Information processing mechanisms in microtubules at physiological temperature: Model predictions for experimental tests

Both direct and indirect experimental evidence has shown signaling, communication and conductivity in microtubules (MTs). Theoretical models have predicted that MTs can be potentially used for both classical and quantum information processing although controversies arose in regard to physiological temperature effects on these capabilities. In this paper, MTs have been studied using well-established principles of classical statistical physics as applied to information processing, information storage and signal propagation. To investigate the existence of information processing in MTs we used cellular automata (CA) models with neighbor rules based on the electrostatic properties of the molecular structure of tubulin, and both synchronous and asynchronous updating methods. We obtained a phase diagram of possible dynamic behaviors in MTs that depend on the values of characteristic physical parameters that can be experimentally verified.     

Rhythmic and non-rhythmic attractors in asynchronous random Boolean networks

In multi-component, discrete systems, such as Boolean networks and cellular automata, the scheme of updating of the individual elements plays a crucial role in determining their dynamic properties and their suitability as models of complex phenomena. Many interesting properties of these systems rely heavily on the use of synchronous updating of the individual elements. Considerations of parsimony have motivated the claim that, if the natural systems being modelled lack any clear evidence of synchronously driven elements, then random asynchronous updating should be used by default. The introduction of a random element precludes the possibility of strictly cyclic behaviour. In principle, this poses the question of whether asynchronously driven Boolean networks, cellular automata, etc., are inherently bad choices at the time of modelling rhythmic phenomena. This paper focuses on this subsidiary issue for the case of Asynchronous Random Boolean Networks (ARBNs). It defines measures of pseudo-periodicity between states and sufficiently relaxed statistical constraints. These measures are used to guide a genetic algorithm to find appropriate examples. Success in this search for a number of cases, and the subsequent statistical analysis lead to the conclusion that ARBNs can indeed be used as models of co-ordinated rhythmic phenomena, which may be stronger precisely because of their in-built asynchrony. The same technique is used to find non-stationary attractors that show no rhythm. Evidence suggests that the latter are more abundant than rhythmic attractor. The methodology is flexible, and allows for more demanding statistical conditions for defining pseudo-periodicity, and constraining the evolutionary search.     

Pigment color patterns of molluscs as an autonomous process generated by asynchronous automata

Pigment color patterns of molluscs are studied from the viewpoint of autonomy. Brownian algebra developed by Spencer-Brown (1969) is extensively used for the expression of cellular-automaton rules. When asynchronous updating is introduced for the transition of cellular automata, various kinds of patterns such as traveling waves, kinks, oscillatory local patterns etc. are generated from the same transitional rule. The type of patterns depends more sensitively on the asynchronous updating relationship rather than the transitional rule itself. Therefore, pattern changes in ontogeny can be explained without any changes in transitional rules or reaction processes. It is proposed that asynchronousness is intrinsic to living systems and that recognition of the intrinsic time is essential in understanding living systems.     

Sociality of an agent during morphogenetic canalization: Asynchronous updating with potential resonance

Canalization is a typical self-organization process leading to complementarity between parts and the whole. In the field of developmental biology, concerns about morphogenesis canalization are often framed as the French flag problem, questioning how each cell knows its own position in the whole system. Although chemical gradients have been suggested to provide positional information, there is no direct evidence that gradients are used to gain positional information. The chemical gradient hypothesis is based on the assumption that agents (e.g., cells) in a domain that locally interact with each other can generate a chemical gradient thanks to a global reference point. Instead of a chemical gradient, we here propose a model based on agents that are equipped with sociality that is based not on a global reference but rather on the ability to sense other neighboring agents, or potential resonance. The interaction among the agents with sociality, developed from undifferentiated types or tokens, is implemented using asynchronous updating automata equipped with potential resonance. We show that these automata can generate a French flag pattern that is very robust against perturbations without positional information by comparing automata with synchronous updating and asynchronous automata without potential resonance.     

ASP-based method for the enumeration of attractors in non-deterministic synchronous and asynchronous multi-valued networks

Background

This paper addresses the problem of finding attractors in biological regulatory networks. We focus here on non-deterministic synchronous and asynchronous multi-valued networks, modeled using automata networks (AN). AN is a general and well-suited formalism to study complex interactions between different components (genes, proteins,...). An attractor is a minimal trap domain, that is, a part of the state-transition graph that cannot be escaped. Such structures are terminal components of the dynamics and take the form of steady states (singleton) or complex compositions of cycles (non-singleton). Studying the effect of a disease or a mutation on an organism requires finding the attractors in the model to understand the long-term behaviors.

