Functional identification of biological neural networks using reservoir adaptation for point processes

The complexity of biological neural networks does not allow to directly relate their biophysical properties to the dynamics of their electrical activity. We present a reservoir computing approach for functionally identifying a biological neural network, i.e. for building an artificial system that is functionally equivalent to the reference biological network. Employing feed-forward and recurrent networks with fading memory, i.e. reservoirs, we propose a point process based learning algorithm to train the internal parameters of the reservoir and the connectivity between the reservoir and the memoryless readout neurons. Specifically, the model is an Echo State Network (ESN) with leaky integrator neurons, whose individual leakage time constants are also adapted. The proposed ESN algorithm learns a predictive model of stimulus-response relations in in vitro and simulated networks, i.e. it models their response dynamics. Receiver Operating Characteristic (ROC) curve analysis indicates that these ESNs can imitate the response signal of a reference biological network. Reservoir adaptation improved the performance of an ESN over readout-only training methods in many cases. This also held for adaptive feed-forward reservoirs, which had no recurrent dynamics. We demonstrate the predictive power of these ESNs on various tasks with cultured and simulated biological neural networks.     

Do mutualistic networks follow power distributions?

Species interactions are central to the structure and dynamics of biological communities. Recently, of particular interest, is the analysis of ecological networks where the number of species to species interactions vary depending on the degree of specialization. For mutualistic networks, species degree has been suggested to follows a power distribution or a truncated power distribution. In this paper, I discuss previously estimated parameters and associated model selection may be unreliable. I use the likelihood approach and compare the results from previous findings and show that the parameter estimates as well as model selection results are indeed very different. Furthermore, the likelihood approach reveals that many mutualistic networks do not follow either power distribution or truncated power distribution.     

Natural selection governs local, but not global, evolutionary gene coexpression networks in Caenorhabditis elegans

Background

Signal duration (e.g. the time over which an active signaling intermediate persists) is a key regulator of biological decisions in myriad contexts such as cell growth, proliferation, and developmental lineage commitments. Accompanying differences in signal duration are numerous downstream biological processes that require multiple steps of biochemical regulation.

Results

Here we present an analysis that investigates how simple biochemical motifs that involve multiple stages of regulation can be constructed to differentially process signals that persist at different time scales. We compute the dynamic, frequency dependent gain within these networks and resulting power spectra to better understand how biochemical networks can integrate signals at different time scales. We identify topological features of these networks that allow for different frequency dependent signal processing properties.

Conclusion

We show that multi-staged cascades are effective in integrating signals of long duration whereas multi-staged cascades that operate in the presence of negative feedback are effective in integrating signals of short duration. Our studies suggest principles for why signal duration in connection with multiple steps of downstream regulation is a ubiquitous motif in biochemical systems.     

Signal transduction networks: topology, response and biochemical processes

Conventionally, biological signal transduction networks are analysed using experimental and theoretical methods to describe specific protein components, interactions, and biochemical processes and to model network behavior under various conditions. While these studies provide crucial information on specific networks, this information is not easily converted to a broader understanding of signal transduction systems. Here, using a specific model of protein interaction we analyse small network topologies to understand their response and general properties. In particular, we catalogue the response for all possible topologies of a given network size to generate a response distribution, analyse the effects of specific biochemical processes on this distribution, and analyse the robustness and diversity of responses with respect to internal fluctuations or mutations in the network. The results show that even three- and four-protein networks are capable of creating diverse and biologically relevant responses, that the distribution of response types changes drastically as a function of biochemical processes at protein level, and that certain topologies strongly pre-dispose a specific response type while others allow for diverse types of responses. This study sheds light on the response types and properties that could be expected from signal transduction networks, provides possible explanations for the role of certain biochemical processes in signal transduction and suggests novel approaches to interfere with signaling pathways at the molecular level. Furthermore it shows that network topology plays a key role on determining response type and properties and that proper representation of network topology is crucial to discover and understand so-called building blocks of large networks.     

