Hard-wired central pattern generators for quadrupedal locomotion

Animal locomotion is generated and controlled, in part, by a central pattern generator (CPG), which is an intraspinal network of neurons capable of producing rhythmic output. In the present work, it is demonstrated that a hard-wired CPG model, made up of four coupled nonlinear oscillators, can produce multiple phase-locked oscillation patterns that correspond to three common quadrupedal gaits — the walk, trot, and bound. Transitions between the different gaits are generated by varying the network's driving signal and/or by altering internal oscillator parameters. The above in numero results are obtained without changing the relative strengths or the polarities of the system's synaptic interconnections, i.e., the network maintains an invariant coupling architecture. It is also shown that the ability of the hard-wired CPG network to produce and switch between multiple gait patterns is a model-independent phenomenon, i.e., it does not depend upon the detailed dynamics of the component oscillators and/or the nature of the inter-oscillator coupling. Three different neuronal oscillator models — the Stein neuronal model, the Van der Pol oscillator, and the FitzHugh-Nagumo model -and two different coupling schemes are incorporated into the network without impeding its ability to produce the three quadrupedal gaits and the aforementioned gait transitions.     

Hybrid neural simulation of a fed-batch bioreactor for a nonideal recombinant fermentation

Fermentations employing genetically modified microbes under industrial conditions are difficult to monitor on line or to describe by simple, good mathematical models. So, a practically convenient approach is to combine mathematical models of some aspects with artificial neural networks of those aspects which are difficult to measure or model. Such hybrid models have been applied earlier to laboratory-scale bioreactors. In the present work, a model based on laboratory data for the synthesis of recombinant #-galactosidase was corrupted by adding imperfect mixing and noise in the feed stream to generate data mimicking a real nonideal operation. These data were used to train a recurrent Elman neural network and a hybrid neural network, and it was seen that a hybrid network provides more accurate estimates of both extra-cellular and intra-cellular variables. The benefit is enhanced by the hybrid network's superiority being more pronounced for the intra-cellular recombinant protein, #-galactosidase, which is the main product of interest.     

A goal programming network for linear programming

Tank and Hopfield have shown that networks of analog neurons can be used to solve linear programming (LP) problems. We have re-examined their approach and found that their network model frequently computes solutions that are only suboptimal or that violate the LP problem's constraints. As their approach has proven unreliable, we have developed a new network model: the goal programming network. To this end, a network model was first developed for goal programming problems, a particular type of LP problems. From the manner the network operates on such problems, it was concluded that overconstrainedness, which is possibly present in an LP formulation, should be removed, and we have provided a simple procedure to accomplish this.     

An Adaptive Complex Network Model for Brain Functional Networks

Brain functional networks are graph representations of activity in the brain, where the vertices represent anatomical regions and the edges their functional connectivity. These networks present a robust small world topological structure, characterized by highly integrated modules connected sparsely by long range links. Recent studies showed that other topological properties such as the degree distribution and the presence (or absence) of a hierarchical structure are not robust, and show different intriguing behaviors. In order to understand the basic ingredients necessary for the emergence of these complex network structures we present an adaptive complex network model for human brain functional networks. The microscopic units of the model are dynamical nodes that represent active regions of the brain, whose interaction gives rise to complex network structures. The links between the nodes are chosen following an adaptive algorithm that establishes connections between dynamical elements with similar internal states. We show that the model is able to describe topological characteristics of human brain networks obtained from functional magnetic resonance imaging studies. In particular, when the dynamical rules of the model allow for integrated processing over the entire network scale-free non-hierarchical networks with well defined communities emerge. On the other hand, when the dynamical rules restrict the information to a local neighborhood, communities cluster together into larger ones, giving rise to a hierarchical structure, with a truncated power law degree distribution.     

