Realistic Neuron Models Research Articles

Is realistic neuronal modeling realistic?

Scientific models are abstractions that aim to explain natural phenomena. A successful model shows how a complex phenomenon arises from relatively simple principles while preserving major physical or biological rules and predicting novel experiments. A model should not be a facsimile of reality; it is an aid for understanding it. Contrary to this basic premise, with the 21st century has come a surge in computational efforts to model biological processes in great detail. Here we discuss the oxymoronic, realistic modeling of single neurons. This rapidly advancing field is driven by the discovery that some neurons don't merely sum their inputs and fire if the sum exceeds some threshold. Thus researchers have asked what are the computational abilities of single neurons and attempted to give answers using realistic models. We briefly review the state of the art of compartmental modeling highlighting recent progress and intrinsic flaws. We then attempt to address two fundamental questions. Practically, can we realistically model single neurons? Philosophically, should we realistically model single neurons? We use layer 5 neocortical pyramidal neurons as a test case to examine these issues. We subject three publically available models of layer 5 pyramidal neurons to three simple computational challenges. Based on their performance and a partial survey of published models, we conclude that current compartmental models are ad hoc, unrealistic models functioning poorly once they are stretched beyond the specific problems for which they were designed. We then attempt to plot possible paths for generating realistic single neuron models.

The Human Brain Project: Parallel technologies for biologically accurate simulation of Granule cells

Studying and understanding human brain is one of the main challenges of 21st century scientists.The Human Brain Project was conceived for addressing this challenge in an innovative way, enabling collaborations between 112 partners spread in 24 European countries.The project is funded by the European Commission and will last until 2023.This paper describes the ongoing activity at one of the Italian units focused on innovative brain simulation through high performance computing technologies. Simulations concern realistic models of neurons belonging to the cerebellar cortex. Due to the level of biological realism, the computational complexity of this model is high, requiring suitable technologies. In this work, simulations have been conducted on high-end Graphical Processing Units (GPUs) and Field Programmable Gate Arrays (FPGAs). The first technology is used during model tuning and validation phases, while the latter allows to achieve real time elaboration, aiming at a possible development of embedded implantable systems. Simulations performance evaluations are discussed in the result section.

A single Markov-type kinetic model reliably accounts for the macroscopic currents of all human voltage-gated sodium channel isoforms

A single Markov-type kinetic model reliably accounts for the macroscopic currents of all human voltage-gated sodium channel isoforms

HCN channels enhance spike phase coherence and regulate the phase of spikes and LFPs in the theta-frequency range

What are the implications for the existence of subthreshold ion channels, their localization profiles, and plasticity on local field potentials (LFPs)? Here, we assessed the role of hyperpolarization-activated cyclic-nucleotide-gated (HCN) channels in altering hippocampal theta-frequency LFPs and the associated spike phase. We presented spatiotemporally randomized, balanced theta-modulated excitatory and inhibitory inputs to somatically aligned, morphologically realistic pyramidal neuron models spread across a cylindrical neuropil. We computed LFPs from seven electrode sites and found that the insertion of an experimentally constrained HCN-conductance gradient into these neurons introduced a location-dependent lead in the LFP phase without significantly altering its amplitude. Further, neurons fired action potentials at a specific theta phase of the LFP, and the insertion of HCN channels introduced large lags in this spike phase and a striking enhancement in neuronal spike-phase coherence. Importantly, graded changes in either HCN conductance or its half-maximal activation voltage resulted in graded changes in LFP and spike phases. Our conclusions on the impact of HCN channels on LFPs and spike phase were invariant to changes in neuropil size, to morphological heterogeneity, to excitatory or inhibitory synaptic scaling, and to shifts in the onset phase of inhibitory inputs. Finally, we selectively abolished the inductive lead in the impedance phase introduced by HCN channels without altering neuronal excitability and found that this inductive phase lead contributed significantly to changes in LFP and spike phase. Our results uncover specific roles for HCN channels and their plasticity in phase-coding schemas and in the formation and dynamic reconfiguration of neuronal cell assemblies.

