Modelling gene networks at different organisational levels

Approaches to modelling gene regulation networks can be categorized, according to increasing detail, as network parts lists, network topology models, network control logic models, or dynamic models. We discuss the current state of the art for each of these approaches. There is a gap between the parts list and topology models on one hand, and control logic and dynamic models on the other hand. The first two classes of models have reached a genome-wide scale, while for the other model classes high throughput technologies are yet to make a major impact.     

Small Modifications to Network Topology Can Induce Stochastic Bistable Spiking Dynamics in a Balanced Cortical Model

Directed random graph models frequently are used successfully in modeling the population dynamics of networks of cortical neurons connected by chemical synapses. Experimental results consistently reveal that neuronal network topology is complex, however, in the sense that it differs statistically from a random network, and differs for classes of neurons that are physiologically different. This suggests that complex network models whose subnetworks have distinct topological structure may be a useful, and more biologically realistic, alternative to random networks. Here we demonstrate that the balanced excitation and inhibition frequently observed in small cortical regions can transiently disappear in otherwise standard neuronal-scale models of fluctuation-driven dynamics, solely because the random network topology was replaced by a complex clustered one, whilst not changing the in-degree of any neurons. In this network, a small subset of cells whose inhibition comes only from outside their local cluster are the cause of bistable population dynamics, where different clusters of these cells irregularly switch back and forth from a sparsely firing state to a highly active state. Transitions to the highly active state occur when a cluster of these cells spikes sufficiently often to cause strong unbalanced positive feedback to each other. Transitions back to the sparsely firing state rely on occasional large fluctuations in the amount of non-local inhibition received. Neurons in the model are homogeneous in their intrinsic dynamics and in-degrees, but differ in the abundance of various directed feedback motifs in which they participate. Our findings suggest that (i) models and simulations should take into account complex structure that varies for neuron and synapse classes; (ii) differences in the dynamics of neurons with similar intrinsic properties may be caused by their membership in distinctive local networks; (iii) it is important to identify neurons that share physiological properties and location, but differ in their connectivity.     

How affinity influences tolerance in an idiotypic network

Idiotypic network models give one possible justification for the appearance of tolerance for a certain category of cells while maintaining immunization for the others. In this paper, we provide new evidence that the manner in which affinity is defined in an idiotypic network model imposes a definite topology on the connectivity of the potential idiotypic network that can emerge. The resulting topology is responsible for very different qualitative behaviour of the network. We show that using a 2D shape-space model with affinity based on complementary regions, a cluster-free topology results that clearly divides the space into distinct zones; if antigens fall into a zone in which there are no available antibodies to bind to, they are tolerated. On the other hand, if they fall into a zone in which there are highly concentrated antibodies available for binding, then they will be eliminated. On the contrary, using a 2D shape space with an affinity function based on cell similarity, a highly clustered topology emerges in which there is no separation of the space into isolated tolerant and non-tolerant zones. Using a bit-string shape space, both similar and complementary affinity measures also result in highly clustered networks. In the networks whose topologies exhibit high clustering, the tolerant and intolerant zones are so intertwined that the networks either reject all antigen or tolerate all antigen. We show that the distribution and topology of the antibody network defined by the complete set of nodes and links-an autonomous feature of the system-therefore selects which antigens are tolerated and which are eliminated.     

Towards building the silicon cell: a modular approach

Systems Biology aims to understand quantitatively how properties of biological systems can be understood as functions of the characteristics of, and interactions between their macromolecular components. Whereas, traditional biochemistry focused on isolation and characterization of cellular components, the challenge for Systems Biology lies in integration of this knowledge and the knowledge about molecular interactions. Computer models play an important role in this integration. We here discuss an approach with which we aim to link kinetic models on small parts of metabolism together, so as to form detailed kinetic models of larger chunks of metabolism, and ultimately of the entire living cell. Specifically, we will discuss techniques that can be used to model a sub-network in isolation of a larger network of which it is a part, while still maintaining the dynamics of the larger complete network. We will start by outlining the JWS online system, the silicon cell project, and the type of models we propose. JWS online is a model repository, which can be used for the storage, simulation and analysis of kinetic models. We advocate to integrate a top-down approach, where measurements on the complete system are used to derive fluxes in a detailed structural model, with a bottom-up approach, consisting of the integration of molecular mechanism-based detailed kinetic models into the structural model.     

