Introduction

What is the big picture question?

What are the current methods available for addressing this question?

What are the limitations of these methods?

Recently, Lynch and Houghton (2015) have developed a method to predict in vivo response of auditory neurons using an estimated spectrotemporal receptive field (STRF) filter combined with an integrate-and-fire neuron model based on the Izhikevich neuron (Izhikevich, 2003). This model adds an additional adaptive parameter to the integrate-and-fire neuron for enhanced biophysical realism. Optimization is performed iteratively on the parameters of the filter and the parameters of the neuron model using a genetic algorithm in which fitness is evaluated by the van Rossum distance metric (van Rossum, 2001).

Lynch and Houghton’s method fills a clear need in the neuroinformatics field and moves forward the possibilities for neuron modeling in in vivo electrophysiology research. There exist many avenues for further improvement, including models with more biologically interpretable parameters and improved optimization algorithms.

In this paper, we propose a dynamical systems-based neuron model combined with an STRF filter that provides superior prediction accuracy with a computationally efficient optimization algorithm. This method is based on a Hindmarsh-Rose (HR) neuron model (Hindmarsh & Rose, 1984), which strikes a balance between the limited parameter sets of the integrate-and-fire models and the biological realism of the Hodgkin-Huxley ion current models (Hodgkin & Huxley, 1952). The feature space is explored by emcee (Foreman-Mackey et al., 2013), a Python implementation of a Markov chain Monte Carlo (MCMC), to find a local optima using the computational efficient SPIKE synchronization metric (Kreuz et al., 2015) as the fitness function. This combination of algorithms is first tested on simulated data with known parameters, and then validation on a real data set recorded in vivo from auditory neurons in the zebra finch (Taeniopygia guttata).

Methods

The Hindmarsh-Rose Model

The Hindmarsh-Rose model is a simple model of neuronal activity that allows for complex behaviors such as bursting and chaotic spiking (Hindmarsh and Rose 1984). It is described by three coupled first order differential equations with eight parameters.

\[x=y-ax^3+bx^2-z+I\]

\[y=c-dx^2\]

\[z=r(s(x-x_0)-z)\]

All parameters.

x=y−ax3+bx2−z+I(1)

x=y-ax^3+bx^2-z+I

y=c−dx2(2)

y=c-dx^2

z=r(s(x−x0)−z)(3)

z=r(s(x-x_0)-z)

All variables are dimensionless. In these equations, `x` is the membrane potential, `y` is the recovery variable, and `z` is the slow adaptation current. The parameters `a`, `b`, `c`, and `d` model the ion channels that produce action potentials, with `a` and `b` determining spike shape and c and d determining spike frequency. The parameter `r` forces `z` to adjust slowly relative to `x` and `y`, while s controls the tendency to burst and `x0` is the resting potential. Finally, `I` is an applied current from outside the neuron such as from a patch clamp.

The

The HR-neuron model exhibits chaotic characteristics that allow for multiple possible variations on spike times, shape, and quantity. These chaotic dynamics are well studied for many possible parameter combinations (Storace, Linaro, & de Lange, 2008; Shilnikov & Kolomeites, 2008).

Twin 2008).

**Next I think we'll want to talk about extended the HR model with an STRF**

Twin studies with 1D data

Bobby:For the sake of the final I am putting the 1D stuff I have for GA here and in the results.

Genetic Algorithm

Mathematical models such as the HR-neuron provide researchers a framework to understand and predict qualities of a given system of interest. Researchers have developed