biology research

This research is looking at mathematical modeling the permeation of ions through biological membrane channels such as potassium, calcium, sodium and gramicidin channels. Conventionally various theoretical and computational tools such as Molecular dynamics and Brownian dynamics are used to gain physical insight into the permeation processes. This alternative thread of research here is investigating simplified engineering models to capture the significant macroscopic properties of such ion channels.

Keywords: Ion channels, biological membrane channels, molecular dynamics, brownian dynamics, coupled, nonlinear filtering, macroscopic properties, channel kinetics, post-synapic currents, Markov chain,

S. H. Chung and R. A. Kennedy, "Forward-backward nonlinear filtering technique for extracting small biological signals from noise", J. Neurosci. Methods, vol. 40, no. 1, pp. 71-86, November 1991.
Abstract BibTeX
Official: Link DOI: 10.1016/0165-0270(91)90118-J PDF: KennedyJ1991b.pdf Google-Scholar: [30]
Abstract: A novel and computationally efficient, non-linear signal processing technique for reducing background noise to reveal small biological signals is described. The signal estimate is formed by weighting the outputs of a set of causal (forward) and anti-causal (backward) predictors. The weights used to combine the predictors are adaptively determined at each data point to reflect the performance of the respective predictor within a short analysis window. The method is specifically designed for revealing fast transient signals dominated by noise, such as single-channel or post-synaptic currents. Markovian and exponentially decaying signals embedded in the amplifier noise were extracted using this method and compared with the original signals. The results of such simulations demonstrate the advantage of this non-linear method over low-pass filtering. Brief pulses imbedded in a broad-band amplifier noise can be reliably recovered using our non-linear filtering technique. Moreover, the kinetics of a single channel and the time constant of exponentially decaying signals can be measured with acceptable accuracy even when the signals are dominated by noise.
@article{KennedyJ1991b,
    title = {Forward-backward nonlinear filtering technique for extracting small biological signals from noise},
    author = {Chung, S. H. and Kennedy, R. A.},
    journal = {J. Neurosci. Methods},
    volume = {40},
    pages = {71-86},
    month = {November},
    year = {1991}}
S. H. Chung and R. A. Kennedy, "Coupled Markov Chain Model: Characterization of Membrane Channel Currents with Multiple Conductance Sublevels as Partially Coupled Elementary Conducting Pores", Mathematical Biosciences, vol. 133, no. 2, pp. 111-137, March 1996.
Abstract BibTeX
Official: Link DOI: 10.1016/0025-5564(95)00084-4 PDF: KennedyJ1996a.pdf Google-Scholar: [10]
Abstract: A parameterized Markov chain model is developed to represent the characteristics of channel currents that either are the superposition of many single channels or show multiple conductance sublevels. The simplified model takes the form of a set of binary chains that are interdependent according to a simple lumped coupling parameter. When varied, this parameter realizes a range of behaviors from tight coupling to complete independence. Other model parameters describe the intrinsic characteristics of the binary chains. An identification procedure for the model parameters is developed based on hidden Markov modeling ideas but incorporating a novel parameter estimation. The usefulness of the model in analyzing certain types of data is demonstrated with examples of real channel currents.
@article{KennedyJ1996a,
    title = {Coupled Markov Chain Model: Characterization of Membrane Channel Currents with Multiple Conductance Sublevels as Partially Coupled Elementary Conducting Pores},
    author = {Chung, S. H. and Kennedy, R. A.},
    journal = {Mathematical Biosciences},
    volume = {133},
    pages = {111-137},
    month = {March},
    year = {1996}}
G. W. Pulford, J. C. Gallant, R. A. Kennedy, and S. H. Chung, "Evaluation and Estimation of Various Markov Models with Application to Membrane Channel Kinetics", Biometrical Journal, vol. 37, no. 1, pp. 39-63, January 1995.
Abstract BibTeX
Official: Link DOI: 10.1002/bimj.4710370104 PDF: KennedyJ1995a.pdf Google-Scholar: [3]
Abstract: Hidden Markov modelling is a powerful and efficient digital signal processing strategy for extracting the maximum likelihood model from a finite length sample of noisy data. Assuming the number of states in the model is known, then the state levels, transition probabilities, initial state distribution and the noise variance can be estimated. We investigate the applicability of this technique in membrane channel kinetics not only as a parameter estimator, but also as an aid to discriminating between various model types according to their statistical likelihood. \par We survey three representative classes of channel dynamics, namely: aggregated Markov models, semi-Markov models (with asymptotically convergent transition probabilities), and coupled Markov models; reformulating each within a discrete-time hidden Markov model framework. We then provide numerical evidence of the effectiveness of the procedure using simulated channel data and hence show that the correct model, as well as the model parameters, can be discerned. We also demonstrate that the model likelihood can be used to indicate the approximate number of states in the model.
@article{KennedyJ1995a,
    title = {Evaluation and Estimation of Various {M}arkov Models with Application to Membrane Channel Kinetics},
    author = {Pulford, G. W. and Gallant, J. C. and Kennedy, R. A. and Chung, S. H.},
    journal = {Biometrical Journal},
    volume = {37},
    pages = {39-63},
    month = {January},
    year = {1995}}
G. W. Pulford, R. A. Kennedy, and S. H. Chung, "Identification of Individual Channel Kinetics from Recordings Containing Many Identical Channels", Signal Processing, vol. 43, no. 2, pp. 207-221, May 1995.
Abstract BibTeX
Official: Link DOI: 10.1016/0165-1684(94)00154-R PDF: KennedyJ1995c.pdf Google-Scholar: [2]
Abstract: Given a discrete-time signal consisting of N identical, independent, binary Markov chains observed in white noise, we consider the problem of estimating the non-zero state level, the number of chains and the elementary transition probability matrix. We derive formulae for the central moments, first- and second-order auto-correlation functions and the power spectrum of a first-order, discrete-time Markov chain. We show that the mean, variance, third central moment and power spectrum provide sufficient information for the estimation of the parameters of the signal in question. We demonstrate the estimation procedure with numerical examples for both simulated and real biological data, and describe a method for estimating the non-unity eigenvalue of the transition matrix as well as the noise variance from the power spectrum of the noisy signal.
@article{KennedyJ1995c,
    title = {Identification of Individual Channel Kinetics from Recordings Containing Many Identical Channels},
    author = {Pulford, G. W. and Kennedy, R. A. and Chung, S. H.},
    journal = {Signal Processing},
    volume = {43},
    pages = {207-221},
    month = {May},
    year = {1995}}