RuleMonkey: software for stochastic simulation of rule-based models

Background  

The system-level dynamics of many molecular interactions, particularly protein-protein interactions, can be conveniently represented using reaction rules, which can be specified using model-specification languages, such as the BioNetGen language (BNGL). A set of rules implicitly defines a (bio)chemical reaction network. The reaction network implied by a set of rules is often very large, and as a result, generation of the network implied by rules tends to be computationally expensive. Moreover, the cost of many commonly used methods for simulating network dynamics is a function of network size. Together these factors have limited application of the rule-based modeling approach. Recently, several methods for simulating rule-based models have been developed that avoid the expensive step of network generation. The cost of these "network-free" simulation methods is independent of the number of reactions implied by rules. Software implementing such methods is now needed for the simulation and analysis of rule-based models of biochemical systems.     

Cooperation and Defection at the Crossroads

We study a simple traffic model with a non-signalized road intersection. In this model the car arriving from the right has precedence. The vehicle dynamics far from the crossing are governed by the rules introduced by Nagel and Paczuski, which define how drivers behave when braking or accelerating. We measure the average velocity of the ensemble of cars and its flow as a function of the density of cars on the roadway. An additional set of rules is defined to describe the dynamics at the intersection assuming a fraction of drivers that do not obey the rule of precedence. This problem is treated within a game-theory framework, where the drivers that obey the rule are cooperators and those who ignore it are defectors. We study the consequences of these behaviors as a function of the fraction of cooperators and defectors. The results show that cooperation is the best strategy because it maximizes the flow of vehicles and minimizes the number of accidents. A rather paradoxical effect is observed: for any percentage of defectors the number of accidents is larger when the density of cars is low because of the higher average velocity.     

Neural networks and logical reasoning systems: a translation table

A correspondence is established between the basic elements of logic reasoning systems (knowledge bases, rules, inference and queries) and the structure and dynamical evolution laws of neural networks. The correspondence is pictured as a translation dictionary which might allow to go back and forth between symbolic and network formulations, a desirable step in learning-oriented systems and multicomputer networks. In the framework of Horn clause logics, it is found that atomic propositions with n arguments correspond to nodes with nth order synapses, rules to synaptic intensity constraints, forward chaining to synaptic dynamics and queries either to simple node activation or to a query tensor dynamics.     

Analysis of Discrete Bioregulatory Networks Using Symbolic Steady States

A discrete model of a biological regulatory network can be represented by a discrete function that contains all available information on interactions between network components and the rules governing the evolution of the network in a finite state space. Since the state space size grows exponentially with the number of network components, analysis of large networks is a complex problem. In this paper, we introduce the notion of symbolic steady state that allows us to identify subnetworks that govern the dynamics of the original network in some region of state space. We state rules to explicitly construct attractors of the system from subnetwork attractors. Using the results, we formulate sufficient conditions for the existence of multiple attractors resp. a cyclic attractor based on the existence of positive resp. negative feedback circuits in the graph representing the structure of the system. In addition, we discuss approaches to finding symbolic steady states. We focus both on dynamics derived via synchronous as well as asynchronous update rules. Lastly, we illustrate the results by analyzing a model of T helper cell differentiation.     

Two-category model of task allocation with application to ant societies

In many network models of interacting units such as cells or insects, the coupling coefficients between units are independent of the state of the units. Here we analyze the temporal behavior of units that can switch between two 'category' states according to rules that involve category-dependent coupling coefficients. The behaviors of the category populations resulting from the asynchronous random updating of units are first classified according to the signs of the coupling coefficients using numerical simulations. They range from isolated fixed points to lines of fixed points and stochastic attractors. These behaviors are then explained analytically using iterated function systems and birth-death jump processes. The main inspiration for our work comes from studies of non-hierarchical task allocation in, e.g., harvester ant colonies where temporal fluctuations in the numbers of ants engaged in various tasks occur as circumstances require and depend on interactions between ants. We identify interaction types that produce quick recovery from perturbations to an asymptotic behavior whose characteristics are function of the coupling coefficients between ants as well as between ants and their environment. We also compute analytically the probability density of the population numbers, and show that perturbations in our model decay twice as fast as in a model with random switching dynamics. A subset of the interaction types between ants yields intrinsic stochastic asymptotic behaviors which could account for some of the experimentally observed fluctuations. Such noisy trajectories are shown to be random walks with state-dependent biases in the 'category population' phase space. With an external stimulus, the parameters of the category-switching rules become time-dependent. Depending on the growth rate of the stimulus in comparison to its population-dependent decay rate, the dynamics may qualitatively differ from the case without stimulus. Our simple two-category model provides a framework for understanding the rich variety of behaviors in network dynamics with state-dependent coupling coefficients, and especially in task allocation processes with many tasks.     