A model for integrating elementary neural functions into delayed-response behavior

It is well established that various cortical regions can implement a wide array of neural processes, yet the mechanisms which integrate these processes into behavior-producing, brain-scale activity remain elusive. We propose that an important role in this respect might be played by executive structures controlling the traffic of information between the cortical regions involved. To illustrate this hypothesis, we present a neural network model comprising a set of interconnected structures harboring stimulus-related activity (visual representation, working memory, and planning), and a group of executive units with task-related activity patterns that manage the information flowing between them. The resulting dynamics allows the network to perform the dual task of either retaining an image during a delay (delayed-matching to sample task), or recalling from this image another one that has been associated with it during training (delayed-pair association task). The model reproduces behavioral and electrophysiological data gathered on the inferior temporal and prefrontal cortices of primates performing these same tasks. It also makes predictions on how neural activity coding for the recall of the image associated with the sample emerges and becomes prospective during the training phase. The network dynamics proves to be very stable against perturbations, and it exhibits signs of scale-invariant organization and cooperativity. The present network represents a possible neural implementation for active, top-down, prospective memory retrieval in primates. The model suggests that brain activity leading to performance of cognitive tasks might be organized in modular fashion, simple neural functions becoming integrated into more complex behavior by executive structures harbored in prefrontal cortex and/or basal ganglia.     

Reliability of pattern separation by the cerebellar mossy fiber — granule cell system

As a simple example of a neuronal network in which synaptic connectivity among neurons is probabilistic, Marr's model for the granular layer of cat cerebellar cortex is examined. The mean and variance are computed for the fraction of granule cells activated, and for the extent of pattern separation by granule cells, for various mossy fiber inputs and various values of connectivity and electrical parameters of the network structure. Results suggest different functions for the network, and different optimal ranges for its parameters, depending on whether Golgi cells are present or absent. The model network does not perform the functions originally prescribed for it with high reliability.     

Aedes-AI: Neural network models of mosquito abundance

We present artificial neural networks as a feasible replacement for a mechanistic model of mosquito abundance. We develop a feed-forward neural network, a long short-term memory recurrent neural network, and a gated recurrent unit network. We evaluate the networks in their ability to replicate the spatiotemporal features of mosquito populations predicted by the mechanistic model, and discuss how augmenting the training data with time series that emphasize specific dynamical behaviors affects model performance. We conclude with an outlook on how such equation-free models may facilitate vector control or the estimation of disease risk at arbitrary spatial scales.     

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.

     

A neural network model of the cerebellar cortex performing dynamic associations

The present paper proposes a model which applies formal neural network modeling techniques to construct a theoretical representation of the cerebellar cortex and its performances in motor control. A schema that makes explicit use of propagation delays of neural signals, is introduced to describe the ability to store temporal sequences of patterns in the Golgi-granule cell system. A perceptron association is then performed on these sequences of patterns by the Purkinje cell layer. The model conforms with important biological constraints, such as the known excitatory or inhibitory nature of the various synapses. Also, as suggested by experimental evidence, the synaptic plasticity underlying the learning ability of the model, is confined to the parallel fiber — Purkinje cell synapses, and takes place under the control of the climbing fibers. The result is a neural network model, constructed according to the anatomy of the cerebellar cortex, and capable of learning and retrieval of temporal sequences of patterns. It provides a framework to represent and interpret properties of learning and control of movements by the cerebellum, and to assess the capacity of formal neural network techniques for modeling of real neural systems.     

Newly proposed node segregation index is not suitable for analyzing unimode food webs

Strona and Veech (2015) developed a new node segregation (or node overlap) index for analysing ecological network structure based on the Veech (2013)’s species co-occurrence probabilistic model, which was originally applied to species-site matrices. However, a species-site matrix for analysing species co-occurrence patterns and an adjacency matrix for characterising unimode network structures are different. Directly applying Veech’s species co-occurrence probabilistic model to adjacency matrices in unimode food webs is problematic. The central critical problem is related to the number of free species (or nodes/vertices) in the unimode network that can be the neighbors (have links to connect) of a focused species or a focused pair of species. This number is typically less than the total number of species in real food webs. That is, species are not independent from each other in unimode networks. For a simple undirected unimode network without self-loops, based on the criterion whether there is a link between two species for a focused pair, a correct probabilistic model is developed to accurately compute the probability of observing some shared neighbors for a pair of species in the network. Numerical simulation show that the node overlap calculated using the correct and original probabilistic models present remarkable differences, especially when a unimode network is nested and contains generalists. In summary, The correct probabilistic model should be used if ones want Strona and Veech (2015)’s node segregation index to work for unimode food webs.     

