Reverse engineering of gene regulatory networks: a finite state linear model

We propose a new model for describing gene regulatory networks that can capture discrete (Boolean) and continuous (differential) aspects of gene regulation. After giving some illustrations of the model, we study the problem of the reverse engineering of such networks, i.e., how to construct a network from gene expression data. We prove that for our model there exists an algorithm finding a network compatible with the given data. We demonstrate the model by simulating lambda-phage. We also describe some generalizations of the model, discuss their relevance to the real-world gene networks and formulate a number of open problems.     

A neutral model of community organization

A discrete time simulation model is described which is neutral (sensuCaswell, 1976) with respect to competition-based community organizational hypotheses. The model randomly locates rectangular niches (identified with species) in a two-dimensional resource hyperspace. Populations for each niche are randomly assigned and increase or decrease randomly in the absence of predation. Predation is represented by a “Lnegative niche” (viz., a rectangular region in the two-space) which removes all organisms that lie within it (i.e. reduces the populations in niches that overlap it in proportion to the overlap). Competition is not represented; hence, the model is neutral with respect to hypotheses of the role of competition in organizing communities.The model determines a number of measures of community organization at each time step: average niche size, average overlap between niches, species diversity, number of niches, average population size, average number of neighbors. Statitistical analyses allow comparison of results between runs and with field data.Model behavior is explained by deriving dimensionless variables that relate model parameters to output. These variables were derived using one set of simulations. A second set of simulations is used to validate the relationships. These relationships are interpreted as testable hypotheses of community organization that do not depend on competition. Preliminary tests are given by comparing qualitatively model output with data from lizard and small mammal communities.     

Complex metabolic network of 1,3-propanediol transport mechanisms and its system identification via biological robustness

The bioconversion of glycerol to 1,3-propanediol (1,3-PD) by Klebsiella pneumoniae (K. pneumoniae) can be characterized by an intricate metabolic network of interactions among biochemical fluxes, metabolic compounds, key enzymes and genetic regulation. Since there are some uncertain factors in the fermentation, especially the transport mechanisms of 1,3-PD across cell membrane, the metabolic network contains multiple possible metabolic systems. Considering the genetic regulation of dha regulon and inhibition of 3-hydroxypropionaldehyde to the growth of cells, we establish a 14-dimensional nonlinear hybrid dynamical system aiming to determine the most possible metabolic system and the corresponding optimal parameter. The existence, uniqueness and continuity of solutions are discussed. Taking the robustness index of the intracellular substances together as a performance index, a system identification model is proposed, in which 1,395 continuous variables and 90 discrete variables are involved. The identification problem is decomposed into two subproblems and a parallel particle swarm optimization procedure is constructed to solve them. Numerical results show that it is most possible that 1,3-PD passes the cell membrane by active transport coupled with passive diffusion.     

A Trade-Off between Sample Complexity and Computational Complexity in Learning Boolean Networks from Time-Series Data

A key problem in molecular biology is to infer regulatory relationships between genes from expression data. This paper studies a simplified model of such inference problems in which one or more Boolean variables, modeling, for example, the expression levels of genes, each depend deterministically on a small but unknown subset of a large number of Boolean input variables. Our model assumes that the expression data comprises a time series, in which successive samples may be correlated. We provide bounds on the expected amount of data needed to infer the correct relationships between output and input variables. These bounds improve and generalize previous results for Boolean network inference and continuous-time switching network inference. Although the computational problem is intractable in general, we describe a fixed-parameter tractable algorithm that is guaranteed to provide at least a partial solution to the problem. Most interestingly, both the sample complexity and computational complexity of the problem depend on the strength of correlations between successive samples in the time series but in opposing ways. Uncorrelated samples minimize the total number of samples needed while maximizing computational complexity; a strong correlation between successive samples has the opposite effect. This observation has implications for the design of experiments for measuring gene expression.     

Complementing ODE-Based System Analysis Using Boolean Networks Derived from an Euler-Like Transformation

In this paper, we present a systematic transition scheme for a large class of ordinary differential equations (ODEs) into Boolean networks. Our transition scheme can be applied to any system of ODEs whose right hand sides can be written as sums and products of monotone functions. It performs an Euler-like step which uses the signs of the right hand sides to obtain the Boolean update functions for every variable of the corresponding discrete model. The discrete model can, on one hand, be considered as another representation of the biological system or, alternatively, it can be used to further the analysis of the original ODE model. Since the generic transformation method does not guarantee any property conservation, a subsequent validation step is required. Depending on the purpose of the model this step can be based on experimental data or ODE simulations and characteristics. Analysis of the resulting Boolean model, both on its own and in comparison with the ODE model, then allows to investigate system properties not accessible in a purely continuous setting. The method is exemplarily applied to a previously published model of the bovine estrous cycle, which leads to new insights regarding the regulation among the components, and also indicates strongly that the system is tailored to generate stable oscillations.     