Formation of multi-armed spiral waves in neuronal network induced by adjusting ion channel conductance

The Hodgkin–Huxley neuron model is used to describe the local dynamics of nodes in a two-dimensional regular network with nearest-neighbor connections. Multi-armed spiral waves emerge when a group of spiral waves rotate the same core synchronously. Here we have numerically investigated how multi-armed spiral waves are formed in such a system. Under the appropriate conditions, multi-armed spiral waves were able to develop as a result of adjusting the conductance of ion channels of particular neurons in the network. In a realistic neuron model, it can be practiced by blocking potassium of ion channels embedded in the membrane of neurons. For example, decreasing the potassium channel conductance in some neurons with a certain transient period can lead to the development of a group of double spirals in a localized area of the network. Furthermore, decreasing the excitability and the external forcing current to zero led to the growth of these double spirals and the formation of a stable multi-armed spiral wave that occupied the network under inhomogeneity.

Bilinearity in spatiotemporal integration of synaptic inputs.

Neurons process information via integration of synaptic inputs from dendrites. Many experimental results demonstrate dendritic integration could be highly nonlinear, yet few theoretical analyses have been performed to obtain a precise quantitative characterization analytically. Based on asymptotic analysis of a two-compartment passive cable model, given a pair of time-dependent synaptic conductance inputs, we derive a bilinear spatiotemporal dendritic integration rule. The summed somatic potential can be well approximated by the linear summation of the two postsynaptic potentials elicited separately, plus a third additional bilinear term proportional to their product with a proportionality coefficient . The rule is valid for a pair of synaptic inputs of all types, including excitation-inhibition, excitation-excitation, and inhibition-inhibition. In addition, the rule is valid during the whole dendritic integration process for a pair of synaptic inputs with arbitrary input time differences and input locations. The coefficient is demonstrated to be nearly independent of the input strengths but is dependent on input times and input locations. This rule is then verified through simulation of a realistic pyramidal neuron model and in electrophysiological experiments of rat hippocampal CA1 neurons. The rule is further generalized to describe the spatiotemporal dendritic integration of multiple excitatory and inhibitory synaptic inputs. The integration of multiple inputs can be decomposed into the sum of all possible pairwise integration, where each paired integration obeys the bilinear rule. This decomposition leads to a graph representation of dendritic integration, which can be viewed as functionally sparse.

Effects of low frequency electric fields on synaptic integration in hippocampal CA1 pyramidal neurons: implications for power line emissions.

The possible cognitive effects of low frequency external electric fields (EFs), such as those generated by power lines, are poorly understood. Their functional consequences for mechanisms at the single neuron level are very difficult to study and identify experimentally, especially in vivo. The major open problem is that experimental investigations on humans have given inconsistent or contradictory results, making it difficult to estimate the possible effects of external low frequency electric fields on cognitive functions. Here we investigate this issue with realistic models of hippocampal CA1 pyramidal neurons. Our findings suggest how and why EFs, with environmentally observed frequencies and intensities far lower than what is required for direct neural activation, can perturb dendritic signal processing and somatic firing of neurons that are crucially involved in cognitive tasks such as learning and memory. These results show that individual neuronal morphology, ion channel dendritic distribution, and alignment with the electric field are major determinants of overall effects, and provide a physiologically plausible explanation of why experimental findings can appear to be small and difficult to reproduce, yet deserve serious consideration.

Perceptron-like computation based on biologically-inspired neurons with heterosynaptic mechanisms

Perceptrons are one of the fundamental paradigms in artificial neural networks and a key processing scheme in supervised classification tasks. However, the algorithm they provide is given in terms of unrealistically simple processing units and connections and therefore, its implementation in real neural networks is hard to be fulfilled. In this work, we present a neural circuit able to perform perceptron’s computation based on realistic models of neurons and synapses. The model uses Wang-Buzsaki neurons with coupling provided by axodendritic and axoaxonic synapses (heterosynapsis). The main characteristics of the feedforward perceptron operation are conserved, which allows to combine both approaches: whereas the classical artificial system can be used to learn a particular problem, its solution can be directly implemented in this neural circuit. As a result, we propose a biologically-inspired system able to work appropriately in a wide range of frequencies and system parameters, while keeping robust to noise and error.

