Decay of HCoV-OC43 infectivity is lower in cell debris-containing media than in fresh culture media

In the quantitative description of viral dynamics within cell cultures and, more broadly, in modeling within-host viral infections, a question that commonly arises is whether the degradation of a fraction of the virus could be disregarded in comparison with the massive synthesis of new viral particles. Surprisingly, quantitative data on the synthesis and degradation rates of RNA viruses in cell cultures are scarce. In this study, we investigated the decay of the human betacoronavirus OC43 (HCoV-OC43) infectivity in cell culture lysates and in fresh media. Our findings revealed a significantly slower viral decay rate in the medium containing lysate cells compared to the fresh medium. This observation suggests that the presence of cellular debris from lysed cells may offer protection or stabilize virions, slowing down their degradation. Moreover, the growth rate of HCoV-OC43 infectivity is significantly higher than degradation as long as there are productive cells in the medium, suggesting that, as a first approximation, degradation can be neglected during early infection.

Optimal dispersal and diffusion-enhanced robustness in two-patch metapopulations: origin's saddle-source nature matters

A two-patch logistic metapopulation model is investigated both analytically and numerically focusing on the impact of dispersal on population dynamics. First, the dependence of the global dynamics on the stability type of the full extinction equilibrium point is tackled. Then, the behaviour of the total population with respect to the dispersal is studied analytically. Our findings demonstrate that diffusion plays a crucial role in the preservation of both subpopulations and the full metapopulation under the presence of stochastic perturbations. At low diffusion, the origin is a repulsor, causing the orbits to flow nearly parallel to the axes, risking stochastic extinctions. Higher diffusion turns the repeller into a saddle point. Orbits then quickly converge to the saddle's unstable manifold, reducing extinction chances. This change in the vector field enhances metapopulation robustness. On the other hand, the well-known fact that asymmetric conditions on the patches is beneficial for the total population is further investigated. This phenomenon has been studied in previous works for large enough or small enough values of the dispersal. In this work, we complete the theory for all values of the dispersal. In particular, we derive analytically a formula for the optimal value of the dispersal that maximizes the total population.

Social copying drives a tipping point for nonlinear population collapse

Sudden changes in populations are ubiquitous in ecological systems, especially under perturbations. The agents of global change may increase the frequency and severity of anthropogenic perturbations, but complex populations' responses hamper our understanding of their dynamics and resilience. Furthermore, the long-term environmental and demographic data required to study those sudden changes are rare. Fitting dynamical models with an artificial intelligence algorithm to population fluctuations over 40 y in a social bird reveals that feedback in dispersal after a cumulative perturbation drives a population collapse. The collapse is well described by a nonlinear function mimicking social copying, whereby dispersal made by a few individuals induces others to leave the patch in a behavioral cascade for decision-making to disperse. Once a threshold for deterioration of the quality of the patch is crossed, there is a tipping point for a social response of runaway dispersal corresponding to social copying feedback. Finally, dispersal decreases at low population densities, which is likely due to the unwillingness of the more philopatric individuals to disperse. In providing the evidence of copying for the emergence of feedback in dispersal in a social organism, our results suggest a broader impact of self-organized collective dispersal in complex population dynamics. This has implications for the theoretical study of population and metapopulation nonlinear dynamics, including population extinction, and managing of endangered and harvested populations of social animals subjected to behavioral feedback loops.

Phase transitions in virology

Viruses have established relationships with almost every other living organism on Earth and at all levels of biological organization: from other viruses up to entire ecosystems. In most cases, they peacefully coexist with their hosts, but in most relevant cases, they parasitize them and induce diseases and pandemics, such as the AIDS and the most recent avian influenza and COVID-19 pandemic events, causing a huge impact on health, society, and economy. Viruses play an essential role in shaping the eco-evolutionary dynamics of their hosts, and have been also involved in some of the major evolutionary innovations either by working as vectors of genetic information or by being themselves coopted by the host into their genomes. Viruses can be studied at different levels of biological organization, from the molecular mechanisms of genome replication, gene expression and encapsidation, to global pandemics. All these levels are different and yet connected through the presence of threshold conditions allowing for the formation of a capsid, the loss of genetic information or epidemic spreading. These thresholds, as occurs with temperature separating phases in a liquid, define sharp qualitative types of behaviour. Thesephase transitionsare very well known in physics. They have been studied by means of simple, but powerful models able to capture their essential properties, allowing us to better understand them. Can the physics of phase transitions be an inspiration for our understanding of viral dynamics at different scales? Here we review well-known mathematical models of transition phenomena in virology. We suggest that the advantages of abstract, simplified pictures used in physics are also the key to properly understanding the origins and evolution of complexity in viruses. By means of several examples, we explore this multilevel landscape and how minimal models provide deep insights into a diverse array of problems. The relevance of these transitions in connecting dynamical patterns across scales and their evolutionary and clinical implications are outlined.