An analysis of the class of gene regulatory functions implied by a biochemical model

Understanding the integrated behavior of genetic regulatory networks, in which genes regulate one another's activities via RNA and protein products, is emerging as a dominant problem in systems biology. One widely studied class of models of such networks includes genes whose expression values assume Boolean values (i.e., on or off). Design decisions in the development of Boolean network models of gene regulatory systems include the topology of the network (including the distribution of input- and output-connectivity) and the class of Boolean functions used by each gene (e.g., canalizing functions, post functions, etc.). For example, evidence from simulations suggests that biologically realistic dynamics can be produced by scale-free network topologies with canalizing Boolean functions. This work seeks further insights into the design of Boolean network models through the construction and analysis of a class of models that include more concrete biochemical mechanisms than the usual abstract model, including genes and gene products, dimerization, cis-binding sites, promoters and repressors. In this model, it is assumed that the system consists of N genes, with each gene producing one protein product. Proteins may form complexes such as dimers, trimers, etc. The model also includes cis-binding sites to which proteins may bind to form activators or repressors. Binding affinities are based on structural complementarity between proteins and binding sites, with molecular binding sites modeled by bit-strings. Biochemically plausible gene expression rules are used to derive a Boolean regulatory function for each gene in the system. The result is a network model in which both topological features and Boolean functions arise as emergent properties of the interactions of components at the biochemical level. A highly biased set of Boolean functions is observed in simulations of networks of various sizes, suggesting a new characterization of the subset of Boolean functions that are likely to appear in gene regulatory networks.     

Structure and development of the insect antennodeutocerebral system

The structure and postembryonic development of antennae and deutocerebrum in various insect orders are reviewed. First, the number and/or size of system components, i.e. antennal sensilla, neuroreceptors, deutocerebral neurons and synaptic complexes (glomeruli), are compared in adult insects. Second, the neuronal organization of the system is examined. Evidence of projection of the neuroreceptors from the 2 basal antennal segments (scape and pedicel) in the antennal mechanosensory and motor center and from the distal segments (flagellum) in the antennal lobe is discussed. Third, the types of cerebral neurons found in the antennal lobe are described. Fourth, all synaptic contacts between neurons in the antennal lobe take place in discrete glomeruli whose ultrastructure and neurotransmitters are examined. Evidence of individual identifiability of glomeruli is given. Fifth, various sexual dimorphisms present in the antenna and antennal lobe, related or not to sex pheromone perception, are described at sensillar, neuronal, and glomerular levels. Sixth, the postembryonic development of neurons and glomeruli is analyzed in holo- and hemimetabolous insects. In conclusion, the columnar organization of the system is emphasized, alternative models of antennal-neuron projection into glomeruli are considered, and the functional significance of identified glomeruli is discussed.     

Batch sizes and lead-time performance in flexible manufacturing systems

Production lead-time performance in flexible manufacturing systems is influenced by several factors which include: machine groupings, demand rates, machine processing rates, product batching, material handling system capacity, and so on. Hence, control of lead-time performance can be affected through the manipulation of one or more of these variables. In this article, we investigate the potential of batch sizing as a control variable for lead-time performance through the use of a queueing network model. We establish a functional relationship between the two variables, and incorporate the relationship in an optimization model to determine the optimal batch size(s) which minimizes the sum of annual work-in-process inventory and final inventory costs. The nonlinear batch sizing problem which results is solved by discrete optimization via marginal analysis. Results show that batch sizing can be a cheap and effective variable for controlling flexible manufacturing system throughput.     

Brucellosis, botflies, and brainworms: the impact of edge habitats on pathogen transmission and species extinction

Ecological interactions between species that prefer different habitat types but come into contact in edge regions at the interfaces between habitat types are modeled via reaction-diffusion systems. The primary sort of interaction described by the models is competition mediated by pathogen transmission. The models are somewhat novel because the spatial domains for the variables describing the population densities of the interacting species overlap but do not coincide. Conditions implying coexistence of the two species or the extinction of one species are derived. The conditions involve the principal eigenvalues of elliptic operators arising from linearizations of the model system around equilibria with only one species present. The conditions for persistence or extinction are made explicit in terms of the parameters of the system and the geometry of the underlying spatial domains via estimates of the principal eigenvalues. The implications of the models with respect to conservation and refuge design are discussed. Received: 10 June 1999 / Revised version: 7 July 2000 / Published online: 20 December 2000     

Feedback regulation in preparative elution chromatography.

