Nonlinear dynamical modeling of single neurons and its application to analysis of long-term potentiation (LTP).

摘要

Neuron spike-train to spike-train temporal transformation is very important to the functions of neurons. Neurons receive presynaptic (input) spike-trains and transform them into postsynaptic (output) spike-trains. This input-output transformation is a highly nonlinear dynamic process which depends on complex nonlinear physiological processes. Mathematically capturing and quantifying neuron spike-train to spike-train transformation are important to understand the information processing done by neurons.;Compartmental modeling methodology is to simulate and interpret detail neuron physiological mechanisms/processes. The Hodgkin-Huxley model is the most prominent example in this category. However, model structure/parameter of compartmental modeling is specific to the targeted neuron (or type of neurons) and not applicable to the others, and the modeling result is vulnerable to biased or incomplete knowledge. Hence, the number of open parameters is often large, making it computationally inefficient. Integrate-and-fire neuron model is a computationally efficient methodology that received a lot of attention in the past two decades. It is perfect for large-scale simulation, and provides qualitative neuron characterization. However, it is over simplified and provides no or little mechanistic implications or quantifications. Lastly, input-output modeling methodology, which is applied in this study is another major approach to characterize neuron spike-train transformation. Input-output models are data-driven. This leads to an important property that it avoids modeling errors due to biased or incomplete knowledge. The number of open parameters is limited, making the model relatively computationally efficient. In other words, input-output model provides is well balanced between the common modeling dilemma: accuracy and efficiency.;In my study, the purpose is to build a single neuron model that (1) captures both sub- and supra-threshold dynamics based on neuron intracellular activity, (2) is sufficiently general to be applied to all spike-input, spike-output neurons, (3) is computationally efficient.;A nonlinear dynamical single neuron model was developed using Volterra kernels based on patch-clamp recordings. There were two phases in developing this model. In the first phase, a single neuron model with constant threshold was developed. It consists: (1) feedforward kernels (up to third-order) which transform presynaptic spikes into postsynaptic potentials (PSPs), (2) a constant threshold which represents the spike generation process, and (3) a feedback kernel (first-order) which describes spike-triggered after-potentials. The model was applied to CA1 pyramidal cells as they were electrically stimulated with broadband impulse trains through the Schaffer collaterals. This synaptically driven broadband intracellular activities contains a broad range of nonlinear dynamics resulted from the interactions of underlying mechanisms. The model performances were evaluated separately with respect to: PSP waveforms and the occurrence of spikes. The average normalized mean square error (NMSE) of PSP prediction is 14.4%. The average spike prediction error rate (SPER) is 18.8%.;In the second phase, inspired by literatures, a dynamical model was developed to study threshold nonlinear dynamics according to the action potential (AP) firing history. To develop the model, we measured the turning point of AP by analyzing its third-order derivative. The AP turning point has a constant offset relationship with the threshold. In other words, variation to the AP turning point represents the nonlinearities of threshold dynamics. To perform accurate spike prediction, it requires an additional spike prediction validation to optimize that offset (the linearity). This dynamic threshold model was implemented using up to third-order Volterra kernels constrained by synaptically driven intracellular activity described before. This threshold model was integrated into the single neuron model to replace its original constant threshold and showed 33% SPER improvement.;This single neuron model is a hybrid, combining both mechanistic (parametric) and input-output (non-parametric) components. The principles of neuronal signal generation common to all spike-input, spike-output determine the model structure. On the other hand, the specific properties that are variable from neuron to neuron are captured and quantified with descriptive model parameters, which are directly constrained by intracellular recording data. This hybrid representation of both parametric and nonparametric model components partitions data variance with respect to mechanistic sources and thus imposes physiological definitions to the model components and facilitates the biological interpretations of the parameters.;This single neuron model was further applied to analyze long-term potentiation (LTP) in single neurons. The purpose of this application is to separate and quantify the pre- and post-synaptic mechanisms both before and after LTP induction. The single neuron model is modified to be a two-stage cascade model. The first-stage represents presynaptic mechanisms, taking presynaptic spikes as input and excitatory postsynaptic currents (EPSCs) as output. The second-stages represents postsynaptic mechanisms, taking EPSCs as input and excitatory postsynaptic potentials (EPSPs) as output. Preliminary data shows that LTP intensifies the linear responses and reduces the nonlinearities.