Refinement of the solution structure of the DNA hexamer 5'd(GCATGC)2: combined use of nuclear magnetic resonance and restrained molecular dynamics

The solution structure of the self-complementary DNA hexamer 5'd(GCATGC)2 comprising the specific target site for the restriction endonuclease Sph 1 is investigated by using nuclear magnetic resonance spectroscopy and restrained molecular dynamics. All the nonexchangeable proton resonances are assigned sequentially, and from time-dependent nuclear Overhauser enhancement measurements a set of 158 approximate interproton distances are determined. These distances are used as the basis of a structure refinement using restrained molecular dynamics in which the interproton distances are incorporated into the total energy function of the system in the form of an effective potential term. Two restrained molecular dynamics simulations are carried out, starting from classical B- and A-DNA [atomic root mean square (rms) difference 3.3 A]. In both cases convergence is achieved to essentially identical structures satisfying the experimental restraints and having a root mean square difference of only 0.3 A between them, which is within the rms fluctuations of the atoms about their average positions. These results suggest that the restrained molecular dynamics structures represent reasonable approximations of the solution structure. The converged structures are of the B type and exhibit clear sequence-dependent variations of helical parameters, some of which follow Calladine's rules and can be attributed to the relief of interstrand purine-purine clash at adjacent base pairs. In addition, the converged restrained dynamics structures appear bent with a radius of curvature of approximately 20 A. This bending appears to be due almost entirely to the large positive base roll angles, particularly at the Pyr-Pur steps. Further, the global and local helix axes are not coincident, and the global helix axis represents a superhelical axis which the bent DNA, when extended into an "infinite" helix by repeated translation and rotation, wraps around.     

On learning dynamics underlying the evolution of learning rules

In order to understand the development of non-genetically encoded actions during an animal’s lifespan, it is necessary to analyze the dynamics and evolution of learning rules producing behavior. Owing to the intrinsic stochastic and frequency-dependent nature of learning dynamics, these rules are often studied in evolutionary biology via agent-based computer simulations. In this paper, we show that stochastic approximation theory can help to qualitatively understand learning dynamics and formulate analytical models for the evolution of learning rules. We consider a population of individuals repeatedly interacting during their lifespan, and where the stage game faced by the individuals fluctuates according to an environmental stochastic process. Individuals adjust their behavioral actions according to learning rules belonging to the class of experience-weighted attraction learning mechanisms, which includes standard reinforcement and Bayesian learning as special cases. We use stochastic approximation theory in order to derive differential equations governing action play probabilities, which turn out to have qualitative features of mutator-selection equations. We then perform agent-based simulations to find the conditions where the deterministic approximation is closest to the original stochastic learning process for standard 2-action 2-player fluctuating games, where interaction between learning rules and preference reversal may occur. Finally, we analyze a simplified model for the evolution of learning in a producer–scrounger game, which shows that the exploration rate can interact in a non-intuitive way with other features of co-evolving learning rules. Overall, our analyses illustrate the usefulness of applying stochastic approximation theory in the study of animal learning.     

Chaotic neural network applied to two-dimensional motion control

Chaotic dynamics generated in a chaotic neural network model are applied to 2-dimensional (2-D) motion control. The change of position of a moving object in each control time step is determined by a motion function which is calculated from the firing activity of the chaotic neural network. Prototype attractors which correspond to simple motions of the object toward four directions in 2-D space are embedded in the neural network model by designing synaptic connection strengths. Chaotic dynamics introduced by changing system parameters sample intermediate points in the high-dimensional state space between the embedded attractors, resulting in motion in various directions. By means of adaptive switching of the system parameters between a chaotic regime and an attractor regime, the object is able to reach a target in a 2-D maze. In computer experiments, the success rate of this method over many trials not only shows better performance than that of stochastic random pattern generators but also shows that chaotic dynamics can be useful for realizing robust, adaptive and complex control function with simple rules.     

