Mathematical Model Of Neuron Research Articles

The Gamma renewal process as an output of the diffusion leaky integrate-and-fire neuronal model.

Statistical properties of spike trains as well as other neurophysiological data suggest a number of mathematical models of neurons. These models range from entirely descriptive ones to those deduced from the properties of the real neurons. One of them, the diffusion leaky integrate-and-fire neuronal model, which is based on the Ornstein-Uhlenbeck (OU) stochastic process that is restricted by an absorbing barrier, can describe a wide range of neuronal activity in terms of its parameters. These parameters are readily associated with known physiological mechanisms. The other model is descriptive, Gamma renewal process, and its parameters only reflect the observed experimental data or assumed theoretical properties. Both of these commonly used models are related here. We show under which conditions the Gamma model is an output from the diffusion OU model. In some cases, we can see that the Gamma distribution is unrealistic to be achieved for the employed parameters of the OU process.

Restoring the encoding properties of a stochastic neuron model by an exogenous noise.

Here we evaluate the possibility of improving the encoding properties of an impaired neuronal system by superimposing an exogenous noise to an external electric stimulation signal. The approach is based on the use of mathematical neuron models consisting of stochastic HH-like circuit, where the impairment of the endogenous presynaptic inputs is described as a subthreshold injected current and the exogenous stimulation signal is a sinusoidal voltage perturbation across the membrane. Our results indicate that a correlated Gaussian noise, added to the sinusoidal signal can significantly increase the encoding properties of the impaired system, through the Stochastic Resonance (SR) phenomenon. These results suggest that an exogenous noise, suitably tailored, could improve the efficacy of those stimulation techniques used in neuronal systems, where the presynaptic sensory neurons are impaired and have to be artificially bypassed.

A Mathematical Model of a Midbrain Dopamine Neuron Identifies Two Slow Variables Likely Responsible for Bursts Evoked by SK Channel Antagonists and Terminated by Depolarization Block.

Midbrain dopamine neurons exhibit a novel type of bursting that we call “inverted square wave bursting” when exposed to Ca2+-activated small conductance (SK) K+ channel blockers in vitro. This type of bursting has three phases: hyperpolarized silence, spiking, and depolarization block. We find that two slow variables are required for this type of bursting, and we show that the three-dimensional bifurcation diagram for inverted square wave bursting is a folded surface with upper (depolarized) and lower (hyperpolarized) branches. The activation of the L-type Ca2+ channel largely supports the separation between these branches. Spiking is initiated at a saddle node on an invariant circle bifurcation at the folded edge of the lower branch and the trajectory spirals around the unstable fixed points on the upper branch. Spiking is terminated at a supercritical Hopf bifurcation, but the trajectory remains on the upper branch until it hits a saddle node on the upper folded edge and drops to the lower branch. The two slow variables contribute as follows. A second, slow component of sodium channel inactivation is largely responsible for the initiation and termination of spiking. The slow activation of the ether-a-go-go-related (ERG) K+ current is largely responsible for termination of the depolarized plateau. The mechanisms and slow processes identified herein may contribute to bursting as well as entry into and recovery from the depolarization block to different degrees in different subpopulations of dopamine neurons in vivo.

Effects of SKF83959 on the excitability of hippocampal CA1 pyramidal neurons: a modeling study.

