The emergence of complex multicellular systems and their associated developmental programs is one of the major problems of evolutionary biology. The advantages of cooperation over individuality seem well known but it is not clear yet how such increase of complexity emerged from unicellular life forms. Current multicellular systems display a complex cell-cell communication machinery, often tied to large-scale controls of body size or tissue homeostasis. Some unicellular life forms are simpler and involve groups of cells cooperating in a tissue-like fashion, as it occurs with biofilms. However, before true gene regulatory interactions were widespread and allowed for controlled changes in cell phenotypes, simple cellular colonies displaying adhesion and interacting with their environments were in place. In this context, models often ignore the physical embedding of evolving cells, thus leaving aside a key component. The potential for evolving pre-developmental patterns is a relevant issue: how far a colony of evolving cells can go? Here we study these pre-conditions for morphogenesis by using CHIMERA, a physically embodied computational model of evolving virtual organisms in a pre-Mendelian world. Starting from a population of identical, independent cells moving in a fluid, the system undergoes a series of changes, from spatial segregation, increased adhesion and the development of generalism. Eventually, a major transition occurs where a change in the flow of nutrients is triggered by a sub-population. This ecosystem engineering phenomenon leads to a subsequent separation of the ecological network into two well defined compartments. The relevance of these results for evodevo and its potential ecological triggers is discussed.
Catastrophic and sudden collapses of ecosystems are sometimes preceded by early warning signals that potentially could be used to predict and prevent a forthcoming catastrophe. Universality of these early warning signals has been proposed, but no formal proof has been provided. Here, we show that in relatively simple ecological models the most commonly used early warning signals for a catastrophic collapse can be silent. We underpin the mathematical reason for this phenomenon, which involves the direction of the eigenvectors of the system. Our results demonstrate that claims on the universality of early warning signals are not correct, and that catastrophic collapses can occur without prior warning. In order to correctly predict a collapse and determine whether early warning signals precede the collapse, detailed knowledge of the mathematical structure of the approaching bifurcation is necessary. Unfortunately, such knowledge is often only obtained after the collapse has already occurred.
Abrupt changes in dynamics of an ecosystem can sometimes be detected using monitoring data. Using nonparametric methods that assume minimal knowledge of the underlying structure, we compute separate estimates of the drift (deterministic) and diffusion (stochastic) components of a general dynamical process, as well as an indicator of the conditional variance. Theory and simulations show that nonparametric conditional variance rises prior to critical transition. Nonparametric diffusion rises also, in cases where the true diffusion function involves a critical transition (sometimes called a noise-induced transition). Thus it is possible to discriminate noise-induced transitions from other kinds of critical transitions by comparing time series for the conditional variance and the diffusion function. Monte Carlo analysis shows that the indicators generally increase prior to the transition, but uncertainties of the indicators become large as the ecosystem approaches the transition point.
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.
We analyzed the relationship between biodiversity and spatial biomass heterogeneity along an ecological succession developed in the laboratory. Periphyton (attached microalgae) biomass spatial patterns at several successional stages were obtained using digital image analysis and at the same time we estimated the species composition and abundance. We show that the spatial pattern was self-similar and as the community developed in an homogeneous environment the pattern is self-organized. To characterize it we estimated the multifractal spectrum of generalized dimensions Dq. Using Dq we analyze the existence of cycles of heterogeneity during succession and the use of the information dimension D1 as an index of successional stage. We did not find cycles but the values of D1 showed an increasing trend as the succession developed and the biomass was higher. D1 was also negatively correlated with Shannon's diversity. Several studies have found this relationship in different ecosystems but here we prove that the community self-organizes and generates its own spatial heterogeneity influencing diversity. If this is confirmed with more experimental and theoretical evidence D1 could be used as an index, easily calculated from remote sensing data, to detect high or low diversity areas.
As indicated early by Charles Darwin, languages behave and change very much like living species. They display high diversity, differentiate in space and time, emerge and disappear. A large body of literature has explored the role of information exchanges and communicative constraints in groups of agents under selective scenarios. These models have been very helpful in providing a rationale on how complex forms of communication emerge under evolutionary pressures. However, other patterns of large-scale organization can be described using mathematical methods ignoring communicative traits. These approaches consider shorter time scales and have been developed by exploiting both theoretical ecology and statistical physics methods. The models are reviewed here and include extinction, invasion, origination, spatial organization, coexistence and diversity as key concepts and are very simple in their defining rules. Such simplicity is used in order to catch the most fundamental laws of organization and those universal ingredients responsible for qualitative traits. The similarities between observed and predicted patterns indicate that an ecological theory of language is emerging, supporting (on a quantitative basis) its ecological nature, although key differences are also present. Here, we critically review some recent advances and outline their implications and limitations as well as highlight problems for future research.
