Conduction velocities in amphibian skeletal muscle fibres exposed to hyperosmotic extracellular solutions

Early quantitative analyses of conduction velocities in unmyelinated nerve studied in a constantly iso-osmotic volume conductor were extended to an analysis of the effects of varying extracellular osmolarities on conduction velocities of surface membrane action potentials in Rana esculenta skeletal muscle fibres. Previous papers had reported that skeletal muscle fibres exposed to a wide range of extracellular sucrose concentrations resemble perfect osmometers with increased extracellular osmolarity proportionally decreasing fibre volume and therefore diminishing fibre radius, a. However, classical electrolyte theory (Robinson and Stokes 1959, Electrolyte solutions 2nd edn. Butterworth & Co. pp 41–42) would then predict that the consequent increases in intracellular ionic strength would correspondingly decrease sarcoplasmic resistivity, Ri. An extension of the original cable analysis then demonstrated that the latter would precisely offset its expected effect of alterations in a on the fibre axial resistance, ri, and leave action potential conduction velocity constant. In contrast, other reports (Hodgkin and Nakajima J Physiol 221:105–120, 1972) had suggested that Riincreased with extracellular osmolarity, owing to alterations in cytosolic viscosity. This led to a prediction of a decreased conduction velocity. These opposing hypotheses were then tested in muscle fibres subject to just-suprathreshold stimulation at a Vaseline seal at one end and measuring action potentials and their first order derivatives, dV/dt, using 5–20 MΩ, 3 M KCl glass microelectrodes at defined distances away from the stimulus sites. Exposures to hyperosmotic, sucrose-containing, Ringer solutions then reversibly reduced both conduction velocity and maximum values of dV/dt. This was compatible with an increase in Ri in the event that conduction depended upon a discharge of membrane capacitance by propagating local circuit currents through initially passive electrical elements. Conduction velocity then showed graded decreases with increasing extracellular osmolarity from 250–750 mOsm. Action potential waveforms through these osmolarity changes remained similar, including both early surface and the late after-depolarisation events reflecting transverse tubular activation. Quantitative comparisons of reduced-χ 2 values derived from a comparison of these results and the differing predictions from the two hypotheses strongly favoured the hypothesis in which Riincreased rather than decreased with hyperosmolarity

Hands-On Parameter Search for Neural Simulations by a MIDI-Controller

Computational neuroscientists frequently encounter the challenge of parameter fitting – exploring a usually high dimensional variable space to find a parameter set that reproduces an experimental data set. One common approach is using automated search algorithms such as gradient descent or genetic algorithms. However, these approaches suffer several shortcomings related to their lack of understanding the underlying question, such as defining a suitable error function or getting stuck in local minima. Another widespread approach is manual parameter fitting using a keyboard or a mouse, evaluating different parameter sets following the users intuition. However, this process is often cumbersome and time-intensive. Here, we present a new method for manual parameter fitting. A MIDI controller provides input to the simulation software, where model parameters are then tuned according to the knob and slider positions on the device. The model is immediately updated on every parameter change, continuously plotting the latest results. Given reasonably short simulation times of less than one second, we find this method to be highly efficient in quickly determining good parameter sets. Our approach bears a close resemblance to tuning the sound of an analog synthesizer, giving the user a very good intuition of the problem at hand, such as immediate feedback if and how results are affected by specific parameter changes. In addition to be used in research, our approach should be an ideal teaching tool, allowing students to interactively explore complex models such as Hodgkin-Huxley or dynamical systems

Simple, Fast and Accurate Implementation of the Diffusion Approximation Algorithm for Stochastic Ion Channels with Multiple States

The phenomena that emerge from the interaction of the stochastic opening and closing of ion channels (channel noise) with the non-linear neural dynamics are essential to our understanding of the operation of the nervous system. The effects that channel noise can have on neural dynamics are generally studied using numerical simulations of stochastic models. Algorithms based on discrete Markov Chains (MC) seem to be the most reliable and trustworthy, but even optimized algorithms come with a non-negligible computational cost. Diffusion Approximation (DA) methods use Stochastic Differential Equations (SDE) to approximate the behavior of a number of MCs, considerably speeding up simulation times. However, model comparisons have suggested that DA methods did not lead to the same results as in MC modeling in terms of channel noise statistics and effects on excitability. Recently, it was shown that the difference arose because MCs were modeled with coupled activation subunits, while the DA was modeled using uncoupled activation subunits. Implementations of DA with coupled subunits, in the context of a specific kinetic scheme, yielded similar results to MC. However, it remained unclear how to generalize these implementations to different kinetic schemes, or whether they were faster than MC algorithms. Additionally, a steady state approximation was used for the stochastic terms, which, as we show here, can introduce significant inaccuracies. We derived the SDE explicitly for any given ion channel kinetic scheme. The resulting generic equations were surprisingly simple and interpretable - allowing an easy and efficient DA implementation. The algorithm was tested in a voltage clamp simulation and in two different current clamp simulations, yielding the same results as MC modeling. Also, the simulation efficiency of this DA method demonstrated considerable superiority over MC methods.Comment: 32 text pages, 10 figures, 1 supplementary text + figur