3-Methyl-6-chloro-7,8-hydroxy-1-(3-methylphenyl)-2,3,4,5-tetrahydro-1H-3-benzazepine (SKF83959) have been shown to affect several types of voltage-dependent channels in hippocampal pyramidal neurons. The aim of this study was to determine how modulation of a individual type of the channels by SKF83959 contributes to the overall excitability of CA1 pyramidal neurons during either direct current injections or synaptic activation. Rat hippocampal slices were prepared. The kinetics of voltage-dependent Na(+) channels and neuronal excitability and depolarization block in CA1 pyramidal neurons were examined using whole-cell recording. A realistic mathematical model of hippocampal CA1 pyramidal neuron was used to simulate the effects of SKF83959 on neuronal excitability. SKF83959 (50 μmol/L) shifted the inactivation curve of Na(+) current by 10.3 mV but had no effect on the activation curve in CA1 pyramidal neurons. The effects of SKF83959 on passive membrane properties, including a decreased input resistance and depolarized resting potential, predicted by our simulations were in agreement with the experimental data. The simulations showed that decreased excitability of the soma by SKF83959 (examined with current injection at the soma) was only observed when the membrane potential was compensated to the control levels, whereas the decreased dendritic excitability (examined with current injection at the dendrite) was found even without membrane potential compensation, which led to a decreased number of action potentials initiated at the soma. Moreover, SKF83959 significantly facilitated depolarization block in CA1 pyramidal neurons. SKF83959 decreased EPSP temporal summation and, of physiologically greater relevance, the synaptic-driven firing frequency. SKF83959 decreased the excitability of CA1 pyramidal neurons even though the drug caused the membrane potential depolarization. The results may reveal a partial mechanism for the drug's anti-Parkinsonian effects and may also suggest that SKF83959 has a potential antiepileptic effect.

Exact computation of the maximum-entropy potential of spiking neural-network models.

Understanding how stimuli and synaptic connectivity influence the statistics of spike patterns in neural networks is a central question in computational neuroscience. The maximum-entropy approach has been successfully used to characterize the statistical response of simultaneously recorded spiking neurons responding to stimuli. However, in spite of good performance in terms of prediction, the fitting parameters do not explain the underlying mechanistic causes of the observed correlations. On the other hand, mathematical models of spiking neurons (neuromimetic models) provide a probabilistic mapping between the stimulus, network architecture, and spike patterns in terms of conditional probabilities. In this paper we build an exact analytical mapping between neuromimetic and maximum-entropy models.

Computational model of midbrain dopaminergic neuron activity in ageing and obesity

Obesity is an increasing health problem in the modern world. Feeding behavior is mostly controlled by homeostatic and hedonic systems. It was already demonstrated in the hypothalamus that diet-induced obesity can change the spontaneous activity of cells involved in homeostatic regulation. It is, however, unclear if the hedonic regulation is also affected by diet-induced obersity. The midbrain dopaminergic (DA) neurons are a key component of the hedonic system. Usually, dopaminergic neurons in brain slice preparations show a highly regular pacemaker-like activity pattern. However it was found in [1], that in mice fed on high fat diet (HFD) a significantly increased proportion of DA neurons fired irregularly as compared to the ones in mice that ware fed on normal diet (NCD). A mathematical model of midbrain dopaminergic neuron (DA) has been developed to better understand the mechanisms underlying the different types of firing patterns that these cells exhibit in vitro. The dopaminergic neuron was modeled using a single compartment which includes voltage and Ca2+-dependent currents described by Hodgkin-Huxley kinetics. The model used in this study is based on an existing DA neuron model [2,3] and some parameters were determined using new voltage-clamp data from HFD and NCD mouse brain slices.

Oxygen dynamics during in vitro seizures

Oxygen is an essential element for brain activity. The brain is a metabolic engine that requires 20% of the body’s metabolic energy, despite being only 2% of the human body mass [1]. Two thirds of brain’s metabolic energy is dedicated to supporting neural spiking activity. Much of the O2 dependent ATP metabolism in single neurons is used by energetic Na/K-ATPase pumps that transport 3Na+ outwards with 2K+ inward against their concentration gradients for each ATP hydrolyzed [2,3]. However, understanding the relationship between seizures and real-time oxygen dynamics has been restricted by current technical limitations. Computational models can offer insight to help understand the measurements from experiments. We have performed experiments relating seizure activity at the cellular level with simultaneous real-time O2 microdomain measurements. In this paper, we build a mathematical neuron model that extends the Hodgkin-Huxley formalism containing leak currents for sodium, potassium and chloride ions, transient sodium currents, and delayed rectifier potassium currents. This neuron was embedded within an extracellular space and a simplified glia-endothelium system. The Na+ and K+ ion concentrations as well as extracellular oxygen density were continuously estimated. Hypoxia was modeled by reducing both neuron and glial Na/K-ATPase pump activities. During seizure events, the extracellular K+ and intracellular Na+ were increased, which further activated the Na/K-ATPase pump activity. Energy (ATP) and O2 demand were simultaneously increased. Therefore, local available [O2] decreased substantially during seizure events, and the apparent O2 debt substantially outlasts the intense electrical activity of a seizure, as shown in Figure ​Figure1.1. This result is consistent with experimental data [4]. We also observed that hypoxia alone can induce seizure like events, which occurs only in a narrow range of bath oxygen pressure, reflecting experimental observations. Lastly, we reproduced the interplay between excitatory and inhibitory neurons seen in experiments. Our model accounts for the different [O2] levels that we have observed during seizures in pyramidal cell layers vs. inhibitory (oriens lacunosum moleculare) cell layers. Our work suggests the critical importance of modeling extracellular ion concentration and oxygen dynamics to properly understand the underlying mechanisms behind seizure and related phenomena. Figure 1 Membrane potentials (top trace), extracellular potassium concentration (middle trace), and oxygen density (bottom trace) from a single model neuron during a seizure event. The time course of [O2] debt is qualitatively similar to that observed experimentally. ...

