Lévy movements and a slowly decaying memory allow efficient collective learning in groups of interacting foragers.

Many animal species benefit from spatial learning to adapt their foraging movements to the distribution of resources. Learning involves the collection, storage and retrieval of information, and depends on both the random search strategies employed and the memory capacities of the individual. For animals living in social groups, spatial learning can be further enhanced by information transfer among group members. However, how individual behavior affects the emergence of collective states of learning is still poorly understood. Here, with the help of a spatially explicit agent-based model where individuals transfer information to their peers, we analyze the effects on the use of resources of varying memory capacities in combination with different exploration strategies, such as ordinary random walks and Lévy flights. We find that individual Lévy displacements associated with a slow memory decay lead to a very rapid collective response, a high group cohesion and to an optimal exploitation of the best resource patches in static but complex environments, even when the interaction rate among individuals is low.

Monitoring lineages of growing and dividing bacteria reveals an inducible memory of mar operon expression.

In Gram negative bacteria, the multiple antibiotic resistance or mar operon, is known to control the expression of multi-drug efflux genes that protect bacteria from a wide range of drugs. As many different chemical compounds can induce this operon, identifying the parameters that govern the dynamics of its induction is crucial to better characterize the processes of tolerance and resistance. Most experiments have assumed that the properties of the mar transcriptional network can be inferred from population measurements. However, measurements from an asynchronous population of cells can mask underlying phenotypic variations of single cells. We monitored the activity of the mar promoter in single Escherichia coli cells in linear micro-colonies and established that the response to a steady level of inducer was most heterogeneous within individual colonies for an intermediate value of inducer. Specifically, sub-lineages defined by contiguous daughter-cells exhibited similar promoter activity, whereas activity was greatly variable between different sub-lineages. Specific sub-trees of uniform promoter activity persisted over several generations. Statistical analyses of the lineages suggest that the presence of these sub-trees is the signature of an inducible memory of the promoter state that is transmitted from mother to daughter cells. This single-cell study reveals that the degree of epigenetic inheritance changes as a function of inducer concentration, suggesting that phenotypic inheritance may be an inducible phenotype.

Resonant learning in scale-free networks.

Large networks of interconnected components, such as genes or machines, can coordinate complex behavioral dynamics. One outstanding question has been to identify the design principles that allow such networks to learn new behaviors. Here, we use Boolean networks as prototypes to demonstrate how periodic activation of network hubs provides a network-level advantage in evolutionary learning. Surprisingly, we find that a network can simultaneously learn distinct target functions upon distinct hub oscillations. We term this emergent property resonant learning, as the new selected dynamical behaviors depend on the choice of the period of the hub oscillations. Furthermore, this procedure accelerates the learning of new behaviors by an order of magnitude faster than without oscillations. While it is well-established that modular network architecture can be selected through evolutionary learning to produce different network behaviors, forced hub oscillations emerge as an alternative evolutionary learning strategy for which network modularity is not necessarily required.

Modeling the role of police corruption in the reduction of organized crime: Mexico as a case study.

Among all types of corruption, police corruption is probably the one that most directly hurts society, as those trusted with protecting the people either side with the criminals that victimize the citizens, or are themselves, criminals. However, both corruption and its effects are very difficult to measure quantitatively other than by perception surveys, but the perception that citizens have of this phenomenon may be different from reality. Using a simple agent-based model, we analyze the effect on crime rates as a result of both corruption and the perception of corruption within law-enforcement corporations. Our results show a phase transition in which crime can propagate across the population even when the majority of police officers are honest. We find that one of the parameters that strongly controls crime incidence is the probability that regular citizens become criminals. In contrast, other actions, such as arresting crime lords, or the amount of crime-associated money that is confiscated, have little impact on the long-term crime incidence. Our results suggest that in addition to combating corruption within law-enforcement institutions, to further reduce the incidence of crime, policymakers should strive to restore confidence in these institutions and the justice system.

Protein concentration fluctuations in the high expression regime: Taylor's law and its mechanistic origin.