Bivalent chromatin as a therapeutic target in cancer: An in silico predictive approach for combining epigenetic drugs

Tumour cell heterogeneity is a major barrier for efficient design of targeted anti-cancer therapies. A diverse distribution of phenotypically distinct tumour-cell subpopulations prior to drug treatment predisposes to non-uniform responses, leading to the elimination of sensitive cancer cells whilst leaving resistant subpopulations unharmed. Few strategies have been proposed for quantifying the variability associated to individual cancer-cell heterogeneity and minimizing its undesirable impact on clinical outcomes. Here, we report a computational approach that allows the rational design of combinatorial therapies involving epigenetic drugs against chromatin modifiers. We have formulated a stochastic model of a bivalent transcription factor that allows us to characterise three different qualitative behaviours, namely: bistable, high- and low-gene expression. Comparison between analytical results and experimental data determined that the so-called bistable and high-gene expression behaviours can be identified with undifferentiated and differentiated cell types, respectively. Since undifferentiated cells with an aberrant self-renewing potential might exhibit a cancer/metastasis-initiating phenotype, we analysed the efficiency of combining epigenetic drugs against the background of heterogeneity within the bistable sub-ensemble. Whereas single-targeted approaches mostly failed to circumvent the therapeutic problems represented by tumour heterogeneity, combinatorial strategies fared much better. Specifically, the more successful combinations were predicted to involve modulators of the histone H3K4 and H3K27 demethylases KDM5 and KDM6A/UTX. Those strategies involving the H3K4 and H3K27 methyltransferases MLL2 and EZH2, however, were predicted to be less effective. Our theoretical framework provides a coherent basis for the development of an in silico platform capable of identifying the epigenetic drugs combinations best-suited to therapeutically manage non-uniform responses of heterogenous cancer cell populations.

Reviewing the reliability of Land Use and Land Cover data in studies relating human health to the environment

BACKGROUND

In recent years, research has been increasingly devoted to understanding the complex human health-environment relationship. Nevertheless, many different measurements have been applied to characterize the environment. Among them, the application of Land Use and Land Cover (LULC) data is becoming more noticeable over time.

AIMS

This research aims to analyse the reliability of Land Use and Land Cover data (LULC) data as a suitable describer of the environment in studies relating human health to the environment. With a specific focus on the methodologies using LULC data, we also examine the study designs and analytical methods that have been commonly performed so far.

MATERIALS AND METHODS

We gathered studies relating human health outcomes to Land Use and Land Cover (LULC) data. A Boolean search limited to reviews was conducted in February 2019 using Web of Science Core Collection search engines. Five reviews were selected as our preliminary starting set of literature and from those, two backward snowballing searches were conducted. The first backward snowballing search used the reference lists of the first 5 reviews and revealed 17 articles. From these, the second search gathered 24 new articles also fulfilling the inclusion criteria established. In total, 41 articles were examined.

RESULTS

Our main results reported that Land Use and Land Cover (LULC) data national level data was preferred over LULC international level data. However, this tendency seems to be strongly related to the specific aims of the articles. They essentially defined the living environment either through buffer zones, using the administrative boundaries wherein the individuals reside, or using the specific location of the individuals assessed. As for the characterization of the environment, authors performed 4 principal methodologies: extracting the percentage of green space, computing the "Land Use mix", recording the type of land cover, and using the percentage of tree canopy. Besides, all the articles included measurements in urban contexts and most of them evaluated the accessibility of individuals to their surroundings. Furthermore, it was clearly stated that the complexity of the topic and the challenging data leads authors to carry out advanced statistical methods and mostly cross-sectional designs with no causal relations.

DISCUSSION AND CONCLUSIONS

Land Use and Land Cover (LULC) data has been demonstrated to be a versatile tool supporting both local-focused studies with few individuals involved and broad territorial-scoped studies with huge populations. Promising synergy has been highlighted between Electronic Health Records (EHR) and LULC data in studies dealing with massive information and broader scopes with regards to the assessment of territorial realities. As this emerging topic matures, investigators should (1) elucidate subjects of ongoing debate such as the measurement of the living environment and its characterization; (2) explore the whole potential of LULC data, using methodologies that encompass both their biophysical and socioeconomic information; (3) perform innovative designs that are able to establish causal relationships among the studied variables (for example, Cellular Automata models), and (4) expand the current set of studied health outcomes leveraging comprehensive and trustworthy health data sources such as EHR.

Increasing temperature alters the within-host competition of viral strains and influences virus genetic variability

Environmental conditions can affect viral accumulation, virulence and adaptation, which have implications in the disease outcomes and efficiency of control measures. Concurrently, mixed viral infections are relevant in plants, being their epidemiology shaped by within-host virus–virus interactions. However, the extent in which the combined effect of variations in abiotic components of the plant ecological niche and the prevalence of mixed infections affect the evolutionary dynamics of viral populations is not well understood. Here, we explore the interplay between ecological and evolutionary factors during viral infections and show that isolates of two strains of Pepino mosaic potexvirus coexisted in tomato plants in a temperature-dependent continuum between neutral and antagonistic interactions. After a long-term infection, the mutational analysis of the evolved viral genomes revealed strain-specific single-nucleotide polymorphisms that were modulated by the interaction between the type of infection and temperature. These results suggest that the temperature is an ecological driver of virus-virus interactions, with an effect on the genetic diversity of individual viruses that are co-infecting an individual host. This research provides insights into the effect that changes in host growth temperatures might have on the evolutionary dynamics of viral populations in mixed infections.

