Toward a classification of isodynamic feed-forward motifs

A preceding study analysed how the topology of network motifs affects the overall rate of the underlying biochemical processes. Surprisingly, it was shown that topologically non-isomorphic motifs can still be isodynamic in the sense that they exhibit the exact same performance rate. Because of the high prevalence of feed-forward functional modules in biological networks, one may hypothesize that evolution tends to favour motifs with faster dynamics. As a step towards ranking the efficiency of feed-forward network motifs, we use a linear flow model to prove theorems establishing that certain classes of motifs are isodynamic. In partitioning the class of all motifs on n nodes into equivalence classes based upon their dynamics, we establish a basis for comparing the efficiency/performance rates of different motifs. The potential biological importance of the theorems is briefly discussed and is the subject of an ongoing large-scale project.     

Design and implementation of three incoherent feed-forward motif based biological concentration sensors

Synthetic biology is a useful tool to investigate the dynamics of small biological networks and to assess our capacity to predict their behavior from computational models. In this work we report the construction of three different synthetic networks in Escherichia coli based upon the incoherent feed-forward loop architecture. The steady state behavior of the networks was investigated experimentally and computationally under different mutational regimes in a population based assay. Our data shows that the three incoherent feed-forward networks, using three different macromolecular inhibitory elements, reproduce the behavior predicted from our computational model. We also demonstrate that specific biological motifs can be designed to generate similar behavior using different components. In addition we show how it is possible to tune the behavior of the networks in a predicable manner by applying suitable mutations to the inhibitory elements. Brian Aufderheide provided material support.     

Some generalized conjugacy theorems and the concepts of fitness and survival in logistic growth models

Current research into the dynamics of iterative ecological and biological models has lead to a number of theorems concerning the existence of various types of iterative dynamical behavior. In particular, much study has been done on the dynamical behavior of the “simplest dynamical system”f _b(x)=bx(1−x), which is just the canonical discrete form of logistic growth equations found in ecology, sociobiology, and population biology. In this paper, we make use of some of the techniques and concepts of topological dynamics to construct a number of generalized conjugacy theorems. These theorems are then used to demonstrate that the mappingf _b has a number of conjugacy classes in which the dynamics of the iterates is equivalent to within a change of variables. The concepts of fitness and survival in logistic equations are then shown to be independent, if we follow certain intuitive definitions for these concepts. This conclusion follows from a comparison of the conjugacy classes of the functionf _b and the extinction sets off _b.     

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.     

Feed-Forward versus Feedback Inhibition in a Basic Olfactory Circuit

Inhibitory interneurons play critical roles in shaping the firing patterns of principal neurons in many brain systems. Despite difference in the anatomy or functions of neuronal circuits containing inhibition, two basic motifs repeatedly emerge: feed-forward and feedback. In the locust, it was proposed that a subset of lateral horn interneurons (LHNs), provide feed-forward inhibition onto Kenyon cells (KCs) to maintain their sparse firing—a property critical for olfactory learning and memory. But recently it was established that a single inhibitory cell, the giant GABAergic neuron (GGN), is the main and perhaps sole source of inhibition in the mushroom body, and that inhibition from this cell is mediated by a feedback (FB) loop including KCs and the GGN. To clarify basic differences in the effects of feedback vs. feed-forward inhibition in circuit dynamics we here use a model of the locust olfactory system. We found both inhibitory motifs were able to maintain sparse KCs responses and provide optimal odor discrimination. However, we further found that only FB inhibition could create a phase response consistent with data recorded in vivo. These findings describe general rules for feed-forward versus feedback inhibition and suggest GGN is potentially capable of providing the primary source of inhibition to the KCs. A better understanding of how inhibitory motifs impact post-synaptic neuronal activity could be used to reveal unknown inhibitory structures within biological networks.     

Discovering adaptation-capable biological network structures using control-theoretic approaches

Constructing biological networks capable of performing specific biological functionalities has been of sustained interest in synthetic biology. Adaptation is one such ubiquitous functional property, which enables every living organism to sense a change in its surroundings and return to its operating condition prior to the disturbance. In this paper, we present a generic systems theory-driven method for designing adaptive protein networks. First, we translate the necessary qualitative conditions for adaptation to mathematical constraints using the language of systems theory, which we then map back as ‘design requirements’ for the underlying networks. We go on to prove that a protein network with different input–output nodes (proteins) needs to be at least of third-order in order to provide adaptation. Next, we show that the necessary design principles obtained for a three-node network in adaptation consist of negative feedback or a feed-forward realization. We argue that presence of a particular class of negative feedback or feed-forward realization is necessary for a network of any size to provide adaptation. Further, we claim that the necessary structural conditions derived in this work are the strictest among the ones hitherto existed in the literature. Finally, we prove that the capability of producing adaptation is retained for the admissible motifs even when the output node is connected with a downstream system in a feedback fashion. This result explains how complex biological networks achieve robustness while keeping the core motifs unchanged in the context of a particular functionality. We corroborate our theoretical results with detailed and thorough numerical simulations. Overall, our results present a generic, systematic and robust framework for designing various kinds of biological networks.     