Seed dispersal in a patchy environment with global age dependence

A model of seed population dynamics proposed by S. A. Levin, A. Hastings, and D. Cohen is presented and analyzed. With the environment considered as a mosaic of patches, patch age is used along with time as an independent variable. Local dynamics depend not only on the local state, but also on the global environment via dispersal modelled by an integral over all patch ages. Basic technical properties of the time varying solutions are examined; necessary and sufficient conditions for nontrivial steady states are given; and general sufficient conditions for global asymptotic stability of these steady states are established. Primary tools of analysis include a hybrid Picard iteration, fixed point methods, monotonicity of solution structure, and upper and lower solutions for differential equations.This work was supported in part by National Science Foundation Grants MCS-7903497 and MCS-790349701     

A computer simulation of a neuron net model as a self-organizing system

A neural net model is simulated on an IBM-1130 digital computer. The model includes rules for learning of the presented patterns. The learning algorithm uses an iteration procedure, in order to compute the ultimate cross coupling-coefficients between the neurons for a specific pattern. The network has a set of latent cyclic modes or reverberations. If the net is stimulated briefly, by presenting a pattern, it will subsequently either return to quiescence or settle into periodic activity in one of its cyclic modes.     

植被层内能量与水分交换的显式解的推导

本文发展了一个求解植被－大气相互作用的稳态分层模式。它结合了Ｎｏｒｍａｎ提出的植被层内辐射能传输模型和Ｗａｓｓｏｎｅｒ及Ｒｅｉｆｓｎｙｄｅｒ提出的求解通量的电路类比模型,推导了来自空中及地表面辐射能在植被层内传递的显式解,还推导了一套通用的联立方程组,把植被层内显热及潜热通量、空气的温度及水汽压等表示为只是叶温的函数。结果避免了以往一些模型不必要迭代．减少了计算机工作量。     

Evaluation of dynamic behavior forecasting parameters in the process of transition rule induction of unidimensional cellular automata

The simulation of the dynamics of a cellular systems based on cellular automata (CA) can be computationally expensive. This is particularly true when such simulation is part of a procedure of rule induction to find suitable transition rules for the CA. Several efforts have been described in the literature to make this problem more treatable. This work presents a study about the efficiency of dynamic behavior forecasting parameters (DBFPs) used for the induction of transition rules of CA for a specific problem: the classification by the majority rule. A total of 8 DBFPs were analyzed for the 31 best-performing rules found in the literature. Some of these DBFPs were highly correlated each other, meaning they yield the same information. Also, most rules presented values of the DBFPs very close each other. An evolutionary algorithm, based on gene expression programming, was developed for finding transition rules according a given preestablished behavior. The simulation of the dynamic behavior of the CA is not used to evaluate candidate transition rules. Instead, the average values for the DBFPs were used as reference. Experiments were done using the DBFPs separately and together. In both cases, the best induced transition rules were not acceptable solutions for the desired behavior of the CA. We conclude that, although the DBFPs represent interesting aspects of the dynamic behavior of CAs, the transition rule induction process still requires the simulation of the dynamics and cannot rely only on the DBFPs.     

Influence of Opinion Dynamics on the Evolution of Games

Under certain circumstances such as lack of information or bounded rationality, human players can take decisions on which strategy to choose in a game on the basis of simple opinions. These opinions can be modified after each round by observing own or others payoff results but can be also modified after interchanging impressions with other players. In this way, the update of the strategies can become a question that goes beyond simple evolutionary rules based on fitness and become a social issue. In this work, we explore this scenario by coupling a game with an opinion dynamics model. The opinion is represented by a continuous variable that corresponds to the certainty of the agents respect to which strategy is best. The opinions transform into actions by making the selection of an strategy a stochastic event with a probability regulated by the opinion. A certain regard for the previous round payoff is included but the main update rules of the opinion are given by a model inspired in social interchanges. We find that the fixed points of the dynamics of the coupled model are different from those of the evolutionary game or the opinion models alone. Furthermore, new features emerge such as the independence of the fraction of cooperators with respect to the topology of the social interaction network or the presence of a small fraction of extremist players.     