Growing biological networks: beyond the gene-duplication model

In this paper we propose a generalized growth model for biological interaction networks, including a set of biological features which have been inspired by a long tradition of simulations of immune system and chemical reaction networks. In our models we include characteristics such as the heterogeneity of biological nodes, the existence of natural hubs, the nodes binding by mutual affinity and the significance of type-based networks as compared with instance-based networks. Under these assumptions, we analyse the importance of the nodes concentration with respect to the selection of incoming nodes. We show that networks with fat-tailed degree distribution and highly clustered structure naturally emerge in systems possessing certain properties: new instances need to be produced through an endogenous source and this source needs to provide a positive feedback favouring nodes with high concentration to receive new connections. Furthermore, we show that understanding the concentration dynamics of each node and the consequent correlation between connectivity and concentration is a more adequate way to capture the global properties of type-based biological networks.     

Invariant properties in coevolutionary networks of plant–animal interactions

Plant–animal mutualistic networks are interaction webs consisting of two sets of entities, plant and animal species, whose evolutionary dynamics are deeply influenced by the outcomes of the interactions, yielding a diverse array of coevolutionary processes. These networks are two‐mode networks sharing many common properties with others such as food webs, social, and abiotic networks. Here we describe generalized patterns in the topology of 29 plant–pollinator and 24 plant–frugivore networks in natural communities. Scale‐free properties have been described for a number of biological, social, and abiotic networks; in contrast, most of the plant–animal mutualistic networks (65.6%) show species connectivity distributions (number of links per species) with a power‐law regime but decaying as a marked cut‐off, i.e. truncated power‐law or broad‐scale networks and few (22.2%) show scale‐invariance. We hypothesize that plant–animal mutualistic networks follow a build‐up process similar to complex abiotic nets, based on the preferential attachment of species. However, constraints in the addition of links such as morphological mismatching or phenological uncoupling between mutualistic partners, restrict the number of interactions established, causing deviations from scale‐invariance. This reveals generalized topological patterns characteristic of self‐organized complex systems. Relative to scale‐invariant networks, such constraints may confer higher robustness to the loss of keystone species that are the backbone of these webs.     

Inference of scale-free networks from gene expression time series

Quantitative time-series observation of gene expression is becoming possible, for example by cell array technology. However, there are no practical methods with which to infer network structures using only observed time-series data. As most computational models of biological networks for continuous time-series data have a high degree of freedom, it is almost impossible to infer the correct structures. On the other hand, it has been reported that some kinds of biological networks, such as gene networks and metabolic pathways, may have scale-free properties. We hypothesize that the architecture of inferred biological network models can be restricted to scale-free networks. We developed an inference algorithm for biological networks using only time-series data by introducing such a restriction. We adopt the S-system as the network model, and a distributed genetic algorithm to optimize models to fit its simulated results to observed time series data. We have tested our algorithm on a case study (simulated data). We compared optimization under no restriction, which allows for a fully connected network, and under the restriction that the total number of links must equal that expected from a scale free network. The restriction reduced both false positive and false negative estimation of the links and also the differences between model simulation and the given time-series data.     

Duplication models for biological networks.

Are biological networks different from other large complex networks? Both large biological and nonbiological networks exhibit power-law graphs (number of nodes with degree k, N(k) approximately k(-beta)), yet the exponents, beta, fall into different ranges. This may be because duplication of the information in the genome is a dominant evolutionary force in shaping biological networks (like gene regulatory networks and protein-protein interaction networks) and is fundamentally different from the mechanisms thought to dominate the growth of most nonbiological networks (such as the Internet). The preferential choice models used for nonbiological networks like web graphs can only produce power-law graphs with exponents greater than 2. We use combinatorial probabilistic methods to examine the evolution of graphs by node duplication processes and derive exact analytical relationships between the exponent of the power law and the parameters of the model. Both full duplication of nodes (with all their connections) as well as partial duplication (with only some connections) are analyzed. We demonstrate that partial duplication can produce power-law graphs with exponents less than 2, consistent with current data on biological networks. The power-law exponent for large graphs depends only on the growth process, not on the starting graph.     