Reduced Computational Models of Serotonin Synthesis, Release, and Reuptake

Multiscale computational models can provide systemic evaluation and prediction of neuropharmacological drug effects. To date, little computational modeling work has been done to bridge from intracellular to neuronal circuit level. A complex model that describes the intracellular dynamics of the presynaptic terminal of a serotonergic neuron has been previously proposed. By systematically perturbing the model's components, we identify the slow and fast dynamical components of the model, and the reduced slow or fast mode of the model is computationally significantly more efficient with accuracy not deviating much from the original model. The reduced fast-mode model is particularly suitable for incorporating into neurobiologically realistic spiking neuronal models, and hence for large-scale realistic computational simulations. We also develop user-friendly software based on the reduced models to allow scientists to rapidly test and predict neuropharmacological drug effects at a systems level.

DYNAMICS OF COLLECTIVE MULTI-STABILITY IN MODELS OF MULTI-UNIT NEURONAL SYSTEMS

In this study, we investigate the correspondence between dynamic patterns of behavior in two types of computational models of neuronal activity. The first model type is the realistic neuronal model; the second model type is the phenomenological or analytical model. In the simplest model set-up of two interconnected units, we define a parameter space for both types of systems where their behavior is similar. Next we expand the analytical model to two sets of 90 fully interconnected units with some overlap, which can display multi-stable behavior. This system can be in three classes of states: (i) a class consisting of a single resting state, where all units of a set are in steady state, (ii) a class consisting of multiple preserving states, where subsets of the units of a set participate in limit cycle, and (iii) a class consisting of a single saturated state, where all units of a set are recruited in a global limit cycle. In the third and final part of the work, we demonstrate that phase synchronization of units can be detected by a single output unit.

A neuromechanical simulation of insect walking and transition to turning of the cockroach Blaberus discoidalis

A neuromechanical simulation of the cockroach Blaberus discoidalis was developed to explore changes in locomotion when the animal transitions from walking straight to turning. The simulation was based upon the biological data taken from three sources. Neural circuitry was adapted from the extensive literature primarily obtained from the studies of neural connections within thoracic ganglia of stick insect and adapted to cockroach. The 3D joint kinematic data on straight, forward walking for cockroach were taken from a paper that describes these movements in all joints simultaneously as the cockroach walked on an oiled-plate tether (Bender et al. in PloS one 5(10):1-15, 2010b). Joint kinematics for turning were only available for some leg joints (Mu and Ritzmann in J Comp Physiol A Neuroethol Sens Neural Behav Physiol 191(11):1037-54, 2005) and thus had to be obtained using the methods that were applied for straight walking by Bender et al. (PloS one 5(10):1-15, 2010b). Once walking, inside turning, and outside turning were characterized, phase and amplitude changes for each joint of each leg were quantified. Apparent reflex reversals and joint activity changes were used to modify sensory coupling pathways between the CPG at each joint of the simulation. Oiled-plate experiments in simulation produced tarsus trajectories in stance similar to those seen in the animal. Simulations including forces that would be experienced if the insect was walking freely (i.e., weight support and friction) again produced similar results. These data were not considered during the design of the simulation, suggesting that the simulation captures some key underlying the principles of walking, turning, and transitioning in the cockroach. In addition, since the nervous system was modeled with realistic neuron models, biologically plausible reflex reversals are simulated, motivating future neurobiological research.

Using Strahler's analysis to reduce up to 200-fold the run time of realistic neuron models

The cellular mechanisms underlying higher brain functions/dysfunctions are extremely difficult to investigate experimentally, and detailed neuron models have proven to be a very useful tool to help these kind of investigations. However, realistic neuronal networks of sizes appropriate to study brain functions present the major problem of requiring a prohibitively high computational resources. Here, building on our previous work, we present a general reduction method based on Strahler's analysis of neuron morphologies. We show that, without any fitting or tuning procedures, it is possible to map any morphologically and biophysically accurate neuron model into an equivalent reduced version. Using this method for Purkinje cells, we demonstrate how run times can be reduced up to 200–fold, while accurately taking into account the effects of arbitrarily located and activated synaptic inputs.

