Modeling the electrical behavior of anatomically complex neurons using a network analysis program: Passive membrane

We describe the application of a popular and widely available electrical circuit simulation program called SPICE to modeling the electrical behavior of neurons with passive membrane properties and arbitrarily complex dendritic trees. Transient responses may be calculated at any location in the cell model following current, voltage or conductance perturbations at any point. A numbering method is described for binary trees which is helpful in transforming complex dendritic structures into a coded list of short cylindrical dendritic segments suitable for input to SPICE. Individual segments are modeled as isopotential compartments comprised of a parallel resistor and capacitor, representing the transmembrane impedance, in series with one or two core resistors. Synaptic current is modeled by a current source controlled by the local membrane potential and an alpha-shaped voltage, thus simulating a conductance change in series with a driving potential. Extensively branched test cell circuits were constructed which satisfied the equivalent cylinder constraints (Rall 1959). These model neurons were perturbed by independent current sources and by synaptic currents. Responses calculated by SPICE are compared with analytical results. With appropriately chosen model parameters, extremely accurate transient calculations may be obtained. Details of the SPICE circuit elements are presented, along with illustrative examples sufficient to allow implementation of passive nerve cell models on a number of common computers. Methods for modeling excitable membrane are presented in the companion paper (Bunow et al. 1985).     

Changes of the neuronal membrane excitability as cellular mechanisms of learning and memory

In the presented review given literature and results of own studies of dynamics of electrical characteristics of neurons, which change are included in processes both an elaboration of learning, and retention of the long-term memory. Literary datas and our results allow to conclusion, that long-term retention of behavioural reactions during learning is accompanied not only by changing efficiency of synaptic transmission, as well as increasing of excitability of command neurons of the defensive reflex. This means, that in the process of learning are involved long-term changes of the characteristics a membrane of certain elements of neuronal network, dependent from the metabolism of the cells. see text). Thou phenomena possible mark as cellular (electrophysiological) correlates of long-term plastic modifications of the behaviour. The analyses of having results demonstrates an important role of membrane characteristics of neurons (their excitability) and parameters an synaptic transmission not only in initial stage of learning, as well as in long-term modifications of the behaviour (long-term memory).     

A simple latency-dependent spiking-neuron model of cricket phonotaxis

 A simple hypothesis regarding the recognition behaviour of crickets for conspecific songs is implemented in a dynamic simulation of spiking neurons and tested on a robot base. The model draws on data from cricket neurophysiology but requires only four neurons to reproduce a wide range of the observed behaviour. The directional response depends on relative latencies in firing onset, and the `recognition' emerges from the implicit filtering properties of leaky-integrate-and-fire neurons. Experimental conditions reproduced include tests of syllable rate preference, song from above with sound from one side, and choice between songs. The robot produces behaviour closely comparable to the cricket in all but a `split-song' condition. A number of properties can be observed in the neural circuit that correspond to cricket neurophysiology including apparent `recognition neurons'. Limitations of the model, extensions and alternative models are discussed. Received: 14 July 1997 / Accepted in revised form: 7 September 1999     

Growth rules for the repair of Asynchronous Irregular neuronal networks after peripheral lesions

