The Neurobiological Basis of Cognition: Identification by Multi-Input, Multioutput Nonlinear Dynamic Modeling: A method is proposed for measuring and modeling human long-term memory formation by mathematical analysis and computer simulation of nerve-cell dynamics

The successful development of neural prostheses requires an understanding of the neurobiological bases of cognitive processes, i.e., how the collective activity of populations of neurons results in a higher level process not predictable based on knowledge of the individual neurons and/or synapses alone. We have been studying and applying novel methods for representing nonlinear transformations of multiple spike train inputs (multiple time series of pulse train inputs) produced by synaptic and field interactions among multiple subclasses of neurons arrayed in multiple layers of incompletely connected units. We have been applying our methods to study of the hippocampus, a cortical brain structure that has been demonstrated, in humans and in animals, to perform the cognitive function of encoding new long-term (declarative) memories. Without their hippocampi, animals and humans retain a short-term memory (memory lasting approximately 1 min), and long-term memory for information learned prior to loss of hippocampal function. Results of more than 20 years of studies have demonstrated that both individual hippocampal neurons, and populations of hippocampal cells, e.g., the neurons comprising one of the three principal subsystems of the hippocampus, induce strong, higher order, nonlinear transformations of hippocampal inputs into hippocampal outputs. For one synaptic input or for a population of synchronously active synaptic inputs, such a transformation is represented by a sequence of action potential inputs being changed into a different sequence of action potential outputs. In other words, an incoming temporal pattern is transformed into a different, outgoing temporal pattern. For multiple, asynchronous synaptic inputs, such a transformation is represented by a spatiotemporal pattern of action potential inputs being changed into a different spatiotemporal pattern of action potential outputs. Our primary thesis is that the encoding of short-term memories into new, long-term memories represents the collective set of nonlinearities induced by the three or four principal subsystems of the hippocampus, i.e., entorhinal cortex-to-dentate gyrus, dentate gyrus-to-CA3 pyramidal cell region, CA3-to-CA1 pyramidal cell region, and CA1-to-subicular cortex. This hypothesis will be supported by studies using in vivo hippocampal multineuron recordings from animals performing memory tasks that require hippocampal function. The implications for this hypothesis will be discussed in the context of "cognitive prostheses"-neural prostheses for cortical brain regions believed to support cognitive functions, and that often are subject to damage due to stroke, epilepsy, dementia, and closed head trauma.

Paired-pulse stimulation at glutamatergic synapses - pre- and postsynaptic components

Paired-pulse stimulation is a standard protocol that has been used for decades to characterize dynamic systems: the differences in responses to two sequential identical stimuli as a function of inter-stimulus interval provide quantitative information on the dynamics of the system. In neuroscience, the paired-pulse protocol is also widely used at multiple levels of analysis, from behavioral conditioning to synaptic plasticity, and in particular to define the biomolecular mechanism of learning and memory. In a system as small and complex as synapses, it is extremely challenging - if not impossible - to experimentally gain access to the multitude of possible readouts. In the present study, we first introduce a computational synaptic modeling platform that we developed and calibrated based on experimental data from both our laboratories and a variety of publications. We then show how this platform allows not only to replicate experimental data, but also to go beyond technological boundaries and investigate the main parameters responsible for regulation of synaptic transmission and plasticity. The results provide critical information regarding the respective role of various subsynaptic processes and of their interactions. Additionally, this approach can strengthen our understanding of potential dysfunctions (pathologies) and suggest potential approaches to re-establish normal function.

Estimating sparse Volterra models using group L1-regularization

Sparse Volterra model (sVM) is defined as a Volterra model (VM) that contains only a subset of its all possible model coefficients corresponding to its significant inputs and the existing terms of those inputs. Compared with ordinary VM, sVM is more efficient and interpretable in representing sparsely connected multiple-input systems, e.g., neuronal networks. In this paper, we formulate a rigorous statistical method of estimating sVM based on the group L1-regularization. It allows simultaneous selection and estimation of the significant groups of coefficients of a VM and results in a sVM. Simulation results show that the actual structure of a sVM can be faithfully recovered even with short input-output data. This method can be extended and applied to the identification of the functional connectivity between neurons.

