Department of Physics, Arizona State University, Tempe, Arizona 85287, United States.
Center for Biological Physics, Arizona State University, Tempe, Arizona 85287, United States.
J Chem Theory Comput. 2024 Sep 10;20(17):7646-7666. doi: 10.1021/acs.jctc.4c00688. Epub 2024 Aug 19.
Kinetic diagrams are commonly used to represent biochemical systems in order to study phenomena such as free energy transduction and ion selectivity. While numerical methods are commonly used to analyze such kinetic networks, the diagram method by King, Altman and Hill makes it possible to construct exact algebraic expressions for steady-state observables in terms of the rate constants of the kinetic diagram. However, manually obtaining these expressions becomes infeasible for models of even modest complexity as the number of the required intermediate diagrams grows with the factorial of the number of states in the diagram. We developed (KDA), a Python library that programmatically generates the relevant diagrams and expressions from a user-defined kinetic diagram. KDA outputs symbolic expressions for state probabilities and cycle fluxes at steady-state that can be symbolically manipulated and evaluated to quantify macroscopic system observables. We demonstrate the KDA approach for examples drawn from the biophysics of active secondary transmembrane transporters. For a generic 6-state antiporter model, we show how the introduction of a single leakage transition reduces transport efficiency by quantifying substrate turnover. We apply KDA to a real-world example, the 8-state free exchange model of the small multidrug resistance transporter EmrE of Hussey et al. (, , , e201912437), where a change in transporter phenotype is achieved by biasing two different subsets of kinetic rates: alternating access and substrate unbinding rates. KDA is made available as open source software under the GNU General Public License version 3.
动力学图通常用于表示生化系统，以便研究自由能转导和离子选择性等现象。虽然数值方法常用于分析此类动力学网络，但 King、Altman 和 Hill 的图方法使得可以根据动力学图的速率常数，用精确的代数表达式来表示稳态观测值。然而，对于甚至是中等复杂度的模型，手动获取这些表达式变得不可行，因为所需中间图的数量随图中状态数的阶乘而增长。我们开发了 (KDA)，这是一个 Python 库，可以根据用户定义的动力学图自动生成相关的图和表达式。KDA 输出稳态下状态概率和循环通量的符号表达式，可以进行符号操作和评估，以量化宏观系统观测值。我们以主动二次跨膜转运蛋白的生物物理学为例展示了 KDA 方法。对于一个通用的 6 态反向转运蛋白模型，我们通过量化底物周转率来展示引入单个泄漏跃迁如何降低转运效率。我们将 KDA 应用于一个真实世界的例子，即 Hussey 等人的小多药耐药转运蛋白 EmrE 的 8 态自由交换模型 (,,, e201912437)，其中通过偏置两个不同的动力学速率子集来实现转运蛋白表型的变化：交替访问和底物解结合速率。KDA 作为开源软件，根据 GNU 通用公共许可证第 3 版发布。
