Pattern Selection by Dynamical Biochemical Signals

The development of multicellular organisms involves cells to decide their fate upon the action of biochemical signals. This decision is often spatiotemporally coordinated such that a spatial pattern arises. The dynamics that drive pattern formation usually involve genetic nonlinear interactions and positive feedback loops. These complex dynamics may enable multiple stable patterns for the same conditions. Under these circumstances, pattern formation in a developing tissue involves a selection process: why is a certain pattern formed and not another stable one? Herein we computationally address this issue in the context of the Notch signaling pathway. We characterize a dynamical mechanism for developmental selection of a specific pattern through spatiotemporal changes of the control parameters of the dynamics, in contrast to commonly studied situations in which initial conditions and noise determine which pattern is selected among multiple stable ones. This mechanism can be understood as a path along the parameter space driven by a sequence of biochemical signals. We characterize the selection process for three different scenarios of this dynamical mechanism that can take place during development: the signal either 1) acts in all the cells at the same time, 2) acts only within a cluster of cells, or 3) propagates along the tissue. We found that key elements for pattern selection are the destabilization of the initial pattern, the subsequent exploration of other patterns determined by the spatiotemporal symmetry of the parameter changes, and the speeds of the path compared to the timescales of the pattern formation process itself. Each scenario enables the selection of different types of patterns and creates these elements in distinct ways, resulting in different features. Our approach extends the concept of selection involved in cellular decision-making, usually applied to cell-autonomous decisions, to systems that collectively make decisions through cell-to-cell interactions.     

Genetic study of plasmid integration into yeast chromosomes. VI. Patterns of the destabilization of chimeric chromosomes and their use in gene mapping

The 2 microns DNA-dependent destabilization of yeast chimeric chromosomes III, IV, V was analysed. The comparison of its peculiarities with the earlier localized sites of episomal plasmid integration allowed to derive genetic regularities of destabilization process. Two destabilization rules that describe patterns of the loss of genetic information in the chromosome were formulated. The usefulness of this for mitotic intrachromosomal gene mapping in yeast was demonstrated using plasmid integration site mapping in chromosome I.     

Simple model of recovery dynamics after mass extinction

Biotic recoveries following mass extinctions are characterized by a complex set of dynamics, including the rebuilding of whole ecologies from low-diversity assemblages of survivors and opportunistic species. Three broad classes of diversity dynamics during recovery have been suggested: an immediate linear response, a logistic recovery, and a simple positive feedback pattern of species interaction. Here we present a simple model of recovery which generates these three scenarios via differences in the extent of species interactions, thus capturing the dynamical logic of the recovery pattern. The model results indicate that the lag time to biotic recovery increases significantly as biotic interactions become more important in the recovery process.     

Learning shapes spontaneous activity itinerating over memorized states

Learning is a process that helps create neural dynamical systems so that an appropriate output pattern is generated for a given input. Often, such a memory is considered to be included in one of the attractors in neural dynamical systems, depending on the initial neural state specified by an input. Neither neural activities observed in the absence of inputs nor changes caused in the neural activity when an input is provided were studied extensively in the past. However, recent experimental studies have reported existence of structured spontaneous neural activity and its changes when an input is provided. With this background, we propose that memory recall occurs when the spontaneous neural activity changes to an appropriate output activity upon the application of an input, and this phenomenon is known as bifurcation in the dynamical systems theory. We introduce a reinforcement-learning-based layered neural network model with two synaptic time scales; in this network, I/O relations are successively memorized when the difference between the time scales is appropriate. After the learning process is complete, the neural dynamics are shaped so that it changes appropriately with each input. As the number of memorized patterns is increased, the generated spontaneous neural activity after learning shows itineration over the previously learned output patterns. This theoretical finding also shows remarkable agreement with recent experimental reports, where spontaneous neural activity in the visual cortex without stimuli itinerate over evoked patterns by previously applied signals. Our results suggest that itinerant spontaneous activity can be a natural outcome of successive learning of several patterns, and it facilitates bifurcation of the network when an input is provided.     