Nonlinear dynamic analyses of single hippocampal neurons before and after long-term potentiation

Long-term potentiation (LTP) has long been considered an important phenomenon involved in learning and memory. However, the current literature lacks systematical analyses of single neuron dynamics before and after LTP induction. In this report, we applied an up to 3rd-order Volterra kernel to analyze the dynamics of single hippocampal neurons before and after LTP induction. Broadband Poisson random impulse trains with a 2 Hz mean frequency, which included physiologically plausible patterns, were applied to stimulate CA1 pyramidal neurons through Schaffer collateral before and after LTP induction. Corresponding somatic sub-threshold excitatory postsynaptic potentials (EPSPs) were recorded from CA1 neurons using whole-cell patch-clamp recording. The result suggests that LTP increases linear responses and depresses nonlinear responses. The phenomenon can be explained with both presynaptic and postsynaptic hypotheses. Further comparisons of voltage-clamp and current-clamp recordings are needed to distinguish the changes of dynamics in presynaptic and/or postsynaptic mechanisms.

Nonlinear dynamic modeling of impaired voice

This paper presents a nonlinear dynamic model for the purpose of modeling vowels uttered by patients who have problem in the control of voice box muscles. The proposed model will be utilized in the detection of speech pathologies and also automatic speech recognition systems to enhance patients' communication capabilities. The model of this study utilizes feedback, and also a sigmoid nonlinear function which is not included in the linear speech production models. The nonlinear function allows for the higher order dynamics of the signal to be captured and feedback increases dynamicity of the model. The model of the current research was applied to discriminate between few voice pathologies and normal cases. The statistical analysis of the parameters of the trained model showed that these parameters can provide independent and distinct features with which pathological classes can be discriminated.

Boolean modeling of neural systems with point-process inputs and outputs. Part II: Application to the rat hippocampus

This paper presents a pilot application of the Boolean-Volterra modeling methodology presented in the companion paper (Part I) that is suitable for the analysis of systems with point-process inputs and outputs (e.g., recordings of the activity of neuronal ensembles). This application seeks to discover the causal links between two neuronal ensembles in the hippocampus of a behaving rat. The experimental data come from multi-unit recordings in the CA3 and CA1 regions of the hippocampus in the form of sequences of action potentials-treated mathematically as point-processes and computationally as spike-trains-that are collected in vivo during two behavioral tasks. The modeling objective is to identify and quantify the causal links among the neurons generating the recorded activity, using Boolean-Volterra models estimated directly from the data according to the methodological framework presented in the companion paper. The obtained models demonstrate the feasibility of the proposed approach using short data-records and provide some insights into the functional properties of the system (e.g., regarding the presence of rhythmic characteristics in the neuronal dynamics of these ensembles), making the proposed methodology an attractive tool for the analysis and modeling of multi-unit recordings from neuronal systems in a practical context.

Boolean modeling of neural systems with point-process inputs and outputs. Part I: theory and simulations

This paper presents a new modeling approach for neural systems with point-process (spike) inputs and outputs that utilizes Boolean operators (i.e. modulo 2 multiplication and addition that correspond to the logical AND and OR operations respectively, as well as the AND_NOT logical operation representing inhibitory effects). The form of the employed mathematical models is akin to a "Boolean-Volterra" model that contains the product terms of all relevant input lags in a hierarchical order, where terms of order higher than first represent nonlinear interactions among the various lagged values of each input point-process or among lagged values of various inputs (if multiple inputs exist) as they reflect on the output. The coefficients of this Boolean-Volterra model are also binary variables that indicate the presence or absence of the respective term in each specific model/system. Simulations are used to explore the properties of such models and the feasibility of their accurate estimation from short data-records in the presence of noise (i.e. spurious spikes). The results demonstrate the feasibility of obtaining reliable estimates of such models, with excitatory and inhibitory terms, in the presence of considerable noise (spurious spikes) in the outputs and/or the inputs in a computationally efficient manner. A pilot application of this approach to an actual neural system is presented in the companion paper (Part II).

