Random distance dependent attachment as a model for neural network generation in the Caenorhabditis elegans

A Game-Theoretical Network Formation Model for C. elegans Neural Network

Studying and understanding human brain structures and functions have become one of the most challenging issues in neuroscience today. However, the mammalian nervous system is made up of hundreds of millions of neurons and billions of synapses. This complexity made it impossible to reconstruct such a huge nervous system in the laboratory. So, most researchers focus on C. elegans neural network. The C. elegans neural network is the only biological neural network that is fully mapped. This nervous system is the simplest neural network that exists. However, many fundamental behaviors like movement emerge from this basic network. These features made C. elegans a convenient case to study the nervous systems. Many studies try to propose a network formation model for C. elegans neural network. However, these studies could not meet all characteristics of C. elegans neural network, such as significant factors that play a role in the formation of C. elegans neural network. Thus, new models are needed to be proposed in order to explain all aspects of C. elegans neural network. In this paper, a new model based on game theory is proposed in order to understand the factors affecting the formation of nervous systems, which meet the C. elegans frontal neural network characteristics. In this model, neurons are considered to be agents. The strategy for each neuron includes either making or removing links to other neurons. After choosing the basic network, the utility function is built using structural and functional factors. In order to find the coefficients for each of these factors, linear programming is used. Finally, the output network is compared with C. elegans frontal neural network and previous models. The results implicate that the game-theoretical model proposed in this paper can better predict the influencing factors in the formation of C. elegans neural network compared to previous models.

An Algorithm for Motif-Based Network Design

A determinant property of the structure of a biological network is the distribution of local connectivity patterns, i.e., network motifs. In this work, a method for creating directed, unweighted networks while promoting a certain combination of motifs is presented. This motif-based network algorithm starts with an empty graph and randomly connects the nodes by advancing or discouraging the formation of chosen motifs. The in- or out-degree distribution of the generated networks can be explicitly chosen. The algorithm is shown to perform well in producing networks with high occurrences of the targeted motifs, both ones consisting of three nodes as well as ones consisting of four nodes. Moreover, the algorithm can also be tuned to bring about global network characteristics found in many natural networks, such as small-worldness and modularity.

Stochastic geometric network models for groups of functional and structural connectomes

Structural and functional connectomes are emerging as important instruments in the study of normal brain function and in the development of new biomarkers for a variety of brain disorders. In contrast to single-network studies that presently dominate the (non-connectome) network literature, connectome analyses typically examine groups of empirical networks and then compare these against standard (stochastic) network models. The current practice in connectome studies is to employ stochastic network models derived from social science and engineering contexts as the basis for the comparison. However, these are not necessarily best suited for the analysis of connectomes, which often contain groups of very closely related networks, such as occurs with a set of controls or a set of patients with a specific disorder. This paper studies important extensions of standard stochastic models that make them better adapted for analysis of connectomes, and develops new statistical fitting methodologies that account for inter-subject variations. The extensions explicitly incorporate geometric information about a network based on distances and inter/intra hemispherical asymmetries (to supplement ordinary degree-distribution information), and utilize a stochastic choice of network density levels (for fixed threshold networks) to better capture the variance in average connectivity among subjects. The new statistical tools introduced here allow one to compare groups of networks by matching both their average characteristics and the variations among them. A notable finding is that connectomes have high "smallworldness" beyond that arising from geometric and degree considerations alone.

Connecting a connectome to behavior: an ensemble of neuroanatomical models of C. elegans klinotaxis

Increased efforts in the assembly and analysis of connectome data are providing new insights into the principles underlying the connectivity of neural circuits. However, despite these considerable advances in connectomics, neuroanatomical data must be integrated with neurophysiological and behavioral data in order to obtain a complete picture of neural function. Due to its nearly complete wiring diagram and large behavioral repertoire, the nematode worm Caenorhaditis elegans is an ideal organism in which to explore in detail this link between neural connectivity and behavior. In this paper, we develop a neuroanatomically-grounded model of salt klinotaxis, a form of chemotaxis in which changes in orientation are directed towards the source through gradual continual adjustments. We identify a minimal klinotaxis circuit by systematically searching the C. elegans connectome for pathways linking chemosensory neurons to neck motor neurons, and prune the resulting network based on both experimental considerations and several simplifying assumptions. We then use an evolutionary algorithm to find possible values for the unknown electrophsyiological parameters in the network such that the behavioral performance of the entire model is optimized to match that of the animal. Multiple runs of the evolutionary algorithm produce an ensemble of such models. We analyze in some detail the mechanisms by which one of the best evolved circuits operates and characterize the similarities and differences between this mechanism and other solutions in the ensemble. Finally, we propose a series of experiments to determine which of these alternatives the worm may be using.

Information diversity in structure and dynamics of simulated neuronal networks

Neuronal networks exhibit a wide diversity of structures, which contributes to the diversity of the dynamics therein. The presented work applies an information theoretic framework to simultaneously analyze structure and dynamics in neuronal networks. Information diversity within the structure and dynamics of a neuronal network is studied using the normalized compression distance. To describe the structure, a scheme for generating distance-dependent networks with identical in-degree distribution but variable strength of dependence on distance is presented. The resulting network structure classes possess differing path length and clustering coefficient distributions. In parallel, comparable realistic neuronal networks are generated with NETMORPH simulator and similar analysis is done on them. To describe the dynamics, network spike trains are simulated using different network structures and their bursting behaviors are analyzed. For the simulation of the network activity the Izhikevich model of spiking neurons is used together with the Tsodyks model of dynamical synapses. We show that the structure of the simulated neuronal networks affects the spontaneous bursting activity when measured with bursting frequency and a set of intraburst measures: the more locally connected networks produce more and longer bursts than the more random networks. The information diversity of the structure of a network is greatest in the most locally connected networks, smallest in random networks, and somewhere in between in the networks between order and disorder. As for the dynamics, the most locally connected networks and some of the in-between networks produce the most complex intraburst spike trains. The same result also holds for sparser of the two considered network densities in the case of full spike trains.