Structure-Dependent Electrical and Concentration Processes in the Dendrites of Pyramidal Neurons of Superficial Neocortical Layers: Model Study

On mathematical models of pyramidal neurons localized in the neocortical layers 2/3, whose reconstructed dendritic arborization possessed passive linear or active nonlinear membrane properties, we studied the effect of morphology of the dendrites on their passive electrical transfer characteristics and also on the formation of patterns of spike discharges at the output of the cell under conditions of tonic activation via uniformly distributed excitatory synapses along the dendrites. For this purpose, we calculated morphometric characteristics of the size, complexity, metric asymmetry, and function of effectiveness of somatopetal transmission of the current (with estimation of the sensitivity of this efficacy to changes in the uniform membrane conductance) for the reconstructed dendritic arborization in general and also for its apical and basal subtrees. Spatial maps of the membrane potential and intracellular calcium concentration, which corresponded to certain temporal patterns of spike discharges generated by the neuron upon different intensities of synaptic activation, were superimposed on the 3D image and dendrograms of the neuron. These maps were considered “spatial autographs” of the above patterns. The main discharge pattern included periodic two-spike bursts (dublets) generated with relatively stable intraburst interspike intervals and interburst intervals decreasing with a rise in the intensity of activation. Under conditions of intense activation, the interburst intervals became close to the intraburst intervals, so the cell began to generate continuous trains of action potentials. Such a repertoire (consisting of two patterns of the activity, periodical dublets and continuous discharges) is considerably scantier than that described earlier in pyramidal neurons of the neocortical layer 5. Under analogous conditions of activation, we observed in the latter cells a variety of patterns of output discharges of different complexities, including stochastic ones. A relatively short length of the apical dendrite subtree of layer 2/3 neurons and, correspondingly, a smaller metric asymmetry (differences between the lengths of the apical and basal dendritic branches and paths), as compared with those in layer 5 pyramidal neurons, are morphological factors responsible for the predominance of periodic spike dublets. As a result, there were two combinations of different electrical states of the sites of dendritic arborization (“spatial autographs”). In the case of dublets, these were high depolarization of the apical dendrites vs. low depolarization of the basal dendrites and a reverse combination; only the latter (reverse) combination corresponded to the case of continuous discharges. The relative simplicity and uniformity of spike patterns in the cells, apparently, promotes the predominance of network interaction in the processes of formation of the activity of pyramidal neurons of layers 2/3 and, thereby, a higher efficiency of the processes of intracortical association.