Nonlinear modeling of neural population dynamics for hippocampal prostheses

Developing a neural prosthesis for the damaged hippocampus requires restoring the transformation of population neural activities performed by the hippocampal circuitry. To bypass a damaged region, output spike trains need to be predicted from the input spike trains and then reinstated through stimulation. We formulate a multiple-input, multiple-output (MIMO) nonlinear dynamic model for the input-output transformation of spike trains. In this approach, a MIMO model comprises a series of physiologically-plausible multiple-input, single-output (MISO) neuron models that consist of five components each: (1) feedforward Volterra kernels transforming the input spike trains into the synaptic potential, (2) a feedback kernel transforming the output spikes into the spike-triggered after-potential, (3) a noise term capturing the system uncertainty, (4) an adder generating the pre-threshold potential, and (5) a threshold function generating output spikes. It is shown that this model is equivalent to a generalized linear model with a probit link function. To reduce model complexity and avoid overfitting, statistical model selection and cross-validation methods are employed to choose the significant inputs and interactions between inputs. The model is applied successfully to the hippocampal CA3-CA1 population dynamics. Such a model can serve as a computational basis for the development of hippocampal prostheses.

Tracking temporal evolution of nonlinear dynamics in hippocampus using time-varying volterra kernels

Hippocampus and other parts of the cortex are not stationary, but change as a function of time and experience. The goal of this study is to apply adaptive modeling techniques to the tracking of multiple-input, multiple-output (MIMO) nonlinear dynamics underlying spike train transformations across brain subregions, e.g. CA3 and CA1 of the hippocampus. A stochastic state point process adaptive filter will be used to track the temporal evolutions of both feedforward and feedback kernels in the natural flow of multiple behavioral events.

Functional connectivity through nonlinear modeling: an application to the rat hippocampus

Implementation of neuroprosthetic devices requires a reliable and accurate quantitative representation of the input-output transformations performed by the involved neuronal populations. Nonparametric, data driven models with predictive capabilities are excellent candidates for these purposes. When modeling input-output relations in multi-input neuronal systems, it is important to select the subset of inputs that are functionally and causally related to the output. Inputs that do not convey information about the actual transformation not only increase the computational burden but also affect the generalization of the model. Moreover, a reliable functional connectivity measure can provide patterns of information flow that can be linked to physiological and anatomical properties of the system. We propose a method based on the Volterra modeling approach that selects distinct subsets of inputs for each output based on the prediction of the respective models and its statistical evaluation. The algorithm builds successive models with increasing number of inputs and examines whether the inclusion of additional inputs benefits the predictive accuracy of the overall model. It also explores possible second-order (inter-modulatory) interactions among the inputs. The method was applied to multi-unit recordings from the CA3 (input) and CA1 (output) regions of the hippocampus in behaving rats, in order to reveal spatiotemporal connectivity maps of the input-output transformation taking place in the CA3-CA1 synapse.

Control theory-based regulation of hippocampal CA1 nonlinear dynamics

We are developing a biomimetic electronic neural prosthesis to replace regions of the hippocampal brain area that have been damaged by disease or insult. Our previous study has shown that the VLSI implementation of a CA3 nonlinear dynamic model can functionally replace the CA3 subregion of the hippocampal slice. As a result, the propagation of temporal patterns of activity from DG-->VLSI-->CA1 reproduces the activity observed experimentally in the biological DG-->CA3-->CA1 circuit. In this project, we incorporate an open-loop controller to optimize the output (CA1) response. Specifically, we seek to optimize the stimulation signal to CA1 using a predictive dentate gyrus (DG)-CA1 nonlinear model (i.e., DG-CA1 trajectory model) and a CA1 input-output model (i.e., CA1 plant model), such that the ultimate CA1 response (i.e., desired output) can be first predicted by the DG-CA1 trajectory model and then transformed to the desired stimulation through the inversed CA1 plant model. Lastly, the desired CA1 output is evoked by the estimated optimal stimulation. This study will be the first stage of formulating an integrated modeling-control strategy for the hippocampal neural prosthetic system.