language dynamics; extinction; diversity; competition; phase transitions
The relapsing-remitting dynamics is a hallmark of autoimmune diseases such as Multiple Sclerosis (MS). Although current understanding of both cellular and molecular mechanisms involved in the pathogenesis of autoimmune diseases is significant, how their activity generates this prototypical dynamics is not understood yet. In order to gain insight about the mechanisms that drive these relapsing-remitting dynamics, we developed a computational model using such biological knowledge. We hypothesized that the relapsing dynamics in autoimmunity can arise through the failure in the mechanisms controlling cross-regulation between regulatory and effector T cells with the interplay of stochastic events (e.g. failure in central tolerance, activation by pathogens) that are able to trigger the immune system.
The model represents five concepts: central tolerance (T-cell generation by the thymus), T-cell activation, T-cell memory, cross-regulation (negative feedback) between regulatory and effector T-cells and tissue damage. We enriched the model with reversible and irreversible tissue damage, which aims to provide a comprehensible link between autoimmune activity and clinical relapses and active lesions in the magnetic resonances studies in patients with Multiple Sclerosis. Our analysis shows that the weakness in this negative feedback between effector and regulatory T-cells, allows the immune system to generate the characteristic relapsing-remitting dynamics of autoimmune diseases, without the need of additional environmental triggers. The simulations show that the timing at which relapses appear is highly unpredictable. We also introduced targeted perturbations into the model that mimicked immunotherapies that modulate effector and regulatory populations. The effects of such therapies happened to be highly dependent on the timing and/or dose, and on the underlying dynamic of the immune system.
The relapsing dynamic in MS derives from the emergent properties of the immune system operating in a pathological state, a fact that has implications for predicting disease course and developing new therapies for MS.
Regardless of genome polarity, intermediaries of complementary sense must be synthesized and used as templates for the production of new genomic strands. Depending on whether these new genomic strands become themselves templates for producing extra antigenomic ones, thus giving rise to geometric growth, or only the firstly synthesized antigenomic strands can be used to this end, thus following Luria's stamping machine model, the abundances and distributions of mutant genomes will be different. Here we propose mathematical and bit string models that allow distinguishing between stamping machine and geometric replication. We have observed that, regardless the topology of the fitness landscape, the critical mutation rate at which the master sequence disappears increases as the mechanism of replication switches from purely geometric to stamping machine. We also found that, for a wide range of mutation rates, large-effect mutations do not accumulate regardless the scheme of replication. However, mild mutations accumulate more in the geometric model. Furthermore, at high mutation rates, geometric growth leads to a population collapse for intermediate values of mutational effects at which the stamping machine still produces master genomes. We observed that the critical mutation rate was weakly dependent on the strength of antagonistic epistasis but strongly dependent on synergistic epistasis. In conclusion, we have shown that RNA viruses may increase their robustness against the accumulation of deleterious mutations by replicating as stamping machines and that the magnitude of this benefit depends on the topology of the fitness landscape assumed.
The ultimate goal of synthetic biology is the conception and construction of genetic circuits that are reliable with respect to their designed function (e.g. oscillators, switches). This task remains still to be attained due to the inherent synergy of the biological building blocks and to an insufficient feedback between experiments and mathematical models. Nevertheless, the progress in these directions has been substantial.
It has been emphasized in the literature that the architecture of a genetic oscillator must include positive (activating) and negative (inhibiting) genetic interactions in order to yield robust oscillations. Our results point out that the oscillatory capacity is not only affected by the interaction polarity but by how it is implemented at promoter level. For a chosen oscillator architecture, we show by means of numerical simulations that the existence or lack of competition between activator and inhibitor at promoter level affects the probability of producing oscillations and also leaves characteristic fingerprints on the associated period/amplitude features.
In comparison with non-competitive binding at promoters, competition drastically reduces the region of the parameters space characterized by oscillatory solutions. Moreover, while competition leads to pulse-like oscillations with long-tail distribution in period and amplitude for various parameters or noisy conditions, the non-competitive scenario shows a characteristic frequency and confined amplitude values. Our study also situates the competition mechanism in the context of existing genetic oscillators, with emphasis on the Atkinson oscillator.
