97 research outputs found
Ergodic directional switching in mobile insect groups
We obtain a Fokker-Planck equation describing experimental data on the
collective motion of locusts. The noise is of internal origin and due to the
discrete character and finite number of constituents of the swarm. The
stationary probability distribution shows a rich phenomenology including
non-monotonic behavior of several order/disorder transition indicators in noise
intensity. This complex behavior arises naturally as a result of the randomness
in the system. Its counterintuitive character challenges standard
interpretations of noise induced transitions and calls for an extension of this
theory in order to capture the behavior of certain classes of biologically
motivated models. Our results suggest that the collective switches of the
group's direction of motion might be due to a random ergodic effect and, as
such, they are inherent to group formation.Comment: Physical Review Focus 26, July 201
Multiscale Computations on Neural Networks: From the Individual Neuron Interactions to the Macroscopic-Level Analysis
We show how the Equation-Free approach for multi-scale computations can be
exploited to systematically study the dynamics of neural interactions on a
random regular connected graph under a pairwise representation perspective.
Using an individual-based microscopic simulator as a black box coarse-grained
timestepper and with the aid of simulated annealing we compute the
coarse-grained equilibrium bifurcation diagram and analyze the stability of the
stationary states sidestepping the necessity of obtaining explicit closures at
the macroscopic level. We also exploit the scheme to perform a rare-events
analysis by estimating an effective Fokker-Planck describing the evolving
probability density function of the corresponding coarse-grained observables
Equation-Free Analysis of Two-Component System Signalling Model Reveals the Emergence of Co-Existing Phenotypes in the Absence of Multistationarity
Phenotypic differences of genetically identical cells under the same environmental conditions have been attributed to the inherent stochasticity of biochemical processes. Various mechanisms have been suggested, including the existence of alternative steady states in regulatory networks that are reached by means of stochastic fluctuations, long transient excursions from a stable state to an unstable excited state, and the switching on and off of a reaction network according to the availability of a constituent chemical species. Here we analyse a detailed stochastic kinetic model of two-component system signalling in bacteria, and show that alternative phenotypes emerge in the absence of these features. We perform a bifurcation analysis of deterministic reaction rate equations derived from the model, and find that they cannot reproduce the whole range of qualitative responses to external signals demonstrated by direct stochastic simulations. In particular, the mixed mode, where stochastic switching and a graded response are seen simultaneously, is absent. However, probabilistic and equation-free analyses of the stochastic model that calculate stationary states for the mean of an ensemble of stochastic trajectories reveal that slow transcription of either response regulator or histidine kinase leads to the coexistence of an approximate basal solution and a graded response that combine to produce the mixed mode, thus establishing its essential stochastic nature. The same techniques also show that stochasticity results in the observation of an all-or-none bistable response over a much wider range of external signals than would be expected on deterministic grounds. Thus we demonstrate the application of numerical equation-free methods to a detailed biochemical reaction network model, and show that it can provide new insight into the role of stochasticity in the emergence of phenotypic diversity
Partial differential equations for self-organization in cellular and developmental biology
Understanding the mechanisms governing and regulating the emergence of structure and heterogeneity within cellular systems, such as the developing embryo, represents a multiscale challenge typifying current integrative biology research, namely, explaining the macroscale behaviour of a system from microscale dynamics. This review will focus upon modelling how cell-based dynamics orchestrate the emergence of higher level structure. After surveying representative biological examples and the models used to describe them, we will assess how developments at the scale of molecular biology have impacted on current theoretical frameworks, and the new modelling opportunities that are emerging as a result. We shall restrict our survey of mathematical approaches to partial differential equations and the tools required for their analysis. We will discuss the gap between the modelling abstraction and biological reality, the challenges this presents and highlight some open problems in the field
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Overview of mathematical approaches used to model bacterial chemotaxis I: the single cell
Mathematical modeling of bacterial chemotaxis systems has been influential and insightful in helping to understand experimental observations. We provide here a comprehensive overview of the range of mathematical approaches used for modeling, within a single bacterium, chemotactic processes caused by changes to external gradients in its environment. Specific areas of the bacterial system which have been studied and modeled are discussed in detail, including the modeling of adaptation in response to attractant gradients, the intracellular phosphorylation cascade, membrane receptor clustering, and spatial modeling of intracellular protein signal transduction. The importance of producing robust models that address adaptation, gain, and sensitivity are also discussed. This review highlights that while mathematical modeling has aided in understanding bacterial chemotaxis on the individual cell scale and guiding experimental design, no single model succeeds in robustly describing all of the basic elements of the cell. We conclude by discussing the importance of this and the future of modeling in this area
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Overview of mathematical approaches used to model bacterial chemotaxis II: bacterial populations