Predicting EMG with generalized Volterra kernel model

Generalized Volterra kernel model (GVM) is developed in spirits of the generalized linear model (GLM) and used to predict EMG signals based on M1 cortical spike trains during a prehension task. The GVM for EMG consists of a cascade of a multiple-input-single-output Volterra kernel model (VM) and an exponential activation function. Without loss of generality, the exponential activation function constrains the unbounded VM output within the positive range, which fully covers the dynamic range of the rectified EMG signals. Results show that GVMs are more accurate than the VMs due to this asymptotic property.

Nonparametric modeling of single neuron

Nonlinear dynamic models were built with Volterra Lagurre kernel method to characterize the input-output properties of single hippocampal CA1 pyramidal neurons. Broadband Poisson random impulse trains with a 2 Hz mean frequency, which include the majorities of the spike patterns in behaving rats, were used to stimulate the Schaffer collaterals. Corresponding random-interval post-synaptic potential (PSP) and spike train data were recorded from the cell bodies using whole-cell recording technique and then analyzed with the nonlinear dynamic model. The model consists of two major components, i.e., a feedforward three order Volterra kernel model characterizing the transformation of presynaptic stimulations to pre-threshold PSPs, and a feedback one order Volterra kernel model capturing the spike-triggered after-potential. Results showed that the model could predict 1) the sub-threshold PSPs trace with a normalized mean square error around 10% and 2) the spikes with accuracy higher than 80%.

Nonstationary modeling of neural population dynamics

A stochastic state point-process adaptive filter was used to track the temporal evolution of several simulated nonlinear dynamical systems. The estimated Laguerre coefficients and Laguerre poles were used to reconstruct the feedforward and feedback kernels in the system. Simulations showed that the proposed method could track the actual underlying changes of nonlinear kernels using spike input and spike output information alone. The estimated models also converge quickly to the actual models after abrupt step changes in kernels. The proposed method can be used to track the functional input-output properties of neural systems as a result of learning, changes in context, aging or other factors in the natural flow of behavioral events.

Nonlinear model of single hippocampal neurons with dynamical thresholds

Neurons transform a series of presynaptic spikes into a series of postsynaptic spikes through a number of nonlinear mechanisms. A nonlinear model with a dynamical threshold was built using a Volterra Laguerre kernel method to characterize the spike train to spike train transformations of hippocampal CA1 pyramidal neurons. Inputs of the model were broadband Poisson random impulse trains with a 2 Hz mean frequency, and outputs of the model were the corresponding evoked post-synaptic potential (PSP) and spike train data recorded from CA1 cell bodies using a whole-cell recording technique. The model consists of four major components, i.e., feedforward kernels representing the transformation of presynaptic spikes to PSPs; a dynamical threshold kernel determining threshold value based on output inter-spike-intervals (ISIs); a spike detector; and a feedback kernel representing the spike-triggered after-potentials.

Using an open-loop inverse control strategy to regulate CA1 nonlinear dynamics for an in vitro hippocampal prosthesis model

A modeling-control paradigm to regulate output of the hippocampus (CA1) for a hippocampal neuroprosthesis was developed and validated using an in vitro slice preparation. Our previous study has shown that the VLSI implementation of a CA3 nonlinear dynamic model can functionally replace the CA3 subregion of the hippocampal slice. The propagation of temporal patterns of activity from DG-->VLSI-->CA1 reproduces the activity observed experimentally in the biological DG-->CA3-->CA1 circuit. In this project, we incorporate an open-loop controller to optimize the output (CA1) response. Specifically, we seek to optimize the stimulation signal to CA1 using a predictive dentate gyrus (DG)-CA1 nonlinear model (i.e., DG-CA1 trajectory model) and a CA1 input-output model (i.e., CA1 plant model), such that the ultimate CA1 response (i.e., desired output) can be first predicted by the DG-CA1 trajectory model and then transformed to the desired stimulation intensity through the CA1 inverse plant model. Laguerre-Volterra kernel model for random - interval, graded - input, contemporaneous - graded -output system is formulated and applied to build the DG-CA1 trajectory model and the CA1 plant model. The inverse model to transform desired output to input is also derived and validated. We validated the paradigm in hippocampal slices, and results showed the CA1 response evoked by the controlled stimulation signal reinstated the CA1 response evoked by the trisynaptic pathway.