Synthetic soil crusts against green-desert transitions: a spatial model

Semiarid ecosystems are threatened by global warming due to longer dehydration times and increasing soil degradation. Mounting evidence indicates that, given the current trends, drylands are likely to expand and possibly experience catastrophic shifts from vegetated to desert states. Here, we explore a recent suggestion based on the concept of ecosystem terraformation, where a synthetic organism is used to counterbalance some of the nonlinear effects causing the presence of such tipping points. Using an explicit spatial model incorporating facilitation and considering a simplification of states found in semiarid ecosystems including vegetation, fertile and desert soil, we investigate how engineered microorganisms can shape the fate of these ecosystems. Specifically, two different, but complementary, terraformation strategies are proposed: Cooperation-based: C-terraformation; and Dispersion-based: D-terraformation. The first strategy involves the use of soil synthetic microorganisms to introduce cooperative loops (facilitation) with the vegetation. The second one involves the introduction of engineered microorganisms improving their dispersal capacity, thus facilitating the transition from desert to fertile soil. We show that small modifications enhancing cooperative loops can effectively modify the aridity level of the critical transition found at increasing soil degradation rates, also identifying a stronger protection against soil degradation by using the D-terraformation strategy. The same results are found in a mean-field model providing insights into the transitions and dynamics tied to these terraformation strategies. The potential consequences and extensions of these models are discussed.

Host-virus evolutionary dynamics with specialist and generalist infection strategies: Bifurcations, bistability, and chaos

In this work, we have investigated the evolutionary dynamics of a generalist pathogen, e.g., a virus population, that evolves toward specialization in an environment with multiple host types. We have particularly explored under which conditions generalist viral strains may rise in frequency and coexist with specialist strains or even dominate the population. By means of a nonlinear mathematical model and bifurcation analysis, we have determined the theoretical conditions for stability of nine identified equilibria and provided biological interpretation in terms of the infection rates for the viral specialist and generalist strains. By means of a stability diagram, we identified stable fixed points and stable periodic orbits, as well as regions of bistability. For arbitrary biologically feasible initial population sizes, the probability of evolving toward stable solutions is obtained for each point of the analyzed parameter space. This probability map shows combinations of infection rates of the generalist and specialist strains that might lead to equal chances for each type becoming the dominant strategy. Furthermore, we have identified infection rates for which the model predicts the onset of chaotic dynamics. Several degenerate Bogdanov-Takens and zero-Hopf bifurcations are detected along with generalized Hopf and zero-Hopf bifurcations. This manuscript provides additional insights into the dynamical complexity of host-pathogen evolution toward different infection strategies.

Synthetic Biology for Terraformation Lessons from Mars, Earth, and the Microbiome

What is the potential for synthetic biology as a way of engineering, on a large scale, complex ecosystems? Can it be used to change endangered ecological communities and rescue them to prevent their collapse? What are the best strategies for such ecological engineering paths to succeed? Is it possible to create stable, diverse synthetic ecosystems capable of persisting in closed environments? Can synthetic communities be created to thrive on planets different from ours? These and other questions pervade major future developments within synthetic biology. The goal of engineering ecosystems is plagued with all kinds of technological, scientific and ethic problems. In this paper, we consider the requirements for terraformation, i.e., for changing a given environment to make it hospitable to some given class of life forms. Although the standard use of this term involved strategies for planetary terraformation, it has been recently suggested that this approach could be applied to a very different context: ecological communities within our own planet. As discussed here, this includes multiple scales, from the gut microbiome to the entire biosphere.

Noise-induced bistability in the quasi-neutral coexistence of viral RNAs under different replication modes

Evolutionary and dynamical investigations into real viral populations indicate that RNA replication can range between the two extremes represented by so-called 'stamping machine replication' (SMR) and 'geometric replication' (GR). The impact of asymmetries in replication for single-stranded (+) sense RNA viruses has been mainly studied with deterministic models. However, viral replication should be better described by including stochasticity, as the cell infection process is typically initiated with a very small number of RNA macromolecules, and thus largely influenced by intrinsic noise. Under appropriate conditions, deterministic theoretical descriptions of viral RNA replication predict a quasi-neutral coexistence scenario, with a line of fixed points involving different strands' equilibrium ratios depending on the initial conditions. Recent research into the quasi-neutral coexistence in two competing populations reveals that stochastic fluctuations fundamentally alter the mean-field scenario, and one of the two species outcompetes the other. In this article, we study this phenomenon for viral RNA replication modes by means of stochastic simulations and a diffusion approximation. Our results reveal that noise has a strong impact on the amplification of viral RNAs, also causing the emergence of noise-induced bistability. We provide analytical criteria for the dominance of (+) sense strands depending on the initial populations on the line of equilibria, which are in agreement with direct stochastic simulation results. The biological implications of this noise-driven mechanism are discussed within the framework of the evolutionary dynamics of RNA viruses with different modes of replication.

Exploiting delayed transitions to sustain semiarid ecosystems after catastrophic shifts

Semiarid ecosystems (including arid, semiarid and dry-subhumid ecosystems) span more than 40% of extant habitats and contain a similar percentage of the human population. Theoretical models and palaeoclimatic data predict a grim future, with rapid shifts towards a desert state, with accelerated diversity losses and ecological collapses. These shifts are a consequence of the special nonlinearities resulting from ecological facilitation. Here, we investigate a simple model of semiarid ecosystems identifying the so-called ghost, which appears after a catastrophic transition from a vegetated to a desert state once a critical rate of soil degradation is overcome. The ghost involves a slowdown of transients towards the desert state, making the ecosystem seem stable even though vegetation extinction is inevitable. We use this model to show how to exploit the ecological ghosts to avoid collapse. Doing so involves the restoration of small fractions of desert areas with vegetation capable of maintaining a stable community once the catastrophic shift condition has been achieved. This intervention method is successfully tested under the presence of demographic stochastic fluctuations.