A Systematic Method for Configuring VLSI Networks of Spiking Neurons

An increasing number of research groups are developing custom hybrid analog/digital very large scale integration (VLSI) chips and systems that implement hundreds to thousands of spiking neurons with biophysically realistic dynamics, with the intention of emulating brainlike real-world behavior in hardware and robotic systems rather than simply simulating their performance on general-purpose digital computers. Although the electronic engineering aspects of these emulation systems is proceeding well, progress toward the actual emulation of brainlike tasks is restricted by the lack of suitable high-level configuration methods of the kind that have already been developed over many decades for simulations on general-purpose computers. The key difficulty is that the dynamics of the CMOS electronic analogs are determined by transistor biases that do not map simply to the parameter types and values used in typical abstract mathematical models of neurons and their networks. Here we provide a general method for resolving this difficulty. We describe a parameter mapping technique that permits an automatic configuration of VLSI neural networks so that their electronic emulation conforms to a higher-level neuronal simulation. We show that the neurons configured by our method exhibit spike timing statistics and temporal dynamics that are the same as those observed in the software simulated neurons and, in particular, that the key parameters of recurrent VLSI neural networks (e.g., implementing soft winner-take-all) can be precisely tuned. The proposed method permits a seamless integration between software simulations with hardware emulations and intertranslatability between the parameters of abstract neuronal models and their emulation counterparts. Most important, our method offers a route toward a high-level task configuration language for neuromorphic VLSI systems.

Modified Pulse Shapes for Effective Neural Stimulation

The electrical stimulation of neuronal structures is used as a treatment for many neurological disorders, e.g., for the treatment of Parkinson’s disease via deep brain stimulation (DBS). To reduce side effects, to avoid tissue or electrode damage, and to increase battery lifetimes, an effective but gentle electrical stimulation is of prime importance. We studied different modified pulse shapes for application in DBS with respect to their efficiency to initiate neuronal activity. Numerical simulations of two mathematical neuron models were performed to investigate the effectiveness of different modified pulse shapes. According to our results, the pulse shapes considered showed a considerably increased efficiency in terms of both activation and entrainment of neural activity. We found that the introduction of a gap with a specific and optimized duration in a biphasic pulse and the reversal of the standard pulse phase order yielded stimulation protocols that could increase the efficiency and therefore reduce the energy consumption of stimulation. The improvements were achieved by simple modifications of existing stimulation techniques. The modification of the pulse shapes resulted in an improvement of up to 50% for both the activation of resting neurons and the entrainment of bursting neurons.

Noise Enhances Subthreshold Oscillations in Injured Primary Sensory Neurons

Noise can play a constructive role in the detection of weak signals in various kinds of peripheral receptors and neurons. What the mechanism underlying the effect of noise is remains unclear. Here, the perforated patch-clamp technique was used on isolated cells from chronic compression of the dorsal root ganglion (DRG) model. Our data provided new insight indicating that, under conditions without external signals, noise can enhance subthreshold oscillations, which was observed in a certain type of neurons with high-frequency (20–100 Hz) intrinsic resonance from injured DRG neurons. The occurrence of subthreshold oscillation considerably decreased the threshold potential for generating repetitive firing. The above effects of noise can be abolished by blocking the persistent sodium current (I_{Na, P}). Utilizing a mathematical neuron model we further simulated the effect of noise on subthreshold oscillation and firing, and also found that noise can enhance the electrical activity through autonomous stochastic resonance. Accordingly, we propose a new concept of the effects of noise on neural intrinsic activity, which suggests that noise may be an important factor for modulating the excitability of neurons and generation of chronic pain signals.

Discovering excitatory relationships using dynamic Bayesian networks

Mining temporal network models from discrete event streams is an important problem with applications in computational neuroscience, physical plant diagnostics, and human–computer interaction modeling. In this paper, we introduce the notion of excitatory networks which are essentially temporal models where all connections are stimulative, rather than inhibitive. The emphasis on excitatory connections facilitates learning of network models by creating bridges to frequent episode mining. Specifically, we show that frequent episodes help identify nodes with high mutual information relationships and that such relationships can be summarized into a dynamic Bayesian network (DBN). This leads to an algorithm that is significantly faster than state-of-the-art methods for inferring DBNs, while simultaneously providing theoretical guarantees on network optimality. We demonstrate the advantages of our approach through an application in neuroscience, where we show how strong excitatory networks can be efficiently inferred from both mathematical models of spiking neurons and several real neuroscience datasets.

Computational model explaining two types of bursting found in inspiratory pacemakers.

