A neural mass model based on single cell dynamics to model pathophysiology

Neural mass models are successful in modeling brain rhythms as observed in macroscopic measurements such as the electroencephalogram (EEG). While the synaptic current is explicitly modeled in current models, the single cell electrophysiology is not taken into account. To allow for investigations of the effects of channel pathologies, channel blockers and ion concentrations on macroscopic activity, we formulate neural mass equations explicitly incorporating the single cell dynamics by using a bottom-up approach. The mean and variance of the firing rate and synaptic input distributions are modeled. The firing rate curve (F(I)-curve) is used as link between the single cell and macroscopic dynamics. We show that this model accurately reproduces the behavior of two populations of synaptically connected Hodgkin-Huxley neurons, also in non-steady state.     

Capturing microscopic features of bone remodeling into a macroscopic model based on biological rationales of bone adaptation

To understand Wolff’s law, bone adaptation by remodeling at the cellular and tissue levels has been discussed extensively through experimental and simulation studies. For the clinical application of a bone remodeling simulation, it is significant to establish a macroscopic model that incorporates clarified microscopic mechanisms. In this study, we proposed novel macroscopic models based on the microscopic mechanism of osteocytic mechanosensing, in which the flow of fluid in the lacuno-canalicular porosity generated by fluid pressure gradients plays an important role, and theoretically evaluated the proposed models, taking biological rationales of bone adaptation into account. The proposed models were categorized into two groups according to whether the remodeling equilibrium state was defined globally or locally, i.e., the global or local uniformity models. Each remodeling stimulus in the proposed models was quantitatively evaluated through image-based finite element analyses of a swine cancellous bone, according to two introduced criteria associated with the trabecular volume and orientation at remodeling equilibrium based on biological rationales. The evaluation suggested that nonuniformity of the mean stress gradient in the local uniformity model, one of the proposed stimuli, has high validity. Furthermore, the adaptive potential of each stimulus was discussed based on spatial distribution of a remodeling stimulus on the trabecular surface. The theoretical consideration of a remodeling stimulus based on biological rationales of bone adaptation would contribute to the establishment of a clinically applicable and reliable simulation model of bone remodeling.     

A spin-glass-like Lyapunov function for a neurotrophic model of neuronal development

 We derive a spin-glass-like energy or Lyapunov function for our previously studied neurotrophic model of anatomical synaptic plasticity and neuronal development. This function is then used in Monte-Carlo simulations of the model applied to the development of ocular dominance columns. We discuss the relationship between our model and other models, and speculate on the implications of underlying spin glass structures in many models of neuronal development, learning and plasticity. Received: 1 October 2001 / Accepted in revised form: 15 January 2002     

Neural dynamics as sampling: a model for stochastic computation in recurrent networks of spiking neurons

The organization of computations in networks of spiking neurons in the brain is still largely unknown, in particular in view of the inherently stochastic features of their firing activity and the experimentally observed trial-to-trial variability of neural systems in the brain. In principle there exists a powerful computational framework for stochastic computations, probabilistic inference by sampling, which can explain a large number of macroscopic experimental data in neuroscience and cognitive science. But it has turned out to be surprisingly difficult to create a link between these abstract models for stochastic computations and more detailed models of the dynamics of networks of spiking neurons. Here we create such a link and show that under some conditions the stochastic firing activity of networks of spiking neurons can be interpreted as probabilistic inference via Markov chain Monte Carlo (MCMC) sampling. Since common methods for MCMC sampling in distributed systems, such as Gibbs sampling, are inconsistent with the dynamics of spiking neurons, we introduce a different approach based on non-reversible Markov chains that is able to reflect inherent temporal processes of spiking neuronal activity through a suitable choice of random variables. We propose a neural network model and show by a rigorous theoretical analysis that its neural activity implements MCMC sampling of a given distribution, both for the case of discrete and continuous time. This provides a step towards closing the gap between abstract functional models of cortical computation and more detailed models of networks of spiking neurons.     

A model of late long-term potentiation simulates aspects of memory maintenance

Late long-term potentiation (L-LTP) denotes long-lasting strengthening of synapses between neurons. L-LTP appears essential for the formation of long-term memory, with memories at least partly encoded by patterns of strengthened synapses. How memories are preserved for months or years, despite molecular turnover, is not well understood. Ongoing recurrent neuronal activity, during memory recall or during sleep, has been hypothesized to preferentially potentiate strong synapses, preserving memories. This hypothesis has not been evaluated in the context of a mathematical model representing ongoing activity and biochemical pathways important for L-LTP. In this study, ongoing activity was incorporated into two such models - a reduced model that represents some of the essential biochemical processes, and a more detailed published model. The reduced model represents synaptic tagging and gene induction simply and intuitively, and the detailed model adds activation of essential kinases by Ca(2+). Ongoing activity was modeled as continual brief elevations of Ca(2+). In each model, two stable states of synaptic strength/weight resulted. Positive feedback between synaptic weight and the amplitude of ongoing Ca(2+) transients underlies this bistability. A tetanic or theta-burst stimulus switches a model synapse from a low basal weight to a high weight that is stabilized by ongoing activity. Bistability was robust to parameter variations in both models. Simulations illustrated that prolonged periods of decreased activity reset synaptic strengths to low values, suggesting a plausible forgetting mechanism. However, episodic activity with shorter inactive intervals maintained strong synapses. Both models support experimental predictions. Tests of these predictions are expected to further understanding of how neuronal activity is coupled to maintenance of synaptic strength. Further investigations that examine the dynamics of activity and synaptic maintenance can be expected to help in understanding how memories are preserved for up to a lifetime in animals including humans.     