Evolved natural systems are known to display some sort of distributed robustness against the loss of individual components. Such type of robustness is not just the result of redundancy. Instead, it seems to be based on degeneracy, i.e. the ability of elements that are structurally different to perform the same function or yield the same output. Here, we explore the problem of how relevant is degeneracy in a class of evolved digital systems formed by NAND gates, and what types of network structures underlie the resilience of evolved designs to the removal or loss of a given unit. It is shown that our fault tolerant circuits are obtained only if robustness arises in a distributed manner. No such reliable systems were reached just by means of redundancy, thus suggesting that reliable designs are necessarily tied to degeneracy.
evolvable hardware; redundancy; degeneracy; robustness; fault tolerance
Two genes are called synthetic lethal (SL) if mutation of either alone is not lethal, but mutation of both leads to death or a significant decrease in organism's fitness. The detection of SL gene pairs constitutes a promising alternative for anti-cancer therapy. As cancer cells exhibit a large number of mutations, the identification of these mutated genes' SL partners may provide specific anti-cancer drug candidates, with minor perturbations to the healthy cells. Since existent SL data is mainly restricted to yeast screenings, the road towards human SL candidates is limited to inference methods.
In the present work, we use phylogenetic analysis and database manipulation (BioGRID for interactions, Ensembl and NCBI for homology, Gene Ontology for GO attributes) in order to reconstruct the phylogenetically-inferred SL gene network for human. In addition, available data on cancer mutated genes (COSMIC and Cancer Gene Census databases) as well as on existent approved drugs (DrugBank database) supports our selection of cancer-therapy candidates.
Our work provides a complementary alternative to the current methods for drug discovering and gene target identification in anti-cancer research. Novel SL screening analysis and the use of highly curated databases would contribute to improve the results of this methodology.
Modularity is known to be one of the most relevant characteristics of biological systems and appears to be present at multiple scales. Given its adaptive potential, it is often assumed to be the target of selective pressures. Under such interpretation, selection would be actively favouring the formation of modular structures, which would specialize in different functions. Here we show that, within the context of cellular networks, no such selection pressure is needed to obtain modularity. Instead, the intrinsic dynamics of network growth by duplication and diversification is able to generate it for free and explain the statistical features exhibited by small subgraphs. The implications for the evolution and evolvability of both biological and technological systems are discussed.
complex networks; modularity; evolvability; tinkering; network biology
Embryonic development is defined by the hierarchical dynamical process that translates genetic information (genotype) into a spatial gene expression pattern (phenotype) providing the positional information for the correct unfolding of the organism. The nature and evolutionary implications of genotype–phenotype mapping still remain key topics in evolutionary developmental biology (evo-devo). We have explored here issues of neutrality, robustness, and diversity in evo-devo by means of a simple model of gene regulatory networks. The small size of the system allowed an exhaustive analysis of the entire fitness landscape and the extent of its neutrality. This analysis shows that evolution leads to a class of robust genetic networks with an expression pattern characteristic of lateral inhibition. This class is a repertoire of distinct implementations of this key developmental process, the diversity of which provides valuable clues about its underlying causal principles.
The diversity of life is a consequence of changes in the genotype (genes and their interdependence), but it is upon the observable organism's morphology (phenotype) that natural selection acts. Thus, the study of genotype–phenotype mapping can reveal key mechanisms driving life's capacity of continuous evolution and resilience in diverse environments. In this context, it has been observed that small numbers of genes form robust functional developmental modules, hierarchically reused throughout development. Here we analyze the evolution of small genetic modules toward higher diversity and robustness. Given the small size of the gene network, we can afford to analyze all possible topologies and thus the entire fitness landscape. This exhaustive study as well as simulations of evolutionary processes uncover a set of genetic interactions producing robust and diverse phenotypes. We single out the distinctive features of these networks responsible for their stability against environmental and structural perturbations. More precisely, all these robust genotypes can be related to the key mechanism of lateral inhibition for which a cell of a given type inhibits its neighbors to keep them from adopting the same type. Their distinctive features can thus shed light on the underlying mechanisms leading to pattern formation through lateral inhibition.