Several homeostatic mechanisms enable the brain to maintain desired levels of neuronal activity. One of these, homeostatic structural plasticity, has been reported to restore activity in networks disrupted by peripheral lesions by altering their neuronal connectivity. While multiple lesion experiments have studied the changes in neurite morphology that underlie modifications of synapses in these networks, the underlying mechanisms that drive these changes are yet to be explained. Evidence suggests that neuronal activity modulates neurite morphology and may stimulate neurites to selective sprout or retract to restore network activity levels. We developed a new spiking network model of peripheral lesioning and accurately reproduced the characteristics of network repair after deafferentation that are reported in experiments to study the activity dependent growth regimes of neurites. To ensure that our simulations closely resemble the behaviour of networks in the brain, we model deafferentation in a biologically realistic balanced network model that exhibits low frequency Asynchronous Irregular (AI) activity as observed in cerebral cortex. Our simulation results indicate that the re-establishment of activity in neurons both within and outside the deprived region, the Lesion Projection Zone (LPZ), requires opposite activity dependent growth rules for excitatory and inhibitory post-synaptic elements. Analysis of these growth regimes indicates that they also contribute to the maintenance of activity levels in individual neurons. Furthermore, in our model, the directional formation of synapses that is observed in experiments requires that pre-synaptic excitatory and inhibitory elements also follow opposite growth rules. Lastly, we observe that our proposed structural plasticity growth rules and the inhibitory synaptic plasticity mechanism that also balances our AI network both contribute to the restoration of the network to pre-deafferentation stable activity levels.     

SPICE: discovery of phenotype-determining component interplays

ABSTRACT: BACKGROUND: A latent behavior of a biological cell is complex. Deriving the underlying simplicity, or the fundamental rules governing this behavior has been the Holy Grail of systems biology. Data-driven prediction of the system components and their component interplays that are responsible for the target system's phenotype is a key and challenging step in this endeavor. RESULTS: The proposed approach, which we call System Phenotype-related Interplaying Components Enumerator (SPICE), iteratively enumerates statistically significant that are hypothesized (1) to play an important role in defining the specificity of the target system's phenotype(s); (2) to exhibit a functionally coherent behavior, namely, act in a coordinated manner to perform the phenotype-specific function; and (3) to improve the predictive skill of the system's phenotype(s) when used collectively in the ensemble of predictive models. When validated, SPICE effectively identified system components related to three target phenotypes: biohydrogen production, motility, and cancer. Manual results curation agreed with the known phenotype-related system components reported in literature. Additionally, using the identified system components as discriminatory features improved the prediction accuracy by 10% on the phenotype-classification task when compared to a number of state-of-the-art methods applied to eight benchmark microarray data sets. CONCLUSION: Conclusion: We formulate a problem--- enumeration of phenotype-determining system component interplays---and propose an effective methodology (SPICE) to address this problem. SPICE improved identification of cancer-related groups of genes from various microarray data sets and detected groups of genes associated with microbial biohydrogen production and motility, many of which were reported in literature. SPICE also improved the predictive skill of the system's phenotype determination compared to individual classifiers and/or other ensemble methods, such as bagging, boosting, random forest, nearest shrunken centroid, and random forest variable selection method. All the supporting data and software can be found in the supplemental files.     

Immunophysical properties and prediction of activities for vaccinia virus complement control protein and smallpox inhibitor of complement enzymes using molecular dynamics and electrostatics

We present immunophysical modeling for VCP, SPICE, and three mutants using MD simulations and Poisson-Boltzmann-type electrostatic calculations. VCP and SPICE are homologous viral proteins that control the complement system by imitating, structurally and functionally, natural regulators of complement activation. VCP and SPICE consist of four CCP modules connected with short flexible loops. MD simulations demonstrate that the rather complex modules of VCP/SPICE and their mutants exhibit a high degree of intermodular spatial mobility, which is affected by surface mutations. Electrostatic calculations using snapshots from the MD trajectories demonstrate variable spatial distribution of the electrostatic potentials, which suggests dynamic binding properties. We use covariance analysis to identify correlated modular oscillations. We also use electrostatic similarity indices to cluster proteins with common electrostatic properties. Our results are compared with experimental data to form correlations between the overall positive electrostatic potential of VCP/SPICE with binding and activity. We show how these correlations can be used to predict binding and activity properties. This work is expected to be useful for understanding the function of native CCP-containing regulators of complement activation and receptors and for the design of antiviral therapeutics and complement inhibitors.     