Synapto-Protective Drugs Evaluation in Reconstructed Neuronal Network

Chronic neurodegenerative syndromes such as Alzheimer’s and Parkinson’s diseases, or acute syndromes such as ischemic stroke or traumatic brain injuries are characterized by early synaptic collapse which precedes axonal and neuronal cell body degeneration and promotes early cognitive impairment in patients. Until now, neuroprotective strategies have failed to impede the progression of neurodegenerative syndromes. Drugs preventing the loss of cell body do not prevent the cognitive decline, probably because they lack synapto-protective effects. The absence of physiologically realistic neuronal network models which can be easily handled has hindered the development of synapto-protective drugs suitable for therapies. Here we describe a new microfluidic platform which makes it possible to study the consequences of axonal trauma of reconstructed oriented mouse neuronal networks. Each neuronal population and sub-compartment can be chemically addressed individually. The somatic, mid axon, presynaptic and postsynaptic effects of local pathological stresses or putative protective molecules can thus be evaluated with the help of this versatile “brain on chip” platform. We show that presynaptic loss is the earliest event observed following axotomy of cortical fibers, before any sign of axonal fragmentation or post-synaptic spine alteration. This platform can be used to screen and evaluate the synapto-protective potential of several drugs. For instance, NAD+ and the Rho-kinase inhibitor Y27632 can efficiently prevent synaptic disconnection, whereas the broad-spectrum caspase inhibitor zVAD-fmk and the stilbenoid resveratrol do not prevent presynaptic degeneration. Hence, this platform is a promising tool for fundamental research in the field of developmental and neurodegenerative neurosciences, and also offers the opportunity to set up pharmacological screening of axon-protective and synapto-protective drugs.

Vestibular integrator neurons have quadratic functions due to voltage dependent conductances

The nonlinear properties of the dendrites of the prepositus hypoglossi nucleus (PHN) neurons are essential for the operation of the vestibular neural integrator that converts a head velocity signal to one that controls eye position. A novel system of frequency probing, namely quadratic sinusoidal analysis (QSA), was used to decode the intrinsic nonlinear behavior of these neurons under voltage clamp conditions. Voltage clamp currents were measured at harmonic and interactive frequencies using specific nonoverlapping stimulation frequencies. Eigenanalysis of the QSA matrix reduces it to a remarkably compact processing unit, composed of just one or two dominant components (eigenvalues). The QSA matrix of rat PHN neurons provides signatures of the voltage dependent conductances for their particular dendritic and somatic distributions. An important part of the nonlinear response is due to the persistent sodium conductance (gNaP), which is likely to be essential for sustained effects needed for a neural integrator. It was found that responses in the range of 10mV peak to peak could be well described by quadratic nonlinearities suggesting that effects of higher degree nonlinearities would add only marginal improvement. Therefore, the quadratic response is likely to sufficiently capture most of the nonlinear behavior of neuronal systems except for extremely large synaptic inputs. Thus, neurons have two distinct linear and quadratic functions, which shows that piecewise linear + quadratic analysis is much more complete than just piecewise linear analysis; in addition quadratic analysis can be done at a single holding potential. Furthermore, the nonlinear neuronal responses contain more frequencies over a wider frequency band than the input signal. As a consequence, they convert limited amplitude and bandwidth input signals to wider bandwidth and more complex output responses. Finally, simulations at subthreshold membrane potentials with realistic PHN neuron models suggest that the quadratic functions are fundamentally dominated by active dendritic structures and persistent sodium conductances.