To satisfy the minimal requirements for life, an information carrying molecular structure must be able to convert resources into building blocks and also be able to adapt to or modify its environment to enhance its own proliferation. Furthermore, new copies of itself must have variable fitness such that evolution is possible. In practical terms, a minimal protocell should be characterized by a strong coupling between its metabolism and genetic subsystem, which is made possible by the container. There is still no general agreement on how such a complex system might have been naturally selected for in a prebiotic environment. However, the historical details are not important for our investigations as they are related to assembling and evolution of protocells in the laboratory. Here, we study three different minimal protocell models of increasing complexity, all of them incorporating the coupling between a ‘genetic template’, a container and, eventually, a toy metabolism. We show that for any local growth law associated with template self-replication, the overall temporal evolution of all protocell's components follows an exponential growth (efficient or uninhibited autocatalysis). Thus, such a system attains exponential growth through coordinated catalytic growth of its component subsystems, independent of the replication efficiency of the involved subsystems. As exponential growth implies the survival of the fittest in a competitive environment, these results suggest that protocell assemblies could be efficient vehicles in terms of evolving through Darwinian selection.
protocell; replicator dynamics; catalytic coupling; prebiotic evolution
The reproduction of a living cell requires a repeatable set of chemical events to be properly coordinated. Such events define a replication cycle, coupling the growth and shape change of the cell membrane with internal metabolic reactions. Although the logic of such process is determined by potentially simple physico-chemical laws, modelling of a full, self-maintained cell cycle is not trivial. Here we present a novel approach to the problem that makes use of so-called symmetry breaking instabilities as the engine of cell growth and division. It is shown that the process occurs as a consequence of the breaking of spatial symmetry and provides a reliable mechanism of vesicle growth and reproduction. Our model opens the possibility of a synthetic protocell lacking information but displaying self-reproduction under a very simple set of chemical reactions.
cells; cell cycle; cell membrane; metabolism; Turing patterns; synthetic biology
The building of minimal self-reproducing systems with a physical embodiment (generically called protocells) is a great challenge, with implications for both theory and applied sciences. Although the classical view of a living protocell assumes that it includes information-carrying molecules as an essential ingredient, a dividing cell-like structure can be built from a metabolism–container coupled system only. An example of such a system, modelled with dissipative particle dynamics, is presented here. This article demonstrates how a simple coupling between a precursor molecule and surfactant molecules forming micelles can experience a growth-division cycle in a predictable manner, and analyses the influence of crucial parameters on this replication cycle. Implications of these results for origins of cellular life and living technology are outlined.
artificial cells; self-replication; micelles; cell division; synthetic biology
Cells are the building blocks of biological complexity. They are complex systems sustained by the coordinated cooperative dynamics of several biochemical networks. Their replication, adaptation and computational features emerge as a consequence of appropriate molecular feedbacks that somehow define what life is. As the last decades have brought the transition from the description-driven biology to the synthesis-driven biology, one great challenge shared by both the fields of bioengineering and the origin of life is to find the appropriate conditions under which living cellular structures can effectively emerge and persist. Here, we review current knowledge (both theoretical and experimental) on possible scenarios of artificial cell design and their future challenges.
cells; cell cycle; cell membrane; metabolism; information; synthetic biology
Biological and technological systems process information by means of cascades of signals. Be they interacting genes, spiking neurons or electronic transistors, information travels across these systems, producing, for each set of external conditions, an appropriate response. In technology, circuits performing specific complex tasks are designed by humans. In biology, however, design has to be ruled out, confronting us with the question of how these systems could have arisen by accumulation of small changes. The key factor is the genotype–phenotype map. With the exception of RNA folding, not much is known about the exact nature of this mapping. Here, we show that structure of the genotype–phenotype map of simple feed-forward circuits is very close to the ones found in RNA; they have a large degree of neutrality, by which a circuit can be completely rewired keeping its input–output function intact, and there is a relatively small neighbourhood of a given circuit containing almost all the phenotypes.
cellular networks; cell signalling; evolution; neutral landscapes
The “survival of the fittest” is the paradigm of Darwinian evolution in which the best-adapted replicators are favored by natural selection. However, at high mutation rates, the fittest organisms are not necessarily the fastest replicators but rather are those that show the greatest robustness against deleterious mutational effects, even at the cost of a low replication rate. This scenario, dubbed the “survival of the flattest”, has so far only been shown to operate in digital organisms. We show that “survival of the flattest” can also occur in biological entities by analyzing the outcome of competition between two viroid species coinfecting the same plant. Under optimal growth conditions, a viroid species characterized by fast population growth and genetic homogeneity outcompeted a viroid species with slow population growth and a high degree of variation. In contrast, the slow-growth species was able to outcompete the fast species when the mutation rate was increased. These experimental results were supported by an in silico model of competing viroid quasispecies.