An algorithm for targeted convergence of Euler or Newton iterations

The concept of multistationarity has become essential for understanding cell differentiation. For this reason theoretical biologists have more and more frequently to determine the steady values, often multiple, of systems of non-linear differential equations. It is well known that iteration processes of current use converge or not towards a fixed point depending on the absolute value of the slope of the iteration function in the vicinity of the considered fixed point. A number of methods have been developed to obtain or accelerate convergence. As biologists, we do not pretend to review these works. Rather, we propose here a simple algorithm which permits to converge at will towards a chosen type of steady state. Others and we have used this procedure extensively for years for the analysis of complex biological systems. A compact program (using Mathematica) is available.     

Real-time fuzzy-knowledge-based control of Baker's yeast production

A real-time fuzzy-knowledge-based system for fault diagnosis and control of bioprocesses was constructed using the object-oriented programming environment Small-talk/V Mac. The basic system was implemented in a Macintosh Quadra 900 computer and built to function connected on line to the process computer. Fuzzy logic was employed in handling uncertainties both in the knowledge and in measurements. The fuzzy sets defined for the process variables could be changed on-line according to process dynamics. Process knowledge was implemented in a graphical two-level hierachical knowledge base. In on-line process control the system first recognizes the current process phase on the basis of top-level rules in the knowledge-base. Then, according to the results of process diagnosis based on measurement data, the appropriate control strategy is subsequently inferred making use of the lower level rules describing the process during the phase in question. (c) 1995 John Wiley & Sons, Inc.     

McComedy: A user-friendly tool for next-generation individual-based modeling of microbial consumer-resource systems

Individual-based modeling is widely applied to investigate the ecological mechanisms driving microbial community dynamics. In such models, the population or community dynamics emerge from the behavior and interplay of individual entities, which are simulated according to a predefined set of rules. If the rules that govern the behavior of individuals are based on generic and mechanistically sound principles, the models are referred to as next-generation individual-based models. These models perform particularly well in recapitulating actual ecological dynamics. However, implementation of such models is time-consuming and requires proficiency in programming or in using specific software, which likely hinders a broader application of this powerful method. Here we present McComedy, a modeling tool designed to facilitate the development of next-generation individual-based models of microbial consumer-resource systems. This tool allows flexibly combining pre-implemented building blocks that represent physical and biological processes. The ability of McComedy to capture the essential dynamics of microbial consumer-resource systems is demonstrated by reproducing and furthermore adding to the results of two distinct studies from the literature. With this article, we provide a versatile tool for developing next-generation individual-based models that can foster understanding of microbial ecology in both research and education.     

保障国家公园体制试点区社区居民利益分享的公平与可持续性——基于社会-生态系统意义认知的研究

建立国家公园旨在保护生态系统完整性并为民众提供多样化的使用机会,保障利益相关者利益分享的公平与可持续性。对国家公园社区居民的资源使用而言,需要他们认可保护地管理中的利益分享规则,从而规范行为,促进系统的稳健性。影响规则认可与相应行为的关键在于各个资源使用者如何评估资源价值,以及如何形成价值共识。基于社会-生态系统理论,研究利用一个界定资源价值与形成使用规则的分析框架,通过对资源价值界定的情境认知、对生态系统的意义认知和对可能规则的态度进行分析,研究武夷山国家公园体制试点建设进程中社区对"利益"的动态认知与形成原因、潜在行为变动对系统"稳健性"的影响和促进利益分享规则形成的路径。分析发现,①在保护地管理发展过程中,社区认为其以往存在和国家公园的出现有利于资源的生计带动;②武夷山生态系统的意义首先在于其多样化的物质供给,其次是作为文化遗产和商品所带来精神满足,同时具有生态保护价值;③社区对利益分享规则的态度取决于规则在时空上的应用是否影响他们对生态系统意义所认定的优先次序。因此,研究提出一个用于规则形成的协商空间,从不同资源使用者利益认知角度引导其认知趋同,最终提高社区对规则的接受程度与行...     