Results

We present a computational logical method based on answer set programming (ASP) to identify all attractors. Performed without any network reduction, the method can be applied on any dynamical semantics. In this paper, we present the two most widespread non-deterministic semantics: the asynchronous and the synchronous updating modes. The logical approach goes through a complete enumeration of the states of the network in order to find the attractors without the necessity to construct the whole state-transition graph. We realize extensive computational experiments which show good performance and fit the expected theoretical results in the literature.

Conclusion

The originality of our approach lies on the exhaustive enumeration of all possible (sets of) states verifying the properties of an attractor thanks to the use of ASP. Our method is applied to non-deterministic semantics in two different schemes (asynchronous and synchronous). The merits of our methods are illustrated by applying them to biological examples of various sizes and comparing the results with some existing approaches. It turns out that our approach succeeds to exhaustively enumerate on a desktop computer, in a large model (100 components), all existing attractors up to a given size (20 states). This size is only limited by memory and computation time.

     

Attractor analysis of asynchronous Boolean models of signal transduction networks

Prior work on the dynamics of Boolean networks, including analysis of the state space attractors and the basin of attraction of each attractor, has mainly focused on synchronous update of the nodes’ states. Although the simplicity of synchronous updating makes it very attractive, it fails to take into account the variety of time scales associated with different types of biological processes. Several different asynchronous update methods have been proposed to overcome this limitation, but there have not been any systematic comparisons of the dynamic behaviors displayed by the same system under different update methods. Here we fill this gap by combining theoretical analysis such as solution of scalar equations and Markov chain techniques, as well as numerical simulations to carry out a thorough comparative study on the dynamic behavior of a previously proposed Boolean model of a signal transduction network in plants. Prior evidence suggests that this network admits oscillations, but it is not known whether these oscillations are sustained. We perform an attractor analysis of this system using synchronous and three different asynchronous updating schemes both in the case of the unperturbed (wild-type) and perturbed (node-disrupted) systems. This analysis reveals that while the wild-type system possesses an update-independent fixed point, any oscillations eventually disappear unless strict constraints regarding the timing of certain processes and the initial state of the system are satisfied. Interestingly, in the case of disruption of a particular node all models lead to an extended attractor. Overall, our work provides a roadmap on how Boolean network modeling can be used as a predictive tool to uncover the dynamic patterns of a biological system under various internal and environmental perturbations.     

缀块性和缀块动态:Ⅱ.描述与分析

在生态学中,“缀块”(patch)的概念早已在植被群落和海洋生态系统中浮游动植物空间分布研究中广泛应用。A.S.Watte早在1947年就强调缀块在植物群落结构分析中的重要性。实际上,缀块存在于地球的任何地方。森林可     

Dynamics of asynchronous random Boolean networks with asynchrony generated by stochastic processes

An asynchronous Boolean network with N nodes whose states at each time point are determined by certain parent nodes is considered. We make use of the models developed by Matache and Heidel [Matache, M.T., Heidel, J., 2005. Asynchronous random Boolean network model based on elementary cellular automata rule 126. Phys. Rev. E 71, 026232] for a constant number of parents, and Matache [Matache, M.T., 2006. Asynchronous random Boolean network model with variable number of parents based on elementary cellular automata rule 126. IJMPB 20 (8), 897-923] for a varying number of parents. In both these papers the authors consider an asynchronous updating of all nodes, with asynchrony generated by various random distributions. We supplement those results by using various stochastic processes as generators for the number of nodes to be updated at each time point. In this paper we use the following stochastic processes: Poisson process, random walk, birth and death process, Brownian motion, and fractional Brownian motion. We study the dynamics of the model through sensitivity of the orbits to initial values, bifurcation diagrams, and fixed-point analysis. The dynamics of the system show that the number of nodes to be updated at each time point is of great importance, especially for the random walk, the birth and death, and the Brownian motion processes. Small or moderate values for the number of updated nodes generate order, while large values may generate chaos depending on the underlying parameters. The Poisson process generates order. With fractional Brownian motion, as the values of the Hurst parameter increase, the system exhibits order for a wider range of combinations of the underlying parameters.     

