A continuum model to study the internal fluctuations in globular proteins

The salient features of the differential equation model to study protein dynamics are presented with results for 19 proteins.     

Waves, bumps, and patterns in neural field theories

Neural field models of firing rate activity have had a major impact in helping to develop an understanding of the dynamics seen in brain slice preparations. These models typically take the form of integro-differential equations. Their non-local nature has led to the development of a set of analytical and numerical tools for the study of waves, bumps and patterns, based around natural extensions of those used for local differential equation models. In this paper we present a review of such techniques and show how recent advances have opened the way for future studies of neural fields in both one and two dimensions that can incorporate realistic forms of axo-dendritic interactions and the slow intrinsic currents that underlie bursting behaviour in single neurons.     

UKF-based closed loop iterative learning control of epileptiform wave in a neural mass model

A novel closed loop control framework is proposed to inhibit epileptiform wave in a neural mass model by external electric field, where the unscented Kalman filter method is used to reconstruct dynamics and estimate unmeasurable parameters of the model. Specifically speaking, the iterative learning control algorithm is introduced into the framework to optimize the control signal. In the proposed method, the control effect can be significantly improved based on the observation of the past attempts. Accordingly, the proposed method can effectively suppress the epileptiform wave as well as showing robustness to noises and uncertainties. Lastly, the simulation is carried out to illustrate the feasibility of the proposed method. Besides, this work shows potential value to design model-based feedback controllers for epilepsy treatment.     

Theta phase coding in a network model of the entorhinal cortex layer II with entorhinal-hippocampal loop connections

We investigated successive firing of the stellate cells within a theta cycle, which replicates the phase coding of place information, using a network model of the entorhinal cortex layer II with loop connections. Layer II of the entorhinal cortex (ECII) sends signals to the hippocampus, and the hippocampus sends signals back to layer V of the entorhinal cortex (ECV). In addition to this major pathway, projection from ECV to ECII also exists. It is, therefore, inferred that reverberation activity readily appears if projections from ECV to ECII are potentiated. The frequency of the reverberation would be in a gamma range because it takes signals 20–30 ms to go around the entorhinal-hippocampal loop circuits. On the other hand, it has been suggested that ECII is a theta rhythm generator. If the reverberation activity appears in the entorhinal-hippocampal loop circuits, gamma oscillation would be superimposed on a theta rhythm in ECII like a gamma-theta oscillation. This is a reminiscence of the theta phase coding of place information. In this paper, first, a network model of ECII will be developed in order to reproduce a theta rhythm. Secondly, we will show that loop connections from one stellate cell to the other one are selectively potentiated by afferent signals to ECII. Frequencies of those afferent signals are different, and transmission delay of the loop connections is 20 ms. As a result, stellate cells fire successively within one cycle of the theta rhythm. This resembles gamma-theta oscillation underlying the phase coding. Our model also replicates the phase precession of stellate cell firing within a cycle of subthreshold oscillation (theta rhythm).     

A linear model for characterization of synchronization frequencies of neural networks

The synchronization frequency of neural networks and its dynamics have important roles in deciphering the working mechanisms of the brain. It has been widely recognized that the properties of functional network synchronization and its dynamics are jointly determined by network topology, network connection strength, i.e., the connection strength of different edges in the network, and external input signals, among other factors. However, mathematical and computational characterization of the relationships between network synchronization frequency and these three important factors are still lacking. This paper presents a novel computational simulation framework to quantitatively characterize the relationships between neural network synchronization frequency and network attributes and input signals. Specifically, we constructed a series of neural networks including simulated small-world networks, real functional working memory network derived from functional magnetic resonance imaging, and real large-scale structural brain networks derived from diffusion tensor imaging, and performed synchronization simulations on these networks via the Izhikevich neuron spiking model. Our experiments demonstrate that both of the network synchronization strength and synchronization frequency change according to the combination of input signal frequency and network self-synchronization frequency. In particular, our extensive experiments show that the network synchronization frequency can be represented via a linear combination of the network self-synchronization frequency and the input signal frequency. This finding could be attributed to an intrinsically-preserved principle in different types of neural systems, offering novel insights into the working mechanism of neural systems.     

Quantum-like model of behavioral response computation using neural oscillators

In this paper we propose the use of neural interference as the origin of quantum-like effects in the brain. We do so by using a neural oscillator model consistent with neurophysiological data. The model used was shown elsewhere to reproduce well the predictions of behavioral stimulus-response theory. The quantum-like effects are brought about by the spreading activation of incompatible oscillators, leading to an interference-like effect mediated by inhibitory and excitatory synapses.     