Connectomic constraints on computation in feedforward networks of spiking neurons

Several efforts are currently underway to decipher the connectome or parts thereof in a variety of organisms. Ascertaining the detailed physiological properties of all the neurons in these connectomes, however, is out of the scope of such projects. It is therefore unclear to what extent knowledge of the connectome alone will advance a mechanistic understanding of computation occurring in these neural circuits, especially when the high-level function of the said circuit is unknown. We consider, here, the question of how the wiring diagram of neurons imposes constraints on what neural circuits can compute, when we cannot assume detailed information on the physiological response properties of the neurons. We call such constraints—that arise by virtue of the connectome—connectomic constraints on computation. For feedforward networks equipped with neurons that obey a deterministic spiking neuron model which satisfies a small number of properties, we ask if just by knowing the architecture of a network, we can rule out computations that it could be doing, no matter what response properties each of its neurons may have. We show results of this form, for certain classes of network architectures. On the other hand, we also prove that with the limited set of properties assumed for our model neurons, there are fundamental limits to the constraints imposed by network structure. Thus, our theory suggests that while connectomic constraints might restrict the computational ability of certain classes of network architectures, we may require more elaborate information on the properties of neurons in the network, before we can discern such results for other classes of networks.     

Structural properties of the MAPK pathway topologies in PC12 cells

In this paper we propose and analyze parameter-free models for the mitogen-activated protein kinase (MAPK) pathway in PC12 rat neural cells. Experiments show that the dynamic behavior of this pathway depends on the input growth factor. The response to epidermal growth factor (EGF) is a short peak followed by a relaxation, while the response to nerve growth factor (NGF) is sustained. In the latter case, the system can be driven to a new state, which persists after the stimulus has vanished. Ultimately, these dynamic behaviors correspond to different cell fates: EFG stimulation induces proliferation, while NGF stimulation induces differentiation. The biochemical mechanisms responsible for the different input-dependent dynamic response are still unclear. One hypothesis is that each input generates a specific interaction topology among the kinases. Starting from experimental results that support this hypothesis, we derive and analyze qualitative models for the two network topologies. Our approach is based on invariant set theory and non-smooth Lyapunov functions. We demonstrate analytically that the network behaviors and stability properties are structurally dependent on the topology, and do not depend on specific parameter values of the underlying biochemical interactions.     

Querying quantitative logic models (Q2LM) to study intracellular signaling networks and cell-cytokine interactions

Mathematical models have substantially improved our ability to predict the response of a complex biological system to perturbation, but their use is typically limited by difficulties in specifying model topology and parameter values. Additionally, incorporating entities across different biological scales ranging from molecular to organismal in the same model is not trivial. Here, we present a framework called "querying quantitative logic models" (Q2LM) for building and asking questions of constrained fuzzy logic (cFL) models. cFL is a recently developed modeling formalism that uses logic gates to describe influences among entities, with transfer functions to describe quantitative dependencies. Q2LM does not rely on dedicated data to train the parameters of the transfer functions, and it permits straight-forward incorporation of entities at multiple biological scales. The Q2LM framework can be employed to ask questions such as: Which therapeutic perturbations accomplish a designated goal, and under what environmental conditions will these perturbations be effective? We demonstrate the utility of this framework for generating testable hypotheses in two examples: (i) a intracellular signaling network model; and (ii) a model for pharmacokinetics and pharmacodynamics of cell-cytokine interactions; in the latter, we validate hypotheses concerning molecular design of granulocyte colony stimulating factor.     

Protein folding pathways and state transitions described by classical equations of motion of an elastic network model

Protein topology defined by the matrix of residue contacts has proved to be a fruitful basis for the study of protein dynamics. The widely implemented coarse-grained elastic network model of backbone fluctuations has been used to describe crystallographic temperature factors, allosteric couplings, and some aspects of the folding pathway. In the present study, we develop a model of protein dynamics based on the classical equations of motion of a damped network model (DNM) that describes the folding path from a completely unfolded state to the native conformation through a single-well potential derived purely from the native conformation. The kinetic energy gained through the collapse of the protein chain is dissipated through a friction term in the equations of motion that models the water bath. This approach is completely general and sufficiently fast that it can be applied to large proteins. Folding pathways for various proteins of different classes are described and shown to correlate with experimental observations and molecular dynamics and Monte Carlo simulations. Allosteric transitions between alternative protein structures are also modeled within the DNM through an asymmetric double-well potential.     

Epidemiologically Optimal Static Networks from Temporal Network Data

One of network epidemiology''s central assumptions is that the contact structure over which infectious diseases propagate can be represented as a static network. However, contacts are highly dynamic, changing at many time scales. In this paper, we investigate conceptually simple methods to construct static graphs for network epidemiology from temporal contact data. We evaluate these methods on empirical and synthetic model data. For almost all our cases, the network representation that captures most relevant information is a so-called exponential-threshold network. In these, each contact contributes with a weight decreasing exponentially with time, and there is an edge between a pair of vertices if the weight between them exceeds a threshold. Networks of aggregated contacts over an optimally chosen time window perform almost as good as the exponential-threshold networks. On the other hand, networks of accumulated contacts over the entire sampling time, and networks of concurrent partnerships, perform worse. We discuss these observations in the context of the temporal and topological structure of the data sets.     