Theoretical conditions for the coexistence of viral strains with differences in phenotypic traits: a bifurcation analysis

We investigate the dynamics of a wild-type viral strain which generates mutant strains differing in phenotypic properties for infectivity, virulence and mutation rates. We study, by means of a mathematical model and bifurcation analysis, conditions under which the wild-type and mutant viruses, which compete for the same host cells, can coexist. The coexistence conditions are formulated in terms of the basic reproductive numbers of the strains, a maximum value of the mutation rate and the virulence of the pathogens. The analysis reveals that parameter space can be divided into five regions, each with distinct dynamics, that are organized around degenerate Bogdanov-Takens and zero-Hopf bifurcations, the latter of which gives rise to a curve of transcritical bifurcations of periodic orbits. These results provide new insights into the conditions by which viral populations may contain multiple coexisting strains in a stable manner.

Viral replication modes in single-peak fitness landscapes: A dynamical systems analysis

Positive-sense, single-stranded RNA viruses are important pathogens infecting almost all types of organisms. Experimental evidence from distributions of mutations and from viral RNA amplification suggest that these pathogens may follow different RNA replication modes, ranging from the stamping machine replication (SMR) to the geometric replication (GR) mode. Although previous theoretical work has focused on the evolutionary dynamics of RNA viruses amplifying their genomes with different strategies, little is known in terms of the bifurcations and transitions involving the so-called error threshold (mutation-induced dominance of mutants) and lethal mutagenesis (extinction of all sequences due to mutation accumulation and demographic stochasticity). Here we analyze a dynamical system describing the intracellular amplification of viral RNA genomes evolving on a single-peak fitness landscape focusing on three cases considering neutral, deleterious, and lethal mutants. We analytically derive the critical mutation rates causing lethal mutagenesis and error threshold, governed by transcritical bifurcations that depend on parameters α (parameter introducing the mode of replication), replicative fitness of mutants (k₁), and on the spontaneous degradation rates of the sequences (ϵ). Our results relate the error catastrophe with lethal mutagenesis in a model with continuous populations of viral genomes. The former case involves dominance of the mutant sequences, while the latter, a deterministic extinction of the viral RNAs during replication due to increased mutation. For the lethal case the critical mutation rate involving lethal mutagenesis is μ_c=1-ɛ/α. Here, the SMR involves lower critical mutation rates, being the system more robust to lethal mutagenesis replicating closer to the GR mode. This result is also found for the neutral and deleterious cases, but for these later cases lethal mutagenesis can shift to the error threshold once the replication mode surpasses a threshold given by α=ϵ/k₁.

Finite-time scaling in local bifurcations

Finite-size scaling is a key tool in statistical physics, used to infer critical behavior in finite systems. Here we have made use of the analogous concept of finite-time scaling to describe the bifurcation diagram at finite times in discrete (deterministic) dynamical systems. We analytically derive finite-time scaling laws for two ubiquitous transitions given by the transcritical and the saddle-node bifurcation, obtaining exact expressions for the critical exponents and scaling functions. One of the scaling laws, corresponding to the distance of the dynamical variable to the attractor, turns out to be universal, in the sense that it holds for both bifurcations, yielding the same exponents and scaling function. Remarkably, the resulting scaling behavior in the transcritical bifurcation is precisely the same as the one in the (stochastic) Galton-Watson process. Our work establishes a new connection between thermodynamic phase transitions and bifurcations in low-dimensional dynamical systems, and opens new avenues to identify the nature of dynamical shifts in systems for which only short time series are available.

Population dynamics of synthetic terraformation motifs

Ecosystems are complex systems, currently experiencing several threats associated with global warming, intensive exploitation and human-driven habitat degradation. Because of a general presence of multiple stable states, including states involving population extinction, and due to the intrinsic nonlinearities associated with feedback loops, collapse in ecosystems could occur in a catastrophic manner. It has been recently suggested that a potential path to prevent or modify the outcome of these transitions would involve designing synthetic organisms and synthetic ecological interactions that could push these endangered systems out of the critical boundaries. In this paper, we investigate the dynamics of the simplest mathematical models associated with four classes of ecological engineering designs, named Terraformation motifs (TMs). These TMs put in a nutshell different ecological strategies. In this context, some fundamental types of bifurcations pervade the systems' dynamics. Mutualistic interactions can enhance persistence of the systems by means of saddle-node bifurcations. The models without cooperative interactions show that ecosystems achieve restoration through transcritical bifurcations. Thus, our analysis of the models allows us to define the stability conditions and parameter domains where these TMs must work.