Darwin's “survival of the fittest” suggests that faster replicators are able to outcompete slower ones. However, when mutation, unavoidably associated with genome replication, is incorporated into the picture, the situation becomes a bit more complicated. At a high mutation rate, being the faster replicator may not always be the best option; in fact, being the more robust against the pernicious effect of mutation may be a better option. If a tradeoff exists between mutational robustness and replication rate—for example, because faster polymerases are more prone to mistakes than slower ones—then selection may favor an organism to replicate faster or to be more robust, but not both at the same time. At a low mutation rate, a faster replicator would displace a robust one. However, beyond a critical mutation rate, the slower replicator should outcompete the faster replicator. This phenomenon is known as the “survival of the flattest”. Here, the authors have confirmed this prediction using a pair of subviral plant pathogens (viroids) competing under normal and mutagenic conditions.
Why are some ecosystems so rich, yet contain so many rare species? High species diversity, together with rarity, is a general trend in neotropical forests and coral reefs. However, the origin of such diversity and the consequences of food web complexity in both species abundances and temporal fluctuations are not well understood. Several regularities are observed in complex, multispecies ecosystems that suggest that these ecologies might be organized close to points of instability. We explore, in greater depth, a recent stochastic model of population dynamics that is shown to reproduce: (i) the scaling law linking species number and connectivity; (ii) the observed distributions of species abundance reported from field studies (showing long tails and thus a predominance of rare species); (iii) the complex fluctuations displayed by natural communities (including chaotic dynamics); and (iv) the species-area relations displayed by rainforest plots. It is conjectured that the conflict between the natural tendency towards higher diversity due to immigration, and the ecosystem level constraints derived from an increasing number of links, leaves the system poised at a critical boundary separating stable from unstable communities, where large fluctuations are expected to occur. We suggest that the patterns displayed by species-rich communities, including rarity, would result from such a spontaneous tendency towards instability.
Biotic recoveries following mass extinctions are characterized by a process in which whole ecologies are reconstructed from low-diversity systems, often characterized by opportunistic groups. The recovery process provides an unexpected window to ecosystem dynamics. In many aspects, recovery is very similar to ecological succession, but important differences are also apparently linked to the innovative patterns of niche construction observed in the fossil record. In this paper, we analyse the similarities and differences between ecological succession and evolutionary recovery to provide a preliminary ecological theory of recoveries. A simple evolutionary model with three trophic levels is presented, and its properties (closely resembling those observed in the fossil record) are compared with characteristic patterns of ecological response to disturbances in continuous models of three-level ecosystems.
The Spanish government recently announced an official fast-track path to citizenship for any individual who is Jewish and whose ancestors were expelled from Spain during the inquisition-related dislocation of Spanish Jews in 1492. It would seem that this policy targets a small subset of the global Jewish population, that is, restricted to individuals who retain cultural practices associated with ancestral origins in Spain. However, the central contribution of this manuscript is to demonstrate how and why the policy is far more likely to apply to a very large fraction (i.e., the vast majority) of Jews. This claim is supported using a series of genealogical models that include transmissible “identities” and preferential intra-group mating. Model analysis reveals that even when intra-group mating is strong and even if only a small subset of a present-day population retains cultural practices typically associated with that of an ancestral group, it is highly likely that nearly all members of that population have direct genealogical links to that ancestral group, given sufficient number of generations have elapsed. The basis for this conclusion is that not having a link to an ancestral group must be a property of all of an individual’s ancestors, the probability of which declines (nearly) superexponentially with each successive generation. These findings highlight unexpected incongruities induced by genealogical dynamics between present-day and ancestral identities.
The effects of habitat fragmentation and their implications for biodiversity is a central issue in conservation biology which still lacks an overall comprehension. There is not yet a clear consensus on how to quantify fragmentation even though it is quite common to couple the effects of habitat loss with habitat fragmentation on biodiversity. Here we address the spatial patterns of species distribution in fragmented landscapes, assuming a neutral community model. To build up the fragmented landscapes, we employ the fractional Brownian motion approach, which in turn permits us to tune the amount of habitat loss and degree of clumping of the landscape independently. The coupling between the neutral community model, here simulated by means of the coalescent method, and fractal neutral landscape models enables us to address how the species–area relationship changes as the spatial patterns of a landscape is varied. The species–area relationship is one of the most fundamental laws in ecology, considered as a central tool in conservation biology, and is used to predict species loss following habitat disturbances. Our simulation results indicate that the level of clumping has a major role in shaping the species–area relationship. For instance, more compact landscapes are more sensitive to the effects of habitat loss and speciation rate. Besides, the level of clumping determines the existence and extension of the power-law regime which is expected to hold at intermediate scales. The distributions of species abundance are strongly influenced by the degree of fragmentation. We also show that the first and second commonest species have approximately self-similar spatial distributions across scales, with the fractal dimensions of the support of the first and second commonest species being very robust to changes in the spatial patterns of the landscape.