The provided MATLAB code snippet appears to be part of a computational neuroscience toolbox designed for fitting various mathematical models to data. This file focuses on loading fittings, both predefined and user-defined, in a structured format. Here's a description of the biological basis that the equations in the code might relate to: ### Biological Basis 1. **Exponential Decay**: - **Equation**: `a*exp(-x/tau)` - **Biological Relevance**: This equation models processes like synaptic transmission or decay of postsynaptic potentials, where neurotransmitter-induced currents in neurons exponentially decline with time. The parameter `tau` often represents the time constant of these decays, crucial for understanding synaptic filtering properties. 2. **Power Laws**: - **Equation**: `a*x^n`, `a*(x+b)^n` - **Biological Relevance**: Power-law functions are often used to describe scaling relationships in neuronal input-output properties, dendritic branching, or the distribution of synaptic weights. In certain contexts, power laws describe how certain neuronal properties scale with cell size or input strength. 3. **Gaussian Functions**: - **Equations**: `exp(-(x^2)/(2*sigma^2))/(2*pi*sigma^2)^(1/2)`, `a*exp(-(x^2)/(2*sigma^2))` - **Biological Relevance**: Gaussian functions are used to model neural responses to stimuli, where the mean of the Gaussian represents a preferred stimulus feature, and the standard deviation (`sigma`) represents variability or tuning width. They can also model noise in synaptic transmission or sensory input. 4. **Sinusoidal Functions**: - **Equation**: `a*sin(b*x) + c`, `a*cos(b*x) + c`, `a*sin(b*x + phi) + c` - **Biological Relevance**: Sinusoidal models are applicable in describing oscillatory activity seen in the nervous system, such as cortical rhythms or membrane potential fluctuations. Such functions could be used in modeling neuronal phase-locking or periodic sensory inputs. 5. **Logarithmic Functions**: - **Equation**: `a*log(b*x)`, `a*log(x) + b` - **Biological Relevance**: Logarithmic functions can represent sensory responses that adopt a logarithmic encoding, such as the Weber-Fechner law, which describes how changes in stimulus magnitude are perceived relative to their baseline levels (e.g., in auditory systems). 6. **Synaptic and Membrane Models**: - **Equation**: `a*exp(-x/tau); a=1; tau=10` - **Biological Relevance**: Often used to model synaptic current dynamics or membrane potential variations where `tau` represents the decay time constant of post-synaptic potentials (PSPs), helping understand passive properties of neuronal membranes. These equations capture a broad spectrum of neuronal dynamics and behaviors, such as synaptic transmission, sensory responses, and oscillatory activity, encompassing both temporal and spatial dynamics in neural tissues. Such mathematical models enable researchers to quantitatively describe and predict the electrical activities and functional interactions among neural components in a variety of biological scenarios.