The what and where of adding channel noise to the Hodgkin-Huxley equations

One of the most celebrated successes in computational biology is the Hodgkin-Huxley framework for modeling electrically active cells. This framework, expressed through a set of differential equations, synthesizes the impact of ionic currents on a cell's voltage -- and the highly nonlinear impact of that voltage back on the currents themselves -- into the rapid push and pull of the action potential. Latter studies confirmed that these cellular dynamics are orchestrated by individual ion channels, whose conformational changes regulate the conductance of each ionic current. Thus, kinetic equations familiar from physical chemistry are the natural setting for describing conductances; for small-to-moderate numbers of channels, these will predict fluctuations in conductances and stochasticity in the resulting action potentials. At first glance, the kinetic equations provide a far more complex (and higher-dimensional) description than the original Hodgkin-Huxley equations. This has prompted more than a decade of efforts to capture channel fluctuations with noise terms added to the Hodgkin-Huxley equations. Many of these approaches, while intuitively appealing, produce quantitative errors when compared to kinetic equations; others, as only very recently demonstrated, are both accurate and relatively simple. We review what works, what doesn't, and why, seeking to build a bridge to well-established results for the deterministic Hodgkin-Huxley equations. As such, we hope that this review will speed emerging studies of how channel noise modulates electrophysiological dynamics and function. We supply user-friendly Matlab simulation code of these stochastic versions of the Hodgkin-Huxley equations on the ModelDB website (accession number 138950) and http://www.amath.washington.edu/~etsb/tutorials.html.Comment: 14 pages, 3 figures, review articl

Consequences of converting graded to action potentials upon neural information coding and energy efficiency

Information is encoded in neural circuits using both graded and action potentials, converting between them within single neurons and successive processing layers. This conversion is accompanied by information loss and a drop in energy efficiency. We investigate the biophysical causes of this loss of information and efficiency by comparing spiking neuron models, containing stochastic voltage-gated Na+ and K+ channels, with generator potential and graded potential models lacking voltage-gated Na+ channels. We identify three causes of information loss in the generator potential that are the by-product of action potential generation: (1) the voltage-gated Na+ channels necessary for action potential generation increase intrinsic noise and (2) introduce non-linearities, and (3) the finite duration of the action potential creates a ‘footprint’ in the generator potential that obscures incoming signals. These three processes reduce information rates by ~50% in generator potentials, to ~3 times that of spike trains. Both generator potentials and graded potentials consume almost an order of magnitude less energy per second than spike trains. Because of the lower information rates of generator potentials they are substantially less energy efficient than graded potentials. However, both are an order of magnitude more efficient than spike trains due to the higher energy costs and low information content of spikes, emphasizing that there is a two-fold cost of converting analogue to digital; information loss and cost inflation

Ion Channel Density Regulates Switches between Regular and Fast Spiking in Soma but Not in Axons

The threshold firing frequency of a neuron is a characterizing feature of its dynamical behaviour, in turn determining its role in the oscillatory activity of the brain. Two main types of dynamics have been identified in brain neurons. Type 1 dynamics (regular spiking) shows a continuous relationship between frequency and stimulation current (f-Istim) and, thus, an arbitrarily low frequency at threshold current; Type 2 (fast spiking) shows a discontinuous f-Istim relationship and a minimum threshold frequency. In a previous study of a hippocampal neuron model, we demonstrated that its dynamics could be of both Type 1 and Type 2, depending on ion channel density. In the present study we analyse the effect of varying channel density on threshold firing frequency on two well-studied axon membranes, namely the frog myelinated axon and the squid giant axon. Moreover, we analyse the hippocampal neuron model in more detail. The models are all based on voltage-clamp studies, thus comprising experimentally measurable parameters. The choice of analysing effects of channel density modifications is due to their physiological and pharmacological relevance. We show, using bifurcation analysis, that both axon models display exclusively Type 2 dynamics, independently of ion channel density. Nevertheless, both models have a region in the channel-density plane characterized by an N-shaped steady-state current-voltage relationship (a prerequisite for Type 1 dynamics and associated with this type of dynamics in the hippocampal model). In summary, our results suggest that the hippocampal soma and the two axon membranes represent two distinct kinds of membranes; membranes with a channel-density dependent switching between Type 1 and 2 dynamics, and membranes with a channel-density independent dynamics. The difference between the two membrane types suggests functional differences, compatible with a more flexible role of the soma membrane than that of the axon membrane

