robustness necessary for the evolutionary diversification of the preimplantation gene regulatory network.

In food webs, many interacting species coexist despite the restrictions imposed by the competitive exclusion principle and apparent competition. For the generalized Lotka-Volterra equations, sustainable coexistence necessitates nonzero determinant of the interaction matrix. Here we show that this requirement is equivalent to demanding that each species be part of a non-overlapping pairing, which substantially constrains the food web structure. We demonstrate that a stable food web can always be obtained if a non-overlapping pairing exists. If it does not, the matrix rank can be used to quantify the lack of niches, corresponding to unpaired species. For the species richness at each trophic level, we derive the food web assembly rules, which specify sustainable combinations. In neighboring levels, these rules allow the higher level to avert competitive exclusion at the lower, thereby incorporating apparent competition. In agreement with data, the assembly rules predict high species numbers at intermediate levels and thinning at the top and bottom. Using comprehensive food web data, we demonstrate how omnivores or parasites with hosts at multiple trophic levels can loosen the constraints and help obtain coexistence in food webs. Hence, omnivory may be the glue that keeps communities intact even under extinction or ecological release of species.

Abstract Eukaryotic transcription involves the synergistic interaction of many different proteins. However, the question remains how eukaryotic promoters achieve ultrasensitive or threshold responses to changes in the concentration or activity of a single transcription factor (TF). We show theoretically that by recruiting a histone‐modifying enzyme, a TF binding non‐cooperatively to a single site can change the balance between opposing positive feedback loops in histone modification to produce a large change in gene expression in response to a small change in concentration of the TF. This mechanism can also generate bistable promoter responses, allowing a gene to be on in some cells and off in others, despite the cells being in identical conditions. In addition, the system provides a simple means by which the activities of many TFs could be integrated at a promoter.

Microbial cells embedded in a self-produced extracellular biofilm matrix cause chronic infections, e. g. by Pseudomonas aeruginosa in the lungs of cystic fibrosis patients. The antibiotic killing of bacteria in biofilms is generally known to be reduced by 100-1000 times relative to planktonic bacteria. This makes such infections difficult to treat. We have therefore proposed that biofilms can be regarded as an independent compartment with distinct pharmacokinetics. To elucidate this pharmacokinetics we have measured the penetration of the tobramycin into seaweed alginate beads which serve as a model of the extracellular polysaccharide matrix in P. aeruginosa biofilm. We find that, rather than a normal first order saturation curve, the concentration of tobramycin in the alginate beads follows a power-law as a function of the external concentration. Further, the tobramycin is observed to be uniformly distributed throughout the volume of the alginate bead. The power-law appears to be a consequence of binding to a multitude of different binding sites. In a diffusion model these results are shown to produce pronounced retardation of the penetration of tobramycin into the biofilm. This filtering of the free tobramycin concentration inside biofilm beads is expected to aid in augmenting the survival probability of bacteria residing in the biofilm.

Populations of species in ecosystems are often constrained by availability of resources within their environment. In effect this means that a growth of one population, needs to be balanced by comparable reduction in populations of others. In neutral models of biodiversity all populations are assumed to change incrementally due to stochastic births and deaths of individuals. Here we propose and model another redistribution mechanism driven by abrupt and severe reduction in size of the population of a single species freeing up resources for the remaining ones. This mechanism may be relevant e.g. for communities of bacteria, with strain-specific collapses caused e.g. by invading bacteriophages, or for other ecosystems where infectious diseases play an important role. The emergent dynamics of our system is characterized by cyclic ''diversity waves'' triggered by collapses of globally dominating populations. The population diversity peaks at the beginning of each wave and exponentially decreases afterwards. Species abundances have bimodal time-aggregated distribution with the lower peak formed by populations of recently collapsed or newly introduced species while the upper peak--species that has not yet collapsed in the current wave. In most waves both upper and lower peaks are composed of several smaller peaks. This self-organized hierarchical peak structure has a long-term memory transmitted across several waves. It gives rise to a scale-free tail of the time-aggregated population distribution with a universal exponent of 1.7. We show that diversity wave dynamics is robust with respect to variations in the rules of our model such as diffusion between multiple environments, species-specific growth and extinction rates, and bet-hedging strategies.

Speciation, diversification, and competition between species challenge the stability of complex ecosystems. Laboratory experiments often focus on one or two species competing under conditions where they may grow exponentially. Field studies, in contrast, emphasize multi-species communities characterized by many types of ecological interactions. A general problem is to understand conditions that support a dynamically maintained coexistence of many species in an ecosystem over a long time span. In the present paper we propose a lattice model of multiple competing and evolving sessile species. When allowing the interspecies interactions to mutate, we obtain coexistence of many species in a complex ecosystem, provided that there is a cost for each interaction. The diversity reached by the model incorporating speciation is found to be substantially higher than in the case when entirely new species appear due to immigration from outside of the considered ecosystem. The species self-organize their spatial distribution through competitive interactions to create many patches, implicitly protecting each other from competitively superior species, and speciation in each patch leads the system to high diversity. We also show that species that exist a long time tend to have a relatively small population, as this allows them to avoid encounter with competitive invaders.