Protein concentration in a living cell fluctuates over time due to noise in growth and division processes. In the high expression regime, variance of the protein concentration in a cell was found to scale with the square of the mean, which belongs to a general phenomenon called Taylor's law (TL). To understand the origin for these fluctuations, we measured protein concentration dynamics in single E. coli cells from a set of strains with a variable expression of fluorescent proteins. The protein expression is controlled by a set of constitutive promoters with different strength, which allows to change the expression level over 2 orders of magnitude without introducing noise from fluctuations in transcription regulators. Our data confirms the square TL, but the prefactor A has a cell-to-cell variation independent of the promoter strength. Distributions of the normalized protein concentration for different promoters are found to collapse onto the same curve. To explain these observations, we used a minimal mechanistic model to describe the stochastic growth and division processes in a single cell with a feedback mechanism for regulating cell division. In the high expression regime where extrinsic noise dominates, the model reproduces our experimental results quantitatively. By using a mean-field approximation in the minimal model, we showed that the stochastic dynamics of protein concentration is described by a Langevin equation with multiplicative noise. The Langevin equation has a scale invariance which is responsible for the square TL. By solving the Langevin equation, we obtained an analytical solution for the protein concentration distribution function that agrees with experiments. The solution shows explicitly how the prefactor A depends on strength of different noise sources, which explains its cell-to-cell variability. By using this approach to analyze our single-cell data, we found that the noise in production rate dominates the noise from cell division. The deviation from the square TL in the low expression regime can also be captured in our model by including intrinsic noise in the production rate.

Self-Propulsion Enhances Polymerization.

Self-assembly is a spontaneous process through which macroscopic structures are formed from basic microscopic constituents (e.g., molecules or colloids). By contrast, the formation of large biological molecules inside the cell (such as proteins or nucleic acids) is a process more akin to self-organization than to self-assembly, as it requires a constant supply of external energy. Recent studies have tried to merge self-assembly with self-organization by analyzing the assembly of self-propelled (or active) colloid-like particles whose motion is driven by a permanent source of energy. Here we present evidence that points to the fact that self-propulsion considerably enhances the assembly of polymers: self-propelled molecules are found to assemble faster into polymer-like structures than non self-propelled ones. The average polymer length increases towards a maximum as the self-propulsion force increases. Beyond this maximum, the average polymer length decreases due to the competition between bonding energy and disruptive forces that result from collisions. The assembly of active molecules might have promoted the formation of large pre-biotic polymers that could be the precursors of the informational polymers we observe nowadays.

Phenotype Heritability in Holobionts: An Evolutionary Model.

Many complex diseases are expressed with high incidence only in certain populations. Genealogy studies determine that these diseases are inherited with a high probability. However, genetic studies have been unable to identify the genomic signatures responsible for such heritability, as identifying the genetic variants that make a population prone to a given disease is not enough to explain its high occurrence within the population. This gap is known as the missing heritability problem. We know that the microbiota plays a very important role in determining many important phenotypic characteristics of its host, in particular the complex diseases for which the missing heritability occurs. Therefore, when computing the heritability of a phenotype, it is important to consider not only the genetic variation in the host but also in its microbiota. Here we test this hypothesis by studying an evolutionary model based on gene regulatory networks. Our results show that the holobiont (the host plus its microbiota) is capable of generating a much larger variability than the host alone, greatly reducing the missing heritability of the phenotype. This result strongly suggests that a considerably large part of the missing heritability can be attributed to the microbiome.

Delay in the dispersal of flocks moving in unbounded space using long-range interactions.

Since the pioneering work by Vicsek and his collaborators on the motion of self-propelled particles, most of the subsequent studies have focused on the onset of ordered states through a phase transition driven by particle density and noise. Usually, the particles in these systems are placed within periodic boundary conditions and interact via short-range velocity alignment forces. However, when the periodic boundaries are eliminated, letting the particles move in open space, the system is not able to organize into a coherently moving group since even small amounts of noise cause the flock to break apart. While the phase transition has been thoroughly studied, the conditions to keep the flock cohesive in open space are still poorly understood. Here we extend the Vicsek model of collective motion by introducing long-range alignment interactions between the particles. We show that just a small number of these interactions is enough for the system to build up long lasting ordered states of collective motion in open space and in the presence of noise. This finding was verified for other models in addition to the Vicsek one, suggesting its generality and revealing the importance that long-range interactions can have for the cohesion of the flock.

Modeling the Role of the Microbiome in Evolution.