We review the application of mathematical modeling to understanding the behavior of populations of chemotactic bacteria. The application of continuum mathematical models, in particular generalized Keller–Segel models, is discussed along with attempts to incorporate the microscale (individual) behavior on the macroscale, modeling the interaction between different species of bacteria, the interaction of bacteria with their environment, and methods used to obtain experimentally verified parameter values. We allude briefly to the role of modeling pattern formation in understanding collective behavior within bacterial populations. Various aspects of each model are discussed and areas for possible future research are postulated
Channeling by Proximity: The Catalytic Advantages of Active Site Colocalization Using Brownian Dynamics
Nature often colocalizes successive steps in a metabolic pathway. Such organization is predicted to increase the effective concentration of pathway intermediates near their recipient active sites and to enhance catalytic efficiency. Here, the pathway of a two-step reaction is modeled using a simple spherical approximation for the enzymes and substrate particles. Brownian dynamics are used to simulate the trajectory of a substrate particle as it diffuses between the active site zones of two different enzyme spheres. The results approximate distances for the most effective reaction pathways, indicating that the most effective reaction pathway is one in which the active sites are closely aligned. However, when the active sites are too close, the ability of the substrate to react with the first enzyme was hindered, suggesting that even the most efficient orientations can be improved for a system that is allowed to rotate or change orientation to optimize the likelihood of reaction at both sites
Metabolomics Unravel Contrasting Effects of Biodiversity on the Performance of Individual Plant Species
In spite of evidence for positive diversity-productivity relationships increasing plant diversity has highly variable effects on the performance of individual plant species, but the mechanisms behind these differential responses are far from being understood. To gain deeper insights into the physiological responses of individual plant species to increasing plant diversity we performed systematic untargeted metabolite profiling on a number of herbs derived from a grassland biodiversity experiment (Jena Experiment). The Jena Experiment comprises plots of varying species number (1, 2, 4, 8, 16 and 60) and number and composition of functional groups (1 to 4; grasses, legumes, tall herbs, small herbs). In this study the metabolomes of two tall-growing herbs (legume: Medicago x varia; non-legume: Knautia arvensis) and three small-growing herbs (legume: Lotus corniculatus; non-legumes: Bellis perennis, Leontodon autumnalis) in plant communities of increasing diversity were analyzed. For metabolite profiling we combined gas chromatography coupled to time-of-flight mass spectrometry (GC-TOF-MS) and UPLC coupled to FT-ICR-MS (LC-FT-MS) analyses from the same sample. This resulted in several thousands of detected m/z-features. ANOVA and multivariate statistical analysis revealed 139 significantly changed metabolites (30 by GC-TOF-MS and 109 by LC-FT-MS). The small-statured plants L. autumnalis, B. perennis and L. corniculatus showed metabolic response signatures to increasing plant diversity and species richness in contrast to tall-statured plants. Key-metabolites indicated C- and N-limitation for the non-leguminous small-statured species B. perennis and L. autumnalis, while the metabolic signature of the small-statured legume L. corniculatus indicated facilitation by other legumes. Thus, metabolomic analysis provided evidence for negative effects of resource competition on the investigated small-statured herbs that might mechanistically explain their decreasing performance with increasing plant diversity. In contrast, taller species often becoming dominant in mixed plant communities did not show modified metabolite profiles in response to altered resource availability with increasing plant diversity. Taken together, our study demonstrates that metabolite profiling is a strong diagnostic tool to assess individual metabolic phenotypes in response to plant diversity and ecophysiological adjustment
Trail formation based on directed pheromone deposition
We propose an Individual-Based Model of ant-trail formation. The ants are
modeled as self-propelled particles which deposit directed pheromones and
interact with them through alignment interaction. The directed pheromones
intend to model pieces of trails, while the alignment interaction translates
the tendency for an ant to follow a trail when it meets it. Thanks to adequate
quantitative descriptors of the trail patterns, the existence of a phase
transition as the ant-pheromone interaction frequency is increased can be
evidenced. Finally, we propose both kinetic and fluid descriptions of this
model and analyze the capabilities of the fluid model to develop trail
patterns. We observe that the development of patterns by fluid models require
extra trail amplification mechanisms that are not needed at the
Individual-Based Model level
Osteochondral defects in the ankle: why painful?
Osteochondral defects of the ankle can either heal and remain asymptomatic or progress to deep ankle pain on weight bearing and formation of subchondral bone cysts. The development of a symptomatic OD depends on various factors, including the damage and insufficient repair of the subchondral bone plate. The ankle joint has a high congruency. During loading, compressed cartilage forces its water into the microfractured subchondral bone, leading to a localized high increased flow and pressure of fluid in the subchondral bone. This will result in local osteolysis and can explain the slow development of a subchondral cyst. The pain does not arise from the cartilage lesion, but is most probably caused by repetitive high fluid pressure during walking, which results in stimulation of the highly innervated subchondral bone underneath the cartilage defect. Understanding the natural history of osteochondral defects could lead to the development of strategies for preventing progressive joint damage
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