Model for Heterogeneous Random Networks Using Continuous Latent Variables and an Application to a Tree–Fungus Network

Summary The mixture model is a method of choice for modeling heterogeneous random graphs, because it contains most of the known structures of heterogeneity: hubs, hierarchical structures, or community structure. One of the weaknesses of mixture models on random graphs is that, at the present time, there is no computationally feasible estimation method that is completely satisfying from a theoretical point of view. Moreover, mixture models assume that each vertex pertains to one group, so there is no place for vertices being at intermediate positions. The model proposed in this article is a grade of membership model for heterogeneous random graphs, which assumes that each vertex is a mixture of extremal hypothetical vertices. The connectivity properties of each vertex are deduced from those of the extreme vertices. In this new model, the vector of weights of each vertex are fixed continuous parameters. A model with a vector of parameters for each vertex is tractable because the number of observations is proportional to the square of the number of vertices of the network. The estimation of the parameters is given by the maximum likelihood procedure. The model is used to elucidate some of the processes shaping the heterogeneous structure of a well‐resolved network of host/parasite interactions.     

Continuous Attractor Network Model for Conjunctive Position-by-Velocity Tuning of Grid Cells

The spatial responses of many of the cells recorded in layer II of rodent medial entorhinal cortex (MEC) show a triangular grid pattern, which appears to provide an accurate population code for animal spatial position. In layer III, V and VI of the rat MEC, grid cells are also selective to head-direction and are modulated by the speed of the animal. Several putative mechanisms of grid-like maps were proposed, including attractor network dynamics, interactions with theta oscillations or single-unit mechanisms such as firing rate adaptation. In this paper, we present a new attractor network model that accounts for the conjunctive position-by-velocity selectivity of grid cells. Our network model is able to perform robust path integration even when the recurrent connections are subject to random perturbations.     

Estimation of Directed Effective Connectivity from fMRI Functional Connectivity Hints at Asymmetries of Cortical Connectome

The brain exhibits complex spatio-temporal patterns of activity. This phenomenon is governed by an interplay between the internal neural dynamics of cortical areas and their connectivity. Uncovering this complex relationship has raised much interest, both for theory and the interpretation of experimental data (e.g., fMRI recordings) using dynamical models. Here we focus on the so-called inverse problem: the inference of network parameters in a cortical model to reproduce empirically observed activity. Although it has received a lot of interest, recovering directed connectivity for large networks has been rather unsuccessful so far. The present study specifically addresses this point for a noise-diffusion network model. We develop a Lyapunov optimization that iteratively tunes the network connectivity in order to reproduce second-order moments of the node activity, or functional connectivity. We show theoretically and numerically that the use of covariances with both zero and non-zero time shifts is the key to infer directed connectivity. The first main theoretical finding is that an accurate estimation of the underlying network connectivity requires that the time shift for covariances is matched with the time constant of the dynamical system. In addition to the network connectivity, we also adjust the intrinsic noise received by each network node. The framework is applied to experimental fMRI data recorded for subjects at rest. Diffusion-weighted MRI data provide an estimate of anatomical connections, which is incorporated to constrain the cortical model. The empirical covariance structure is reproduced faithfully, especially its temporal component (i.e., time-shifted covariances) in addition to the spatial component that is usually the focus of studies. We find that the cortical interactions, referred to as effective connectivity, in the tuned model are not reciprocal. In particular, hubs are either receptors or feeders: they do not exhibit both strong incoming and outgoing connections. Our results sets a quantitative ground to explore the propagation of activity in the cortex.     