Cellular mechanisms of behavioural plasticity in simple nervous systems

In the present study, we will try to single out several principles of the nervous system functioning essential for describing the mechanisms of learning and memory, basing on our own experimental investigation of cellular mechanisms of memory in the nervous system of gastropod molluscs and literature data as follows: (1) Main changes in functioning due to learning occur in the interneurons; (2) Due to learning some synaptic inputs of command neurons selectively change its effectivity; (3) Reinforcement is not related to activity of the neural chain receptor-sensory neuron-interneuron-motoneuron-effector; reinforcement is mediated via activity of modulatory neurons, and in some cases can be exerted by a single neuron; (4) Activity of modulatory neurons is necessary for development of plastic modifications of behaviour (including associative), but is not needed for recall of conditioned responses. At the same time, the modulatory neurons (in fact they constitute a neural reinforcement system) are necessary for recall of context associative memory; (5) Changes due to learning occur at least in two independent loci in the nervous system.     

Substrate versus inhibitor dynamics of P‐glycoprotein

By far the most studied multidrug resistance protein is P‐glycoprotein. Despite recent structural data, key questions about its function remain. P‐glycoprotein (P‐gp) is flexible and undergoes large conformational changes as part of its function and in this respect, details not only of the export cycle, but also the recognition stage are currently lacking. Given the flexibility, molecular dynamics (MD) simulations provide an ideal tool to examine this aspect in detail. We have performed MD simulations to examine the behaviour of P‐gp. In agreement with previous reports, we found that P‐gp undergoes large conformational changes which tended to result in the nucleotide‐binding domains coming closer together. In all simulations, the approach of the NBDs was asymmetrical in agreement with previous observations for other ABC transporter proteins. To validate the simulations, we make extensive comparison to previous cross‐linking data. Our results show very good agreement with the available data. We then went on to compare the influence of inhibitor compounds bound with simulations of a substrate (daunorubicin) bound. Our results suggest that inhibitors may work by keeping the NBDs apart, thus preventing ATP‐hydrolysis. On the other hand, repeat simulations of daunorubicin (substrate) in one particular binding pose suggest that the approach of the NBDs is not impaired and that the structure would be still be competent to perform ATP hydrolysis, thus providing a model for inhibition or substrate transport. Finally we compare the latter to earlier QSAR data to provide a model for the first part of substrate transport within P‐gp. Proteins 2013. © 2013 Wiley Periodicals, Inc.     

Making noise: Emergent stochasticity in collective motion

Individual-based models of self-propelled particles (SPPs) are a popular and promising approach to explain features of the collective motion of animal aggregations. Many models that capture some features of group motion have been suggested but a common framework has yet to emerge. Key to all of these models is the inclusion of “noise” or stochastic errors in the individual behaviour of the SPPs. Here, we present a fully stochastic SPP model in one dimension that demonstrates a new way of introducing noise into SPP models whilst preserving emergent behaviours of previous models such as coherent groups and spontaneous direction switching. This purely individual-to-individual, local model is related to previous models in the literature and can easily be extended to higher dimensions. Its coarse-grained behaviour qualitatively reproduces recently reported locust movement data. We suggest that our approach offers an alternative to current reasoning about model construction and has the potential to offer mechanistic explanations for emergent properties of animal groups in nature.     

A neural circuit model of flexible sensorimotor mapping: learning and forgetting on multiple timescales

Volitional behavior relies on the brain's ability to remap sensory flow to motor programs whenever demanded by a changed behavioral context. To investigate the circuit basis of such flexible behavior, we have developed a biophysically based decision-making network model of spiking neurons for arbitrary sensorimotor mapping. The model quantitatively reproduces behavioral and prefrontal single-cell data from an experiment in which monkeys learn visuomotor associations that are reversed unpredictably from time to time. We show that when synaptic modifications occur on multiple timescales, the model behavior becomes flexible only when needed: slow components of learning usually dominate the decision process. However, if behavioral contexts change frequently enough, fast components of plasticity take over, and the behavior exhibits a quick forget-and-learn pattern. This model prediction is confirmed by monkey data. Therefore, our work reveals a scenario for conditional associative learning that is distinct from instant switching between sets of well-established sensorimotor associations.     