Repetitive firing: a quantitative study of feedback in model encoders

Recognition of nonlinearities in the neuronal encoding of repetitive spike trains has generated a number of models to explain this behavior. Here we develop the mathematics and a set of tests for two such models: the leaky integrator and the variable-gamma model. Both of these are nearly sufficient to explain the dynamic behavior of a number of repetitively firing, sensory neurons. Model parameters can be related to possible underlying basic mechanisms. Summed and nonsummed, spike- locked negative feedback are examined in conjunction with the models. Transfer functions are formulated to predict responses to steady state, steps, and sinusoidally varying stimuli in which output data are the times of spike-train events only. An electrical analog model for the leaky integrator is tested to verify predicted responses. Curve fitting and parameter variation techniques are explored for the purpose of extracting basic model parameters from spike train data. Sinusoidal analysis of spike trains appear to be a very accurate method for determining spike-locked feedback parameters, and it is to a large extent a model independent method that may also be applied to neuronal responses.     

Voltage-dependent gating of Shaker A-type potassium channels in Drosophila muscle

The voltage-dependent gating mechanism of A1-type potassium channels coded for by the Shaker locus of Drosophila was studied using macroscopic and single-channel recording techniques on embryonic myotubes in primary culture. From a kinetic analysis of data from single A1 channels, we have concluded that all of the molecular transitions after first opening, including the inactivation transition, are voltage independent and therefore not associated with charge movement through the membrane. In contrast, at least some of the activation transitions leading to first opening are considerably voltage dependent and account for all of the voltage dependence seen in the macroscopic currents. This mechanism is similar in many ways to that of vertebrate neuronal voltage-sensitive sodium channels, and together with the sequence similarities in the S4 region suggests a conserved mechanism for voltage-dependent gating among channels with different selectivities. By testing independent and coupled models for activation and inactivation we have determined that the final opening transition and inactivation are not likely to arise from the independent action of multiple subunits, each with simple gating transitions, but rather come about through their aggregate properties. A partially coupled model accurately reproduces all of the single-channel and macroscopic data. This model will provide a framework on which to organize and understand alterations in gating that occur in Shaker variants and mutants.     

Neuromechanical representation of fabric-evoked prickliness: a fiber-skin-neuron model

Cutaneous Aδ nociceptors encode the material and geometrical features of fiber ends evoking prickliness sensation by generating neural spikes in response to indentation of human skin, however, understanding of the underlying neuromechanism of fabric-evoked prickliness is still far from clear. This work develops and validates a fiber-skin-neuron (mechanosensitive Aδ-nociceptors) model that combines an analytical model of fiber-skin indentation, a sigmoidal function of neuronal transduction, and a leaky integrate-and-fire model of neuronal dynamics. Firstly, the model is validated to be capable of capturing the typical neurphysiological features of cutaneous Aδ nociceptors and the psychophysical phenomenon. And then, several case studies with respect to statistical features of fiber ends are carried out, and the resulting neural responses are calculated to explore the relationship between statistical features in study and evoked responses. The analysis of predicted action potentials over one second indicates that they systematically change with statistical features of fiber ends protruding above fabric surfaces, and the fitted stimulus–response relationship of Aδ nociceptors is highly similar to the stimulus-sensation relationship of prickliness rating magnitude. It follows that there might exist a linear relationship between fabric-evoked neurophysiological responses and psychophysical responses. These results provide significant new insight into the fabric-evoked prickliness sensation and raise interesting questions for further investigation, and the model described here bridges the gap between those models that transform fiber ends properties to firing rates.     

