Abstract

Based on experimental observations in Daphnia, we introduce an agent-based model for the motion of single and swarms of animals. Each agent is described by a stochastic equation that also considers the conditions for active biological motion. An environmental potential further reflects local conditions for Daphnia, such as attraction to light sources. This model is sufficient to describe the observed cycling behavior of single Daphnia. To simulate vortex swarming of many Daphnia, i.e. the collective rotation of the swarm in one direction, we extend the model by considering avoidance of collisions. Two different ansatzes to model such a behavior are developed and compared. By means of computer simulations of a multi-agent system we show that local avoidance-as a special form of asymmetric repulsion between animals-leads to the emergence of a vortex swarm. The transition from uncorrelated rotation of single agents to the vortex swarming as a function of the swarm size is investigated. Eventually, some evidence of avoidance behavior in Daphnia is provided by comparing experimental and simulation results for two animals.

Abstract

An agent-based approach is used to explain the formation of vortex swarms in biological systems. The dynamics of the multiagent system is described by 3N coupled equations, mod-eling for each agent its position, its velocity and its internal energy depot. The energy depot considers the conditions for active biological motion, such as energy take-up, metabolism, and energy conversion. The equation of motion results from a superposition of deterministic and stochastic terms (random noise). The deterministic part considers indirect interactions with other agents to describe local avoidance behavior, and external influences resulting from an attractive environmental potential. Stochastic computer simulations of the multi-agent system are shown in very good agreement with the behavior observed in Daphnia swarms.

Abstract

Agent-based modeling is a powerful methodology to describe the occurence of complex behavior in biological systems. The interaction of a large number of individuals (agents) may for example lead to the emergence of new forms of collective motion. In this paper, we investigate a particle-based approach to the coherent motion of a swarm with parabolic (i. e. harmonic) interactions between the agents. It is based on generalized Langevin equations for the particle agents, which take into account (i) energetic conditions for active motion, (ii) linear attractive forces between each two agents. The complex collective motion observed can be explained as the result of these different influences: the active motion of the agents, which is driven by the energy-take up, would eventually lead to a spatial dispersion of the swarm, while the mutual interaction of the agents results in a tendency of spatial concentration. In addition to particle-based computer simulations, we also provide a mathematical framework for investigating the collective dynamics.

Abstract

We develop the theory of canonical-dissipative systems, based on the assumption that both the conservative and the dissipative elements of the dynamics are determined by invariants of motion. In this case, known solutions for conservative systems can be used for an extension of the dynamics, which also includes elements such as the take-up/dissipation of energy. This way, a rather complex dynamics can be mapped to an analytically tractable model, while still covering important features of non-equilibrium systems. In our paper, this approach is used to derive a rather general swarm model that considers (a) the energetic conditions of swarming, i.e. for active motion, (b) interactions between the particles based on global couplings. We derive analytical expressions for the non-equilibrium velocity distribution and the mean squared displacement of the swarm. Further, we investigate the influence of different global couplings on the overall behavior of the swarm by means of particle-based computer simulations and compare them with the analytical estimations.

Abstract

We develop an agent-based model of the motion and pattern formation of vesicles. These intracellular particles can be found in four different modes of (undirected and directed) motion and can fuse with other vesicles. While the size of vesicles follows a log-normal distribution that changes over time due to fusion processes, their spatial distribution gives rise to distinct patterns. Their occurrence depends on the concentration of proteins which are synthesized based on the transcriptional activities of some genes. Hence, differences in these spatio-temporal vesicle patterns allow indirect conclusions about the (unknown) impact of these genes. By means of agent-based computer simulations we are able to reproduce such patterns on real temporal and spatial scales. Our modeling approach is based on Brownian agents with an internal degree of freedom, $θ$, that represents the different modes of motion. Conditions inside the cell are modeled by an effective potential that differs for agents dependent on their value $θ$. Agent’s motion in this effective potential is modeled by an overdampted Langevin equation, changes of $θ$ are modeled as stochastic transitions with values obtained from experiments, and fusion events are modeled as space-dependent stochastic transitions. Our results for the spatio-temporal vesicle patterns can be used for a statistical comparison with experiments. We also derive hypotheses of how the silencing of some genes may affect the intracellular transport, and point to generalizations of the model.