Noise-induced bistability in the fate of cancer phenotypic quasispecies: a bit-strings approach

Tumor cell populations are highly heterogeneous. Such heterogeneity, both at genotypic and phenotypic levels, is a key feature during tumorigenesis. How to investigate the impact of this heterogeneity in the dynamics of tumors cells becomes an important issue. Here we explore a stochastic model describing the competition dynamics between a pool of heterogeneous cancer cells with distinct phenotypes and healthy cells. This model is used to explore the role of demographic fluctuations on the transitions involving tumor clearance. Our results show that for large population sizes, when demographic fluctuations are negligible, there exists a sharp transition responsible for tumor cells extinction at increasing tumor cells' mutation rates. This result is consistent with a mean field model developed for the same system. The mean field model reveals only monostability scenarios, in which either the dominance of the tumor cells or the dominance of the healthy cells is found. Interestingly, the stochastic model shows that for small population sizes the monostability behavior disappears, involving the presence of noise-induced bistability. The impact of the initial populations of cells in the fate of the cell populations is investigated, as well as the transient times towards the healthy and the cancer states.

Trans-heteroclinic bifurcation: a novel type of catastrophic shift

Global and local bifurcations are extremely important since they govern the transitions between different qualitative regimes in dynamical systems. These transitions or tipping points, which are ubiquitous in nature, can be smooth or catastrophic. Smooth transitions involve a continuous change in the steady state of the system until the bifurcation value is crossed, giving place to a second-order phase transition. Catastrophic transitions involve a discontinuity of the steady state at the bifurcation value, giving place to first-order phase transitions. Examples of catastrophic shifts can be found in ecosystems, climate, economic or social systems. Here we report a new type of global bifurcation responsible for a catastrophic shift. This bifurcation, identified in a family of quasi-species equations and named as trans-heteroclinic bifurcation, involves an exchange of stability between two distant and heteroclinically connected fixed points. Since the two fixed points interchange the stability without colliding, a catastrophic shift takes place. We provide an exhaustive description of this new bifurcation, also detailing the structure of the replication-mutation matrix of the quasi-species equation giving place to this bifurcation. A perturbation analysis is provided around the bifurcation value. At this value the heteroclinic connection is replaced by a line of fixed points in the quasi-species model. But it is shown that, if the replication-mutation matrix satisfies suitable conditions, then, under a small perturbation, the exchange of heteroclinic connections is preserved, except on a tiny range around the bifurcation value whose size is of the order of magnitude of the perturbation. The results presented here can help to understand better novel mechanisms behind catastrophic shifts and contribute to a finer identification of such transitions in theoretical models in evolutionary biology and other dynamical systems.

Predicting the Stability of Homologous Gene Duplications in a Plant RNA Virus

One of the striking features of many eukaryotes is the apparent amount of redundancy in coding and non-coding elements of their genomes. Despite the possible evolutionary advantages, there are fewer examples of redundant sequences in viral genomes, particularly those with RNA genomes. The factors constraining the maintenance of redundant sequences in present-day RNA virus genomes are not well known. Here, we use Tobacco etch virus, a plant RNA virus, to investigate the stability of genetically redundant sequences by generating viruses with potentially beneficial gene duplications. Subsequently, we tested the viability of these viruses and performed experimental evolution. We found that all gene duplication events resulted in a loss of viability or in a significant reduction in viral fitness. Moreover, upon analyzing the genomes of the evolved viruses, we always observed the deletion of the duplicated gene copy and maintenance of the ancestral copy. Interestingly, there were clear differences in the deletion dynamics of the duplicated gene associated with the passage duration and the size and position of the duplicated copy. Based on the experimental data, we developed a mathematical model to characterize the stability of genetically redundant sequences, and showed that fitness effects are not enough to predict genomic stability. A context-dependent recombination rate is also required, with the context being the duplicated gene and its position. Our results therefore demonstrate experimentally the deleterious nature of gene duplications in RNA viruses. Beside previously described constraints on genome size, we identified additional factors that reduce the likelihood of the maintenance of duplicated genes.

Abrupt transitions to tumor extinction: a phenotypic quasispecies model

The dynamics of heterogeneous tumor cell populations competing with healthy cells is an important topic in cancer research with deep implications in biomedicine. Multitude of theoretical and computational models have addressed this issue, especially focusing on the nature of the transitions governing tumor clearance as some relevant model parameters are tuned. In this contribution, we analyze a mathematical model of unstable tumor progression using the quasispecies framework. Our aim is to define a minimal model incorporating the dynamics of competition between healthy cells and a heterogeneous population of cancer cell phenotypes involving changes in replication-related genes (i.e., proto-oncogenes and tumor suppressor genes), in genes responsible for genomic stability, and in house-keeping genes. Such mutations or loss of genes result into different phenotypes with increased proliferation rates and/or increased genomic instabilities. Despite bifurcations in the classical deterministic quasispecies model are typically given by smooth, continuous shifts (i.e., transcritical bifurcations), we here identify a novel type of bifurcation causing an abrupt transition to tumor extinction. Such a bifurcation, named as trans-heteroclinic, is characterized by the exchange of stability between two distant fixed points (that do not collide) involving tumor persistence and tumor clearance. The increase of mutation and/or the decrease of the replication rate of tumor cells involves this catastrophic shift of tumor cell populations. The transient times near bifurcation thresholds are also characterized, showing a power law dependence of exponent [Formula: see text] of the transients as mutation is changed near the bifurcation value. These results are discussed in the context of targeted cancer therapy as a possible therapeutic strategy to force a catastrophic shift by simultaneously delivering mutagenic and cytotoxic drugs inside tumor cells.