Dynamic network rewiring determines temporal regulatory functions in Drosophila melanogaster development processes

The identification of network motifs has been widely considered as a significant step towards uncovering the design principles of biomolecular regulatory networks. To date, time‐invariant networks have been considered. However, such approaches cannot be used to reveal time‐specific biological traits due to the dynamic nature of biological systems, and hence may not be applicable to development, where temporal regulation of gene expression is an indispensable characteristic. We propose a concept of a “temporal sequence of network motifs”, a sequence of network motifs in active sub‐networks constructed over time, and investigate significant network motifs in the active temporal sub‐networks of Drosophila melanogaster . Based on this concept, we find a temporal sequence of network motifs which changes according to developmental stages and thereby cannot be identified from the whole static network. Moreover, we show that the temporal sequence of network motifs corresponding to each developmental stage can be used to describe pivotal developmental events.     

Colored motifs reveal computational building blocks in the C. elegans brain

Background

Complex networks can often be decomposed into less complex sub-networks whose structures can give hints about the functional organization of the network as a whole. However, these structural motifs can only tell one part of the functional story because in this analysis each node and edge is treated on an equal footing. In real networks, two motifs that are topologically identical but whose nodes perform very different functions will play very different roles in the network.

Methodology/Principal Findings

Here, we combine structural information derived from the topology of the neuronal network of the nematode C. elegans with information about the biological function of these nodes, thus coloring nodes by function. We discover that particular colorations of motifs are significantly more abundant in the worm brain than expected by chance, and have particular computational functions that emphasize the feed-forward structure of information processing in the network, while evading feedback loops. Interneurons are strongly over-represented among the common motifs, supporting the notion that these motifs process and transduce the information from the sensor neurons towards the muscles. Some of the most common motifs identified in the search for significant colored motifs play a crucial role in the system of neurons controlling the worm''s locomotion.

Conclusions/Significance

The analysis of complex networks in terms of colored motifs combines two independent data sets to generate insight about these networks that cannot be obtained with either data set alone. The method is general and should allow a decomposition of any complex networks into its functional (rather than topological) motifs as long as both wiring and functional information is available.     

Failure tolerance of motif structure in biological networks

Complex networks serve as generic models for many biological systems that have been shown to share a number of common structural properties such as power-law degree distribution and small-worldness. Real-world networks are composed of building blocks called motifs that are indeed specific subgraphs of (usually) small number of nodes. Network motifs are important in the functionality of complex networks, and the role of some motifs such as feed-forward loop in many biological networks has been heavily studied. On the other hand, many biological networks have shown some degrees of robustness in terms of their efficiency and connectedness against failures in their components. In this paper we investigated how random and systematic failures in the edges of biological networks influenced their motif structure. We considered two biological networks, namely, protein structure network and human brain functional network. Furthermore, we considered random failures as well as systematic failures based on different strategies for choosing candidate edges for removal. Failure in the edges tipping to high degree nodes had the most destructive role in the motif structure of the networks by decreasing their significance level, while removing edges that were connected to nodes with high values of betweenness centrality had the least effect on the significance profiles. In some cases, the latter caused increase in the significance levels of the motifs.     

Unraveling the design principle for motif organization in signaling networks

Cellular signaling networks display complex architecture. Defining the design principle of this architecture is crucial for our understanding of various biological processes. Using a mathematical model for three-node feed-forward loops, we identify that the organization of motifs in specific manner within the network serves as an important regulator of signal processing. Further, incorporating a systemic stochastic perturbation to the model we could propose a possible design principle, for higher-order organization of motifs into larger networks in order to achieve specific biological output. The design principle was then verified in a large, complex human cancer signaling network. Further analysis permitted us to classify signaling nodes of the network into robust and vulnerable nodes as a result of higher order motif organization. We show that distribution of these nodes within the network at strategic locations then provides for the range of features displayed by the signaling network.     