There is undeniable evidence showing that bacteria have strongly influenced the evolution and biological functions of multicellular organisms. It has been hypothesized that many host-microbial interactions have emerged so as to increase the adaptive fitness of the holobiont (the host plus its microbiota). Although this association has been corroborated for many specific cases, general mechanisms explaining the role of the microbiota in the evolution of the host are yet to be understood. Here we present an evolutionary model in which a network representing the host adapts in order to perform a predefined function. During its adaptation, the host network (HN) can interact with other networks representing its microbiota. We show that this interaction greatly accelerates and improves the adaptability of the HN without decreasing the adaptation of the microbial networks. Furthermore, the adaptation of the HN to perform several functions is possible only when it interacts with many different bacterial networks in a specialized way (each bacterial network participating in the adaptation of one function). Disrupting these interactions often leads to non-adaptive states, reminiscent of dysbiosis, where none of the networks the holobiont consists of can perform their respective functions. By considering the holobiont as a unit of selection and focusing on the adaptation of the host to predefined but arbitrary functions, our model predicts the need for specialized diversity in the microbiota. This structural and dynamical complexity in the holobiont facilitates its adaptation, whereas a homogeneous (non-specialized) microbiota is inconsequential or even detrimental to the holobiont's evolution. To our knowledge, this is the first model in which symbiotic interactions, diversity, specialization and dysbiosis in an ecosystem emerge as a result of coevolution. It also helps us understand the emergence of complex organisms, as they adapt more easily to perform multiple tasks than non-complex ones.

The Human Microbiome and the Missing Heritability Problem.

The "missing heritability" problem states that genetic variants in Genome-Wide Association Studies (GWAS) cannot completely explain the heritability of complex traits. Traditionally, the heritability of a phenotype is measured through familial studies using twins, siblings and other close relatives, making assumptions on the genetic similarities between them. When this heritability is compared to the one obtained through GWAS for the same traits, a substantial gap between both measurements arise with genome wide studies reporting significantly smaller values. Several mechanisms for this "missing heritability" have been proposed, such as epigenetics, epistasis, and sequencing depth. However, none of them are able to fully account for this gap in heritability. In this paper we provide evidence that suggests that in order for the phenotypic heritability of human traits to be broadly understood and accounted for, the compositional and functional diversity of the human microbiome must be taken into account. This hypothesis is based on several observations: (A) The composition of the human microbiome is associated with many important traits, including obesity, cancer, and neurological disorders. (B) Our microbiome encodes a second genome with nearly a 100 times more genes than the human genome, and this second genome may act as a rich source of genetic variation and phenotypic plasticity. (C) Human genotypes interact with the composition and structure of our microbiome, but cannot by themselves explain microbial variation. (D) Microbial genetic composition can be strongly influenced by the host's behavior, its environment or by vertical and horizontal transmissions from other hosts. Therefore, genetic similarities assumed in familial studies may cause overestimations of heritability values. We also propose a method that allows the compositional and functional diversity of our microbiome to be incorporated to genome wide association studies.

Evolving Ecosystems: Inheritance and Selection in the Light of the Microbiome.

The importance of microorganisms in human biology is undeniable. The amount of research that supports that microbes have a fundamental role in animal and plant physiology is substantial and increasing every year. Even though we are only beginning to comprehend the broadness and complexity of microbial communities, evolutionary theories need to be recast in the light of such discoveries to fully understand and incorporate the role of microbes in our evolution. Fundamental evolutionary concepts such as diversity, heredity, selection, speciation, etc., which constitute the modern synthesis, are now being challenged, or at least expanded, by the emerging notion of the holobiont, which defines the genetic and metabolic networks of the host and its microbes as a single evolutionary unit. Several concepts originally developed to study ecosystems, can be used to understand the physiology and evolution of such complex systems that constitute "individuals." In this review, we discuss these ecological concepts and also provide examples that range from squids, insects and koalas to other mammals and humans, suggesting that microorganisms have a fundamental role not only in physiology but also in evolution. Current evolutionary theories need to take into account the dynamics and interconnectedness of the host-microbiome network, as animals and plants not only owe their symbiogenetic origin to microbes, but also share a long evolutionary history together.

Adaptive resistance to antibiotics in bacteria: a systems biology perspective.

Despite all the major breakthroughs in antibiotic development and treatment procedures, there is still no long-term solution to the bacterial antibiotic resistance problem. Among all the known types of resistance, adaptive resistance (AdR) is particularly inconvenient. This phenotype is known to emerge as a consequence of concentration gradients, as well as contact with subinhibitory concentrations of antibiotics, both known to occur in human patients and livestock. Moreover, AdR has been repeatedly correlated with the appearance of multidrug resistance, although the biological processes behind its emergence and evolution are not well understood. Epigenetic inheritance, population structure and heterogeneity, high mutation rates, gene amplification, efflux pumps, and biofilm formation have all been reported as possible explanations for its development. Nonetheless, these concepts taken independently have not been sufficient to prevent AdR's fast emergence or to predict its low stability. New strains of resistant pathogens continue to appear, and none of the new approaches used to kill them (mixed antibiotics, sequential treatments, and efflux inhibitors) are completely efficient. With the advent of systems biology and its toolsets, integrative models that combine experimentally known features with computational simulations have significantly improved our understanding of the emergence and evolution of the adaptive-resistant phenotype. Apart from outlining these findings, we propose that one of the main cornerstones of AdR in bacteria, is the conjunction of two types of mechanisms: one rapidly responding to transient environmental challenges but not very efficient, and another much more effective and specific, but developing on longer time scales. WIREs Syst Biol Med 2016, 8:253-267. doi: 10.1002/wsbm.1335 For further resources related to this article, please visit the WIREs website.

