Dendritic and Synaptic Effects in Systems of Coupled Cortical Oscillators

We explore the influence of synaptic location and form on the behavior of networks of coupled cortical oscillators. First, we develop a model of two coupled somatic oscillators that includes passive dendritic cables. Using a phase model approach, we show that the synchronous solution can change from a stable solution to an unstable one as the cable lengthens and the synaptic position moves further from the soma. We confirm this prediction using a system of coupled compartmental models. We also demonstrate that when the synchronous solution becomes unstable, a bifurcation occurs and a pair of asynchronous stable solutions appear, causing a phase lag between the cells in the system. Then using a variety of coupling functions and different synaptic positions, we show that distal connections and broad synaptic time courses encourage phase lags that can be reduced, eliminated, or enhanced by the presence of active currents in the dendrite. This mechanism may appear in neural systems where proximal connections could be used to encourage synchrony, and distal connections and broad synaptic time courses could be used to produce phase lags that can be modulated by active currents.     

The necessity of connection structures in neural models of variable binding

In his review of neural binding problems, Feldman (Cogn Neurodyn 7:1–11, 2013) addressed two types of models as solutions of (novel) variable binding. The one type uses labels such as phase synchrony of activation. The other (‘connectivity based’) type uses dedicated connections structures to achieve novel variable binding. Feldman argued that label (synchrony) based models are the only possible candidates to handle novel variable binding, whereas connectivity based models lack the flexibility required for that. We argue and illustrate that Feldman’s analysis is incorrect. Contrary to his conclusion, connectivity based models are the only viable candidates for models of novel variable binding because they are the only type of models that can produce behavior. We will show that the label (synchrony) based models analyzed by Feldman are in fact examples of connectivity based models. Feldman’s analysis that novel variable binding can be achieved without existing connection structures seems to result from analyzing the binding problem in a wrong frame of reference, in particular in an outside instead of the required inside frame of reference. Connectivity based models can be models of novel variable binding when they possess a connection structure that resembles a small-world network, as found in the brain. We will illustrate binding with this type of model with episode binding and the binding of words, including novel words, in sentence structures.     

Deterministic epidemic models on contact networks: correlations and unbiological terms

The relationship between system-level and subsystem-level master equations is investigated and then utilised for a systematic and potentially automated derivation of the hierarchy of moment equations in a susceptible-infectious-removed (SIR) epidemic model. In the context of epidemics on contact networks we use this to show that the approximate nature of some deterministic models such as mean-field and pair-approximation models can be partly understood by the identification of implicit anomalous terms. These terms describe unbiological processes which can be systematically removed up to and including the nth order by nth order moment closure approximations. These terms lead to a detailed understanding of the correlations in network-based epidemic models and contribute to understanding the connection between individual-level epidemic processes and population-level models. The connection with metapopulation models is also discussed. Our analysis is predominantly made at the individual level where the first and second order moment closure models correspond to what we term the individual-based and pair-based deterministic models, respectively. Matlab code is included as supplementary material for solving these models on transmission networks of arbitrary complexity.     

Two-point heterogeneous connections in a continuum neural field model

We examine a novel heterogeneous connection scheme in a 1D continuum neural field model. Multiple two-point connections are added to a local connection function in order to model the “patchy” connections seen in, for example visual cortex. We use a numerical approach to solve the equations, choosing the locations of the two-point connections stochastically. We observe self-sustained persistent fluctuations of activity which can be classified into two types (one of which is similar to that seen in network models of discrete excitable neurons, the other being particular to this model). We study the effect of parameters such as system size and the range, number and strength of connections, on the probability that a particular realisation of the connections is able to exhibit persistent fluctuations.     

Mathematical modeling and optimization of cellulase protein production using Trichoderma reesei RL-P37

The enzyme cellulase, a multienzyme complex made up of several proteins, catalyzes the conversion of cellulose to glucose in an enzymatic hydrolysis-based biomass-to-ethanol process. Production of cellulase enzyme proteins in large quantities using the fungus Trichoderma reesei requires understanding the dynamics of growth and enzyme production. The method of neural network parameter function modeling, which combines the approximation capabilities of neural networks with fundamental process knowledge, is utilized to develop a mathematical model of this dynamic system. In addition, kinetic models are also developed. Laboratory data from bench-scale fermentations involving growth and protein production by T. reesei on lactose and xylose are used to estimate the parameters in these models. The relative performances of the various models and the results of optimizing these models on two different performance measures are presented. An approximately 33% lower root-mean-squared error (RMSE) in protein predictions and about 40% lower total RMSE is obtained with the neural network-based model as opposed to kinetic models. Using the neural network-based model, the RMSE in predicting optimal conditions for two performance indices, is about 67% and 40% lower, respectively, when compared with the kinetic models. Thus, both model predictions and optimization results from the neural network-based model are found to be closer to the experimental data than the kinetic models developed in this work. It is shown that the neural network parameter function modeling method can be useful as a "macromodeling" technique to rapidly develop dynamic models of a process.     

Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns

This study deals with neurophysiologically based models simulating electrical brain activity (i.e., the electroencephalogram or EEG, and evoked potentials or EPs). A previously developed lumped-parameter model of a single cortical column was implemented using a more accurate computational procedure. Anatomically acceptable values for the various model parameters were determined, and a multi-dimensional exploration of the model parameter-space was conducted. It was found that the model could produce a large variety of EEG-like waveforms and rhythms. Coupling two models, with delays in the interconnections to simulate the synaptic connections within and between cortical areas, made it possible to replicate the spatial distribution of alpha and beta activity. EPs were simulated by presenting pulses to the input of the coupled models. In general, the responses were more realistic than those produced using a single model. Our simulations also suggest that the scalp-recorded EP is at least partially due to a phase reordering of the ongoing activity.     

Transitory memory retrieval in a biologically plausible neural network model

A number of memory models have been proposed. These all have the basic structure that excitatory neurons are reciprocally connected by recurrent connections together with the connections with inhibitory neurons, which yields associative memory (i.e., pattern completion) and successive retrieval of memory. In most of the models, a simple mathematical model for a neuron in the form of a discrete map is adopted. It has not, however, been clarified whether behaviors like associative memory and successive retrieval of memory appear when a biologically plausible neuron model is used. In this paper, we propose a network model for associative memory and successive retrieval of memory based on Pinsky-Rinzel neurons. The state of pattern completion in associative memory can be observed with an appropriate balance of excitatory and inhibitory connection strengths. Increasing of the connection strength of inhibitory interneurons changes the state of memory retrieval from associative memory to successive retrieval of memory. We investigate this transition.     

On the mechanistic underpinning of discrete-time population models with complex dynamics

We present a mechanistic underpinning for various discrete-time population models that can produce limit cycles and chaotic dynamics. Specific examples include the discrete-time logistic model and the Hassell model, which for a long time eluded convincing mechanistic interpretations, and also the Ricker- and Beverton-Holt models. We first formulate a continuous-time resource consumption model for the dynamics within a year, and from that we derive a discrete-time model for the between-year dynamics. Without influx of resources from the outside into the system, the resulting between-year dynamics is always overcompensating and hence may produce complex dynamics as well as extinction in finite time. We recover a connection between various standard types of continuous-time models for the resource dynamics within a year on the one hand and various standard types of discrete-time models for the population dynamics between years on the other. The model readily generalizes to several resource and consumer species as well as to more than two trophic levels for the within-year dynamics.     

Effect of electric field gradients on lipid monolayer membranes.

Externally applied nonuniform electric fields can strongly affect thermodynamic phases in a lipid monolayer when applied under conditions of temperature, pressure, and composition that are near phase boundaries. Under such conditions nonuniform applied fields can produce or suppress phase separations. Field-induced phase-separated domains have sizes that are in good agreement with calculations. Field gradients can also produce large concentration gradients in binary mixtures just above their critical points. The present work elaborates our earlier studies of these field effects using thermodynamic models of the phase behavior of two-component liquid mixtures. The calculations are of interest in connection with biological membranes that, at the growth temperature, are in a liquid state close to a phase boundary.     

Intersegmental coordination in the lamprey: simulations using a network model without segmental boundaries

