Dependence of DNA length on binding affinity between TrpR and trpO of DNA

Abstract

We scrutinize the length dependency of the binding affinity of bacterial repressor TrpR protein to trpO (specific site) on DNA. A footprinting experiment shows that the longer the DNA length, the larger the affinity of TrpR to the specific site on DNA. This effect termed “antenna effect” might be interpreted as follows: longer DNA provides higher probability for TrpR to access to the specific site aided by one-dimensional diffusion along the nonspecific sites of DNA. We show that, however, the antenna effect cannot be explained while detailed balance holds among three kinetic states, that is, free protein/DNA, nonspecific complexes, and specific complex. We propose a working hypothesis that slow degree(s) of freedom in the system switch(es) different potentials of mean force causing transitions among the three states. This results in a deviation from detailed balance on the switching timescale. We then derive a simple reaction diffusion/binding model that describes the antenna effect on TrpR binding to its target operator. Possible scenarios for such slow degree(s) of freedom in TrpR–DNA complex are addressed.

One-dimensional diffusion of TrpR along DNA enhances its affinity for the operator by chemical ratchet mechanism

“…As discussed later in more detail, if some of the reaction component molecules alter their intrinsic affinity/stability according to oscillating conformational changes with random phases, the latter is possible to be established to show a macroscopic affinity but the rule does not hold in the non-equilibrium state. We named the mechanism “chemical ratchet”, which is consistent with the 10,000-fold antenna effect of TrpR- trpO binding 12 .…”

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

“…The scenario shown above is one of the possible candidates for molecular models of chemical ratchets. As shown in Figure 4 b, the observed values of the dissociation equilibrium constant, the inverse of the affinity, are well fitted by the solution of the differential equation composed of the diffusion equation and the rate equation (blue curve in Figure 4 b) [ 16 ]. For short DNA, where sliding is assumed to be equilibrated before dissociation from the DNA, the concentration of the complex can be dynamically determined from kinetic equations.…”

“…For a long time, the first step in kinetic analysis was to define the homogeneous reactants. However, one must first determine whether the reaction contains a chemical ratchet, which was proposed recently for protein–DNA binding [ 16 ]. This new concept is an extension of the ratchet mechanism in physics, whose driving force was originally an external energy source [ 17 ], but the force has been extended to internal ones [ 18 , 19 ], which is the case for chemical ratchet also.…”

“…The theoretical framework of chemical ratchet was proposed by Toda based on the experimental results and interpretation by Kinebuchi and Shimamoto with mathematical support by Nara et al [ 16 ]. In the experiment of E. coli TrpR binding to trpO , the apparent dissociation equilibrium constant changed by 10,000-fold according to the length of the DNA harboring trpO , which was denoted as the antenna effect [ 10 , 20 ].…”

“…The values of the dissociation constant (closed circles) were obtained with the site-specific hydroxyl radical footprinting of TrpR on trpO DNA of various lengths. The differential equations composed of rate equations and diffusion equations corresponding to the one-dimensional diffusion of TrpR along the DNA were solved in a stationary state to provide the best-fit curve (blue line) with a site size of 18 bp and a diffusion distance of 625 bp (blue) [ 16 ]. Another theoretical calculation of chemical ratchet under the assumption of rapid diffusion for short DNA gave the best-fit curve with a site size of 18 bp (red curve) [ 21 ], where Panel b is taken from.…”