How Complex, Probable, and Predictable is Genetically Driven Red Queen Chaos?

Coevolution between two antagonistic species has been widely studied theoretically for both ecologically- and genetically-driven Red Queen dynamics. A typical outcome of these systems is an oscillatory behavior causing an endless series of one species adaptation and others counter-adaptation. More recently, a mathematical model combining a three-species food chain system with an adaptive dynamics approach revealed genetically driven chaotic Red Queen coevolution. In the present article, we analyze this mathematical model mainly focusing on the impact of species rates of evolution (mutation rates) in the dynamics. Firstly, we analytically proof the boundedness of the trajectories of the chaotic attractor. The complexity of the coupling between the dynamical variables is quantified using observability indices. By using symbolic dynamics theory, we quantify the complexity of genetically driven Red Queen chaos computing the topological entropy of existing one-dimensional iterated maps using Markov partitions. Co-dimensional two bifurcation diagrams are also built from the period ordering of the orbits of the maps. Then, we study the predictability of the Red Queen chaos, found in narrow regions of mutation rates. To extend the previous analyses, we also computed the likeliness of finding chaos in a given region of the parameter space varying other model parameters simultaneously. Such analyses allowed us to compute a mean predictability measure for the system in the explored region of the parameter space. We found that genetically driven Red Queen chaos, although being restricted to small regions of the analyzed parameter space, might be highly unpredictable.

Computational implementation of a tunable multicellular memory circuit for engineered eukaryotic consortia

Cells are complex machines capable of processing information by means of an entangled network of molecular interactions. A crucial component of these decision-making systems is the presence of memory and this is also a specially relevant target of engineered synthetic systems. A classic example of memory devices is a 1-bit memory element known as the flip-flop. Such system can be in principle designed using a single-cell implementation, but a direct mapping between standard circuit design and a living circuit can be cumbersome. Here we present a novel computational implementation of a 1-bit memory device using a reliable multicellular design able to behave as a set-reset flip-flop that could be implemented in yeast cells. The dynamics of the proposed synthetic circuit is investigated with a mathematical model using biologically-meaningful parameters. The circuit is shown to behave as a flip-flop in a wide range of parameter values. The repression strength for the NOT logics is shown to be crucial to obtain a good flip-flop signal. Our model also shows that the circuit can be externally tuned to achieve different memory states and dynamics, such as persistent and transient memory. We have characterized the parameter domains for robust memory storage and retrieval as well as the corresponding time response dynamics.

Bifurcations analysis of oscillating hypercycles

We investigate the dynamics and transitions to extinction of hypercycles governed by periodic orbits. For a large enough number of hypercycle species (n>4) the existence of a stable periodic orbit has been previously described, showing an apparent coincidence of the vanishing of the periodic orbit with the value of the replication quality factor Q where two unstable (non-zero) equilibrium points collide (named QSS). It has also been reported that, for values below QSS, the system goes to extinction. In this paper, we use a suitable Poincaré map associated to the hypercycle system to analyze the dynamics in the bistability regime, where both oscillatory dynamics and extinction are possible. The stable periodic orbit is identified, together with an unstable periodic orbit. In particular, we are able to unveil the vanishing mechanism of the oscillatory dynamics: a saddle-node bifurcation of periodic orbits as the replication quality factor, Q, undergoes a critical fidelity threshold, QPO. The identified bifurcation involves the asymptotic extinction of all hypercycle members, since the attractor placed at the origin becomes globally stable for values Q<QPO. Near the bifurcation, these extinction dynamics display a periodic remnant that provides the system with an oscillating delayed transition. Surprisingly, we found that the value of QPO is slightly higher than QSS, thus identifying a gap in the parameter space where the oscillatory dynamics has vanished while the unstable equilibrium points are still present. We also identified a degenerate bifurcation of the unstable periodic orbits for Q=1.

Can a minimal replicating construct be identified as the embodiment of cancer?

Genomic instability is a hallmark of cancer. Cancer cells that exhibit abnormal chromosomes are characteristic of most advanced tumours, despite the potential threat represented by accumulated genetic damage. Carcinogenesis involves a loss of key components of the genetic and signalling molecular networks; hence some authors have suggested that this is part of a trend of cancer cells to behave as simple, minimal replicators. In this study, we explore this conjecture and suggest that, in the case of cancer, genomic instability has an upper limit that is associated with a minimal cancer cell network. Such a network would include (for a given microenvironment) the basic molecular components that allow cells to replicate and respond to selective pressures. However, it would also exhibit internal fragilities that could be exploited by appropriate therapies targeting the DNA repair machinery. The implications of this hypothesis are discussed.