一类具有非单调发生率SIS流行病模型的分析

该文讨论了具有非单调发生率SIS流行病模型,分别建立了带有分布时滞和离散时滞形式的感染个体的恢复时滞模型,同时分析了系统平衡态的稳定性．     

Tissue mechanical behavior of tendinous fibers under statistical and dynamic requirements

With a device for dynamical processes tension tests were performed on bundles of collagen fibres of human and bovin origin. Part of the studies were performed under statical condition with an universal materials testing machine, equipped with a closed loop feed back control system. If the force is to be kept constant subsequently to a strain process on a collagen fiber bundle (isotonic condition), the fiber length must increase (creep phenomenon, retardation). The force decreases under constant length after a preceding strain process (relaxation). In analogy to the statical relaxation, statical isorheological line, and statical force recovery curve the dynamical (cyclic) relaxation, dynamical (cyclic) isorheological curve, and dynamical (cyclic) force recovery curve are described. The mechanical-rheological properties collagen fiber bundles are discussed in relation to functional anatomy.     

Modeling epithelial cell homeostasis: Assessing recovery and control mechanisms

Critical to epithelial cell viability is prompt and direct recovery, following a perturbation of cellular conditions. Although a number of transporters are known to be activated by changes in cell volume, cell pH, or cell membrane potential, their importance to cellular homeostasis has been difficult to establish. Moreover, the coordination among such regulated transporters to enhance recovery has received no attention in mathematical models of cellular function. In this paper, a previously developed model of proximal tubule (Weinstein, 1992, Am. J. Physiol. 263, F784–F798), has been approximated by its linearization about a reference condition. This yields a system of differential equations and auxiliary linear equations, which estimate cell volume and composition and transcellular fluxes in response to changes in bath conditions or membrane transport coefficients. Using the singular value decomposition, this system is reduced to a linear dynamical system, which is stable and reproduces the full model behavior in a useful neighborhood of the reference. Cost functions on trajectories formulated in the model variables (e.g., time for cell volume recovery) are translated into cost functions for the dynamical system. When the model is extended by the inclusion of linear dependence of membrane transport coefficients on model variables, the impact of each such controller on the recovery cost can be estimated with the solution of a Lyapunov matrix equation. Alternatively, solution of an algebraic Riccati equation provides the ensemble of controllers that constitute optimal state feedback for the dynamical system. When translated back into the physiological variables, the optimal controller contains some expected components, as well as unanticipated controllers of uncertain significance. This approach provides a means of relating cellular homeostasis to optimization of a dynamical system.     

Oscillations in cyclical neutropenia: new evidence based on mathematical modeling

We present a dynamical model of the production and regulation of circulating blood neutrophil number. This model is derived from physiologically relevant features of the hematopoietic system, and is analysed using both analytic and numerical methods. Supercritical Hopf bifurcations and saddle-node bifurcations of limit cycles are shown to exist. We make the estimation of kinetic parameters for dogs and then apply the model to cyclical neutropenia (CN) in the grey collie, a rare disorder in which oscillations in all blood cell counts are found. We conclude that the major cause of the oscillations in CN is an increased rate of apoptosis of neutrophil precursors which leads to a destabilization of the hematopoietic stem cell compartment.     

Pattern recognition and associative memory as dynamical processes in a synergetic system

We consider a model for associative memory and pattern recognition which was devised by Haken (1987b). This model treats the activity of the neurons as continuous variables and exploits an analogy with pattern formation in synergetic systems. The capability of such a system to act as associative memory is demonstrated by the reconstruction of faces which are partially offered to the system, and which are restored by the corresponding dynamical process. We demonstrate how this model can be cast into a form which is translation invariant and how partially hidden faces in scenes can be recognized by means of the control of attention parameters of specific patterns.     

Recovery after mass extinction: evolutionary assembly in large-scale biosphere dynamics

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.     

Identification of tissue differentiation rates in a mechanobiological model of fracture healing

As a basis for model-based analysis of the processes in secondary fracture healing, a dynamical model is presented that characterises the physiological status in the fracture area by the location-dependent composition of tissues. Five types of tissue are distinguished: connective tissue, cartilage, bone, haematoma and avascular bone. A rule base is given that describes dynamical tissue differentiation processes. The rules consider not only a mechanical stimulus but also osteogenic and a vasculative factors as biological stimuli. Within this model structure, it is possible, e.g., to distinguish intramembranous from endochondral ossification processes. An objective function is introduced to assess accordance between the model-based simulation results and reference healing stages. By minimising this objective function, relevant tissue differentiation rates can be determined. For a reference process of secondary fracture healing it could be shown that the intramembranous ossification rate of 0.313%/day (from connective tissue to bone) is much smaller than the endochondral ossification rate of 1.136%/day (from cartilage to bone). In order to verify the model approach, it is transferred to simulate long bone distraction. Results show that healing patterns of bone distraction can be predicted. Using this method, it is possible to identify model parameters for individual subjects. This will allow a patient-specific analysis of tissue healing processes in future.     