Nonlinear modeling of causal interrelationships in neuronal ensembles

The increasing availability of multiunit recordings gives new urgency to the need for effective analysis of "multidimensional" time-series data that are derived from the recorded activity of neuronal ensembles in the form of multiple sequences of action potentials--treated mathematically as point-processes and computationally as spike-trains. Whether in conditions of spontaneous activity or under conditions of external stimulation, the objective is the identification and quantification of possible causal links among the neurons generating the observed binary signals. A multiple-input/multiple-output (MIMO) modeling methodology is presented that can be used to quantify the neuronal dynamics of causal interrelationships in neuronal ensembles using spike-train data recorded from individual neurons. These causal interrelationships are modeled as transformations of spike-trains recorded from a set of neurons designated as the "inputs" into spike-trains recorded from another set of neurons designated as the "outputs." The MIMO model is composed of a set of multiinput/single-output (MISO) modules, one for each output. Each module is the cascade of a MISO Volterra model and a threshold operator generating the output spikes. The Laguerre expansion approach is used to estimate the Volterra kernels of each MISO module from the respective input-output data using the least-squares method. The predictive performance of the model is evaluated with the use of the receiver operating characteristic (ROC) curve, from which the optimum threshold is also selected. The Mann-Whitney statistic is used to select the significant inputs for each output by examining the statistical significance of improvements in the predictive accuracy of the model when the respective inputs is included. Illustrative examples are presented for a simulated system and for an actual application using multiunit data recordings from the hippocampus of a behaving rat.

Parametric and non-parametric modeling of short-term synaptic plasticity. Part I: Computational study

Parametric and non-parametric modeling methods are combined to study the short-term plasticity (STP) of synapses in the central nervous system (CNS). The nonlinear dynamics of STP are modeled by means: (1) previously proposed parametric models based on mechanistic hypotheses and/or specific dynamical processes, and (2) non-parametric models (in the form of Volterra kernels) that transforms the presynaptic signals into postsynaptic signals. In order to synergistically use the two approaches, we estimate the Volterra kernels of the parametric models of STP for four types of synapses using synthetic broadband input-output data. Results show that the non-parametric models accurately and efficiently replicate the input-output transformations of the parametric models. Volterra kernels provide a general and quantitative representation of the STP.

Parametric and non-parametric modeling of short-term synaptic plasticity. Part II: Experimental study

This paper presents a synergistic parametric and non-parametric modeling study of short-term plasticity (STP) in the Schaffer collateral to hippocampal CA1 pyramidal neuron (SC) synapse. Parametric models in the form of sets of differential and algebraic equations have been proposed on the basis of the current understanding of biological mechanisms active within the system. Non-parametric Poisson-Volterra models are obtained herein from broadband experimental input-output data. The non-parametric model is shown to provide better prediction of the experimental output than a parametric model with a single set of facilitation/depression (FD) process. The parametric model is then validated in terms of its input-output transformational properties using the non-parametric model since the latter constitutes a canonical and more complete representation of the synaptic nonlinear dynamics. Furthermore, discrepancies between the experimentally-derived non-parametric model and the equivalent non-parametric model of the parametric model suggest the presence of multiple FD processes in the SC synapses. Inclusion of an additional set of FD process in the parametric model makes it replicate better the characteristics of the experimentally-derived non-parametric model. This improved parametric model in turn provides the requisite biological interpretability that the non-parametric model lacks.

Statistical selection of multiple-input multiple-output nonlinear dynamic models of spike train transformation

Multiple-input multiple-output nonlinear dynamic model of spike train to spike train transformations was previously formulated for hippocampal-cortical prostheses. This paper further described the statistical methods of selecting significant inputs (self-terms) and interactions between inputs (cross-terms) of this Volterra kernel-based model. In our approach, model structure was determined by progressively adding self-terms and cross-terms using a forward stepwise model selection technique. Model coefficients were then pruned based on Wald test. Results showed that the reduced kernel models, which contained much fewer coefficients than the full Volterra kernel model, gave good fits to the novel data. These models could be used to analyze the functional interactions between neurons during behavior.