A more efficient search strategy for aging genes based on connectivity

MOTIVATION: Many aging genes have been found from unbiased screens in model organisms. Genetic interventions promoting longevity are usually quantitative, while in many other biological fields (e.g. development) null mutations alone have been very informative. Therefore, in the case of aging the task is larger and the need for a more efficient genetic search strategy is especially strong. RESULTS: The topology of genetic and metabolic networks is organized according to a scale-free distribution, in which hubs with large numbers of links are present. We have developed a computational model of aging genes as the hubs of biological networks. The computational model shows that, after generalized damage, the function of a network with scale-free topology can be significantly restored by a limited intervention on the hubs. Analyses of data on aging genes and biological networks support the applicability of the model to biological aging. The model also might explain several of the properties of aging genes, including the high degree of conservation across different species. The model suggests that aging genes tend to have a higher number of connections and therefore supports a strategy, based on connectivity, for prioritizing what might otherwise be a random search for aging genes.     

Protein interaction networks of Saccharomyces cerevisiae, Caenorhabditis elegans and Drosophila melanogaster: large-scale organization and robustness

High-throughput screens have begun to reveal protein interaction networks in several organisms. To understand the general properties of these protein interaction networks, a systematic analysis of topological structure and robustness was performed on the protein interaction networks of Saccharomyces cerevisiae, Caenorhabditis elegans and Drosophila melanogaster. It shows that the three protein interaction networks have a scale-free and high-degree clustering nature as the consequence of their hierarchical organization. It also shows that they have the small-world property with similar diameter at 4-5. Evaluation of the consequences of random removal of both proteins and interactions from the protein interaction networks suggests their high degree of robustness. Simulation of a protein's removal shows that the protein interaction network's error tolerance is accompanied by attack vulnerability. These fundamental analyses of the networks might serve as a starting point for further exploring complex biological networks and the coming research of "systems biology".     

Simulating the evolution of signal transduction pathways

We use a generic model of a network of proteins that can activate or deactivate each other to explore the emergence and evolution of signal transduction networks and to gain a basic understanding of their general properties. Starting with a set of non-interacting proteins, we evolve a signal transduction network by random mutation and selection to fulfill a complex biological task. In order to validate this approach we base selection on a fitness function that captures the essential features of chemotactic behavior as seen in bacteria. We find that a system of as few as three proteins can evolve into a network mediating chemotaxis-like behavior by acting as a "derivative sensor". Furthermore, we find that the dynamics and topology of such networks show many similarities to the natural chemotaxis pathway, that the response magnitude can increase with increasing network size and that network behavior shows robustness towards variations in some of the internal parameters. We conclude that simulating the evolution of signal transduction networks to mediate a certain behavior may be a promising approach for understanding the general properties of the natural pathway for that behavior.     

Probabilistic inference of molecular networks from noisy data sources

Information on molecular networks, such as networks of interacting proteins, comes from diverse sources that contain remarkable differences in distribution and quantity of errors. Here, we introduce a probabilistic model useful for predicting protein interactions from heterogeneous data sources. The model describes stochastic generation of protein-protein interaction networks with real-world properties, as well as generation of two heterogeneous sources of protein-interaction information: research results automatically extracted from the literature and yeast two-hybrid experiments. Based on the domain composition of proteins, we use the model to predict protein interactions for pairs of proteins for which no experimental data are available. We further explore the prediction limits, given experimental data that cover only part of the underlying protein networks. This approach can be extended naturally to include other types of biological data sources.     