Embedding Responses in Spontaneous Neural Activity Shaped through Sequential Learning

Recent experimental measurements have demonstrated that spontaneous neural activity in the absence of explicit external stimuli has remarkable spatiotemporal structure. This spontaneous activity has also been shown to play a key role in the response to external stimuli. To better understand this role, we proposed a viewpoint, “memories-as-bifurcations,” that differs from the traditional “memories-as-attractors” viewpoint. Memory recall from the memories-as-bifurcations viewpoint occurs when the spontaneous neural activity is changed to an appropriate output activity upon application of an input, known as a bifurcation in dynamical systems theory, wherein the input modifies the flow structure of the neural dynamics. Learning, then, is a process that helps create neural dynamical systems such that a target output pattern is generated as an attractor upon a given input. Based on this novel viewpoint, we introduce in this paper an associative memory model with a sequential learning process. Using a simple Hebbian-type learning, the model is able to memorize a large number of input/output mappings. The neural dynamics shaped through the learning exhibit different bifurcations to make the requested targets stable upon an increase in the input, and the neural activity in the absence of input shows chaotic dynamics with occasional approaches to the memorized target patterns. These results suggest that these dynamics facilitate the bifurcations to each target attractor upon application of the corresponding input, which thus increases the capacity for learning. This theoretical finding about the behavior of the spontaneous neural activity is consistent with recent experimental observations in which the neural activity without stimuli wanders among patterns evoked by previously applied signals. In addition, the neural networks shaped by learning properly reflect the correlations of input and target-output patterns in a similar manner to those designed in our previous study.     

A stochastic carcinogenesis model incorporating genomic instability fitted to colon cancer data

A generalization of the two-mutation stochastic carcinogenesis model of Moolgavkar, Venzon and Knudson and certain models constructed by Little is developed; the model incorporates progressive genomic instability and an arbitrary number of mutational stages. This model is shown to have the property that, at least in the case when the parameters of the model are eventually constant, the excess relative and absolute cancer rates following changes in any of the parameters will eventually tend to zero. It is also shown that when the parameters governing the processes of cell division, death, or additional mutation (whether of the normal sort or that resulting in genomic destabilization) at the penultimate stage are subject to perturbations, there are relatively large fluctuations in the hazard function for the model, which start almost as soon as the parameters are changed. The model is fitted to US Caucasian colon cancer incidence data. A model with five stages and two levels of genomic destabilization fits the data well. Comparison with patterns of excess risk in the Japanese atomic bomb survivor colon cancer incidence data indicate that radiation might act on early mutation rates in the model; a major role for radiation in initiating genomic destabilization is less likely.     

Stabilization of bimanual coordination due to active interhemispheric inhibition: a dynamical account

Based on recent brain-imaging data and congruent theoretical insights, a dynamical model is derived to account for the patterns of brain activity observed during stable performance of bimanual multifrequency patterns, as well as during behavioral instabilities in the form of phase transitions between such patterns. The model incorporates four dynamical processes, defined over both motor and premotor cortices, which are coupled through inhibitory and excitatory inter- and intrahemispheric connections. In particular, the model underscores the crucial role of interhemispheric inhibition in reducing the interference between disparate frequencies during stable performance, as well as the failure of this reduction during behavioral transitions. As an aside, the model also accounts for in- and antiphase preferences during isofrequency movements. The viability of the proposed model is illustrated by magnetoencephalographic signals that were recorded from an experienced subject performing a polyrhythmic tapping task that was designed to induce transitions between multifrequency patterns. Consistent with the models dynamics, contra- and ipsilateral cortical areas of activation were frequency- and phase-locked, while their activation strength changed markedly in the vicinity of transitions in coordination.     

Chemotaxis-induced spatio-temporal heterogeneity in multi-species host-parasitoid systems

When searching for hosts, parasitoids are observed to aggregate in response to chemical signalling cues emitted by plants during host feeding. In this paper we model aggregative parasitoid behaviour in a multi-species host-parasitoid community using a system of reaction-diffusion-chemotaxis equations. The stability properties of the steady-states of the model system are studied using linear stability analysis which highlights the possibility of interesting dynamical behaviour when the chemotactic response is above a certain threshold. We observe quasi-chaotic dynamic heterogeneous spatio-temporal patterns, quasi-stationary heterogeneous patterns and a destabilisation of the steady-states of the system. The generation of heterogeneous spatio-temporal patterns and destabilisation of the steady state are due to parasitoid chemotactic response to hosts. The dynamical behaviour of our system has both mathematical and ecological implications and the concepts of chemotaxis-driven instability and coexistence and ecological change are discussed. I. G. Pearce gratefully acknowledges the financial support of the NERC.     

