The state model of nerve excitation by Hodgkin and Huxley has been a backbone of neuroscience for over sixty years. Mathematical models are compact summaries of data that can recreate the features of interest. Those features inevitably change as new experiments provide new data and as a priori information is collected from the literature. This evolution of models characterizes all of science. Newton’s laws were the classic laws (models) of mechanics; they needed tuning by Einstein. The ability to create and test models allows us to summarize what we know about the laws of nature. We would rather look at a model with few parameters, than at gigabytes of raw data. Furthermore, model-based-analyses make explicit the assumptions used to create the model, and they provide quantitative parameters with testable conclusions. In the biologically and medically relevant case of channelopathies, models can provide insights as how to assay therapeutic drugs. A change in rate constants can cause a disease, and therapy should try to restore those rates to normal.
In the case of ion channel kinetics, the rate constants between states predict the free energy differences between states and those changes need to be reproduced from structural models of channels. The free energies can be further dissected into entropic and enthalpic contributions by varying the temperature, thus providing insight into physical mechanisms that dominate the molecular dynamics. The flow of energy in a system of states is contained in the topology of the connections between states, the rates between them, and the dependence of those rates on stimuli. Ion channels are the quantum units of cell excitability, so that understanding ion channel kinetics is essential to understanding excitability of the brain and other tissues.
We began writing programs to analyze single channel kinetics in the early days of patch clamp since manual analysis was not only subjective but time consuming. Furthermore, stimulus driven data could not be readily analyzed manually. Over the last thirty years, our software grew into what we have named QuB (Q for the rate transition matrix and UB for University of Buffalo). QuB can treat single or multiple discrete channel data where the rates can be stimulus driven with arbitrary stimuli. It can also analyze multichannel data as collected from whole-cell recordings. Given multichannel data, QuB’s algorithms not only provide the rate constants of a multistate model, but by utilizing the variance of the data they provide estimates of the number of channels in the activatable pool and the unitary current amplitude. Fitting state models of channel kinetics is fast, commonly interactive on PC, Mac or Linux, and can employ video array processors when available.
The modeling implemented in our software is applicable not only to ion channels, but to state models in general. For example, Markov models are applied to DNA sequencing and to the sleep cycles in mice where the states are awake, REM and delta. The software has also been used for the analysis of single molecule optical data and molecular motor data and solid state physics.
Anyone who has studied the kinetics of multistate models knows how difficult it can be to extract the rates for a collection of different models, yet QuB is sufficiently interactive to make that kind of modeling routine. QuB allows you to read data in a variety of formats including those used by commercial data acquisition software such as PClamp and HEKA, to select and edit the data to be analyzed, to fit the data to defaulted or customized models with rates that may be stimulus driven. QuB delivers the rates, their dependence upon the stimulus, and satisfies any a priori constraints such as detailed balance of loops. The program provides error estimates on all parameters, the likelihoods of models, and a variety of information criteria that include allowance for the degrees of freedom. It can globally fit data from multiple files such as those taken with different environmental variables such as concentration, voltage, temperature, or mechanical stress.