Input-output models utilizing discrete variables are developed for elution chromatography and used together with control theory to investigate behavior patterns between output variables (e.g., yield, purity, and production rate) and input variables (e.g., cut point locations and feed slug size). Variable interactions and controllability characteristics for isocratic and stepwise gradient elution in linear and nonlinear chromatography are investigated by using the relative gain array, singular value decomposition, and direct simulation. Inverse-based regulatory systems are evaluated for updating process inputs by using information on process outputs such that product quality and system performance parameters are efficiently maintained for the case where the column is overloaded and the solute peaks overlap with each other. Strategies for feedback optimizing control are also discussed.     

Genetic network inference: from co-expression clustering to reverse engineering

MOTIVATION: Advances in molecular biological, analytical and computational technologies are enabling us to systematically investigate the complex molecular processes underlying biological systems. In particular, using high-throughput gene expression assays, we are able to measure the output of the gene regulatory network. We aim here to review datamining and modeling approaches for conceptualizing and unraveling the functional relationships implicit in these datasets. Clustering of co-expression profiles allows us to infer shared regulatory inputs and functional pathways. We discuss various aspects of clustering, ranging from distance measures to clustering algorithms and multiple-cluster memberships. More advanced analysis aims to infer causal connections between genes directly, i.e. who is regulating whom and how. We discuss several approaches to the problem of reverse engineering of genetic networks, from discrete Boolean networks, to continuous linear and non-linear models. We conclude that the combination of predictive modeling with systematic experimental verification will be required to gain a deeper insight into living organisms, therapeutic targeting and bioengineering.     

Prey diversity as a driver of resource partitioning between river‐dwelling fish species

Although food resource partitioning among sympatric species has often been explored in riverine systems, the potential influence of prey diversity on resource partitioning is little known. Using empirical data, we modeled food resource partitioning (assessed as dietary overlap) of coexisting juvenile Atlantic salmon (Salmo salar) and alpine bullhead (Cottus poecilopus). Explanatory variables incorporated into the model were fish abundance, benthic prey diversity and abundance, and several dietary metrics to give a total of seventeen potential explanatory variables. First, a forward stepwise procedure based on the Akaike information criterion was used to select explanatory variables with significant effects on food resource partitioning. Then, linear mixed‐effect models were constructed using the selected explanatory variables and with sampling site as a random factor. Food resource partitioning between salmon and bullhead increased significantly with increasing prey diversity, and the variation in food resource partitioning was best described by the model that included prey diversity as the only explanatory variable. This study provides empirical support for the notion that prey diversity is a key driver of resource partitioning among competing species.     

Genetic network models and statistical properties of gene expression data in knock-out experiments

It is shown here how gene knock-out experiments can be simulated in Random Boolean Networks (RBN), which are well-known simplified models of genetic networks. The results of the simulations are presented and compared with those of actual experiments in S. cerevisiae. RBN with two incoming links per node have been considered, and the Boolean functions have been chosen at random among the set of so-called canalizing functions. Genes are knocked-out (i.e. silenced) one at a time, and the variations in the expression levels of the other genes, with respect to the unperturbed case, are considered. Two important variables are defined: (i) avalanches, which measure the size of the perturbation generated by knocking out a single gene, and (ii) susceptibilities, which measure how often the expression of a given gene is modified in these experiments. A remarkable observation is that the distributions of avalanches and susceptibilities are very robust, i.e. they are very similar in different random networks; this should be contrasted with the distribution of other variables that show a high variance in RBN. Moreover, the distribution of avalanches and susceptibilities of the RBN models are close to those observed in actual experiments performed with S. cerevisiae, where the changes in gene expression levels have been recorded with DNA microarrays. These findings suggest that these distributions might be "generic" properties, common to a wide range of genetic models and real genetic networks. The importance of such generic properties is discussed.     

Variables aggregation in a time discrete linear model

In this work we extend approximate aggregation methods to deal with a very general linear time discrete model. Approximate aggregation consists in describing some features of the dynamics of a general system in terms of the dynamics of a reduced system governed by a few global variables. We present a time discrete model for a structured population (i.e., the population is subdivided in subpopulations) in which we can distinguish two processes of a general nature and whose corresponding time scales are very different from each other. We transform the general system to make the global variables appear and obtain the reduced system. These global variables are, for each subpopulation, a certain linear combination of the corresponding state variables. We show that, under quite general conditions, the asymptotic behavior of the reduced system can be known in terms of the corresponding behavior for the reduced system. The general method is applied to aggregate a multiregional Leslie model in which the demographic process is supposed to be fast with respect to migration.     