Dynamics of Nephron-Vascular Network

The paper presents a modeling study of the spatial dynamics of a nephro-vascular network consisting of individual nephrons connected via a tree-like vascular branching structure. We focus on the effects of nonlinear mechanisms that are?responsible for the formation of synchronous patterns in order to learn about processes not directly amenable to experimentation. We demonstrate that: (i) the nearest nephrons are synchronized in-phase due to a vascular propagated electrical coupling, (ii) the next few branching levels display a formation of phase-shifted patterns due to hemodynamic coupling and mode elimination, and (iii) distantly located areas show asynchronous behavior or, if all nephrons and branches are perfectly identical, an infinitely long transient behavior. These results contribute to the understanding of mechanisms responsible for the highly dynamic and limited synchronization observed among groups of nephrons despite of the fairly strong interaction between the individual units.     

Library-based numerical reduction of the Hodgkin–Huxley neuron for network simulation

We present an efficient library-based numerical method for simulating the Hodgkin–Huxley (HH) neuronal networks. The key components in our numerical method involve (i) a pre-computed high resolution data library which contains typical neuronal trajectories (i.e., the time-courses of membrane potential and gating variables) during the interval of an action potential (spike), thus allowing us to avoid resolving the spikes in detail and to use large numerical time steps for evolving the HH neuron equations; (ii) an algorithm of spike-spike corrections within the groups of strongly coupled neurons to account for spike-spike interactions in a single large time step. By using the library method, we can evolve the HH networks using time steps one order of magnitude larger than the typical time steps used for resolving the trajectories without the library, while achieving comparable resolution in statistical quantifications of the network activity, such as average firing rate, interspike interval distribution, power spectra of voltage traces. Moreover, our large time steps using the library method can break the stability requirement of standard methods (such as Runge–Kutta (RK) methods) for the original dynamics. We compare our library-based method with RK methods, and find that our method can capture very well phase-locked, synchronous, and chaotic dynamics of HH neuronal networks. It is important to point out that, in essence, our library-based HH neuron solver can be viewed as a numerical reduction of the HH neuron to an integrate-and-fire (I&F) neuronal representation that does not sacrifice the gating dynamics (as normally done in the analytical reduction to an I&F neuron).     

An Efficient Algorithm for Computing Attractors of Synchronous And Asynchronous Boolean Networks

Biological networks, such as genetic regulatory networks, often contain positive and negative feedback loops that settle down to dynamically stable patterns. Identifying these patterns, the so-called attractors, can provide important insights for biologists to understand the molecular mechanisms underlying many coordinated cellular processes such as cellular division, differentiation, and homeostasis. Both synchronous and asynchronous Boolean networks have been used to simulate genetic regulatory networks and identify their attractors. The common methods of computing attractors are that start with a randomly selected initial state and finish with exhaustive search of the state space of a network. However, the time complexity of these methods grows exponentially with respect to the number and length of attractors. Here, we build two algorithms to achieve the computation of attractors in synchronous and asynchronous Boolean networks. For the synchronous scenario, combing with iterative methods and reduced order binary decision diagrams (ROBDD), we propose an improved algorithm to compute attractors. For another algorithm, the attractors of synchronous Boolean networks are utilized in asynchronous Boolean translation functions to derive attractors of asynchronous scenario. The proposed algorithms are implemented in a procedure called geneFAtt. Compared to existing tools such as genYsis, geneFAtt is significantly faster in computing attractors for empirical experimental systems.

Availability

The software package is available at https://sites.google.com/site/desheng619/download.     

Cell cycle characteristics of synchronized and asynchronous populations of human cells and effect of cooling of selected mitotic cells.

The method of synchronizing cells by means of mitotic selection has been adapted to the human line NHIK 3025. Increase in cell number as a function of time in asynchronous and synchronous populations was studied as well as mitotic index as a function of time after selection of synchronized populations. Phase durations of the cell cycle of synchronous populations were determined by 3H-thymidine incorporation and scintillation counting. The relative phase durations of exponentially growing asynchronous populations were determined by mathematical analysis of DNA-histograms recorded by flow cytofluorimetry. Both the generation time and the various phase durations of the cell cycle were found to be the same in asynchronous and synchronous populations. It was found that NHIK 3025 cells are damaged by cooling to 4 and 0 degrees C so that cooling of selected cells in order to increase the yield would reduce the quality of the synchronized populations.     

