RNA Polymerase and Transcription Mechanisms: The Forefront of Physicochemical Studies of Chemical Reactions

Single-molecule evidence for a chemical ratchet in binding between the cam repressor and its operator

The affinity for regulator-operator binding on DNA sometimes depends on the length of the DNA harboring the operator, which is known as the antenna effect. One-dimensional diffusion along DNA has been suggested to be the cause, but this may contradict the binding affinity independent of the reaction pathways, which is derived from the detailed balance of the reaction at equilibrium. Recently, the chemical ratchet was proposed to solve this contradiction by suggesting a stationary state containing microscopic non-equilibrium. In a single-molecule observation, P. putida CamR molecules associate with their operator via one-dimensional diffusion along the DNA, while they mostly dissociated from the operator without the diffusion. Consistently, the observed overall association rate was dependent on the DNA length, while the overall dissociation rate was not, leading to an antenna effect. E. coli RNA polymerase did not show this behavior, and thus it is a specific property of a protein. The bipartite interaction domains containing the helix-turn-helix motif are speculated to be one of the possible causes. The biological significance of the chemical ratchet and a model for its microscopic mechanism are also discussed.

The Limitation of the Combination of Transition State Theory and Thermodynamics for the Reactions of Proteins and Nucleic Acids

When a reaction is accompanied by a change with the speed close to or slower than the reaction rate, a circulating reaction flow can exist among the reaction states in the macroscopic stationary state. If the accompanying change were at equilibrium in the timescale of the relevant reaction, the transition-state theory would hold to eliminate the flow.

Ideas and methods of nonlinear mathematics and theoretical physics in DNA science: the McLaughlin-Scott equation and its application to study the DNA open state dynamics

The review is devoted to a new and rapidly developing area related to the application of ideas and methods of nonlinear mathematics and theoretical physics to study the internal dynamics of DNA and, in particular, the behavior of the open states of DNA. There are two main competing approaches to this research. The first approach is based on the molecular dynamics method, which takes into account the motions of all structural elements of the DNA molecule and all interactions between them. The second approach is based on prior selection of the main (dominant) motions and their mathematical description using a small number of model equations. This review describes the results of the study of the open states of DNA performed within the framework of the second approach using the McLaughlin-Scott equation. We present the results obtained both in the case of homogeneous sequences: poly (A), poly (T), poly (G) and poly (C), and in the inhomogeneous case when the McLaughlin-Scott equation has been used for studying the dynamics of open states activated in the promoters A1, A2 and A3 of the bacteriophage T7 genome, in the genes IFNA17, ADRB2, NOS1 and IL-5, in the pBR322 and pTTQ18 plasmids. Particular attention is paid to the results concerning the effect of various external fields on the behavior of open states. In the concluding part of the review, new possibilities and prospects for the development of the considered approach and especially of the McLaughlin-Scott equation are discussed.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s12551-021-00801-0.