Passive Dendrites Enable Single Neurons to Compute Linearly Non-separable Functions

Local supra-linear summation of excitatory inputs occurring in pyramidal cell dendrites, the so-called dendritic spikes, results in independent spiking dendritic sub-units, which turn pyramidal neurons into two-layer neural networks capable of computing linearly non-separable functions, such as the exclusive OR. Other neuron classes, such as interneurons, may possess only a few independent dendritic sub-units, or only passive dendrites where input summation is purely sub-linear, and where dendritic sub-units are only saturating. To determine if such neurons can also compute linearly non-separable functions, we enumerate, for a given parameter range, the Boolean functions implementable by a binary neuron model with a linear sub-unit and either a single spiking or a saturating dendritic sub-unit. We then analytically generalize these numerical results to an arbitrary number of non-linear sub-units. First, we show that a single non-linear dendritic sub-unit, in addition to the somatic non-linearity, is sufficient to compute linearly non-separable functions. Second, we analytically prove that, with a sufficient number of saturating dendritic sub-units, a neuron can compute all functions computable with purely excitatory inputs. Third, we show that these linearly non-separable functions can be implemented with at least two strategies: one where a dendritic sub-unit is sufficient to trigger a somatic spike; another where somatic spiking requires the cooperation of multiple dendritic sub-units. We formally prove that implementing the latter architecture is possible with both types of dendritic sub-units whereas the former is only possible with spiking dendrites. Finally, we show how linearly non-separable functions can be computed by a generic two-compartment biophysical model and a realistic neuron model of the cerebellar stellate cell interneuron. Taken together our results demonstrate that passive dendrites are sufficient to enable neurons to compute linearly non-separable functions.

Investigating the computational power of spiking neurons with non-standard behaviors

Spiking neural networks have been called the third generation of neural networks. Their main difference with respect to the previous two generations is the use of realistic neuron models. Their computational power has been well studied with respect to threshold gates and sigmoidal neurons. However, biologically realistic models of spiking neurons can produce behaviors that can be computationally relevant, but their power has not been assessed in the same way. This paper studies the computational power of neurons with different behaviors based on the previous analyses conducted by Maass and Schmitt. The studied behaviors are rebound spiking, resonance and bursting. The results of the analysis are presented. A theoretical motivation for this study is presented and a discussion is done on the possible implications of the findings for using networks of spiking neurons for performing computations.

Phenomenological incorporation of nonlinear dendritic integration using integrate-and-fire neuronal frameworks.

It has been discovered recently in experiments that the dendritic integration of excitatory glutamatergic inputs and inhibitory GABAergic inputs in hippocampus CA1 pyramidal neurons obeys a simple arithmetic rule as , where , and are the respective voltage values of the summed somatic potential, the excitatory postsynaptic potential (EPSP) and the inhibitory postsynaptic potential measured at the time when the EPSP reaches its peak value. Moreover, the shunting coefficient in this rule only depends on the spatial location but not the amplitude of the excitatory or inhibitory input on the dendrite. In this work, we address the theoretical issue of how much the above dendritic integration rule can be accounted for using subthreshold membrane potential dynamics in the soma as characterized by the conductance-based integrate-and-fire (I&F) model. Then, we propose a simple I&F neuron model that incorporates the spatial dependence of the shunting coefficient by a phenomenological parametrization. Our analytical and numerical results show that this dendritic-integration-rule-based I&F (DIF) model is able to capture many experimental observations and it also yields predictions that can be used to verify the validity of the DIF model experimentally. In addition, the DIF model incorporates the dendritic integration effects dynamically and is applicable to more general situations than those in experiments in which excitatory and inhibitory inputs occur simultaneously in time. Finally, we generalize the DIF neuronal model to incorporate multiple inputs and obtain a similar dendritic integration rule that is consistent with the results obtained by using a realistic neuronal model with multiple compartments. This generalized DIF model can potentially be used to study network dynamics that may involve effects arising from dendritic integrations.

Finite Element Method for Population Density Approach for Large-Scale Neuronal Networks

The population density approach has been used for modeling the dynamics of large-scale neuronal networks to consider the stochastic nature of the signal processing in the brain. From the conservation principle, the time evolution of population density can be described by a nonlinear partial differential equation (PDE). The finite difference method (FDM) has been proposed for solving this PDE. However, FDM is sensitive to the density gradient of the solution and is confined to problems that have a regular state space. An irregular state space is always obtained if realistic neuronal models are considered. In this study, the finite element method (FEM) is formulated to solve this POE and apply it to solve the orientation tuning problem. The results show that when the state space discretization is coarse, FEM retains high accuracy whereas FDM does not. Furthermore, FEM reduces computation time by 90% compared to that required for FDM. In addition, FEM can easily handle the existence of a point source without any modifications. Due to its superior accuracy, efficiency, and consistency, FEM may be a better numerical technique for applying the population density approach to large-scale neuronal networks.