生物分子网络弹性研究进展

弹性是生物分子网络重要且基础的属性之一,一方面弹性赋予生物分子网络抵抗内部噪声与环境干扰并维持其自身基本功能的能力,另一方面,弹性为网络状态的恢复制造了阻力。生物分子网络弹性研究试图回答如下3个问题：a. 生物分子网络弹性的产生机理是什么？b. 弹性影响下生物分子网络的状态如何发生转移？c. 如何预测生物网络状态转换临界点,以防止系统向不理想的状态演化？因此,研究生物分子网络弹性有助于理解生物系统内部运作机理,同时对诸如疾病发生临界点预测、生物系统状态逆转等临床应用具有重要的指导意义。鉴于此,本文主要针对以上生物分子网络弹性领域的3个热点研究问题,在研究方法和生物学应用上进行了系统地综述,并对未来生物分子网络弹性的研究方向进行了展望。     

PANET: A GPU-Based Tool for Fast Parallel Analysis of Robustness Dynamics and Feed-Forward/Feedback Loop Structures in Large-Scale Biological Networks

It has been a challenge in systems biology to unravel relationships between structural properties and dynamic behaviors of biological networks. A Cytoscape plugin named NetDS was recently proposed to analyze the robustness-related dynamics and feed-forward/feedback loop structures of biological networks. Despite such a useful function, limitations on the network size that can be analyzed exist due to high computational costs. In addition, the plugin cannot verify an intrinsic property which can be induced by an observed result because it has no function to simulate the observation on a large number of random networks. To overcome these limitations, we have developed a novel software tool, PANET. First, the time-consuming parts of NetDS were redesigned to be processed in parallel using the OpenCL library. This approach utilizes the full computing power of multi-core central processing units and graphics processing units. Eventually, this made it possible to investigate a large-scale network such as a human signaling network with 1,609 nodes and 5,063 links. We also developed a new function to perform a batch-mode simulation where it generates a lot of random networks and conducts robustness calculations and feed-forward/feedback loop examinations of them. This helps us to determine if the findings in real biological networks are valid in arbitrary random networks or not. We tested our plugin in two case studies based on two large-scale signaling networks and found interesting results regarding relationships between coherently coupled feed-forward/feedback loops and robustness. In addition, we verified whether or not those findings are consistently conserved in random networks through batch-mode simulations. Taken together, our plugin is expected to effectively investigate various relationships between dynamics and structural properties in large-scale networks. Our software tool, user manual and example datasets are freely available at http://panet-csc.sourceforge.net/.     

Structural principles for periodic orbits in glass networks

A piecewise-linear differential equation model framework for gene regulatory interactions (Glass networks) has allowed considerable analysis of qualitative dynamics in such systems, including periodicity, an important class of regulatory behaviors. Here, we present new results relating the structure of the network to its dynamics (structural principles). The structure we refer to is the state space of the network, which is a digraph on an n-cube in the case of a single threshold per gene. In particular, we show that for a wide class of cycles in the state space there exist parameter values, consistent with the graph structure, for which a periodic orbit exists in the network. For some classes, we show in addition that stable periodic orbits exist. These results extend greatly earlier work by Glass and Pasternack (J Math Biol 6:207–223, 1978).     

A unified neural model of spatiotemporal processing in X and Y retinal ganglion cells

This work presents unified analyses of spatial and temporal visual information processing in a feed-forward network of neurons that obey membrane, or shunting equations. The feed-forward shunting network possesses properties that make it well suited for processing of static, spatial information. However, it is shown here that those same properties of the shunting network that lead to good spatial processing imply poor temporal processing characteristics. This article presents an extension of the feed-forward shunting network model that solves this problem by means of preprocessing layers. The anatomical interpretation of the resulting model is structurally analogous to recently discovered data on a retinal circuit connecting cones to retinal ganglion cells through pairs of pushpull bipolar cells. Mathematical analysis of the lumped model leads to the hypothesis that X and Y retinal ganglion cells may consist of a single mechanism acting in different parameter ranges. This hypothesis is confirmed in the companion article, wherein the model in conjunction with a nonlinear temporal adaptation mechanism — is used to reproduce experimental data of both X and Y cells by simple changes in morphological and physiological parameters.     

Information processing in social insect networks

Investigating local-scale interactions within a network makes it possible to test hypotheses about the mechanisms of global network connectivity and to ask whether there are general rules underlying network function across systems. Here we use motif analysis to determine whether the interactions within social insect colonies resemble the patterns exhibited by other animal associations or if they exhibit characteristics of biological regulatory systems. Colonies exhibit a predominance of feed-forward interaction motifs, in contrast to the densely interconnected clique patterns that characterize human interaction and animal social networks. The regulatory motif signature supports the hypothesis that social insect colonies are shaped by selection for network patterns that integrate colony functionality at the group rather than individual level, and demonstrates the utility of this approach for analysis of selection effects on complex systems across biological levels of organization.