Path lengths in protein-protein interaction networks and biological complexity

We investigated the biological significance of path lengths in 12 protein-protein interaction (PPI) networks. We put forward three predictions, based on the idea that biological complexity influences path lengths. First, at the network level, path lengths are generally longer in PPIs than in random networks. Second, this pattern is more pronounced in more complex organisms. Third, within a PPI network, path lengths of individual proteins are biologically significant. We found that in 11 of the 12 species, average path lengths in PPI networks are significantly longer than those in randomly rewired networks. The PPI network of the malaria parasite Plasmodium falciparum, however, does not exhibit deviation from rewired networks. Furthermore, eukaryotic PPIs exhibit significantly greater deviation from randomly rewired networks than prokaryotic PPIs. Thus our study highlights the potentially meaningful variation in path lengths of PPI networks. Moreover, node eccentricity, defined as the longest path from a protein to others, is significantly correlated with the levels of gene expression and dispensability in the yeast PPI network. We conclude that biological complexity influences both global and local properties of path lengths in PPI networks. Investigating variation of path lengths may provide new tools to analyze the evolution of functional modules in biological systems.     

生物网络研究进展述评

生物网络是一类典型的复杂适应性系统,包含了许多个体的多层次的各种相互作用和关系,在过去的十年里,利用复杂网络理论对生物网络进行研究引起了人们的注意并获得了快速发展.本文首先从从度分布、聚类系数及鲁棒性等角度对现阶段生物网络性质的研究进行了简要介绍,后进一步对生物网络的聚类算法及主要建模理论做出了概括.今后的研究趋势在于如何建立合理的生物网络模型,以深入研究生物网络的各种性质.     

Graph-based methods for analysing networks in cell biology

Availability of large-scale experimental data for cell biology is enabling computational methods to systematically model the behaviour of cellular networks. This review surveys the recent advances in the field of graph-driven methods for analysing complex cellular networks. The methods are outlined on three levels of increasing complexity, ranging from methods that can characterize global or local structural properties of networks to methods that can detect groups of interconnected nodes, called motifs or clusters, potentially involved in common elementary biological functions. We also briefly summarize recent approaches to data integration and network inference through graph-based formalisms. Finally, we highlight some challenges in the field and offer our personal view of the key future trends and developments in graph-based analysis of large-scale datasets.     

Modeling of Hysteresis in Gene Regulatory Networks

Hysteresis, observed in many gene regulatory networks, has a pivotal impact on biological systems, which enhances the robustness of cell functions. In this paper, a general model is proposed to describe the hysteretic gene regulatory network by combining the hysteresis component and the transient dynamics. The Bouc-Wen hysteresis model is modified to describe the hysteresis component in the mammalian gene regulatory networks. Rigorous mathematical analysis on the dynamical properties of the model is presented to ensure the bounded-input-bounded-output (BIBO) stability and demonstrates that the original Bouc-Wen model can only generate a clockwise hysteresis loop while the modified model can describe both clockwise and counter clockwise hysteresis loops. Simulation studies have shown that the hysteresis loops from our model are consistent with the experimental observations in three mammalian gene regulatory networks and two E.coli gene regulatory networks, which demonstrate the ability and accuracy of the mathematical model to emulate natural gene expression behavior with hysteresis. A comparison study has also been conducted to show that this model fits the experiment data significantly better than previous ones in the literature. The successful modeling of the hysteresis in all the five hysteretic gene regulatory networks suggests that the new model has the potential to be a unified framework for modeling hysteresis in gene regulatory networks and provide better understanding of the general mechanism that drives the hysteretic function.     

The incorporation of epigenetics in artificial gene regulatory networks

Artificial gene regulatory networks are computational models that draw inspiration from biological networks of gene regulation. Since their inception they have been used to infer knowledge about gene regulation and as methods of computation. These computational models have been shown to possess properties typically found in the biological world, such as robustness and self organisation. Recently, it has become apparent that epigenetic mechanisms play an important role in gene regulation. This paper describes a new model, the Artificial Epigenetic Regulatory Network (AERN) which builds upon existing models by adding an epigenetic control layer. Our results demonstrate that AERNs are more adept at controlling multiple opposing trajectories when applied to a chaos control task within a conservative dynamical system, suggesting that AERNs are an interesting area for further investigation.