Tempo and mode of plant RNA virus escape from RNA interference-mediated resistance

A biotechnological application of artificial microRNAs (amiRs) is the generation of plants that are resistant to virus infection. This resistance has proven to be highly effective and sequence specific. However, before these transgenic plants can be deployed in the field, it is important to evaluate the likelihood of the emergence of resistance-breaking mutants. Two issues are of particular interest: (i) whether such mutants can arise in nontransgenic plants that may act as reservoirs and (ii) whether a suboptimal expression level of the transgene, resulting in subinhibitory concentrations of the amiR, would favor the emergence of escape mutants. To address the first issue, we experimentally evolved independent lineages of Turnip mosaic virus (TuMV) (family Potyviridae) in fully susceptible wild-type Arabidopsis thaliana plants and then simulated the spillover of the evolving virus to fully resistant A. thaliana transgenic plants. To address the second issue, the evolution phase took place with transgenic plants that expressed the amiR at subinhibitory concentrations. Our results show that TuMV populations replicating in susceptible hosts accumulated resistance-breaking alleles that resulted in the overcoming of the resistance of fully resistant plants. The rate at which resistance was broken was 7 times higher for TuMV populations that experienced subinhibitory concentrations of the antiviral amiR. A molecular characterization of escape alleles showed that they all contained at least one nucleotide substitution in the target sequence, generally a transition of the G-to-A and C-to-U types, with many instances of convergent molecular evolution. To better understand the viral population dynamics taking place within each host, as well as to evaluate relevant population genetic parameters, we performed in silico simulations of the experiments. Together, our results contribute to the rational management of amiR-based antiviral resistance in plants.

Quasispecies spatial models for RNA viruses with different replication modes and infection strategies

Empirical observations and theoretical studies suggest that viruses may use different replication strategies to amplify their genomes, which impact the dynamics of mutation accumulation in viral populations and therefore, their fitness and virulence. Similarly, during natural infections, viruses replicate and infect cells that are rarely in suspension but spatially organized. Surprisingly, most quasispecies models of virus replication have ignored these two phenomena. In order to study these two viral characteristics, we have developed stochastic cellular automata models that simulate two different modes of replication (geometric vs stamping machine) for quasispecies replicating and spreading on a two-dimensional space. Furthermore, we explored these two replication models considering epistatic fitness landscapes (antagonistic vs synergistic) and different scenarios for cell-to-cell spread, one with free superinfection and another with superinfection inhibition. We found that the master sequences for populations replicating geometrically and with antagonistic fitness effects vanished at low critical mutation rates. By contrast, the highest critical mutation rate was observed for populations replicating geometrically but with a synergistic fitness landscape. Our simulations also showed that for stamping machine replication and antagonistic epistasis, a combination that appears to be common among plant viruses, populations further increased their robustness by inhibiting superinfection. We have also shown that the mode of replication strongly influenced the linkage between viral loci, which rapidly reached linkage equilibrium at increasing mutations for geometric replication. We also found that the strategy that minimized the time required to spread over the whole space was the stamping machine with antagonistic epistasis among mutations. Finally, our simulations revealed that the multiplicity of infection fluctuated but generically increased along time.

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.

Dynamics of a plant RNA virus intracellular accumulation: stamping machine vs. geometric replication

The tremendous evolutionary potential of RNA viruses allows them to thrive despite host defense mechanisms and endows them with properties such as emergence, host switching, and virulence. The frequency of mutant viruses after an infectious process results from the interplay between the error rate of the viral replicase, from purifying mechanisms acting after transcription on aberrant RNAs, and from the amplification dynamics of virus RNA positive (+) and negative (-) strands. Two extreme scenarios describing viral RNA amplification are the geometric growth, in which each RNA strand serves as template for the synthesis of complementary strands with the same efficiency, and the stamping machine, where a strand is reiteratively used as template to synthesize multiple copies of the complementary. The resulting mutation frequencies are completely different, being geometric growth largely more mutagenic than stamping machine. In this work we evaluate the contribution of geometric growth and stamping machine to the overall genome amplification of the plant (+)-strand RNA virus turnip mosaic virus (TuMV). By means of transfection experiments of Nicotiana benthamiana protoplasts with a TuMV cDNA infectious clone and by using strand-specific quantitative real-time PCR, we determined the amplification dynamics of viral (+) and (-) RNA during a single-cell infectious process. A mathematical model describing the amplification of each viral strand was fitted to the data. Analyses of the model parameters showed that TuMV (+) and (-) RNA amplification occurs through a mixed strategy with ∼93% of genomes produced via stamping machine and only ∼7% resulting from geometric growth.

Differences in accumulation and virulence determine the outcome of competition during Tobacco etch virus coinfection

Understanding the evolution of virulence for RNA viruses is essential for developing appropriate control strategies. Although it has been usually assumed that virulence is a consequence of within-host replication of the parasite, viral strains may be highly virulent without experiencing large accumulation as a consequence of immunopathological host responses. Using two strains of Tobacco etch potyvirus (TEV) that show a negative relationship between virulence and accumulation rate, we first explored the evolution of virulence and fitness traits during simple and mixed infections. Short-term evolution experiments initiated with each strain independently confirmed the genetic and evolutionary stability of virulence and viral load, although infectivity significantly increased for both strains. Second, competition experiments between hypo- and hypervirulent TEV strains have shown that the outcome of competition is driven by differences in replication rate. A simple mathematical model has been developed to analyze the dynamics of these two strains during coinfection. The model qualitatively reproduced the experimental results using biologically meaningful parameters. Further analyses of the model also revealed a wide parametric region in which a low-fitness but hypovirulent virus can still outcompete a high-fitness but hypervirulent one. These results provide additional support to the observation that virulence and within-host replication may not necessarily be strongly tied in plant RNA viruses.