Swimming in vertebrates such as eel and lamprey involves the coordination of alternating left and right activity in each segment. Forward swimming is achieved by a lag between the onset of activity in consecutive segments rostrocaudally along the spinal cord. The intersegmental phase lag is approximately 1% of the cycle duration per segment and is independent of the swimming frequency. Since the lamprey has approximately 100 spinal segments, at any given time one wave of activity is propagated along the body. Most previous simulations of intersegmental coordination in the lamprey have treated the cord as a chain of coupled oscillators or well-defined segments. Here a network model without segmental boundaries is described which can produce coordinated activity with a phase lag. This ‘continuous’ pattern-generating network is composed of a column of 420 excitatory interneurons (E1 to E420) and 300 inhibitory interneurons (C1 to C300) on each half of the simulated spinal cord. The interneurons are distributed evenly along the simulated spinal cord, and their connectivity is chosen to reflect the behavior of the intact animal and what is known about the length and strength of the synaptic connections. For example, E100 connects to all interneurons between E51 and E149, but at varying synaptic strengths, while E101 connects to all interneurons between E52 and E150. This unsegmented E-C network generates a motor pattern that is sampled by output elements similar to motoneurons (M cells), which are arranged along the cell column so that they receive input from seven E and five C interneurons. The M cells thus represent the summed excitatory and inhibitory input at different points along the simulated spinal cord and can be regarded as representing the ventral root output to the myotomes along the spinal cord. E and C interneurons have five simulated compartments and Hodgkin-Huxley based dynamics. The simulated network produces rhythmic output over a wide range of frequencies (1–11 Hz) with a phase lag constant over most of the length, with the exception of the ‘cut’ ends due to reduced synaptic input. As the inhibitory C interneurons in the simulation have more extensive caudal than rostral projections, the output of the simulation has positive phase lags, as occurs in forward swimming. However, unlike the biological network, phase lags in the simulation increase significantly with burst frequency, from 0.5% to 2.3% over the range of frequencies of the simulation. Local rostral or caudal increases in excitatory drive in the simulated network are sufficient to produce motor patterns with increased or decreased phase lags, respectively. Received: 15 December 1995 / Accepted in revised form: 17 September 1996     

Chloride-driven Electromechanical Phase Lags at Acoustic Frequencies Are Generated by SLC26a5, the Outer Hair Cell Motor Protein

Outer hair cells (OHC) possess voltage-dependent membrane bound molecular motors, identified as the solute carrier protein SLC26a5, that drive somatic motility at acoustic frequencies. The electromotility (eM) of OHCs provides for cochlear amplification, a process that enhances auditory sensitivity by up to three orders of magnitude. In this study, using whole cell voltage clamp and mechanical measurement techniques, we identify disparities between voltage sensing and eM that result from stretched exponential electromechanical behavior of SLC26a5, also known as prestin, for its fast responsiveness. This stretched exponential behavior, which we accurately recapitulate with a new kinetic model, the meno presto model of prestin, influences the protein’s responsiveness to chloride binding and provides for delays in eM relative to membrane voltage driving force. The model predicts that in the frequency domain, these delays would result in eM phase lags that we confirm by measuring OHC eM at acoustic frequencies. These lags may contribute to canceling viscous drag, a requirement for many models of cochlear amplification.     

Dual phase lag bio-heat transfer during cryosurgery of lung cancer: Comparison of three heat transfer models

The Pennes bio-heat model is based on Fourier's law of heat conduction, which assumed that a thermal signal propagate with infinite speed. This gives contradiction in physical situation. Also, the hyperbolic bio-heat model considers the micro scale response in time, but it does not explain the micro scale response in space. Therefore, to consider the thermal behaviour which is not captured by the Fourier's law and to take into account the microstructural effect in space, a dual phase lag (DPL) bio-heat conduction model would be advantageous. In this paper, a two dimensional DPL model is proposed to study the phase change heat transfer process during cryosurgery of lung cancer. The governing equations are solved numerically by enthalpy based finite difference method. The non-ideal behaviour of tissue and heat source terms, metabolism and blood perfusion are also considered. This study is made to examine the effects of phase lags in heat flux and temperature gradient on interface positions and temperature distribution during freezing process. A comparative study of DPL, parabolic and hyperbolic conduction models is thoroughly investigated. It is found that the phase lags of temperature gradient and heat flux have significant effect on interface positions and temperature distribution.     

Sea Surface Temperature Influence on Terrestrial Gross Primary Production along the Southern California Current

Some land and ocean processes are related through connections (and synoptic-scale teleconnections) to the atmosphere. Synoptic-scale atmospheric (El Niño/Southern Oscillation [ENSO], Pacific Decadal Oscillation [PDO], and North Atlantic Oscillation [NAO]) decadal cycles are known to influence the global terrestrial carbon cycle. Potentially, smaller scale land-ocean connections influenced by coastal upwelling (changes in sea surface temperature) may be important for local-to-regional water-limited ecosystems where plants may benefit from air moisture transported from the ocean to terrestrial ecosystems. Here we use satellite-derived observations to test potential connections between changes in sea surface temperature (SST) in regions with strong coastal upwelling and terrestrial gross primary production (GPP) across the Baja California Peninsula. This region is characterized by an arid/semiarid climate along the southern California Current. We found that SST was correlated with the fraction of photosynthetic active radiation (fPAR; as a proxy for GPP) with lags ranging from 0 to 5 months. In contrast ENSO was not as strongly related with fPAR as SST in these coastal ecosystems. Our results show the importance of local-scale changes in SST during upwelling events, to explain the variability in GPP in coastal, water-limited ecosystems. The response of GPP to SST was spatially-dependent: colder SST in the northern areas increased GPP (likely by influencing fog formation), while warmer SST at the southern areas was associated to higher GPP (as SST is in phase with precipitation patterns). Interannual trends in fPAR are also spatially variable along the Baja California Peninsula with increasing secular trends in subtropical regions, decreasing trends in the most arid region, and no trend in the semi-arid regions. These findings suggest that studies and ecosystem process based models should consider the lateral influence of local-scale ocean processes that could influence coastal ecosystem productivity.     