CELL CYCLE CHARACTERISTICS OF SYNCHRONIZED AND ASYNCHRONOUS POPULATIONS OF HUMAN CELLS AND EFFECT OF COOLING OF SELECTED MITOTIC CELLS

The method of synchronizing cells by means of mitotic selection has been adapted to the human line NHIK 3025. Increase in cell number as a function of time in asynchronous and synchronous populations was studied as well as mitotic index as a function of time after selection of synchronized populations. Phase durations of the cell cycle of synchronous populations were determined by ³ H-thymidine incorporation and scintillation counting. The relative phase durations of exponentially growing asynchronous populations were determined by mathematical analysis of DNA-histograms recorded by flow cytofluorimetry. Both the generation time and the various phase durations of the cell cycle were found to be the same in asynchronous and synchronous populations. It was found that NHIK 3025 cells are damaged by cooling to 4 and 0°C so that cooling of selected cells in order to increase the yield would reduce the quality of the synchronized populations.     

Periodic synchronisation of dengue epidemics in Thailand over the last 5 decades driven by temperature and immunity

The spatial distribution of dengue and its vectors (spp. Aedes) may be the widest it has ever been, and projections suggest that climate change may allow the expansion to continue. However, less work has been done to understand how climate variability and change affects dengue in regions where the pathogen is already endemic. In these areas, the waxing and waning of immunity has a large impact on temporal dynamics of cases of dengue haemorrhagic fever. Here, we use 51 years of data across 72 provinces and characterise spatiotemporal patterns of dengue in Thailand, where dengue has caused almost 1.5 million cases over the last 30 years, and examine the roles played by temperature and dynamics of immunity in giving rise to those patterns. We find that timescales of multiannual oscillations in dengue vary in space and time and uncover an interesting spatial phenomenon: Thailand has experienced multiple, periodic synchronisation events. We show that although patterns in synchrony of dengue are similar to those observed in temperature, the relationship between the two is most consistent during synchronous periods, while during asynchronous periods, temperature plays a less prominent role. With simulations from temperature-driven models, we explore how dynamics of immunity interact with temperature to produce the observed patterns in synchrony. The simulations produced patterns in synchrony that were similar to observations, supporting an important role of immunity. We demonstrate that multiannual oscillations produced by immunity can lead to asynchronous dynamics and that synchrony in temperature can then synchronise these dengue dynamics. At higher mean temperatures, immune dynamics can be more predominant, and dengue dynamics more insensitive to multiannual fluctuations in temperature, suggesting that with rising mean temperatures, dengue dynamics may become increasingly asynchronous. These findings can help underpin predictions of disease patterns as global temperatures rise.

This study shows that spatially large-scale shifts in temperature can synchronize dengue dynamics across Thailand; however, as average temperatures rise, dengue dynamics may increasingly be dictated by dynamics of immunity, which may in turn mean fewer synchronous outbreaks in the future.     

Two-patch dispersal-linked compensatory-overcompensatory spatially discrete population models

We study the role of asynchronous and synchronous dispersals on discrete-time two-patch dispersal-linked population models, where the pre-dispersal local patch dynamics are of mixed compensatory and overcompensatory types. Single-species dispersal-linked models behave as single-species single-patch models whenever all pre-dispersal local patch dynamics are compensatory and dispersal is synchronous. However, the dynamics of the corresponding two-patch population model connected by asynchronous dispersal depends on the dispersal rates. The species goes extinct on at least one patch when the asynchronous dispersal rates are high, while it persists when the rates are low. We use numerical simulations to show that in both synchronous and asynchronous mixed compensatory and overcompensatory systems, symmetric and asymmetric dispersals can control and impede the onset of cyclic population oscillations via period-doubling reversal bifurcations. Also, we show that in mixed systems both asynchronous and synchronous dispersals are capable of altering the pre-dispersal local patch dynamics from overcompensatory to compensatory dynamics. Dispersal-linked population models with ‘unstructured’ overcompensatory pre-dispersal local dynamics connected by synchronous dispersal can generate multiple attractors with fractal basin boundaries. However, mixed compensatory and overcompensatory systems appear to exhibit single attractors and not coexisting (multiple) attractors.     