The Dynamic Consequences of Cooperation and Competition in Small-World Networks

We present a study of the social dynamics among cooperative and competitive actors interacting on a complex network that has a small-world topology. In this model, the state of each actor depends on its previous state in time, its inertia to change, and the influence of its neighboring actors. Using numerical simulations, we determine how the distribution of final states of the actors and measures of the distances between the values of the actors at local and global levels, depend on the number of cooperative to competitive actors and the connectivity of the actors in the network. We find that similar numbers of cooperative and competitive actors yield the lowest values for the local and global measures of the distances between the values of the actors. On the other hand, when the number of either cooperative or competitive actors dominate the system, then the divergence is largest between the values of the actors. Our findings make new testable predictions on how the dynamics of a conflict depends on the strategies chosen by groups of actors and also have implications for the evolution of behaviors.     

Susceptible-infected-recovered epidemics in dynamic contact networks

Contact patterns in populations fundamentally influence the spread of infectious diseases. Current mathematical methods for epidemiological forecasting on networks largely assume that contacts between individuals are fixed, at least for the duration of an outbreak. In reality, contact patterns may be quite fluid, with individuals frequently making and breaking social or sexual relationships. Here, we develop a mathematical approach to predicting disease transmission on dynamic networks in which each individual has a characteristic behaviour (typical contact number), but the identities of their contacts change in time. We show that dynamic contact patterns shape epidemiological dynamics in ways that cannot be adequately captured in static network models or mass-action models. Our new model interpolates smoothly between static network models and mass-action models using a mixing parameter, thereby providing a bridge between disparate classes of epidemiological models. Using epidemiological and sexual contact data from an Atlanta high school, we demonstrate the application of this method for forecasting and controlling sexually transmitted disease outbreaks.     

BraX-Ray: An X-Ray of the Brazilian Computer Science Graduate Programs

Research productivity assessment is increasingly relevant for allocation of research funds. On one hand, this assessment is challenging because it involves both qualitative and quantitative analysis of several characteristics, most of them subjective in nature. On the other hand, current tools and academic social networks make bibliometric data web-available to everyone for free. Those tools, especially when combined with other data, are able to create a rich environment from which information on research productivity can be extracted. In this context, our work aims at characterizing the Brazilian Computer Science graduate programs and the relationship among themselves. We (i) present views of the programs from different perspectives, (ii) rank the programs according to each perspective and a combination of them, (iii) show correlation between assessment metrics, (iv) discuss how programs relate to another, and (v) infer aspects that boost programs'' research productivity. The results indicate that programs with a higher insertion in the coauthorship network topology also possess a higher research productivity between 2004 and 2009.     

Predicting network topology of mistletoe–host interactions: do mistletoes really mimic their hosts?

Network analysis provides a unified framework for investigating different types of species interactions at the community level. Network analysis is typically based on null models that test for specific patterns in network topology. Here we use a novel predictive approach to investigate the topology of a mistletoe–host network. It has been hypothesised that Australian mistletoes mimic the phenotype of their preferred hosts to avoid herbivory. We developed a deterministic model based on phenotypic similarity to predict the topology of a quantitative network between Lauranthaceaous mistletoes and their hosts. We quantified mistletoe–host interactions in a semi‐arid woodland central Australia, along with the size, shape and colour of leaves produced by both players in the interaction. Traditional null model analyses showed support for negative co‐occurrence patterns, web specialisation and strong links between species pairs. However, our deterministic model showed that the observed network topology could not be predicted by phenotypic similarity, suggesting that Australian mistletoes do not mimic their hosts.     

Uncovering Gene Regulatory Networks from Time-Series Microarray Data with Variational Bayesian Structural Expectation Maximization

We investigate in this paper reverse engineering of gene regulatory networks from time-series microarray data. We apply dynamic Bayesian networks (DBNs) for modeling cell cycle regulations. In developing a network inference algorithm, we focus on soft solutions that can provide a posteriori probability (APP) of network topology. In particular, we propose a variational Bayesian structural expectation maximization algorithm that can learn the posterior distribution of the network model parameters and topology jointly. We also show how the obtained APPs of the network topology can be used in a Bayesian data integration strategy to integrate two different microarray data sets. The proposed VBSEM algorithm has been tested on yeast cell cycle data sets. To evaluate the confidence of the inferred networks, we apply a moving block bootstrap method. The inferred network is validated by comparing it to the KEGG pathway map.     