The respiratory rhythm is generated within the network of inspiratory neurons in the pre-Botzinger complex (pBC) and persists under highly variable neuronal input. The mechanism of pBC rhythm generation at the level of the network is an active area of debate and inquiry. A fraction of these inspiratory pBC neurons generate a stable bursting rhythm even when pharmacologically isolated from the network and likely contribute to the rhythm. Experiments indicate that the intrinsic bursting mechanism of these pacemaker neurons depends on either persistent sodium current or changes in intracellular Ca2+. Motivated by experimental evidence obtained from these subpopulations of bursting neurons, we developed a two-compartment mathematical model of a pBC pacemaker neuron with two independent bursting mechanisms. The model explains a number of contradictory experimental results and is able to generate a robust bursting rhythm over a large range of parameters, with a frequency adjusted by neuromodulators. For the somatic compartment of our model, we used a previously developed model of pBC pacemaker neurons [1]. In this model, action potentials are generated by a fast sodium current (INa) and a delayed rectifier potassium current (IK), and the burst is terminated by slow inactivation of a persistent sodium current (INaP). The bursting in the dendritic compartment of our model follows the Ca2+ oscillations arising from periodic Ca2+ release from intracellular stores. Briefly, the activation of a Gq-protein cascade leads to an increase in the concentration of IP3, which binds to its receptor on the surface of the endoplasmic reticulum and initiates Ca2+ influx into the cytosol. A calcium-activated nonspecific cation current (ICaN) then depolarizes the cell membrane in response to the increase in intracellular Ca2+ concentration. This depolarizing potential spreads to the soma and activates action potential-generating currents (INa and IK), thus initiating the burst. Finally, the action potential propagates to the dendrite, producing a dendritic burst of smaller amplitude. The model predicts that in synaptically isolated cells, the bursting mechanism depends on neuromodulators, endogenously released within the pBC. The neuromodulatory tone can bias the neuron to a somatic (INaP) or dendritic (Ca2+ and ICaN) mode of bursting, or a hybrid of the two. In the dendritic mode, the period of bursting is largely modulated by the IP3 concentration, whereas in the somatic mode the burst duration is modulated by the persistent sodium current. This model displays changes in burst duration and period that are consistent with experimentally published pharmacological manipulations, such as the application of ion channel blockers (FFA and Riluzole) as well as neuromodulatory manipulations.

Spectrum measurement of fast optical signal of neural activity in brain tissue and its theoretical origin

Functional brain imaging technologies have enabled recent advances in understanding human brain function. In particular, a noninvasive and fast optical technique will become one of the most promising tools for future studies. As a fundamental ex vivo study for the development of such a technique, this paper demonstrates the spectral measurement of fast optical changes associated with neural activity in bulk brain tissue. For this purpose, a high-speed confocal near-infrared spectrometer was built and used. The results verified that observed transient optical responses (tORs) are associated with neural activity by showing that the following: tORs were concurrent and correlated with local field potentials (LFPs); tORs disappeared following tetrodotoxin application; and tORs were reproducibly observed across preparations. In addition, the amplitude of tORs was statistically significantly larger in longer wavelengths (∼1200nm). The time course of tORs, however, is quite different from that of LFPs. Since this difference implies that tORs may originate not directly from the electric potential variation but from other neurophysiological events accompanying excitation, this paper tested the hypothesis that tORs are attributed to transient cellular volume changes (tCVCs). With no previous dynamic equation to elucidate such different temporal dynamics of the optical responses, a novel mathematical neuron model to describe tCVCs was developed. This neuron model, along with finite-difference time-domain simulations, showed that tCVCs and tORs were similar in the temporal dynamics, order of magnitude, response direction, and detectability in the bulk tissue; thus supporting the hypothesis.

Nonlinear electronic circuit with neuron like bursting and spiking dynamics

It is difficult to design electronic nonlinear devices capable of reproducing complex oscillations because of the lack of general constructive rules, and because of stability problems related to the dynamical robustness of the circuits. This is particularly true for current analog electronic circuits that implement mathematical models of bursting and spiking neurons. Here we describe a novel, four-dimensional and dynamically robust nonlinear analog electronic circuit that is intrinsic excitable, and that displays frequency adaptation bursting and spiking oscillations. Despite differences from the classical Hodgkin–Huxley (HH) neuron model, its bifurcation sequences and dynamical properties are preserved, validating the circuit as a neuron model. The circuit's performance is based on a nonlinear interaction of fast–slow circuit blocks that can be clearly dissected, elucidating burst's starting, sustaining and stopping mechanisms, which may also operate in real neurons. Our analog circuit unit is easily linked and may be useful in building networks that perform in real-time.