Two-patch dispersal-linked compensatory-overcompensatory spatially discrete population models

We study the role of asynchronous and synchronous dispersals on discrete-time two-patch dispersal-linked population models, where the pre-dispersal local patch dynamics are of mixed compensatory and overcompensatory types. Single-species dispersal-linked models behave as single-species single-patch models whenever all pre-dispersal local patch dynamics are compensatory and dispersal is synchronous. However, the dynamics of the corresponding two-patch population model connected by asynchronous dispersal depends on the dispersal rates. The species goes extinct on at least one patch when the asynchronous dispersal rates are high, while it persists when the rates are low. We use numerical simulations to show that in both synchronous and asynchronous mixed compensatory and overcompensatory systems, symmetric and asymmetric dispersals can control and impede the onset of cyclic population oscillations via period-doubling reversal bifurcations. Also, we show that in mixed systems both asynchronous and synchronous dispersals are capable of altering the pre-dispersal local patch dynamics from overcompensatory to compensatory dynamics. Dispersal-linked population models with 'unstructured' overcompensatory pre-dispersal local dynamics connected by synchronous dispersal can generate multiple attractors with fractal basin boundaries. However, mixed compensatory and overcompensatory systems appear to exhibit single attractors and not coexisting (multiple) attractors.     

Predictability in Cellular Automata

Modelled as finite homogeneous Markov chains, probabilistic cellular automata with local transition probabilities in (0, 1) always posses a stationary distribution. This result alone is not very helpful when it comes to predicting the final configuration; one needs also a formula connecting the probabilities in the stationary distribution to some intrinsic feature of the lattice configuration. Previous results on the asynchronous cellular automata have showed that such feature really exists. It is the number of zero-one borders within the automaton''s binary configuration. An exponential formula in the number of zero-one borders has been proved for the 1-D, 2-D and 3-D asynchronous automata with neighborhood three, five and seven, respectively. We perform computer experiments on a synchronous cellular automaton to check whether the empirical distribution obeys also that theoretical formula. The numerical results indicate a perfect fit for neighbourhood three and five, which opens the way for a rigorous proof of the formula in this new, synchronous case.     

Comparison of Methods of Cell Cycle Analysis in Paramecium tetraurelia

ABSTRACT. Four methods are commonly used to study cell cycle processes in Paramecium tetraurelia. These include stage frequency analysis in asynchronous cultures, hand selection of synchronous dividing cells, selection of newly divided cells by elutriation centrifugation, and the sister cell method. We have compared the timing and resolution of stages of oral morphogenesis and micronuclear mitosis with each method. The temporal resolution obtainable with the sister cell method was inadequate to position the timing of morphogenesis stages within the cell cycle. Both the asynchronous method and the hand-selected synchronous samples methods are prone to bias. Elutriation centrifuge synchronization provides large samples with resolution comparable to that of hand selected samples. The elutriation method is the least prone to bias when <5% of the parent culture of Paramecium is selected.     

Proliferation of anchorage-dependent contact-inhibited cells: I. Development of theoretical models based on cellular automata

We report the development of new class of discrete models that can accurately describe the contact-inhibited proliferation of anchorage-dependent cells. The models are based on cellular automata, and they quantitatively account for contact inhibition phenomena occurring during all stages of the proliferation process: (a) the initial stage of "exponential" growth of cells without contact inhibition; (b) the second stage where cell colonies form and grow with few colony mergings; and (c) the final stage where proliferation rates are dominated by colony merging events. Model prediction are presented and analyzed to study the complicated dynamics of large cell populations and determine how the initial spatial cell distribution, the seeding density, and the geometry of the growth surface affect the observed proliferation rates. Finally, we present a model variant that can simulate contact-inhibited proliferation of asynchronous cell populations with arbitrary cell cycle-time distribution. The latter model can also compute the percentage of cells that are in a specific phase of their division cycle at a given time.     

Asynchronous, irregular automata nets: the path not taken

This is a prelude to, and an extension of the original paper Artificial tissue models (Stark, R., 1994. The topology and analysis of asynchronous processes. http://www.math.usf.edu/ approximately stark/documents). However, this exposition is designed for a broader audience - anyone working in biological information processing. A primary objective is to demonstrate that irregular asynchronous automata nets, as opposed to cellular automata, are a realistic approach to modeling biological information processing. Also, new material is presented. Sections 1 and 2 review the early history of von Neumann's attempt explore biological information processing and finally the emergence of cellular automata. The history is guided by the question of why John von Neumann knowingly (we believe) compromised his investigation of biological information processing by falling back to the model we now know as cellular automata. Section 3 defines and explores examples of cellular automata and artificial tissue. Sections 4 and 5 contain philosophical observations which unify our paper, and propose an answer to the original question. A new model for Turing's leopards' spot problem is presented. The asynchronous models are defined by a cell program and a local commumications protocol only. Computational freedom comes from asynchronous activity, while global organization emerges from the entropy reducing nature of the cell programs.