Entrainment ranges of forced phase oscillators

In the vertebrate spinal cord, a neural circuit called the central pattern generator produces the basic locomotory rhythm. Short and long distance intersegmental connections serve to maintain coordination along the length of the body. As a way of examining the influence of such connections, we consider a model of a chain of coupled phase oscillators in which one oscillator receives a periodic forcing stimulus. For a certain range of forcing frequencies, the chain will match the stimulus frequency, a phenomenon called entrainment. Motivated by recent experiments in lampreys, we derive analytical expressions for the range of forcing frequencies that entrain the chain, and how that range depends on the forcing location. For short intersegmental connections, in which an oscillator is connected only to its nearest neighbors, we describe two ways in which entrainment is lost: internally, in which oscillators within the chain no longer oscillate at the same frequency; and externally, in which the the chain no longer has the same frequency as the forcing. By analyzing chains in which every oscillator is connected to every other oscillator (i.e., all-to-all connections), we show that the presence of connections with lengths greater than one do not necessarily change the entrainment ranges based on the nearest–neighbor model. We derive a criterion for the ratio of connection strengths under which the connections of length greater than one do not change the entrainment ranges produced in the nearest–neighbor model, provided entrainment is lost externally. However, when this criterion holds, the range of entrained frequencies is a monotonic function of forcing location, unlike experimental results, in which entrainment ranges are larger near the middle of the chain than at the ends. Numerically, we show that similar non-monotonic entrainment ranges are possible if the ratio criterion does not hold, suggesting that in the lamprey central pattern generator, intersegmental connection strengths are not a simple function of the connection length.     

Causes of cyclicity of Epirrita autumnata (Lepidoptera, Geometridae): grandiose theory and tedious practice

Creating multiyear cycles in population density demands, in traditional models, causal factors that operate on local populations in a density-dependent way with time lags. However, cycles of the geometrid Epirrita autumnata in northern Europe may be regional, not local; i.e., successive outbreaks occur in different localities. We review possible causes of cycles of E. autumnata under both local and regional scenarios, including large-scale synchrony. Assuming cyclicity is a local phenomenon, individual populations of E. autumnata display peaks but populations all over the outbreak range fluctuate in synchrony. This concept assumes that the peaks at most localities are so low that they do not lead to visible defoliation and easily remain unnoticed. In this scenario, populations are able to start recovery a few years after the crash, i.e., at the time of the mitigation of detrimental delayed density-dependent factors, such as delayed inducible resistance of the host plant or parasitism. In that case, the same factors that lead to crashes also explain the periodicity of cyclic fluctuations. According to the regional cyclicity scenario, different factors can be important in different phases of the cycle. The key is to identify the factors that tend to produce outbreaks with a periodicity of about 10 years. Initiation of the increase phase seems to coincide with maxima in sunspot activity, but causal connections remain unclear. Climatic factor(s) associated with the solar cycle could contribute to the large-scale geographic synchrony.     

Plastic inducible morphologies are not always adaptive: The importance of time delays in a stochastic environment

Summary We present a mathematical model for predicting the expected fitness of phenotypically plastic organisms experiencing a variable environment. We assume that individuals experience two discrete environments probabilistically in time (as a Markov process) and that there are two different phenotypic states, each yielding the highest fitness in one of the two environments. We compare the expected fitness of a phenotypically fixed individual to that of an individual whose phenotype is induced to produce the better phenotype in each environment with a time lag between experiencing a new environment and realization of the new phenotype. Such time lags are common in organisms where phenotypically plastic, inducible traits have been documented. We find that although plasticity is generally adaptive when time lags are short (relative to the time scale of environmental variability), plasticity can be disadvantageous for longer lag times. Asymmetries in environmental change probabilities and/or the relative fitnesses of each phenotype strongly influence whether plasticity is favoured. In contrast to other models, our model does not require costs for plasticity to be disadvantageous; costs affect the results quantitatively, not qualitatively.     