Adaptive resistance in bacteria requires epigenetic inheritance, genetic noise, and cost of efflux pumps.

Adaptive resistance emerges when populations of bacteria are subjected to gradual increases of antibiotics. It is characterized by a rapid emergence of resistance and fast reversibility to the non-resistant phenotype when the antibiotic is removed from the medium. Recent work shows that adaptive resistance requires epigenetic inheritance and heterogeneity of gene expression patterns that are, in particular, associated with the production of porins and efflux pumps. However, the precise mechanisms by which inheritance and variability govern adaptive resistance, and what processes cause its reversibility remain unclear. Here, using an efflux pump regulatory network (EPRN) model, we show that the following three mechanisms are essential to obtain adaptive resistance in a bacterial population: 1) intrinsic variability in the expression of the EPRN transcription factors; 2) epigenetic inheritance of the transcription rate of EPRN associated genes; and 3) energetic cost of the efflux pumps activity that slows down cell growth. While the first two mechanisms acting together are responsible for the emergence and gradual increase of the resistance, the third one accounts for its reversibility. In contrast with the standard assumption, our model predicts that adaptive resistance cannot be explained by increased mutation rates. Our results identify the molecular mechanism of epigenetic inheritance as the main target for therapeutic treatments against the emergence of adaptive resistance. Finally, our theoretical framework unifies known and newly identified determinants such as the burden of efflux pumps that underlie bacterial adaptive resistance to antibiotics.

Criticality is an emergent property of genetic networks that exhibit evolvability.

Accumulating experimental evidence suggests that the gene regulatory networks of living organisms operate in the critical phase, namely, at the transition between ordered and chaotic dynamics. Such critical dynamics of the network permits the coexistence of robustness and flexibility which are necessary to ensure homeostatic stability (of a given phenotype) while allowing for switching between multiple phenotypes (network states) as occurs in development and in response to environmental change. However, the mechanisms through which genetic networks evolve such critical behavior have remained elusive. Here we present an evolutionary model in which criticality naturally emerges from the need to balance between the two essential components of evolvability: phenotype conservation and phenotype innovation under mutations. We simulated the Darwinian evolution of random Boolean networks that mutate gene regulatory interactions and grow by gene duplication. The mutating networks were subjected to selection for networks that both (i) preserve all the already acquired phenotypes (dynamical attractor states) and (ii) generate new ones. Our results show that this interplay between extending the phenotypic landscape (innovation) while conserving the existing phenotypes (conservation) suffices to cause the evolution of all the networks in a population towards criticality. Furthermore, the networks produced by this evolutionary process exhibit structures with hubs (global regulators) similar to the observed topology of real gene regulatory networks. Thus, dynamical criticality and certain elementary topological properties of gene regulatory networks can emerge as a byproduct of the evolvability of the phenotypic landscape.

Pattern recognition in neural networks with competing dynamics: coexistence of fixed-point and cyclic attractors.

We study the properties of the dynamical phase transition occurring in neural network models in which a competition between associative memory and sequential pattern recognition exists. This competition occurs through a weighted mixture of the symmetric and asymmetric parts of the synaptic matrix. Through a generating functional formalism, we determine the structure of the parameter space at non-zero temperature and near saturation (i.e., when the number of stored patterns scales with the size of the network), identifying the regions of high and weak pattern correlations, the spin-glass solutions, and the order-disorder transition between these regions. This analysis reveals that, when associative memory is dominant, smooth transitions appear between high correlated regions and spurious states. In contrast when sequential pattern recognition is stronger than associative memory, the transitions are always discontinuous. Additionally, when the symmetric and asymmetric parts of the synaptic matrix are defined in terms of the same set of patterns, there is a discontinuous transition between associative memory and sequential pattern recognition. In contrast, when the symmetric and asymmetric parts of the synaptic matrix are defined in terms of independent sets of patterns, the network is able to perform both associative memory and sequential pattern recognition for a wide range of parameter values.