Exploring global distortions of biological macromolecules and assemblies from low-resolution structural information and elastic network theory

A theory of elastic normal modes is described for the exploration of global distortions of biological structures and their assemblies based upon low-resolution image data. Structural information at low resolution, e.g. from density maps measured by cryogenic electron microscopy (cryo-EM), is used to construct discrete multi-resolution models for the electron density using the techniques of vector quantization. The elastic normal modes computed based on these discretized low-resolution models are found to compare well with the normal modes obtained at atomic resolution. The quality of the normal modes describing global displacements of the molecular system is found to depend on the resolution of the synthetic EM data and the extent of reductionism in the discretized representation. However, models that reproduce the functional rearrangements of our test set of molecules are achieved for realistic values of experimental resolution. Thus large conformational changes as occur during the functioning of biological macromolecules and assemblies can be elucidated directly from low-resolution structural data through the application of elastic normal mode theory and vector quantization.     

Modeling discrete and rhythmic movements through motor primitives: a review

Rhythmic and discrete movements are frequently considered separately in motor control, probably because different techniques are commonly used to study and model them. Yet the increasing interest in finding a comprehensive model for movement generation requires bridging the different perspectives arising from the study of those two types of movements. In this article, we consider discrete and rhythmic movements within the framework of motor primitives, i.e., of modular generation of movements. In this way we hope to gain an insight into the functional relationships between discrete and rhythmic movements and thus into a suitable representation for both of them. Within this framework we can define four possible categories of modeling for discrete and rhythmic movements depending on the required command signals and on the spinal processes involved in the generation of the movements. These categories are first discussed in terms of biological concepts such as force fields and central pattern generators and then illustrated by several mathematical models based on dynamical system theory. A discussion on the plausibility of theses models concludes the work.     

Modelling motor units in 3D: influence on muscle contraction and joint force via a proof of concept simulation

Functional heterogeneity is a skeletal muscle’s ability to generate diverse force vectors through localised motor unit (MU) recruitment. Existing 3D macroscopic continuum-mechanical finite element (FE) muscle models neglect MU anatomy and recruit muscle volume simultaneously, making them unsuitable for studying functional heterogeneity. Here, we develop a method to incorporate MU anatomy and information in 3D models. Virtual fibres in the muscle are grouped into MUs via a novel “virtual innervation” technique, which can control the units’ size, shape, position, and overlap. The discrete MU anatomy is then mapped to the FE mesh via statistical averaging, resulting in a volumetric MU distribution. Mesh dependency is investigated using a 2D idealised model and revealed that the amount of MU overlap is inversely proportional to mesh dependency. Simultaneous recruitment of a MU’s volume implies that action potentials (AP) propagate instantaneously. A 3D idealised model is used to verify this assumption, revealing that neglecting AP propagation results in a slightly less-steady force, advanced in time by approximately 20 ms, at the tendons. Lastly, the method is applied to a 3D, anatomically realistic model of the masticatory system to demonstrate the functional heterogeneity of masseter muscles in producing bite force. We found that the MU anatomy significantly affected bite force direction compared to bite force magnitude. MU position was much more efficacious in bringing about bite force changes than MU overlap. These results highlight the relevance of MU anatomy to muscle function and joint force, particularly for muscles with complex neuromuscular architecture.

     

Higher mental functions and the systems analysis of behavior under conditions of uncertainty

Superior psychical functions (skills) are usually formed in great subjective uncertainty conditions. Because of that exact knowledge of information mechanisms of behavior activity under uncertainty conditions is very importent. Some difficulties of traditional notions (classic behavior act model developed by P. K. Anokhin, systems quantization of behavior) are discussed. The model of probabilitive training allows to describe various training uncertainty conditions, and it operates as the Anokhin model in a specific case. The system-shaping factor in this model is an adaptive result. Afferent synthesis, aim for action, acceptor of the action result and the programme of actions have the traditional senses. Besides those it is proposed to use a concept of probability decision to alter the program of action, as well as an idea of memory buffer (results of search reactions). The organizational features of the functional system of behavior under great uncertainty conditions should be taken into account while specifying the informational mechanism responsible for systems quantization of behavior. The above mechanism can be used for explain the discreteness of an action in the program alteration process when the same quantum of behavior is implemented. These ideas are profitable for systems analysis of superior psychical functions, based on the reflex formation under environmental uncertainty conditions.