Modeling the electrical behavior of anatomically complex neurons using a network analysis program: Excitable membrane

We present methods for using the generalpurpose network analysis program, SPICE, to construct computer models of excitable membrane displaying Hodgkin-Huxley-like kinetics. The four non-linear partial differential equations of Hodgkin and Huxley (H-H; 1952) are implemented using electrical circuit elements. The H-H rate constants, and , are approximated by polynomial functions rather than exponential functions, since the former are handled more efficiently by SPICE. The process of developing code to implement the H-H sodium conductance is described in detail. The Appendix contains a complete listing of the code required to simulate an H-H action potential. The behavior of models so constructed is validated by comparison with the space-clamped and propagating action potentials of Hodgkin and Huxley. SPICE models of multiply branched axons were tested and found to behave as predicted by previous numerical solutions for propagation in inhomogeneous axons. New results are presented for two cases. First, a detailed, anatomically based model is constructed of group Ia input to an -motoneuron with an excitable soma, a myelinated axon and passive dendrites. Second, we simulate interactions among clusters of mixed excitable and passive dendritic spines on an idealized neuron. The methods presented in this paper and its companion (Segev et al. 1985) should permit neurobiologists to construct and explore models which simulate much more closely the real morphological and physiological characteristics of nerve cells.     

Choline Transporter regulates olfactory habituation via a neuronal triad of excitatory,inhibitory and mushroom body neurons

Choline is an essential component of Acetylcholine (ACh) biosynthesis pathway which requires high-affinity Choline transporter (ChT) for its uptake into the presynaptic terminals of cholinergic neurons. Previously, we had reported a predominant expression of ChT in memory processing and storing region of the Drosophila brain called mushroom bodies (MBs). It is unknown how ChT contributes to the functional principles of MB operation. Here, we demonstrate the role of ChT in Habituation, a non-associative form of learning. Odour driven habituation traces are laid down in ChT dependent manner in antennal lobes (AL), projection neurons (PNs), and MBs. We observed that reduced habituation due to knock-down of ChT in MBs causes hypersensitivity towards odour, suggesting that ChT also regulates incoming stimulus suppression. Importantly, we show for the first time that ChT is not unique to cholinergic neurons but is also required in inhibitory GABAergic neurons to drive habituation behaviour. Our results support a model in which ChT regulates both habituation and incoming stimuli through multiple circuit loci via an interplay between excitatory and inhibitory neurons. Strikingly, the lack of ChT in MBs shows characteristics similar to the major reported features of Autism spectrum disorders (ASD), including attenuated habituation, sensory hypersensitivity as well as defective GABAergic signalling. Our data establish the role of ChT in habituation and suggest that its dysfunction may contribute to neuropsychiatric disorders like ASD.     

Dynamic Excitatory and Inhibitory Gain Modulation Can Produce Flexible,Robust and Optimal Decision-making