A multi-input modeling approach to quantify hippocampal nonlinear dynamic transformations

A multi-input modeling approach is introduced to quantify hippocampal neural dynamics. It is based on the Volterra modeling approach extended to multiple inputs. The computed Volterra kernels allow quantitative description of hippocampal transformations and define a predictive model that can produce responses to arbitrary input patterns. Electrophysiological data from several CA3 and CA1 cells in behaving rats were recorded simultaneously using an array of penetrating electrodes. This activity was used to compute kernels up to third order for single and multiple input cases. Representative sets of kernels illustrate the variability of the dynamics of the CA3-CA1 transformations. Our model's predictive accuracy was evaluated using ROC curves.

Pathological voice assessment

While there are number of guidelines and methods used in practice, there is no standard universally agreed upon system for assessment of pathological voices. Pathological voices are primarily labeled based on the perceptual judgments of specialists, a process that may result in different label(s) being assigned to a given voice sample. This paper focuses on the recognition of five specific pathologies. The main goal is to compare two different classification methods. The first method considers single label classification by assigning a new label (single label) to the ensembles to which they most likely belong. The second method employs all labels originally assigned to the voice samples. Our results show that the pathological voice assessment performance in the second method is improved with respect to the first method.

Modeling the nonlinear properties of the in vitro hippocampal perforant path-dentate system using multielectrode array technology

A modeling approach to characterize the nonlinear dynamic transformations of the dentate gyrus of the hippocampus is presented and experimentally validated. The dentate gyrus is the first region of the hippocampus which receives and integrates sensory information via the perforant path. The perforant path is composed of two distinct pathways: 1) the lateral path and 2) the medial perforant path. The proposed approach examines and captures the short-term dynamic characteristics of these two pathways using a nonparametric, third-order Poisson-Volterra model. The nonlinear characteristics of the two pathways are represented by Poisson-Volterra kernels, which are quantitative descriptors of the nonlinear dynamic transformations. The kernels were computed with experimental data from in vitro hippocampal slices. The electrophysiological activity was measured with custom-made multielectrode arrays, which allowed selective stimulation with random impulse trains and simultaneous recordings of extracellular field potential activity. The results demonstrate that this mathematically rigorous approach is suitable for the multipathway complexity of the hippocampus and yields interpretable models that have excellent predictive capabilities. The resulting models not only accurately predict previously reported electrophysiological descriptors, such as paired pulses, but more important, can be used to predict the electrophysiological activity of dentate granule cells to arbitrary stimulation patterns at the perforant path.

Interaction of short-term neuronal plasticity and synaptic plasticity revealed by nonlinear systems analysis in dentate granule cells

Dentate granule cells receive inputs from the entorhinal cortex as the "perforant path". There are two components of the perforant path: the lateral component (LPP) and the medial component (MPP). LPP and MPP convey different sensory modality information. It remains elusive as to how signals from different inputs interact and integrate at the granule cell level. We attempted to address this issue by using nonlinear systems analytic methods. Granule cell EPSPs and action potentials were recorded intracellularly from in vitro hippocampal slices of the rat. MPP and LPP were activated simultaneously by two independent Poisson random trains. Poisson-Volterra kernel models were estimated using Laguerre expansion of Volterra kernel technique. In the kernel models, self-kernels represent the intrinsic input/output properties of each pathway, while cross-kernels quantify the interactions between the two inputs. Short-term plasticity (STP) was revealed by both 2nd order self and cross kernels. We reason that the underlying mechanisms of the STP are diffusely distributed along input-specific synapses, dendritic tree and soma. The plasticity held by the dendritic tree/soma and synapses can be divided and referred to as neuronal and synaptic plasticity respectively. We argue that the cross kernel properties are determined primarily by neuronal plasticity while the self kernel properties are controlled largely by synaptic plasticity. Our experimental data suggest that linear summation of the membrane potential of the postsynaptic neuron can only partially explain the neuronal plasticity. Both supra- and sublinear summations were observed. Thus, the neuronal plasticity is likely to be the product of passive and active processes of the postsynaptic neuron and plays a pivotal role in multiple inputs integration.