A modified Ising model of Barabási–Albert network with gene-type spins

The central question of systems biology is to understand how individual components of a biological system such as genes or proteins cooperate in emerging phenotypes resulting in the evolution of diseases. As living cells are open systems in quasi-steady state type equilibrium in continuous exchange with their environment, computational techniques that have been successfully applied in statistical thermodynamics to describe phase transitions may provide new insights to the emerging behavior of biological systems. Here we systematically evaluate the translation of computational techniques from solid-state physics to network models that closely resemble biological networks and develop specific translational rules to tackle problems unique to living systems. We focus on logic models exhibiting only two states in each network node. Motivated by the apparent asymmetry between biological states where an entity exhibits boolean states i.e. is active or inactive, we present an adaptation of symmetric Ising model towards an asymmetric one fitting to living systems here referred to as the modified Ising model with gene-type spins. We analyze phase transitions by Monte Carlo simulations and propose a mean-field solution of a modified Ising model of a network type that closely resembles a real-world network, the Barabási–Albert model of scale-free networks. We show that asymmetric Ising models show similarities to symmetric Ising models with the external field and undergoes a discontinuous phase transition of the first-order and exhibits hysteresis. The simulation setup presented herein can be directly used for any biological network connectivity dataset and is also applicable for other networks that exhibit similar states of activity. The method proposed here is a general statistical method to deal with non-linear large scale models arising in the context of biological systems and is scalable to any network size.

     

Learning generative models of molecular dynamics

We introduce three algorithms for learning generative models of molecular structures from molecular dynamics simulations. The first algorithm learns a Bayesian-optimal undirected probabilistic model over user-specified covariates (e.g., fluctuations, distances, angles, etc). L1 regularization is used to ensure sparse models and thus reduce the risk of over-fitting the data. The topology of the resulting model reveals important couplings between different parts of the protein, thus aiding in the analysis of molecular motions. The generative nature of the model makes it well-suited to making predictions about the global effects of local structural changes (e.g., the binding of an allosteric regulator). Additionally, the model can be used to sample new conformations. The second algorithm learns a time-varying graphical model where the topology and parameters change smoothly along the trajectory, revealing the conformational sub-states. The last algorithm learns a Markov Chain over undirected graphical models which can be used to study and simulate kinetics. We demonstrate our algorithms on multiple molecular dynamics trajectories.     

A comparison of two cell regulatory models entailing high dimensional attractors representing phenotype

Two models for mammalian cell regulation that invoke the concept of cellular phenotype represented by high dimensional dynamic attractor states are compared. In one model the attractors are derived from an experimentally determined genetic regulatory network (GRN) for the cell type. As the state space architecture within which the attractors are embedded is determined by the binding sites on proteins and the recognition sites on DNA the attractors can be described as “hard-wired” in the genome through the genomic DNA sequence. In the second model attractors arising from the interactions between active gene products (mainly proteins) and independent of the genomic sequence, are descended from a pre-cellular state from which life originated. As this model is based on the cell as an open system the attractor acts as the interface between the cell and its environment. Environmental sources of stress can serve to trigger attractor and therefore phenotypic, transitions without entailing genotypic sequence changes.It is asserted that the evidence from cell and molecular biological research and logic, favours the second model. If correct there are important implications for understanding how environmental factors impact on evolution and may be implicated in hereditary and somatic disease.     

Mixed‐Effects State‐Space Models for Analysis of Longitudinal Dynamic Systems

Summary The rapid development of new biotechnologies allows us to deeply understand biomedical dynamic systems in more detail and at a cellular level. Many of the subject‐specific biomedical systems can be described by a set of differential or difference equations that are similar to engineering dynamic systems. In this article, motivated by HIV dynamic studies, we propose a class of mixed‐effects state‐space models based on the longitudinal feature of dynamic systems. State‐space models with mixed‐effects components are very flexible in modeling the serial correlation of within‐subject observations and between‐subject variations. The Bayesian approach and the maximum likelihood method for standard mixed‐effects models and state‐space models are modified and investigated for estimating unknown parameters in the proposed models. In the Bayesian approach, full conditional distributions are derived and the Gibbs sampler is constructed to explore the posterior distributions. For the maximum likelihood method, we develop a Monte Carlo EM algorithm with a Gibbs sampler step to approximate the conditional expectations in the E‐step. Simulation studies are conducted to compare the two proposed methods. We apply the mixed‐effects state‐space model to a data set from an AIDS clinical trial to illustrate the proposed methodologies. The proposed models and methods may also have potential applications in other biomedical system analyses such as tumor dynamics in cancer research and genetic regulatory network modeling.