Gatenby Robert A
Department of Integrated Mathematical Oncology, Moffitt Cancer Center, Tampa, Florida.
bioRxiv. 2023 Sep 17:2023.09.15.557926. doi: 10.1101/2023.09.15.557926.
Living systems use genomic information to maintain a stable highly ordered state far from thermodynamic equilibrium but the specific mechanisms and general principles governing the interface of genetics and thermodynamics has not been extensively investigated. Genetic information is quantified in unitless bits termed "Shannon entropy", which does not directly relate to thermodynamic entropy or energy. Thus, it is unclear how the Shannon entropy of genetic information is converted into thermodynamic work necessary to maintain the non-equilibrium state of living systems. Here we investigate the interface of genetic information and cellular thermodynamics in enzymatic acceleration of a chemical reaction , where and are substrate and enzyme, is the enzyme substrate complex and product. The rate of any intracellular chemical reaction is determined by probability functions at macroscopic (Boltzmann distribution of the reactant kinetic energies governed by temperature) or microscopic (overlap of reactant quantum wave functions) scales - described, respectively, by the Arrhenius and Knudsen equations. That is, the reaction rate, in the absence of a catalyst, is governed by temperature which determines the kinetic energy of the interacting molecules. Genetic information can act upon a when the encoded string of amino acids folds into a 3-deminsional structure that permits a lock/key spatial matching with the reactants. By optimally superposing the reactants' wave functions, the information in the enzyme increases the reaction rate by up to15 orders of magnitude under isothermal conditions. In turn, the accelerated reaction rate alters the intracellular thermodynamics environment as the products are at lower Gibbs free energy which permits thermodynamic work . Mathematically and biologically, the critical event that allows genetic information to produce thermodynamic work is the folding of the amino acid string specified by the gene into a 3-dimensional shape determined by its lowest energy state. Biologically, this allows the amino acid string to bind substrate and place them in an optimal spatial orientation. These key-lock are mathematically characterized by Kullback-Leibler Divergence and the interactions with the reaction channel now represent Fisher Information (the second derivative Kullback-Leibler divergence), which can take on the units of the process to which it is applied. Interestingly, Shannon is typically derived by "coarse graining" Shannon information. Thus, living system, by acting at a quantum level, "fine grain" Shannon information.
生命系统利用基因组信息来维持一个远离热力学平衡的稳定的高度有序状态，但控制遗传学与热力学界面的具体机制和一般原理尚未得到广泛研究。遗传信息以称为“香农熵”的无量纲比特进行量化，它与热力学熵或能量并无直接关联。因此，尚不清楚遗传信息的香农熵是如何转化为维持生命系统非平衡状态所需的热力学功的。在此，我们在化学反应的酶促加速过程中研究遗传信息与细胞热力学的界面，其中S和E分别是底物和酶，ES是酶 - 底物复合物，P是产物。任何细胞内化学反应的速率由宏观尺度（由温度控制的反应物动能的玻尔兹曼分布）或微观尺度（反应物量子波函数的重叠）的概率函数决定——分别由阿伦尼乌斯方程和克努森方程描述。也就是说，在没有催化剂的情况下，反应速率由温度决定，温度决定了相互作用分子的动能。当编码的氨基酸序列折叠成三维结构，允许与反应物进行锁钥式空间匹配时，遗传信息就可以作用于底物。通过最优地叠加反应物的波函数，酶中的信息在等温条件下可将反应速率提高多达15个数量级。反过来，加速的反应速率会改变细胞内的热力学环境，因为产物具有更低的吉布斯自由能，这允许进行热力学功。在数学和生物学上，使遗传信息能够产生热力学功的关键事件是基因指定的氨基酸序列折叠成由其最低能量状态决定的三维形状。在生物学上，这使得氨基酸序列能够结合底物并将它们置于最佳空间取向。这些锁钥关系在数学上由库尔贝克 - 莱布勒散度表征，并且与反应通道的相互作用现在代表费希尔信息（库尔贝克 - 莱布勒散度的二阶导数），它可以采用其所应用过程的单位。有趣的是，香农熵通常是通过对香农信息进行“粗粒化”得到的。因此，生命系统通过在量子水平上起作用，对香农信息进行“细粒化”。