The dynamical analogy between microbial growth on mixtures of substrates and population growth of competing species

There is a similarity between the metabolic dynamics of a microbial species growing on a mixture of two substrates and the dynamics of growth of two competing populations. Specifically, the enzymes catalyzing the uptake and catabolism of substrates exhibit phenomena analogous to extinction and coexistence."Extinction" of the enzymes associated with one of the substrates results in sequential utilization of the substrates (diauxie) (Monod, 1942). "Coexistence" of the enzymes associated with the substrates results in simultaneous utilization of the substrates (Egli, 1995). Here, we formulate a simple model that shows the basis for this dynamical similarity: The equations describing the evolution of the enzyme levels are dynamical analogs of the Lotka-Volterra model for two competing species. The analogy suggests ways of capturing the experimentally observed preculture-dependent growth patterns, i.e., growth patterns that vary depending on the physiological state of the preculture.     

Biological Evolution of Replicator Systems: Towards a Quantitative Approach

The aim of this work is to study the features of a simple replicator chemical model of the relation between kinetic stability and entropy production under the action of external perturbations. We quantitatively explore the different paths leading to evolution in a toy model where two independent replicators compete for the same substrate. To do that, the same scenario described originally by Pross (J Phys Org Chem 17:312–316, 2004) is revised and new criteria to define the kinetic stability are proposed. Our results suggest that fast replicator populations are continually favored by the effects of strong stochastic environmental fluctuations capable to determine the global population, the former assumed to be the only acting evolution force. We demonstrate that the process is continually driven by strong perturbations only, and that population crashes may be useful proxies for these catastrophic environmental fluctuations. As expected, such behavior is particularly enhanced under very large scale perturbations, suggesting a likely dynamical footprint in the recovery patterns of new species after mass extinction events in the Earth’s geological past. Furthermore, the hypothesis that natural selection always favors the faster processes may give theoretical support to different studies that claim the applicability of maximum principles like the Maximum Metabolic Flux (MMF) or Maximum Entropy Productions Principle (MEPP), seen as the main goal of biological evolution.     

Software Sensors to Monitor the Dynamics of Microbial Communities: Application to Anaerobic Digestion

A mass balance based model has been derived to represent the dynamical behavior of the ecosystem contained in an anaerobic digester. The model considers two bacterial populations: acidogenic and methanogenic bacteria. It forms the basis for the design of a software sensor considering both a model of the biological system and on-line gaseous measurements. The software sensor computes the concentration of inorganic carbon and volatile fatty acids (VFA) in the digester. Another software sensor is dedicated to the estimation of the bacterial biomasses. The predictions of the software sensors for a real experiment are very close to the actual off-line measurements. The software sensors monitor the accumulation of VFA and thus very early detect a destabilization of the digester due to overloading. The presented methodology demonstrates the usefulness of advanced monitoring techniques for an improved understanding of the internal working of a biological system.     

The effect of predator limitation on the dynamics of simple food chains

We investigate the influence of competition between predators on the dynamics of bitrophic predator–prey systems and of tritrophic food chains. Competition between predators is implemented either as interference competition, or as a density-dependent mortality rate. With interference competition, the paradox of enrichment is reduced or completely suppressed, but otherwise, the dynamical behavior of the systems is not fundamentally different from that of the Rosenzweig–MacArthur model, which contains no predator competition and shows only continuous transitions between fixed points or periodic oscillations. In contrast, with density-dependent predator mortality, the system shows a surprisingly rich dynamical behavior. In particular, decreasing the density regulation of the predator can induce catastrophic shifts from a stable fixed point to a large oscillation where the predator chases the prey through a cycle that brings both species close to the threshold of extinction. Other catastrophic bifurcations, such as subcritical Hopf bifurcations and saddle-node bifurcations of limit cycles, do also occur. In tritrophic food chains, we find again that fixed points in the model with predator interference become unstable only through Hopf bifurcations, which can also be subcritical, in contrast to the bitrophic situation. The model with a density limitation shows again catastrophic destabilization of fixed points and various nonlocal bifurcations. In addition, chaos occurs for both models in appropriate parameter ranges.