Behavioural and neurophysiological studies in primates have increasingly shown the involvement of urgency signals during the temporal integration of sensory evidence in perceptual decision-making. Neuronal correlates of such signals have been found in the parietal cortex, and in separate studies, demonstrated attention-induced gain modulation of both excitatory and inhibitory neurons. Although previous computational models of decision-making have incorporated gain modulation, their abstract forms do not permit an understanding of the contribution of inhibitory gain modulation. Thus, the effects of co-modulating both excitatory and inhibitory neuronal gains on decision-making dynamics and behavioural performance remain unclear. In this work, we incorporate time-dependent co-modulation of the gains of both excitatory and inhibitory neurons into our previous biologically based decision circuit model. We base our computational study in the context of two classic motion-discrimination tasks performed in animals. Our model shows that by simultaneously increasing the gains of both excitatory and inhibitory neurons, a variety of the observed dynamic neuronal firing activities can be replicated. In particular, the model can exhibit winner-take-all decision-making behaviour with higher firing rates and within a significantly more robust model parameter range. It also exhibits short-tailed reaction time distributions even when operating near a dynamical bifurcation point. The model further shows that neuronal gain modulation can compensate for weaker recurrent excitation in a decision neural circuit, and support decision formation and storage. Higher neuronal gain is also suggested in the more cognitively demanding reaction time than in the fixed delay version of the task. Using the exact temporal delays from the animal experiments, fast recruitment of gain co-modulation is shown to maximize reward rate, with a timescale that is surprisingly near the experimentally fitted value. Our work provides insights into the simultaneous and rapid modulation of excitatory and inhibitory neuronal gains, which enables flexible, robust, and optimal decision-making.     

A database of computational models of a half-center oscillator for analyzing how neuronal parameters influence network activity

A half-center oscillator (HCO) is a common circuit building block of central pattern generator networks that produce rhythmic motor patterns in animals. Here we constructed an efficient relational database table with the resulting characteristics of the Hill et al.’s (J Comput Neurosci 10:281–302, 2001) HCO simple conductance-based model. The model consists of two reciprocally inhibitory neurons and replicates the electrical activity of the oscillator interneurons of the leech heartbeat central pattern generator under a variety of experimental conditions. Our long-range goal is to understand how this basic circuit building block produces functional activity under a variety of parameter regimes and how different parameter regimes influence stability and modulatability. By using the latest developments in computer technology, we simulated and stored large amounts of data (on the order of terabytes). We systematically explored the parameter space of the HCO and corresponding isolated neuron models using a brute-force approach. We varied a set of selected parameters (maximal conductance of intrinsic and synaptic currents) in all combinations, resulting in about 10 million simulations. We classified these HCO and isolated neuron model simulations by their activity characteristics into identifiable groups and quantified their prevalence. By querying the database, we compared the activity characteristics of the identified groups of our simulated HCO models with those of our simulated isolated neuron models and found that regularly bursting neurons compose only a small minority of functional HCO models; the vast majority was composed of spiking neurons.     

Experimental analysis and computational modeling of interburst intervals in spontaneous activity of cortical neuronal culture

Rhythmic bursting is the most striking behavior of cultured cortical networks and may start in the second week after plating. In this study, we focus on the intervals between spontaneously occurring bursts, and compare experimentally recorded values with model simulations. In the models, we use standard neurons and synapses, with physiologically plausible parameters taken from literature. All networks had a random recurrent architecture with sparsely connected neurons. The number of neurons varied between 500 and 5,000. We find that network models with homogeneous synaptic strengths produce asynchronous spiking or stable regular bursts. The latter, however, are in a range not seen in recordings. By increasing the synaptic strength in a (randomly chosen) subset of neurons, our simulations show interburst intervals (IBIs) that agree better with in vitro experiments. In this regime, called weakly synchronized, the models produce irregular network bursts, which are initiated by neurons with relatively stronger synapses. In some noise-driven networks, a subthreshold, deterministic, input is applied to neurons with strong synapses, to mimic pacemaker network drive. We show that models with such "intrinsically active neurons" (pacemaker-driven models) tend to generate IBIs that are determined by the frequency of the fastest pacemaker and do not resemble experimental data. Alternatively, noise-driven models yield realistic IBIs. Generally, we found that large-scale noise-driven neuronal network models required synaptic strengths with a bimodal distribution to reproduce the experimentally observed IBI range. Our results imply that the results obtained from small network models cannot simply be extrapolated to models of more realistic size. Synaptic strengths in large-scale neuronal network simulations need readjustment to a bimodal distribution, whereas small networks do not require such changes.     