Many toxin-antitoxin operons are regulated by the toxin/antitoxin ratio by mechanisms collectively coined "conditional cooperativity". Toxin and antitoxin form heteromers with different stoichiometric ratios, and the complex with the intermediate ratio works best as a transcription repressor. This allows transcription at low toxin level, strong repression at intermediate toxin level, and then again transcription at high toxin level. Such regulation has two interesting features; firstly, it provides a non-monotonous response to the concentration of one of the proteins, and secondly, it opens for ultra-sensitivity mediated by the sequestration of the functioning heteromers. We explore possible functions of conditional regulation in simple feedback motifs, and show that it can provide bistability for a wide range of parameters. We then demonstrate that the conditional cooperativity in toxin-antitoxin systems combined with the growth-inhibition activity of free toxin can mediate bistability between a growing state and a dormant state.

ABSTRACT Even within similar bacterial strains, it has been found that the clustered, regularly interspaced short palindromic repeat (CRISPR) shows a large variability of spacers. Modeling bacterial strains with different levels of immunity to infection by a single virulent phage, we find that coexistence in a well-mixed environment is possible only when these levels are distinctly different. When bacterial strains are similar, one subpopulation collapses. In the case of bacteria with various levels of CRISPR immunity to a range of phages, small differences in spacer composition will accordingly be suppressed under well-mixed conditions. Using a numerical model of populations spreading in space, we predict that it is the Lamarckian nature of CRISPR evolution that combines with spatial correlations to sustain the experimentally observed distribution of spacer diversity.

Nucleosomes can be covalently modified by addition of various chemical groups on several of their exposed histone amino acids. These modifications are added and removed by enzymes (writers) and can be recognized by nucleosome-binding proteins (readers). Linking a reader domain and a writer domain that recognize and create the same modification state should allow nucleosomes in a particular modification state to recruit enzymes that create that modification state on nearby nucleosomes. This positive feedback has the potential to provide the alternative stable and heritable states required for epigenetic memory. However, analysis of simple histone codes involving interconversions between only two or three types of modified nucleosomes has revealed only a few circuit designs that allow heritable bistability. Here we show by computer simulations that a histone code involving alternative modifications at two histone positions, producing four modification states, combined with reader-writer proteins able to distinguish these states, allows for hundreds of different circuits capable of heritable bistability. These expanded possibilities result from multiple ways of generating two-step cooperativity in the positive feedback--through alternative pathways and an additional, novel cooperativity motif. Our analysis reveals other properties of such epigenetic circuits. They are most robust when the dominant nucleosome types are different at both modification positions and are not the type inserted after DNA replication. The dominant nucleosome types often recruit enzymes that create their own type or destroy the opposing type, but never catalyze their own destruction. The circuits appear to be evolutionary accessible; most circuits can be changed stepwise into almost any other circuit without losing heritable bistability. Thus, our analysis indicates that systems that utilize an expanded histone code have huge potential for generating stable and heritable nucleosome modification states and identifies the critical features of such systems.

Localization of activity is ubiquitous in life, and also within sub-cellular compartments. Localization provides potential advantages as different proteins involved in the same cellular process may supplement each other on a fast timescale. It might also prevent proteins from being active in other regions of the cell. However localization is at odds with the spreading of unbound molecules by diffusion. We model the cost and gain for specific enzyme activity using localization strategies based on binding to sites of intermediate specificity. While such bindings in themselves decrease the activity of the protein on its target site, they may increase protein activity if stochastic motion allows the acting protein to touch both the intermediate binding site and the specific site simultaneously. We discuss this strategy in view of recent suggestions on long non-coding RNA as a facilitator of localized activity of chromatin modifiers.

ABSTRACT Genes of prokaryotes and Archaea are often organized in cotranscribed groups, or operons. In contrast, eukaryotic genes are generally transcribed independently. Here we show that there is a substantial economic gain for the cell to cotranscribe genes encoding protein complexes because it synchronizes the fluctuations, or noise, in the levels of the different components. This correlation substantially reduces the shortfall in production of the complex. This benefit is relatively large in small cells such as bacterial cells, in which there are few mRNAs and proteins per cell, and is diminished in larger cells such as eukaryotic cells.

Pathogens and parasites are ubiquitous in the living world, being limited only by availability of suitable hosts. The ability to transmit a particular disease depends on competing infections as well as on the status of host immunity. Multiple diseases compete for the same resource and their fate is coupled to each other. Such couplings have many facets, for example cross-immunization between related influenza strains, mutual inhibition by killing the host, or possible even a mutual catalytic effect if host immunity is impaired. We here introduce a minimal model for an unlimited number of unrelated pathogens whose interaction is simplified to simple mutual exclusion. The model incorporates an ongoing development of host immunity to past diseases, while leaving the system open for emergence of new diseases. The model exhibits a rich dynamical behavior with interacting infection waves, leaving broad trails of immunization in the host population. This obtained immunization pattern depends only on the system size and on the mutation rate that initiates new diseases.