Dynamics of outgrowth in a continuum model of neurite elongation

Neurite outgrowth (dendrites and axons) should be a stable, but easily regulated process to enable a neuron to make its appropriate network connections during development. We explore the dynamics of outgrowth in a mathematical continuum model of neurite elongation. The model describes the construction of the internal microtubule cytoskeleton, which results from the production and transport of tubulin dimers and their assembly into microtubules at the growing neurite tip. Tubulin is assumed to be largely synthesised in the cell body from where it is transported by active mechanisms and by diffusion along the neurite. It is argued that this construction process is a fundamental limiting factor in neurite elongation. In the model, elongation is highly stable when tubulin transport is dominated by either active transport or diffusion, but oscillations in length may occur when both active transport and diffusion contribute. Autoregulation of tubulin production can eliminate these oscillations. In all cases a stable steady-state length is reached, provided there is intrinsic decay of tubulin. Small changes in growth parameters, such as the tubulin production rate, can lead to large changes in length. Thus cytoskeleton construction can be both stable and easily regulated, as seems necessary for neurite outgrowth during nervous system development. Action Editor: Upinder Bhalla     

Towards a unifying model of neural net activity in the visual cortex

A neural net model describing the non-linear interactions between axonal spikes is presented. It reconciles aspects of pattern recognition (as action of an associative memory) with those of spike synchronization and phase locking. The stability of the synchronized state is studied in detail.     

A neural network model of attention-modulated neurodynamics

Visual attention appears to modulate cortical neurodynamics and synchronization through various cholinergic mechanisms. In order to study these mechanisms, we have developed a neural network model of visual cortex area V4, based on psychophysical, anatomical and physiological data. With this model, we want to link selective visual information processing to neural circuits within V4, bottom-up sensory input pathways, top-down attention input pathways, and to cholinergic modulation from the prefrontal lobe. We investigate cellular and network mechanisms underlying some recent analytical results from visual attention experimental data. Our model can reproduce the experimental findings that attention to a stimulus causes increased gamma-frequency synchronization in the superficial layers. Computer simulations and STA power analysis also demonstrate different effects of the different cholinergic attention modulation action mechanisms.     

Inactivation of Cdc42 in neural crest cells causes craniofacial and cardiovascular morphogenesis defects

Neural crest cells (NCCs) are physically responsible for craniofacial skeleton formation, pharyngeal arch artery remodeling and cardiac outflow tract septation during vertebrate development. Cdc42 (cell division cycle 42) is a Rho family small GTP-binding protein that works as a molecular switch to regulate cytoskeleton remodeling and the establishment of cell polarity. To investigate the role of Cdc42 in NCCs during embryonic development, we deleted Cdc42 in NCCs by crossing Cdc42 flox mice with Wnt1-cre mice. We found that the inactivation of Cdc42 in NCCs caused embryonic lethality with craniofacial deformities and cardiovascular developmental defects. Specifically, Cdc42 NCC knockout embryos showed fully penetrant cleft lips and short snouts. Alcian Blue and Alizarin Red staining of the cranium exhibited an unfused nasal capsule and palatine in the mutant embryos. India ink intracardiac injection analysis displayed a spectrum of cardiovascular developmental defects, including persistent truncus arteriosus, hypomorphic pulmonary arteries, interrupted aortic arches, and right-sided aortic arches. To explore the underlying mechanisms of Cdc42 in the formation of the great blood vessels, we generated Wnt1Cre-Cdc42-Rosa26 reporter mice. By beta-galactosidase staining, a subpopulation of Cdc42-null NCCs was observed halting in their migration midway from the pharyngeal arches to the conotruncal cushions. Phalloidin staining revealed dispersed, shorter and disoriented stress fibers in Cdc42-null NCCs. Finally, we demonstrated that the inactivation of Cdc42 in NCCs impaired bone morphogenetic protein 2 (BMP2)-induced NCC cytoskeleton remodeling and migration. In summary, our results demonstrate that Cdc42 plays an essential role in NCC migration, and inactivation of Cdc42 in NCCs impairs craniofacial and cardiovascular development in mice.     

Control of continuous fed-batch fermentation process using neural network based model predictive controller

Cell growth and metabolite production greatly depend on the feeding of the nutrients in fed-batch fermentations. A strategy for controlling the glucose feed rate in fed-batch baker’s yeast fermentation and a novel controller was studied. The difference between the specific carbon dioxide evolution rate and oxygen uptake rate (Q _c − Q _o) was used as controller variable. The controller evaluated was neural network based model predictive controller and optimizer. The performance of the controller was evaluated by the set point tracking. Results showed good performance of the controller.     