Complex sequencing rules of birdsong can be explained by simple hidden Markov processes

Complex sequencing rules observed in birdsongs provide an opportunity to investigate the neural mechanism for generating complex sequential behaviors. To relate the findings from studying birdsongs to other sequential behaviors such as human speech and musical performance, it is crucial to characterize the statistical properties of the sequencing rules in birdsongs. However, the properties of the sequencing rules in birdsongs have not yet been fully addressed. In this study, we investigate the statistical properties of the complex birdsong of the Bengalese finch (Lonchura striata var. domestica). Based on manual-annotated syllable labeles, we first show that there are significant higher-order context dependencies in Bengalese finch songs, that is, which syllable appears next depends on more than one previous syllable. We then analyze acoustic features of the song and show that higher-order context dependencies can be explained using first-order hidden state transition dynamics with redundant hidden states. This model corresponds to hidden Markov models (HMMs), well known statistical models with a large range of application for time series modeling. The song annotation with these models with first-order hidden state dynamics agreed well with manual annotation, the score was comparable to that of a second-order HMM, and surpassed the zeroth-order model (the Gaussian mixture model; GMM), which does not use context information. Our results imply that the hierarchical representation with hidden state dynamics may underlie the neural implementation for generating complex behavioral sequences with higher-order dependencies.     

Cis-regulatory evolution of chalcone-synthase expression in the genus Arabidopsis

The contribution of cis-regulation to adaptive evolutionary change is believed to be essential, yet little is known about the evolutionary rules that govern regulatory sequences. Here, we characterize the short-term evolutionary dynamics of a cis-regulatory region within and among two closely related species, A. lyrata and A. halleri, and compare our findings to A. thaliana. We focused on the cis-regulatory region of chalcone synthase (CHS), a key enzyme involved in the synthesis of plant secondary metabolites. We observed patterns of nucleotide diversity that differ among species but do not depart from neutral expectations. Using intra- and interspecific F1 progeny, we have evaluated functional cis-regulatory variation in response to light and herbivory, environmental cues, which are known to induce CHS expression. We find that substantial cis-regulatory variation segregates within and among populations as well as between species, some of which results from interspecific genetic introgression. We further demonstrate that, in A. thaliana, CHS cis-regulation in response to herbivory is greater than in A. lyrata or A. halleri. Our work indicates that the evolutionary dynamics of a cis-regulatory region is characterized by pervasive functional variation, achieved mostly by modification of response modules to one but not all environmental cues. Our study did not detect the footprint of selection on this variation.     

A 3-D model of tumor progression based on complex automata driven by particle dynamics

The dynamics of a growing tumor involving mechanical remodeling of healthy tissue and vasculature is neglected in most of the existing tumor models. This is due to the lack of efficient computational framework allowing for simulation of mechanical interactions. Meanwhile, just these interactions trigger critical changes in tumor growth dynamics and are responsible for its volumetric and directional progression. We describe here a novel 3-D model of tumor growth, which combines particle dynamics with cellular automata concept. The particles represent both tissue cells and fragments of the vascular network. They interact with their closest neighbors via semi-harmonic central forces simulating mechanical resistance of the cell walls. The particle dynamics is governed by both the Newtonian laws of motion and the cellular automata rules. These rules can represent cell life-cycle and other biological interactions involving smaller spatio-temporal scales. We show that our complex automata, particle based model can reproduce realistic 3-D dynamics of the entire system consisting of the tumor, normal tissue cells, blood vessels and blood flow. It can explain phenomena such as the inward cell motion in avascular tumor, stabilization of tumor growth by the external pressure, tumor vascularization due to the process of angiogenesis, trapping of healthy cells by invading tumor, and influence of external (boundary) conditions on the direction of tumor progression. We conclude that the particle model can serve as a general framework for designing advanced multiscale models of tumor dynamics and it is very competitive to the modeling approaches presented before.