Visiome Platform in Retinal Modeling

Event Abstract Back to Event Visiome Platform in Retinal Modeling Yoshimi Kamiyama1* and Shiro Usui2 1 Aichi Prefectural University, Information Science and Technology, Japan 2 RIKEN Brain Science Institute, Japan Recently computational models and tools are increasingly popularized in Vision science to assist in the exploration and interpretation of complex visual functions and phenomena. There is a critical need for a database where published data can be archived so that they can be accessed, uploaded, downloaded, and tested. Visiome Platform is being developed to answer this need as a web-based database system with a variety of digital research resources in vision science. We have been constructing a website, http://platform.visiome.neuroinf.jp/, which includes contents such as mathematical models, experimental data, illusion designs, visual stimulus generation codes, demonstration movies and analytical software tools.Since reproducibility is a key principle of the scientific method, it is essential that published results be testable by other researchers using the same method. However, for example, most modeling articles do not contain enough information that is necessary for readers to be able to reproduce and verify the results due to lack of initial conditions, incomplete parameter values and so on. Visiome Platform has been designed to make the items reusable. The platform accepts and provides archive files including any formats of model, data or visual stimulus with files of explanatory figures, program sources, readme and other related files.Users can browse Visiome Platform to surf the field of vision science, or seek specific topics of interests. Mathematical models of the vertebrate retina are typical contents in the platform. The retina is an excellent preparation for studying brain structure and function as well as neural signal processing in the brain because of its accessibility and suitability for neuroscientific investigation. Consequently, large amount of research results on all aspects of retinal visual information processing are available. We have been developing mathematical models of retinal neurons and network based on neurophysiological experimental findings. Models we developed are now browsed and downloaded and users can be able to reproduce simulation results in the original papers. In addition to our own models, we have been re-implementing published models of the retina such as a historical model of the photoreceptor and a recent systematic model of the cone-horizontal cell network. Here, we show the mathematical models of the retinal neurons, and demonstrate the electrical responses are quantitatively accounted for by the models in the platform. Visiome Platform now contains a growing collection of the published models of the retina, and the platform supports the field of neuroinformatics by making high-quality retinal models readily available. Conference: Neuroinformatics 2009, Pilsen, Czechia, 6 Sep - 8 Sep, 2009. Presentation Type: Oral Presentation Topic: Computational neuroscience Citation: Kamiyama Y and Usui S (2019). Visiome Platform in Retinal Modeling. Front. Neuroinform. Conference Abstract: Neuroinformatics 2009. doi: 10.3389/conf.neuro.11.2009.08.111 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 25 May 2009; Published Online: 09 May 2019. * Correspondence: Yoshimi Kamiyama, Aichi Prefectural University, Information Science and Technology, Aichi, Japan, kamiyama@ist.aichi-pu.ac.jp Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Yoshimi Kamiyama Shiro Usui Google Yoshimi Kamiyama Shiro Usui Google Scholar Yoshimi Kamiyama Shiro Usui PubMed Yoshimi Kamiyama Shiro Usui Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

Computational neuroscience grand challenges - a humble attempt at future forecast