Novel tracking function of moving target using chaotic dynamics in a recurrent neural network model

Chaotic dynamics introduced in a recurrent neural network model is applied to controlling an object to track a moving target in two-dimensional space, which is set as an ill-posed problem. The motion increments of the object are determined by a group of motion functions calculated in real time with firing states of the neurons in the network. Several cyclic memory attractors that correspond to several simple motions of the object in two-dimensional space are embedded. Chaotic dynamics introduced in the network causes corresponding complex motions of the object in two-dimensional space. Adaptively real-time switching of control parameter results in constrained chaos (chaotic itinerancy) in the state space of the network and enables the object to track a moving target along a certain trajectory successfully. The performance of tracking is evaluated by calculating the success rate over 100 trials with respect to nine kinds of trajectories along which the target moves respectively. Computer experiments show that chaotic dynamics is useful to track a moving target. To understand the relations between these cases and chaotic dynamics, dynamical structure of chaotic dynamics is investigated from dynamical viewpoint.     

Derivation of a field equation of brain activity

We present a nonlinear field theory of the brain under realistic anatomical connectivity conditions describing the interaction between functional units within the brain. This macroscopic field theory is derived from the quasi-microscopic conversion properties of neural populations occurring at synapses and somas. Functional units are treated as inhomogeneities within a nonlinear neural tissue.     

A hybrid model for the neural representation of complex mental processing in the human brain

In the present conceptual review several theoretical and empirical sources of information were integrated, and a hybrid model of the neural representation of complex mental processing in the human brain was proposed. Based on empirical evidence for strategy-related and inter-individually different task-related brain activation networks, and further based on empirical evidence for a remarkable overlap of fronto-parietal activation networks across different complex mental processes, it was concluded by the author that there might be innate and modular organized neuro-developmental starting regions, for example, in intra-parietal, and both medial and middle frontal brain regions, from which the neural organization of different kinds of complex mental processes emerge differently during individually shaped learning histories. Thus, the here proposed model provides a hybrid of both massive modular and holistic concepts of idiosyncratic brain physiological elaboration of complex mental processing. It is further concluded that 3-D information, obtained by respective methodological approaches, are not appropriate to identify the non-linear spatio-temporal dynamics of complex mental process-related brain activity in a sufficient way. How different participating network parts communicate with each other seems to be an indispensable aspect, which has to be considered in particular to improve our understanding of the neural organization of complex cognition.     

Percolation on heterogeneous networks as a model for epidemics

We consider a spatial model related to bond percolation for the spread of a disease that includes variation in the susceptibility to infection. We work on a lattice with random bond strengths and show that with strong heterogeneity, i.e. a wide range of variation of susceptibility, patchiness in the spread of the epidemic is very likely, and the criterion for epidemic outbreak depends strongly on the heterogeneity. These results are qualitatively different from those of standard models in epidemiology, but correspond to real effects. We suggest that heterogeneity in the epidemic will affect the phylogenetic distance distribution of the disease-causing organisms. We also investigate small world lattices, and show that the effects mentioned above are even stronger.     

Parsing recursive sentences with a connectionist model including a neural stack and synaptic gating

It is supposed that humans are genetically predisposed to be able to recognize sequences of context-free grammars with centre-embedded recursion while other primates are restricted to the recognition of finite state grammars with tail-recursion. Our aim was to construct a minimalist neural network that is able to parse artificial sentences of both grammars in an efficient way without using the biologically unrealistic backpropagation algorithm. The core of this network is a neural stack-like memory where the push and pop operations are regulated by synaptic gating on the connections between the layers of the stack. The network correctly categorizes novel sentences of both grammars after training. We suggest that the introduction of the neural stack memory will turn out to be substantial for any biological ‘hierarchical processor’ and the minimalist design of the model suggests a quest for similar, realistic neural architectures.     

A neural circuit model for changing the amount of information maintained in short-term memory depending on stimuli relationships

We propose a neural circuit model of changes in amount of information maintained in short-term memory depending on stimuli relationships. The relationships between stimuli are represented by the synchronous firings of overlapping neuronal groups for semantically related stimuli and the excitatory mutual connections for semantically unrelated but simultaneously presented stimuli. We conduct computer simulations to confirm our proposed neural circuit model. The resultant numbers of stored informational input patterns are almost consistent with the maximum numbers in the psychological experiments for both semantically related and unrelated stimuli. This agreement with the psychological experiments suggests that the structure and informational representation of the proposed model are appropriate.