AI 中文总结
针对基因组规模建模与实验技术在反应动力学研究上的矛盾，提出变分动力学方法，通过数学重新表述和指数圆锥优化，满足稳态反应动力学，放宽非线性约束，经计算验证该方法可处理多种相关情况。
AI 中文摘要
基因组规模建模方法主要预测反应通量，而成熟的高通量实验技术主要测量分子种类。出现这种看似矛盾的情况是因为在不借助方便但不准确的近似或仅在参考状态附近有效的展开的情况下，实施代表反应动力学速率方程的非线性约束具有挑战性。我们提出了一个数学和计算上易于处理的解决方案。首先，我们用矩阵向量表示法对代谢反应和反应动力学的现有知识进行数学重新表述。然后，我们提出了变分动力学，一种通过指数圆锥优化在基因组规模上满足稳态反应动力学的新方法。非线性速率定律约束被放宽为指数锥，这使得可行集是凸的，并且通过在该集合上最小化一个严格凹的优值函数来恢复基元动力学的满足情况，当且仅当每个速率定律成立时该优值函数为零。我们确定了一个特定的圆锥优化问题序列收敛到这个优值函数的一个驻点，并且每个这样的驻点都是满足基元动力学的稳态。部分守恒、对基元动力学参数的热力学约束、正则化稳态和外部反应速率的线性优化都包含在同一个圆锥公式中。我们在一个基因组规模的代谢模型上通过计算证明了该方法。
英文摘要
Genome-scale modelling methods primarily predict reaction fluxes, whereas established high throughput experimental technologies primarily measure molecular species concentrations. This apparently paradoxical situation has arisen because implementing the non-linear constraints that represent reaction kinetic rate equations is challenging without resorting to convenient yet inaccurate approximations or to expansions that are valid only near a reference state. We present a mathematically and computationally tractable solution to this problem. First, we introduce a mathematical reformulation of established knowledge of metabolic reactions and reaction kinetics in matrix-vector notation. We then present variational kinetics, a novel approach that satisfies steady state reaction kinetics at genome scale by exponential conic optimisation. The non-linear rate law constraints are relaxed to exponential cones, which renders the feasible set convex, and satisfaction of elementary kinetics is recovered by minimising a strictly concave merit function over that set, which attains zero if, and only if, every rate law holds. We establish that a particular sequence of conic optimisation problems converges to a stationary point of this merit function, and that every such stationary point is a steady state satisfying elementary kinetics. Moiety conservation, thermodynamic constraints on elementary kinetic parameters, regularised steady states and linear optimisation of external reaction rates are each accommodated within the same conic formulation. We demonstrate the approach computationally on a genome-scale metabolic model.
Comments54 pages, 5 figures