Computational Neuroscience is a still nascent field, aspiring to imitate the great success of theoretical physics. The crucial advance of theoretical physics that transformed our understanding of the material world around us beyond recognition was the demonstration that various physical processes, no matter how complicated and rich they may appear to an observer, are governed by a well-defined set of simple principles that are formulated with the precise language of mathematical equations. Are there simple mathematical laws that capture the fundamental laws that govern the operation of neural systems? Will we one day understand the brain to a similar degree as we now understand the material world? If so, we will be able to quantitatively predict complicated cognitive behaviours under arbitrary external and internal conditions and build good brain emulators, very much as we can predict the trajectory of an asteroid or design a bridge with a given safety level. A mere acceptance of such a possibility should not be taken for granted however, as it might put us in a shaky position with respect to some deeply entrenched (and hotly debated) concepts, such as e.g. free will and related issues. This simple consideration illustrates in my view that even the ultimate goals of computational neuroscience should continually be debated and refined. Theoretical studies of the brain are pursued along several disjoint scientific approaches. We have rather accurate mathematical models of ion channels, neurons and synapses, at the level approaching physics. These are formulated with the language of dynamical systems theory, and have reasonable predictive capacity. Extending this approach to larger systems, giving rise to neural network theory, resulted in some profound and imaginative ideas about such complex cognitive phenomena as learning and memory, object recognition and spatial navigation. Predictive capacity of neural network models is however much more limited, and there are still profound uncertainties about their validity, explained among other things by still inadequate experimental techniques of measuring activity of large neuronal ensembles and anatomy of neuronal interactions. Moreover, neural networks models still have a rather poor repertoire of cognitive behaviours that they were applied to. Another approach is to view the brain as a biological implementation of a complex computer, and correspondingly to study it with the tools of computer science. In a sense, a researcher tries to formulate a certain computational task that the brain is performing, and then tries to imagine which algorithm he/she would use to perform the task on a computer. Neuronal architectures may be then used to put certain constrains on the possible algorithm, depending on the particular problem in question. Some examples of a successful application of this approach are the reinforcement theory of learning, computer vision and Bayesian inference framework for the information processing in the brain. Despite of significant achievements, this approach still appears to be largely detached from more biologically inspired modelling. Yet another direction could be called ‘data-driven approach’, who's proponents are mainly concerned with developing sophisticated techniques for analyzing multidimensional data that is generated by various experimental tools such as optical imaging and fMRI. What are the goals that computational neuroscience can realistically achieve in the observable future? I believe the first challenge is to see how far the neural networks theory can be pushed to get close to explaining high-level brain functions. Any cognitive process, vision as an example, involves multi-stage stream of processing with progressive specialized brain areas having similar overall architecture but different aspects of information representation and processing. Neural networks for the most part were confined to functionally uniform neuronal populations. The second challenge that computational neuroscience will have to meet in order to make a progress will be to partially break with the tradition of trying to explain all the richness of the brain with networks of simple elements and complex architectures. This tradition was probably a necessary first step that allowed the researchers to set the stage for the new field and borrow the techniques and intuitions developed in physics, but it resulted in a certain degree of ignorance about the incredible complexity of the neuronal hardware in the brain. It appears reasonable to predict that the full-fledged neuronal network theory will have to seriously consider the effects of neuromodulation, neuronal and synaptic adaptation on various spatial and time scales, incredible diversity of neuron types, the role of glia cells, etc etc etc. Finally, different theoretical approaches mentioned above will have to be more closely integrated into a unified theoretical framework. Thus, theoreticians who come from different scientific traditions not only should make bridges to their experimental colleagues, they should also talk much more to each other, which sometimes, paradoxically, appears to be even more challenging.

Spike Train Probability Models for Stimulus-Driven Leaky Integrate-and-Fire Neurons

Mathematical models of neurons are widely used to improve understanding of neuronal spiking behavior. These models can produce artificial spike trains that resemble actual spike train data in important ways, but they are not very easy to apply to the analysis of spike train data. Instead, statistical methods based on point process models of spike trains provide a wide range of data-analytical techniques. Two simplified point process models have been introduced in the literature: the time-rescaled renewal process (TRRP) and the multiplicative inhomogeneous Markov interval (m-IMI) model. In this letter we investigate the extent to which the TRRP and m-IMI models are able to fit spike trains produced by stimulus-driven leaky integrate-and-fire (LIF) neurons. With a constant stimulus, the LIF spike train is a renewal process, and the m-IMI and TRRP models will describe accurately the LIF spike train variability. With a time-varying stimulus, the probability of spiking under all three of these models depends on both the experimental clock time relative to the stimulus and the time since the previous spike, but it does so differently for the LIF, m-IMI, and TRRP models. We assessed the distance between the LIF model and each of the two empirical models in the presence of a time-varying stimulus. We found that while lack of fit of a Poisson model to LIF spike train data can be evident even in small samples, the m-IMI and TRRP models tend to fit well, and much larger samples are required before there is statistical evidence of lack of fit of the m-IMI or TRRP models. We also found that when the mean of the stimulus varies across time, the m-IMI model provides a better fit to the LIF data than the TRRP, and when the variance of the stimulus varies across time, the TRRP provides the better fit.