Distributed sensory coding applied to simulations of iconic storage and metacontrast

If information is coded in the combination of activities of many neurons operating in parallel, then information present in a network can be defined by the correlation of present network activity with the activity which had been elicited by a stimulus in the past; a high correlation indicates the presence of the previously encoded stimulus. Information is distributed in the network because coding is dependent upon the activities of all cells. A model based on Hartline-Ratliff lateral inhibition with a time delay shows that lateral inhibition can distribute information across a parallel network, reduce output noise, and also briefly store information. With no changes in model parameters, and the use of a correlation measure for recognition, the model can stimulate psychophysical results in eleven variations of the metacontrast masking paradigm.     

Evolution of specificity in an immune network

A dynamic antigen response of the immune network is discussed, based on shape-space modelling. The present model extends the shape-space modelling by introducing the evolution of specificity of idiotypes. When the amount of external antigen increases, a measure of stability of the immune network is lost and thus the network can respond to the antigen. It is shown that specific and non-specific responses emerge as a function of antigen amounts. A specific response is observed with a fixed-point attractor, and a non-specific response is observed with a chaotic attractor for the lymphocyte population dynamics. The network topology also changes between fixed-point and chaotic attractors. For some antigen amounts, chaotic attractors will vanish or become long-lived super-transient states. A dynamic bell-shaped response function will thus emerge. The relevance of long-lived chaotic transient states embedded in fixed-point attractors is discussed with respect to immune functions.     

Endothelial cell apoptosis in capillary network remodeling

We hypothesized that the regulation of apoptosis is an important determinant of capillary network structure. Using human umbilical vein endothelial cells (HUVEC) in in vitro model systems of capillary tube formation, we initially documented that apoptosis is a prominent feature of network formation. Perturbations of integrin-matrix signaling by the administration of either colchicine or an anti-αvβ3 antibody resulted in the dissolution of the tubular network in association with increased apoptosis. The activation of the αvβ3 integrin induced increased expression of the anti-apoptotic gene bcl-2 and conferred resistance to the proapoptotic effect of TGF-β1. In contrast to the stable networks formed by HUVEC, bovine aortic endothelial cells (BAEC) exhibited a more dynamic process of network formation and spontaneous involution. The inhibition of BAEC apoptosis by stable transfection of bcl-2 prevented the involution of the network. We hypothesized that TGF-β1 present within the model system mediated network involution by inducing BAEC death. Indeed, blockade of TGF-β1 with neutralizing antibodies reduced BAEC apoptosis and preserved the network structure. As observed with HUVEC networks, stable BAEC networks formed during blockade of TGF-β1 were also dependent on the survival-promoting effects of matrix-integrin interactions. This study suggests that capillary network structure is determined by the balance of proapoptotic vs. anti-apoptotic signals mediated by the engagement of cytokine and integrin receptors within the milieu. J. Cell. Physiol. 178:359–370, 1999. © 1999 Wiley-Liss, Inc.     

On the Complexity of Life Cycle Inventory Networks: Role of Life Cycle Processes with Network Analysis

Determining the relevance and importance of a technosphere process or a cluster of processes in relation to the rest of the industrial network can provide insights into the sustainability of supply chains: those that need to be optimized or controlled/safeguarded. Network analysis (NA) can offer a broad framework of indicators to tackle this problem. In this article, we present a detailed analysis of a life cycle inventory (LCI) model from an NA perspective. Specifically, the network is represented as a directed graph and the “emergy” numeraire is used as the weight associated with the arcs of the network. The case study of a technological system for drinking water production is presented. We investigate the topological and structural characteristics of the network representation of this system and compare properties of its weighted and unweighted network, as well as the importance of nodes (i.e., life cycle unit processes). By identifying a number of advantages and limitations linked to the modeling complexity of such emergy‐LCI networks, we classify the LCI technosphere network of our case study as a complex network belonging to the scale‐free network family. The salient feature of this network family is represented by the presence of “hubs”: nodes that connect with many other nodes. Hub failures may imply relevant changes, decreases, or even breaks in the connectedness with other smaller hubs and nodes of the network. Hence, by identifying node centralities, we can rank and interpret the relevance of each node for its special role in the life cycle network.     