Gene regulatory networks (GRNs) that make reliable decisions should have design features to cope with random fluctuations in the levels or activities of biological molecules. The phage λ GRN makes a lysis-lysogeny decision informed by the number of phages infecting the cell. To analyse the design of decision making GRNs, we generated random in silico GRNs comprised of two or three transcriptional regulators and selected those able to perform a λ-like decision in the presence of noise. Various two-protein networks analogous to the λ CI-Cro GRN worked in noise-less conditions but failed when noise was introduced. Adding a λ CII-like protein significantly improved robustness to noise. CII relieves the CI-like protein of its 'decider' function, allowing CI to be optimized as a decision 'maintainer'. CII's lysogenic decider function was improved by its instability and rapid removal once the decision was taken, preventing its interference with maintenance. A more reliable decision also resulted from simulated co-transcription of the genes for CII and the Cro-like protein, which correlates fluctuations in these opposing decider functions and makes their ratio less noisy. Thus, the λ decision network contains design features for reducing and resisting noise.

BACKGROUND: Proper cellular function requires uptake of small molecules from the environment. In response to changes in extracellular conditions cells alter the import and utilization of small molecules. For a wide variety of small molecules the cellular response is regulated by a network motif that combines two feedback loops, one which regulates the transport and the other which regulates the subsequent metabolism. RESULTS: We analyze the dynamic behavior of two widespread but logically distinct two-loop motifs. These motifs differ in the logic of the feedback loop regulating the uptake of the small molecule. Our aim is to examine the qualitative features of the dynamics of these two classes of feedback motifs. We find that the negative feedback to transport is accompanied by overshoot in the intracellular amount of small molecules, whereas a positive feedback to transport removes overshoot by boosting the final steady state level. On the other hand, the negative feedback allows for a rapid initial response, whereas the positive feedback is slower. We also illustrate how the dynamical deficiencies of one feedback motif can be mitigated by an additional loop, while maintaining the original steady-state properties. CONCLUSIONS: Our analysis emphasizes the core of the regulation found in many motifs at the interface between the metabolic network and the environment of the cell. By simplifying the regulation into uptake and the first metabolic step, we provide a basis for elaborate studies of more realistic network structures. Particularly, this theoretical analysis predicts that FeS cluster formation plays an important role in the dynamics of iron homeostasis.

Noise in the expression of a gene produces fluctuations in the concentration of the gene product. These fluctuations can interfere with optimal function or can be exploited to generate beneficial diversity between cells; gene expression noise is therefore expected to be subject to evolutionary pressure. Shifts between modes of high and low rates of transcription initiation at a promoter appear to contribute to this noise both in eukaryotes and prokaryotes. However, models invoked for eukaryotic promoter noise such as stable activation scaffolds or persistent nucleosome alterations seem unlikely to apply to prokaryotic promoters. We consider the relative importance of the steps required for transcription initiation. The 3-step transcription initiation model of McClure is extended into a mathematical model that can be used to predict consequences of additional promoter properties. We show in principle that the transcriptional bursting observed at an E. coli promoter by Golding et al. (2005) can be explained by stimulation of initiation by the negative supercoiling behind a transcribing RNA polymerase (RNAP) or by the formation of moribund or dead-end RNAP-promoter complexes. Both mechanisms are tunable by the alteration of promoter kinetics and therefore allow the optimization of promoter mediated noise.

Escherichia coli bacteria respond to DNA damage by a highly orchestrated series of events known as the SOS response, regulated by transcription factors, protein-protein binding, and active protein degradation. We present a dynamical model of the UV-induced SOS response, incorporating mutagenesis by the error-prone polymerase, Pol V. In our model, mutagenesis depends on a combination of two key processes: damage counting by the replication forks and a long-term memory associated with the accumulation of UmuD'. Together, these provide a tight regulation of mutagenesis, resulting, we show, in a "digital" turn-on and turn-off of Pol V. Our model provides a compact view of the topology and design of the SOS network, pinpointing the specific functional role of each of the regulatory processes. In particular, we suggest that the recently observed second peak in the activity of promoters in the SOS regulon (Friedman et al., 2005, PLoS Biology 3(7): e238) is the result of positive feedback from Pol V to RecA filaments.

The relationship between the design and functionality of molecular networks is now a key issue in biology. Comparison of regulatory networks performing similar tasks can provide insights into how network architecture is constrained by the functions it directs. Here, we discuss methods of network comparison based on network architecture and signaling logic. Introducing local and global signaling scores for the difference between two networks, we quantify similarities between evolutionarily closely and distantly related bacteriophages. Despite the large evolutionary separation between phage lambda and 186, their networks are found to be similar when difference is measured in terms of global signaling. We finally discuss how network alignment can be used to pinpoint protein similarities viewed from the network perspective.