Modeling and simulation of retinal neurons and the neuroinformatics tools

Event Abstract Back to Event Modeling and simulation of retinal neurons and the neuroinformatics tools Yoshimi Kamiyama1* and Shiro Usui2 1 Aichi Prefectural University, Japan 2 RIKEN Brain Science Institute, Japan The retina transforms the light into nerve spikes which are carried by the optic nerve to the brain. The retina has been thought to be a window to the brain because of its accessibility and suitability for neuroscientific investigation. It is thought to be one of the few parts of the vertebrate brain where we can reasonably explain its purpose and how it works. The retina is an attractive model system for approaching the question of the information processing role of biological mechanisms of neurons. The physiology and anatomy of the retina are relatively well known. Physiological studies of the retina have uncovered a number of cellular and subcellular mechanisms such as phototransduction and the characteristics of the ion channels found in retinal neurons. Neuroanatomical studies have revealed the morphological principles govering the structure of the retina. The former data provide information about the functional role of ion channels in generating and shaping the light response of the retinal neurons. It is as yet impossible to provide a complete model of the retina. But it is now possible to identify some computational operations that the retina perfoms and to relate them to specific physiological mechanisms, on the basis of computational modeling work. Over the last decade, we have developed mathematical models of retinal neurons based on neurophysiological details. These models can reveal what happens if a particular ionic current is active or inactive. One can then ask what advantages are given on the visual system by having the particular class of ion channel present in the neuron. Here, we show the mathematical models of the retinal neurons, and demonstrate that the electircal responses are quantitatively accounted for by the models. The models we have developed provide a unified framework for the undestanding of the functional role of cellular mechanisms of retinal neurons and their integrative functions. In the present study, we analyzed the underlying mechanisms of a rod photoreceptor that behaves as a bandpass filter which has long been a mystery. We discovered that the kinetics of the calcium dependent ionic currents characterize the bandpass filtering of rod signals. We also developed a stochastic model of spike generation in retinal ganglion cells. The stochastic model showed precise and reliable spikes to randomly fluctuating current similar to those of experimental data. We found the spike timing was much influenced by the outward currents, not by the sodium current which riggers spikes. The simulation analysis with these models requires some software tools. We developed three software systems; (1) XML-based retinal neuron modeling language which stores not only mathematical models, but also all calculation conditions and improves model reproducibility, (2)Grid portal simulation environment which provides seamless access to computing resources over the network, (3)Realtime retinal neuron simulator with USB camera device for understanding the role of retinal neurons in visual information processing. These tools highly improved simulation efficiency for retinal modeling and simulation. 81b tn_07-29-2008-10-52_81b tn_81b 07-29-2008-10-52_81b Conference: Neuroinformatics 2008, Stockholm, Sweden, 7 Sep - 9 Sep, 2008. Presentation Type: Oral Presentation Topic: Live Demonstrations Citation: Kamiyama Y and Usui S (2008). Modeling and simulation of retinal neurons and the neuroinformatics tools. Front. Neuroinform. Conference Abstract: Neuroinformatics 2008. doi: 10.3389/conf.neuro.11.2008.01.121 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 28 Jul 2008; Published Online: 28 Jul 2008. * Correspondence: Yoshimi Kamiyama, Aichi Prefectural University, Aichi, Japan, usuishiro@riken.jp Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract Supplemental Data The Authors in Frontiers Yoshimi Kamiyama Shiro Usui Google Yoshimi Kamiyama Shiro Usui Google Scholar Yoshimi Kamiyama Shiro Usui PubMed Yoshimi Kamiyama Shiro Usui Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

Computational model of a modulatory cell type in the feeding network of the snail, Lymnaea stagnalis

Realistic mathematical models of single neurons are significant in assessing the contribution of specific ionic conductances to neuronal excitability. This study presents a detailed computational model of the Cerebral Giant Cells (CGCs), a pair of serotonergic neurons in the feeding network of Lymnaea stagnalis, which are critical for the expression of motor behaviour (feeding) and the formation of long-term memory.