Enter Your Search:
Results 1-3 (3)
Go to page number:
Select a Filter Below
Annals of Biomedical Engineering (1)
BMC Genomics (1)
PLoS Computational Biology (1)
Buzzard, Gregery T. (2)
Bazil, Jason N. (1)
Beard, Daniel A. (1)
Buzzard, Gregery T (1)
Cordeiro, Jonathan M. (1)
Fox, Jeffrey J. (1)
Karim, Shahriar (1)
Miller, Robert E. (1)
Rundell, Ann E. (1)
Siso-Nadal, Fernando (1)
Umulis, David M (1)
Zhou, Qinlian (1)
Zygmunt, Andrew C. (1)
Year of Publication
Did you mean:
author:("Buzzard, gregory T")
Efficient calculation of steady state probability distribution for stochastic biochemical reaction network
Umulis, David M
The Steady State (SS) probability distribution is an important quantity needed to characterize the steady state behavior of many stochastic biochemical networks. In this paper, we propose an efficient and accurate approach to calculating an approximate SS probability distribution from solution of the Chemical Master Equation (CME) under the assumption of the existence of a unique deterministic SS of the system. To find the approximate solution to the CME, a truncated state-space representation is used to reduce the state-space of the system and translate it to a finite dimension. The subsequent ill-posed eigenvalue problem of a linear system for the finite state-space can be converted to a well-posed system of linear equations and solved. The proposed strategy yields efficient and accurate estimation of noise in stochastic biochemical systems. To demonstrate the approach, we applied the method to characterize the noise behavior of a set of biochemical networks of ligand-receptor interactions for Bone Morphogenetic Protein (BMP) signaling. We found that recruitment of type II receptors during the receptor oligomerization by itself doesn't not tend to lower noise in receptor signaling, but regulation by a secreted co-factor may provide a substantial improvement in signaling relative to noise. The steady state probability approximation method shortened the time necessary to calculate the probability distributions compared to earlier approaches, such as Gillespie's Stochastic Simulation Algorithm (SSA) while maintaining high accuracy.
Modeling Mitochondrial Bioenergetics with Integrated Volume Dynamics
Bazil, Jason N.
Rundell, Ann E.
Beard, Daniel A.
PLoS Computational Biology
Mathematical models of mitochondrial bioenergetics provide powerful analytical tools to help interpret experimental data and facilitate experimental design for elucidating the supporting biochemical and physical processes. As a next step towards constructing a complete physiologically faithful mitochondrial bioenergetics model, a mathematical model was developed targeting the cardiac mitochondrial bioenergetic based upon previous efforts, and corroborated using both transient and steady state data. The model consists of several modified rate functions of mitochondrial bioenergetics, integrated calcium dynamics and a detailed description of the K+-cycle and its effect on mitochondrial bioenergetics and matrix volume regulation. Model simulations were used to fit 42 adjustable parameters to four independent experimental data sets consisting of 32 data curves. During the model development, a certain network topology had to be in place and some assumptions about uncertain or unobserved experimental factors and conditions were explicitly constrained in order to faithfully reproduce all the data sets. These realizations are discussed, and their necessity helps contribute to the collective understanding of the mitochondrial bioenergetics.
Mathematically modeling biological systems challenges our current understanding of the physical and biochemical events contributing to the observed dynamics. It requires careful consideration of hypothesized mechanisms, model development assumptions and details regarding the experimental conditions. We have adopted a modeling approach to translate these factors that explicitly considers the thermodynamic constraints, biochemical states and reaction mechanisms during model development. Such models have numerous constant parameters that must be determined. Integrating thermodynamics and detailed mechanistic representation of the principal phenomena help constrain these parameter values; therefore, only a handful of the total number of model parameters (∼10%) must be adjusted during parameter estimation through model simulations. Additionally, all models must undergo some form of corroboration prior to application. In practice, this corroboration should challenge all possible dynamics of the model, but it is recognized that in this data rich world, we are surprisingly data poor. Eventually such developed and corroborated models are capable of supporting current hypotheses, guiding experimental designs and contributing to the overall knowledge base of biological processes.
Identification of IKr Kinetics and Drug Binding in Native Myocytes
Zygmunt, Andrew C.
Cordeiro, Jonathan M.
Miller, Robert E.
Fox, Jeffrey J.
Annals of Biomedical Engineering
Determining the effect of a compound on IKr is a standard screen for drug safety. Often the effect is described using a single IC50 value, which is unable to capture complex effects of a drug. Using verapamil as an example, we present a method for using recordings from native myocytes at several drug doses along with qualitative features of IKr from published studies of HERG current to estimate parameters in a mathematical model of the drug effect on IKr. IKr was recorded from canine left ventricular myocytes using ruptured patch techniques. A voltage command protocol was used to record tail currents at voltages from −70 to −20 mV, following activating pulses over a wide range of voltages and pulse durations. Model equations were taken from a published IKr Markov model and the drug was modeled as binding to the open state. Parameters were estimated using a combined global and local optimization algorithm based on collected data with two additional constraints on IKrI–V relation and IKr inactivation. The method produced models that quantitatively reproduce both the control IKr kinetics and dose dependent changes in the current. In addition, the model exhibited use and rate dependence. The results suggest that: (1) the technique proposed here has the practical potential to develop data-driven models that quantitatively reproduce channel behavior in native myocytes; (2) the method can capture important drug effects that cannot be reproduced by the IC50 method. Although the method was developed for IKr, the same strategy can be applied to other ion channels, once appropriate channel-specific voltage protocols and qualitative features are identified.
Electronic supplementary material
The online version of this article (doi:10.1007/s10439-009-9690-5) contains supplementary material, which is available to authorized users.
Mathematical modeling; Drug–ion current interaction; Parameter estimation; Global optimization; Verapamil; Cardiac electrophysiology
Results 1-3 (3)
Go to page number:
Remove citation from clipboard
Add citation to clipboard
This will clear all selections from your clipboard. Do you wish proceed?
Clipboard is full! Please remove an item and try again.
PubMed Central Canada is a service of the
Canadian Institutes of Health Research
(CIHR) working in partnership with the National Research Council's
Canada Institute for Scientific and Technical Information
in cooperation with the
National Center for Biotechnology Information
U.S. National Library of Medicine
(NCBI/NLM). It includes content provided to the
PubMed Central International archive
by participating publishers.