Impact of neuronal heterogeneity on correlated colored noise-induced synchronization

Synchronization plays an important role in neural signal processing and transmission. Many hypotheses have been proposed to explain the origin of neural synchronization. In recent years, correlated noise-induced synchronization has received support from many theoretical and experimental studies. However, many of these prior studies have assumed that neurons have identical biophysical properties and that their inputs are well modeled by white noise. In this context, we use colored noise to induce synchronization between oscillators with heterogeneity in both phase-response curves and frequencies. In the low noise limit, we derive novel analytical theory showing that the time constant of colored noise influences correlated noise-induced synchronization and that oscillator heterogeneity can limit synchronization. Surprisingly, however, heterogeneous oscillators may synchronize better than homogeneous oscillators given low input correlations. We also find resonance of oscillator synchronization to colored noise inputs when firing frequencies diverge. Collectively, these results prove robust for both relatively high noise regimes and when applied to biophysically realistic spiking neuron models, and further match experimental recordings from acute brain slices.

Individual differences in leech heart motor neuron models

Motor neurons are frequently overlooked as critical contributors to the programming of motor output except where they directly play a role in central pattern generators (CPGs). Leech heart motor neurons have been shown to contribute significant phase shifts to the rhythmic motor patterns they produce [1-3], although the most important factor in pattern formation is the interaction of CPG output and synaptic weights from the CPG onto the motor neurons [3]. We seek to address the question of which neural parameters, in particular active conductances, are important for functional pattern formation, and how they influence it. We are well positioned to address this question, as we have a unique dataset comprising the complete leech heart motor neuron input pattern, output pattern, and synaptic weights for multiple ganglia in many individual animals. We have begun to exploit these data to develop more realistic Hodgkin-Huxley style biophysical models of the leech heart motor neurons by constraining models optimized by a multi-objective evolutionary algorithm to fit this animal-specific data. In particular, we extended the single compartment Garcia model [1] to a multi-compartmental model and added a slow calcium and a calcium sensitive potassium channel, currents known to be present in the living motor neurons. Our model’s dimensions are derived from reconstructions of fluorophore filled leech heart motor neurons in segments 8-12. Membrane currents were distributed according to experimental data and the result of hand tuning; e.g., the fast sodium current is only present in the axonal compartment. This base model was then parameterized such that the maximal conductances of the active currents present in each compartment, as well as the electrical coupling conductance between each pair of motor neurons, were allowed to vary as free parameters in our evolutionary algorithm. We then utilized our input-output data by delivering a particular input pattern (specific animal and motor neuron pair) to a model motor neuron and then comparing the resulting output with that recorded in the same animal. In this manner, we constrained our definition of an ‘acceptable’ model by the input/output pattern recorded in individual animals – such a model must transform the input into the correct output within some reasonable error bound. To generate acceptable models we use a Multi Objective Evolutionary Algorithm (MOEA) to create a population of models from which a subset achieves ‘acceptable’ status. In this framework, multiple independent fitness functions are evaluated separately – the phase, duty cycle, spike height, slow-wave height, and within-burst inter-spike interval (ISI) for the two phases produced. The targets for these parameters are drawn from the same individual animal as the input/output data, and error bounds are based on the within-animal variability, although slightly widened for parameters such as ISI, slow-wave and spike height, as they vary greatly between animals (derived primarily from within-animal experimental variability). Acceptable model simulation traces were all but indistinguishable from intracellular recordings from the living system, with the exception of measurement noise, even though they are constrained by a small number of functional parameters. In order to identify key parameters and relationships between synaptic weights and membrane conductances which are constrained by the functional requirements of the system, we will conduct a sensitivity analysis of the acceptable models and inspect the dimensional stacking [4] of acceptable and failed models. The identified conductances can then be perturbed in the living system either via dynamic clamp or pharmacological manipulation to validate the modeling results.