Smooth muscle length adaptation and actin filament length: a network model of the cytoskeletal dysregulation

Length adaptation of the airway smooth muscle cell is attributable to cytoskeletal remodeling. It has been proposed that dysregulated actin filaments may become longer in asthma, and that such elongation would prevent a parallel-to-series transition of contractile units, thus precluding the well-known beneficial effects of deep inspirations and tidal breathing. To test the potential effect that actin filament elongation could have in overall muscle mechanics, we present an extremely simple model. The cytoskeleton is represented as a 2-D network of links (contractile filaments) connecting nodes (adhesion plaques). Such a network evolves in discrete time steps by forming and dissolving links in a stochastic fashion. Links are formed by idealized contractile units whose properties are either those from normal or elongated actin filaments. Oscillations were then imposed on the network to evaluate both the effects of breathing and length adaptation. In response to length oscillation, a network with longer actin filaments showed smaller decreases of force, smaller increases in compliance, and higher shortening velocities. Taken together, these changes correspond to a network that is refractory to the effects of breathing and therefore approximates an asthmatic scenario. Thus, an extremely simple model seems to capture some relatively complex mechanics of airway smooth muscle, supporting the idea that dysregulation of actin filament length may contribute to excessive airway narrowing.     

Structure-based rebuilding of coevolutionary information reveals functional modules in rhodopsin structure

Correlated mutation analysis (CMA) has been used to investigate protein functional sites. However, CMA has suffered from low signal-to-noise ratio caused by meaningless phylogenetic signals or structural constraints. We present a new method, Structure-based Correlated Mutation Analysis (SCMA), which encodes coevolution scores into a protein structure network. A path-based network model is adapted to describe information transfer between residues, and the statistical significance is estimated by network shuffling. This model intrinsically assumes that residues in physical contact have a more reliable coevolution score than distant residues, and that coevolution in distant residues likely arises from a series of contacting and coevolving residues. In addition, coevolutionary coupling is statistically controlled to remove the structural effects. When applied to the rhodopsin structure, the SCMA method identified a much higher percentage of functional residues than the typical coevolution score (61% vs. 22%). In addition, statistically significant residues are used to construct the coevolved residue-residue subnetwork. The network has one highly connected node (retinal bound Lys296), indicating that Lys296 can induce and regulate most other coevolved residues in a variety of locations. The coevolved network consists of a few modular clusters which have distinct functional roles. This article is part of a Special Issue entitled: Computational Methods for Protein Interaction and Structural Prediction.     

A modelling-experimental approach reveals insulin receptor substrate (IRS)-dependent regulation of adenosine monosphosphate-dependent kinase (AMPK) by insulin

Mammalian target of rapamycin (mTOR) kinase responds to growth factors, nutrients and cellular energy status and is a central controller of cellular growth. mTOR exists in two multiprotein complexes that are embedded into a complex signalling network. Adenosine monophosphate-dependent kinase (AMPK) is activated by energy deprivation and shuts off adenosine 5'-triphosphate (ATP)-consuming anabolic processes, in part via the inactivation of mTORC1. Surprisingly, we observed that AMPK not only responds to energy deprivation but can also be activated by insulin, and is further induced in mTORC1-deficient cells. We have recently modelled the mTOR network, covering both mTOR complexes and their insulin and nutrient inputs. In the present study we extended the network by an AMPK module to generate the to date most comprehensive data-driven dynamic AMPK-mTOR network model. In order to define the intersection via which AMPK is activated by the insulin network, we compared simulations for six different hypothetical model structures to our observed AMPK dynamics. Hypotheses ranking suggested that the most probable intersection between insulin and AMPK was the insulin receptor substrate (IRS) and that the effects of canonical IRS downstream cues on AMPK would be mediated via an mTORC1-driven negative-feedback loop. We tested these predictions experimentally in multiple set-ups, where we inhibited or induced players along the insulin-mTORC1 signalling axis and observed AMPK induction or inhibition. We confirmed the identified model and therefore report a novel connection within the insulin-mTOR-AMPK network: we conclude that AMPK is positively regulated by IRS and can be inhibited via the negative-feedback loop.