A Mathematical model for Astrocytes mediated LTP at Single Hippocampal Synapses

Many contemporary studies have shown that astrocytes play a significant role in modulating both short and long form of synaptic plasticity. There are very few experimental models which elucidate the role of astrocyte over Long-term Potentiation (LTP). Recently, Perea & Araque (2007) demonstrated a role of astrocytes in induction of LTP at single hippocampal synapses. They suggested a purely pre-synaptic basis for induction of this N-methyl-D- Aspartate (NMDA) Receptor-independent LTP. Also, the mechanisms underlying this pre-synaptic induction were not investigated. Here, in this article, we propose a mathematical model for astrocyte modulated LTP which successfully emulates the experimental findings of Perea & Araque (2007). Our study suggests the role of retrograde messengers, possibly Nitric Oxide (NO), for this pre-synaptically modulated LTP.Comment: 51 pages, 15 figures, Journal of Computational Neuroscience (to appear

A Reconfigurable Architecture for Implementing Locally Connected Neural Arrays

Moore’s law is rapidly approaching a long-predicted decline, and with it the performance gains of conventional processors are becoming ever more marginal. Cognitive computing systems based on neural networks have the potential to provide a solution to the decline of Moore’s law. Identifying common traits in neural systems can lead to the design of more efficient, robust and adaptable processors. Despite the potentials, large-scale neural systems remain difficult to implement due to constraints on scalability. Here we introduce a new hardware architecture for implementing locally connected neural networks that can model biological systems with a high level of scalability. We validate our architecture using a full model of the locomotion system of the Caenorhabditis elegans. Further, we show that our proposed architecture archives a nine-fold increase in clock speed over existing hardware models. Importantly the clock speed for our architecture is found to be independent of system size, providing an unparalleled level of scalability. Our approach can be applied to the modelling of large neural networks, with greater performance, easier configuration and a high level of scalability

A Cognitive Architecture Based on a Learning Classifier System with Spiking Classifiers

© 2015, Springer Science+Business Media New York. Learning classifier systems (LCS) are population-based reinforcement learners that were originally designed to model various cognitive phenomena. This paper presents an explicitly cognitive LCS by using spiking neural networks as classifiers, providing each classifier with a measure of temporal dynamism. We employ a constructivist model of growth of both neurons and synaptic connections, which permits a genetic algorithm to automatically evolve sufficiently-complex neural structures. The spiking classifiers are coupled with a temporally-sensitive reinforcement learning algorithm, which allows the system to perform temporal state decomposition by appropriately rewarding “macro-actions”, created by chaining together multiple atomic actions. The combination of temporal reinforcement learning and neural information processing is shown to outperform benchmark neural classifier systems, and successfully solve a robotic navigation task

SPE-44 Implements Sperm Cell Fate

The sperm/oocyte decision in the hermaphrodite germline of Caenorhabditis elegans provides a powerful model for the characterization of stem cell fate specification and differentiation. The germline sex determination program that governs gamete fate has been well studied, but direct mediators of cell-type-specific transcription are largely unknown. We report the identification of spe-44 as a critical regulator of sperm gene expression. Deletion of spe-44 causes sperm-specific defects in cytokinesis, cell cycle progression, and organelle assembly resulting in sterility. Expression of spe-44 correlates precisely with spermatogenesis and is regulated by the germline sex determination pathway. spe-44 is required for the appropriate expression of several hundred sperm-enriched genes. The SPE-44 protein is restricted to the sperm-producing germline, where it localizes to the autosomes (which contain sperm genes) but is excluded from the transcriptionally silent X chromosome (which does not). The orthologous gene in other Caenorhabditis species is similarly expressed in a sex-biased manner, and the protein likewise exhibits autosome-specific localization in developing sperm, strongly suggestive of an evolutionarily conserved role in sperm gene expression. Our analysis represents the first identification of a transcriptional regulator whose primary function is the control of gamete-type-specific transcription in this system