Adaptive and phase selective spike timing dependent plasticity in synaptically coupled neuronal oscillators

We consider and analyze the influence of spike-timing dependent plasticity (STDP) on homeostatic states in synaptically coupled neuronal oscillators. In contrast to conventional models of STDP in which spike-timing affects weights of synaptic connections, we consider a model of STDP in which the time lags between pre- and/or post-synaptic spikes change internal state of pre- and/or post-synaptic neurons respectively. The analysis reveals that STDP processes of this type, modeled by a single ordinary differential equation, may ensure efficient, yet coarse, phase-locking of spikes in the system to a given reference phase. Precision of the phase locking, i.e. the amplitude of relative phase deviations from the reference, depends on the values of natural frequencies of oscillators and, additionally, on parameters of the STDP law. These deviations can be optimized by appropriate tuning of gains (i.e. sensitivity to spike-timing mismatches) of the STDP mechanism. However, as we demonstrate, such deviations can not be made arbitrarily small neither by mere tuning of STDP gains nor by adjusting synaptic weights. Thus if accurate phase-locking in the system is required then an additional tuning mechanism is generally needed. We found that adding a very simple adaptation dynamics in the form of slow fluctuations of the base line in the STDP mechanism enables accurate phase tuning in the system with arbitrary high precision. Adaptation operating at a slow time scale may be associated with extracellular matter such as matrix and glia. Thus the findings may suggest a possible role of the latter in regulating synaptic transmission in neuronal circuits.     

The emergence of Up and Down states in cortical networks

The cerebral cortex is continuously active in the absence of external stimuli. An example of this spontaneous activity is the voltage transition between an Up and a Down state, observed simultaneously at individual neurons. Since this phenomenon could be of critical importance for working memory and attention, its explanation could reveal some fundamental properties of cortical organization. To identify a possible scenario for the dynamics of Up–Down states, we analyze a reduced stochastic dynamical system that models an interconnected network of excitatory neurons with activity-dependent synaptic depression. The model reveals that when the total synaptic connection strength exceeds a certain threshold, the phase space of the dynamical system contains two attractors, interpreted as Up and Down states. In that case, synaptic noise causes transitions between the states. Moreover, an external stimulation producing a depolarization increases the time spent in the Up state, as observed experimentally. We therefore propose that the existence of Up–Down states is a fundamental and inherent property of a noisy neural ensemble with sufficiently strong synaptic connections.     

Dynamic Neural Network Models of the Premotoneuronal Circuitry Controlling Wrist Movements in Primates

Dynamic recurrent neural networks were derived to simulate neuronal populations generating bidirectional wrist movements in the monkey. The models incorporate anatomical connections of cortical and rubral neurons, muscle afferents, segmental interneurons and motoneurons; they also incorporate the response profiles of four populations of neurons observed in behaving monkeys. The networks were derived by gradient descent algorithms to generate the eight characteristic patterns of motor unit activations observed during alternating flexion-extension wrist movements. The resulting model generated the appropriate input-output transforms and developed connection strengths resembling those in physiological pathways. We found that this network could be further trained to simulate additional tasks, such as experimentally observed reflex responses to limb perturbations that stretched or shortened the active muscles, and scaling of response amplitudes in proportion to inputs. In the final comprehensive network, motor units are driven by the combined activity of cortical, rubral, spinal and afferent units during step tracking and perturbations.The model displayed many emergent properties corresponding to physiological characteristics. The resulting neural network provides a working model of premotoneuronal circuitry and elucidates the neural mechanisms controlling motoneuron activity. It also predicts several features to be experimentally tested, for example the consequences of eliminating inhibitory connections in cortex and red nucleus. It also reveals that co-contraction can be achieved by simultaneous activation of the flexor and extensor circuits without invoking features specific to co-contraction.     

主动联想记忆神经网络模型

在信息编码能提高联想记忆的存贮能力和脑内存在主动活动机制的启发下,提出一个主动联想记忆模型。模型包括两个神经网络,其一为输入和输出网络,另一个为在学习时期能自主产生兴奋模式的主动网络。两个网络的神经元之间有突触联系。由于自主产生的兴奋模式与输入无关,并可能接近于相互正交,因此,本模型有较高的存贮能力。初步分析和计算机仿真证明：本模型确有比通常联想记忆模型高的存贮能力,特别是在输入模式间有高度相关情况下、最后,对提出的模型与双向自联想记忆和光学全息存贮机制的关系作了讨论。