Abstract

We revisit a recently proposed agent-based model of active biological motion and compare its predictions with own experimental findings for the speed distribution of bacterial cells, Salmonella typhimurium. Agents move according to a stochastic dynamics and use energy stored in an internal depot for metabolism and active motion. We discuss different assump-tions of how the conversion from internal to kinetic energy d(v) may depend on the actual speed, to conclude that d2v$ξ$ with either $ξ$ = 2 or 1 < $ξ$ < 2 are promising hypotheses. To test these, we compare the model’s prediction with the speed distribution of bacteria which were obtained in media of different nutrient concentration and at different times. We find that both hypotheses are in line with the experimental observations, with $ξ$ between 1.67 and 2.0. Regarding the influence of a higher nutrient concentration, we conclude that the take-up of energy by bacterial cells is indeed increased. But this energy is not used to increase the speed, with 40µm/s as the most probable value of the speed distribution, but is rather spend on metabolism and growth.

Abstract

After summarizing basic features of self-organization such as entropy export, feedbacks and nonlinear dynamics, we discuss several examples in biology. The main part of the paper is devoted to a model of active Brownian motion that allows a stochastic description of the active motion of biological entities based on energy consumption and conversion. This model is applied to the dynamics of swarms with external and interaction potentials. By means of analytical results, we can distiguish between translational, rotational and amoebic modes of swarm motion. We further investigate swarms of active Brownian particles interacting via chemical fields and demonstrate the application of this model to phenomena such as biological aggregation and trail formation in insects.

Abstract

Recently, Markov models of codon substitution have come into the spotlight. By incorporating the structure of the genetic code and the selection intensity at the protein level they provide a more realistic representation of protein-coding sequences than nucleotide or amino acid models. Thus, for protein-coding genes phylogenetic inference is expected to be more accurate under codon models. So far, phylogeny reconstruction under codon models has been elusive due to computational difficulties of dealing with high dimension matrices. Here we present a fast maximum likelihood package for phylogenetic inference, CodonPhyML offering hundreds of different codon models, the largest variety to date, for phylogeny inference by maximum likelihood. CodonPhyML is tested on simulated and real data, and is shown to offer excellent speed and convergence properties. In addition, CodonPhyML includes most recent fast methods for estimating phylogenetic branch supports, and provides an integral framework for models selection, including amino acid and DNA models.

Remarks

Zanetti and Gil contributed equally to the article.

Abstract

An understanding of bacterial diversity and evolution in any environment requires knowledge of phenotypic diversity. In this study, the underlying factors leading to phenotypic clustering were analyzed and interpreted using a novel approach based on a four-tiered graph. Bacterial isolates were organized into equivalence classes based on their phenotypic profile. Likewise, phenotypes were organized in equivalence classes based on the bacteria that manifest them. The linking of these equivalence classes in a four-tiered graph allowed for a quick visual identification of the phenotypic measurements leading to the clustering patterns deduced from principal component analyses. For evaluation of the method, we investigated phenotypic variation in enzyme production and carbon assimilation of members of the genera Pseudomonas and Serratia, isolated from the Aletsch Glacier in Switzerland. The analysis indicates that the genera isolated produce at least six common enzymes and can exploit a wide range of carbon resources, though some specialist species within the pseudomonads were also observed. We further found that pairwise distances between enzyme profiles strongly correlate with distances based on carbon profiles. However, phenotypic distances weakly correlate with phylogenetic distances. The method developed in this study facilitates a more comprehensive understanding of phenotypic clustering than what would be deduced from principal component analysis alone.

Remarks

Miro Svercel, Manuela Filippini and Nicolas Perony contributed equally to the study.

Abstract

We study the collective dynamics of an ensemble of coupled identical FitzHugh-Nagumo elements in their excitable regime. We show that collective firing, where all the elements perform their individual firing cycle synchronously, can be induced by random changes in the interaction pattern. Specifically, on a sparse evolving network where, at any time, each element is connected with at most one partner, collective firing occurs for intermediate values of the rewiring frequency. Thus, network dynamics can play the role of noise and connectivity in inducing this kind of self-organised behaviour in highly disconnected systems which, otherwise, would not allow for the spreading of coherent evolution.

Abstract

Understanding the patterns and processes of diversification of life in the planet is a key challenge of science. The Tree of Life represents such diversification processes through the evolutionary relationships among the different taxa, and can be extended down to intra-specific relationships. Here we examine the topological properties of a large set of interspecific and intraspecific phylogenies and show that the branching patterns follow allometric rules conserved across the different levels in the Tree of Life, all significantly departing from those expected from the standard null models. The finding of non-random universal patterns of phylogenetic differentiation suggests that similar evolutionary forces drive diversification across the broad range of scales, from macro-evolutionary to micro-evolutionary processes, shaping the diversity of life on the planet.