Quantifying chaos for ecological stoichiometry

The theory of ecological stoichiometry considers ecological interactions among species with different chemical compositions. Both experimental and theoretical investigations have shown the importance of species composition in the outcome of the population dynamics. A recent study of a theoretical three-species food chain model considering stoichiometry [B. Deng and I. Loladze, Chaos 17, 033108 (2007)] shows that coexistence between two consumers predating on the same prey is possible via chaos. In this work we study the topological and dynamical measures of the chaotic attractors found in such a model under ecological relevant parameters. By using the theory of symbolic dynamics, we first compute the topological entropy associated with unimodal Poincaré return maps obtained by Deng and Loladze from a dimension reduction. With this measure we numerically prove chaotic competitive coexistence, which is characterized by positive topological entropy and positive Lyapunov exponents, achieved when the first predator reduces its maximum growth rate, as happens at increasing δ1. However, for higher values of δ1 the dynamics become again stable due to an asymmetric bubble-like bifurcation scenario. We also show that a decrease in the efficiency of the predator sensitive to prey's quality (increasing parameter ζ) stabilizes the dynamics. Finally, we estimate the fractal dimension of the chaotic attractors for the stoichiometric ecological model.

Simple genomes, complex interactions: epistasis in RNA virus

Owed to their reduced size and low number of proteins encoded, RNA viruses and other subviral pathogens are often considered as being genetically too simple. However, this structural simplicity also creates the necessity for viral RNA sequences to encode for more than one protein and for proteins to carry out multiple functions, all together resulting in complex patterns of genetic interactions. In this work we will first review the experimental studies revealing that the architecture of viral genomes is dominated by antagonistic interactions among loci. Second, we will also review mathematical models and provide a description of computational tools for the study of RNA virus dynamics and evolution. As an application of these tools, we will finish this review article by analyzing a stochastic bit-string model of in silico virus replication. This model analyzes the interplay between epistasis and the mode of replication on determining the population load of deleterious mutations. The model suggests that, for a given mutation rate, the deleterious mutational load is always larger when epistasis is predominantly antagonistic than when synergism is the rule. However, the magnitude of this effect is larger if replication occurs geometrically than if it proceeds linearly.

Chaos and crises in a model for cooperative hunting: a symbolic dynamics approach

In this work we investigate the population dynamics of cooperative hunting extending the McCann and Yodzis model for a three-species food chain system with a predator, a prey, and a resource species. The new model considers that a given fraction sigma of predators cooperates in prey's hunting, while the rest of the population 1-sigma hunts without cooperation. We use the theory of symbolic dynamics to study the topological entropy and the parameter space ordering of the kneading sequences associated with one-dimensional maps that reproduce significant aspects of the dynamics of the species under several degrees of cooperative hunting. Our model also allows us to investigate the so-called deterministic extinction via chaotic crisis and transient chaos in the framework of cooperative hunting. The symbolic sequences allow us to identify a critical boundary in the parameter spaces (K,C(0)) and (K,sigma) which separates two scenarios: (i) all-species coexistence and (ii) predator's extinction via chaotic crisis. We show that the crisis value of the carrying capacity K(c) decreases at increasing sigma, indicating that predator's populations with high degree of cooperative hunting are more sensitive to the chaotic crises. We also show that the control method of Dhamala and Lai [Phys. Rev. E 59, 1646 (1999)] can sustain the chaotic behavior after the crisis for systems with cooperative hunting. We finally analyze and quantify the inner structure of the target regions obtained with this control method for wider parameter values beyond the crisis, showing a power law dependence of the extinction transients on such critical parameters.

Bifurcations and phase transitions in spatially extended two-member hypercycles

Mounting theoretical and experimental evidence indicates that the success of molecular replicators is strongly tied to the local nature of their interactions. Local dispersal in a given spatial domain, particularly on surfaces, might strongly enhance the growth and selection of fit molecules and their resistance to parasites. In this work the spatial dynamics of a simple hypercycle model consisting of two molecular species is analysed. In order to characterize it, both mean field models and stochastic, spatially explicit approaches are considered. The mean field approach predicts the presence of a saddle-node bifurcation separating a phase involving stable hypercycles from extinction, consistently with spatially explicit models, where an absorbing first-order phase transition is shown to exist and diffusion is explicitly introduced. The saddle-node bifurcation is shown to leave a ghost in the phase plane. A metapopulation-based model is also developed in order to account for the observed phases when both diffusion and reaction are considered. The role of information and diffusion as well as the relevance of these phases and the underlying spatial structures are discussed, and their potential implications for the evolution of early replicators are outlined.

Information catastrophe in RNA viruses through replication thresholds

RNA viruses are known to replicate at very high mutation rates. These rates are actually known to be close to their so-called error threshold. This threshold is in fact a critical point beyond which genetic information is lost through a so-called error catastrophe. However, the transition from a stable quasispecies to genetic drift and loss of information can also occur by crossing replication thresholds, below some replication rates, the viral population is suddenly unable to survive. Available data from hepatitis C virus population analysis [Mas, A., Ulloa, E., Bruguera, M., Furcić, I., Garriga, D., Fábregas, S., Andreu, D., Saiz, J.C., Díez, J., 2004. Hepatitis C virus population analysis of a single-source nosocomial outbreak reveals an inverse correlation between viral load and quasispecies complexity. J. Gen. Virol. 85, 3619-3626] can be interpreted through this theoretical view, providing evidence for such a replication threshold. Here a simple model is used in order to provide evidence for such a phenomenon, consistent with available data.