Transition between two excitabilities in mesencephalic V neurons

Neurons can make different responses to identical inputs. According to the emerging frequency of repetitive firing, neurons are classified into two types: type 1 and type 2 excitability. Though in mathematical simulations, minor modifications of parameters describing ionic currents can result in transitions between these two excitabilities, empirical evidence to support these theoretical possibilities is scarce. Here we report a joint theoretical and experimental study to test the hypothesis that changes in parameters describing ionic currents cause predictable transitions between the two excitabilities in mesencephalic V (Mes V) neurons. We developed a simple mathematical model of Mes V neurons. Using bifurcation analysis and model simulation, we then predicted that changes in conductance of two low-threshold currents would result in transitions between type 1 and type 2. Finally, by applying specific channel blockers, we observed the transition between two excitabilities forecast by the mathematical model.     

Computational modeling of cardiovascular response to orthostatic stress.

The objective of this study is to develop a model of the cardiovascular system capable of simulating the short-term (< or = 5 min) transient and steady-state hemodynamic responses to head-up tilt and lower body negative pressure. The model consists of a closed-loop lumped-parameter representation of the circulation connected to set-point models of the arterial and cardiopulmonary baroreflexes. Model parameters are largely based on literature values. Model verification was performed by comparing the simulation output under baseline conditions and at different levels of orthostatic stress to sets of population-averaged hemodynamic data reported in the literature. On the basis of experimental evidence, we adjusted some model parameters to simulate experimental data. Orthostatic stress simulations are not statistically different from experimental data (two-sided test of significance with Bonferroni adjustment for multiple comparisons). Transient response characteristics of heart rate to tilt also compare well with reported data. A case study is presented on how the model is intended to be used in the future to investigate the effects of post-spaceflight orthostatic intolerance.     

Hamiltonian energy and coexistence of hidden firing patterns from bidirectional coupling between two different neurons

In this paper, bidirectional-coupled neurons through an asymmetric electrical synapse are investigated. These coupled neurons involve 2D Hindmarsh–Rose (HR) and 2D FitzHugh–Nagumo (FN) neurons. The equilibria of the coupled neurons model are investigated, and their stabilities have revealed that, for some values of the electrical synaptic weight, the model under consideration can display either self-excited or hidden firing patterns. In addition, the hidden coexistence of chaotic bursting with periodic spiking, chaotic spiking with period spiking, chaotic bursting with a resting pattern, and the coexistence of chaotic spiking with a resting pattern are also found for some sets of electrical synaptic coupling. For all the investigated phenomena, the Hamiltonian energy of the model is computed. It enables the estimation of the amount of energy released during the transition between the various electrical activities. Pspice simulations are carried out based on the analog circuit of the coupled neurons to support our numerical results. Finally, an STM32F407ZE microcontroller development board is exploited for the digital implementation of the proposed coupled neurons model.     

The functional role of sequentially neuromodulated synaptic plasticity in behavioural learning

To survive, animals have to quickly modify their behaviour when the reward changes. The internal representations responsible for this are updated through synaptic weight changes, mediated by certain neuromodulators conveying feedback from the environment. In previous experiments, we discovered a form of hippocampal Spike-Timing-Dependent-Plasticity (STDP) that is sequentially modulated by acetylcholine and dopamine. Acetylcholine facilitates synaptic depression, while dopamine retroactively converts the depression into potentiation. When these experimental findings were implemented as a learning rule in a computational model, our simulations showed that cholinergic-facilitated depression is important for reversal learning. In the present study, we tested the model’s prediction by optogenetically inactivating cholinergic neurons in mice during a hippocampus-dependent spatial learning task with changing rewards. We found that reversal learning, but not initial place learning, was impaired, verifying our computational prediction that acetylcholine-modulated plasticity promotes the unlearning of old reward locations. Further, differences in neuromodulator concentrations in the model captured mouse-by-mouse performance variability in the optogenetic experiments. Our line of work sheds light on how neuromodulators enable the learning of new contingencies.