Regulatory design governing progression of population growth phases in bacteria.

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

Discrete dynamics model for the speract-activated Ca2+ signaling network relevant to sperm motility.

Understanding how spermatozoa approach the egg is a central biological issue. Recently a considerable amount of experimental evidence has accumulated on the relation between oscillations in intracellular calcium ion concentration ([Ca2+]i) in the sea urchin sperm flagellum, triggered by peptides secreted from the egg, and sperm motility. Determination of the structure and dynamics of the signaling pathway leading to these oscillations is a fundamental problem. However, a biochemically based formulation for the comprehension of the molecular mechanisms operating in the axoneme as a response to external stimulus is still lacking. Based on experiments on the S. purpuratus sea urchin spermatozoa, we propose a signaling network model where nodes are discrete variables corresponding to the pathway elements and the signal transmission takes place at discrete time intervals according to logical rules. The validity of this model is corroborated by reproducing previous empirically determined signaling features. Prompted by the model predictions we performed experiments which identified novel characteristics of the signaling pathway. We uncovered the role of a high voltage-activated Ca2+ channel as a regulator of the delay in the onset of fluctuations after activation of the signaling cascade. This delay time has recently been shown to be an important regulatory factor for sea urchin sperm reorientation. Another finding is the participation of a voltage-dependent calcium-activated K+ channel in the determination of the period of the [Ca2+]i fluctuations. Furthermore, by analyzing the spread of network perturbations we find that it operates in a dynamically critical regime. Our work demonstrates that a coarse-grained approach to the dynamics of the signaling pathway is capable of revealing regulatory sperm navigation elements and provides insight, in terms of criticality, on the concurrence of the high robustness and adaptability that the reproduction processes are predicted to have developed throughout evolution.

Floral morphogenesis: stochastic explorations of a gene network epigenetic landscape.

In contrast to the classical view of development as a preprogrammed and deterministic process, recent studies have demonstrated that stochastic perturbations of highly non-linear systems may underlie the emergence and stability of biological patterns. Herein, we address the question of whether noise contributes to the generation of the stereotypical temporal pattern in gene expression during flower development. We modeled the regulatory network of organ identity genes in the Arabidopsis thaliana flower as a stochastic system. This network has previously been shown to converge to ten fixed-point attractors, each with gene expression arrays that characterize inflorescence cells and primordial cells of sepals, petals, stamens, and carpels. The network used is binary, and the logical rules that govern its dynamics are grounded in experimental evidence. We introduced different levels of uncertainty in the updating rules of the network. Interestingly, for a level of noise of around 0.5-10%, the system exhibited a sequence of transitions among attractors that mimics the sequence of gene activation configurations observed in real flowers. We also implemented the gene regulatory network as a continuous system using the Glass model of differential equations, that can be considered as a first approximation of kinetic-reaction equations, but which are not necessarily equivalent to the Boolean model. Interestingly, the Glass dynamics recover a temporal sequence of attractors, that is qualitatively similar, although not identical, to that obtained using the Boolean model. Thus, time ordering in the emergence of cell-fate patterns is not an artifact of synchronous updating in the Boolean model. Therefore, our model provides a novel explanation for the emergence and robustness of the ubiquitous temporal pattern of floral organ specification. It also constitutes a new approach to understanding morphogenesis, providing predictions on the population dynamics of cells with different genetic configurations during development.

Intrinsic and extrinsic noise effects on phase transitions of network models with applications to swarming systems.

We analyze order-disorder phase transitions driven by noise that occur in two kinds of network models closely related to the self-propelled model proposed by Vicsek [Phys. Rev. Lett. 75, 1226 (1995)] to describe the collective motion of groups of organisms. Two different types of noise, which we call intrinsic and extrinsic, are considered. The intrinsic noise, the one used by Vicsek in their original work, is related to the decision mechanism through which the particles update their positions. In contrast, the extrinsic noise, later introduced by Grégoire and Chaté [Phys. Rev. Lett. 92, 025702 (2004)], affects the signal that the particles receive from the environment. The network models presented here can be considered as mean-field representations of the self-propelled model. We show analytically and numerically that, for these two network models, the phase transitions driven by the intrinsic noise are continuous, whereas the extrinsic noise produces discontinuous phase transitions. This is true even for the small-world topology, which induces strong spatial correlations between the network elements. We also analyze the case where both types of noise are present simultaneously. In this situation, the phase transition can be continuous or discontinuous depending upon the amplitude of each type of noise.