Analysis of the response properties of a computationally efficient spike initiator model

 A simple model for neuronal spike initiation is presented. It comprises two linear differential equations and is based on the work of Hill, Rashevsky and Monnier (Rashevsky 1933; Monnier 1934; Hill 1936). Three different versions of the model and the corresponding assumptions are described. The intrinsic noise model used with the deterministic equations is described. The equations are analyzed through the direct solution of relevant equations and the technique of phase plane analysis. The analysis reveals that a subset of the model parameters is responsible for the distinction between spike initiator models which fire a single spike and those that fire repetitively in the presence of a sustained stimulus. Relationships between stimulus intensity and different modes of operation are derived. The effects of the three different versions of the model are compared analytically. Received: 5 August 1993/Accepted in revised form: 24 February 1994     

Realistic model of a solid substrate fermentation packed-bed pilot bioreactor

For any given large-scale solid substrate fermentation (SSF) bioreactor, to assess how well a control system will work in practice requires the most realistic model possible. This model needs to account fully for complicated dynamic reactor behaviour and, in addition, has to include a specific noise model that is capable of reproducing the disturbances observed in SSF bioreactor measurements. In this work, noisy data collected historically from SSF pilot scale fermentations was used to develop such a model. Applying standard signal processing techniques, each measured variable was separated into deterministic and noise signals. Deterministic signals were used to calibrate a previously developed phenomenological model of the bioreactor. Noise signals were used to construct a realistic noise model for each measured variable in turn. Finally, the two models were combined to attain simulations that compared well with real measurements. This integrated model will provide realistic simulations that will prove useful in the design of effective control systems for intermittently mixed SSF bioreactors.     

Hyperlipidemic chicken as a model of non-alcoholic steatohepatitis

Non-alcoholic steatohepatitis (NASH) is part of the spectrum of non-alcoholic fatty liver disease (NAFLD), currently the most common cause of abnormal liver tests. Given the difficulty of studying all the factors involved in it in human populations, studies in animal models might provide crucial insights in the pathogenesis of steatohepatitis. Several physiological features predispose birds to fat deposition in the liver. The present study was conceived to explore the possibilities of the chicken fed a cholesterol and fat enriched diet as a model for steatohepatitis. We used two different diets: a standard growing mash (control group) and a standard growing mash enriched with 2% cholesterol and 20% palm oil (hyperlipidemic group). We investigated the effect of feeding a cholesterol and fat enriched diet, on plasma lipid levels, liver enzymes and hepatic histopathology. Semiquantitative and quantitative assessment by image analysis was performed to determine changes in lipid deposits and inflammatory infiltration. Statistically significant increases were observed in all plasma lipid parameters, liver macroscopic features, fat deposits and cell-ballooning of hepatocytes between control and hyperlipidemic animals. Significant differences were also observed in the inflammatory infiltration parameters (number of foci, density, area and maximal diameter). Results show that diet-induced hypercholesterolemia and hypertriglyceridemia are associated with severe impairment of liver histology (fat accumulation, inflammation and cell-ballooning), reproducing histological features of human NAFLD. This model, which is easy and reproducible, offers economic and technical advantages. Furthermore, the reversibility of the pathologic changes makes it suitable for drug intervention studies of steatohepatitis.     

Functional model of biological neural networks

A functional model of biological neural networks, called temporal hierarchical probabilistic associative memory (THPAM), is proposed in this paper. THPAM comprises functional models of dendritic trees for encoding inputs to neurons, a first type of neuron for generating spike trains, a second type of neuron for generating graded signals to modulate neurons of the first type, supervised and unsupervised Hebbian learning mechanisms for easy learning and retrieving, an arrangement of dendritic trees for maximizing generalization, hardwiring for rotation-translation-scaling invariance, and feedback connections with different delay durations for neurons to make full use of present and past informations generated by neurons in the same and higher layers. These functional models and their processing operations have many functions of biological neural networks that have not been achieved by other models in the open literature and provide logically coherent answers to many long-standing neuroscientific questions. However, biological justifications of these functional models and their processing operations are required for THPAM to qualify as a macroscopic model (or low-order approximate) of biological neural networks.     

Pairwise differences under a general model of population subdivision

A number of different migration and isolation models of population subdivision have been studied. In this paper I analyse a general model of two populations derived from a common ancestral population at some time in the past. The two populations may exchange migrants, but they may also be completely isolated from each other. I derive the expectation and variance of the number of differences between two sequences sampled from the two populations. These are then compared to the corresponding results from two other much-used models: equilibrium migration and complete isolation.     

From single molecule fluctuations to muscle contraction: a brownian model of A.F. Huxley's hypotheses

Muscular force generation in response to external stimuli is the result of thermally fluctuating, cyclical interactions between myosin and actin, which together form the actomyosin complex. Normally, these fluctuations are modelled using transition rate functions that are based on muscle fiber behaviour, in a phenomenological fashion. However, such a basis reduces the predictive power of these models. As an alternative, we propose a model which uses direct single molecule observations of actomyosin fluctuations reported in the literature. We precisely estimate the actomyosin potential bias and use diffusion theory to obtain a brownian ratchet model that reproduces the complete cross-bridge cycle. The model is validated by simulating several macroscopic experimental conditions, while its interpretation is compatible with two different force-generating scenarios.     

Prolegomena to a joint model of the contractile system of striated muscle

On the basis of some known properties of the contractile apparatus of muscle and, employing speculative premises, a mathematical model was formulated which makes it possible to express the relations between some macroscopic phenomena of muscle contraction and activities of idealized molecular generators of force quantitatively. With the exception of the sliding filament theory, which is generally accepted, no other published models have, as yet, been taken into consideration.