Maxwell relations for single-DNA experiments: Monitoring protein binding and double-helix torque with force-extension measurements

Abstract

Single-DNA stretching and twisting experiments provide a sensitive means to detect binding of proteins, via detection of their modification of DNA mechanical properties. However, it is often difficult or impossible to determine the numbers of proteins bound in such experiments, especially when the proteins interact nonspecifically (bind stably at any sequence position) with DNA. Here we discuss how analogs of the Maxwell relations of classical thermodynamics may be defined and used to determine changes in numbers of bound proteins, from measurements of extension as a function of bulk protein concentration. We include DNA twisting in our analysis, which allows us to show how changes in torque along single DNA molecules may be determined from measurements of extension as a function of DNA linking number. We focus on relations relevant to common experimental situations (e.g., magnetic and optical tweezers with or without controlled torque or linking number). The relation of our results to Gibbs adsorption is discussed.

Soliton Propagation in Homogeneous and Inhomogeneous Models for DNA Torsion Dynamics

“…have been quite successful in several aspects, and in particular in analyzing DNA elastic properties (also involving global DNA torsion dynamics) and structural transitions [17][18][19][20][21][22][23][24][25][26][27][28][29][30]; SME can also be performed for DNA unzipping, and actually the base sequence can be reconstructed from such measurements [31]; similarly, base stacking forces can be directly measured in SME [32]. SME testing the Peyrard-Bishop-Dauxois model [9] have been recently proposed [33].…”

Role of chain entropy in an analytic model of protein binding in single-DNA stretching experiments

“…In order to take this into account, we consider the entropy of a Gaussian chain of contour length and segment length , constrained to have a fixed end-to-end distance . The entropy of this chain had been calculated by Neumann a long time ago [11]: (8) The entropic force between the ends is given by [11,12] (9) Setting the entropic force to zero determines the most probable end-to-end separation : (10) Substituting this value into Eqn. (8), one obtains the zero-force entropy of a Gaussian chain (11a)…”

“…Therefore understanding the effect of protein binding on DNA is an important topic in cell biology. Of particular value in such studies [4][5][6][7][8][9] are micromanipulation techniques, which use magnetic tweezers to measure the extension-versus-force characteristics of single DNA molecules in solution in the presence of known concentrations of proteins.…”

Abziehen eines einzelnen Polymers von einem Substrat erschließt thermodynamische Parameter der Kosolutbindung

“…[8] In dieser Ausführung der klassischen Adsorptionsisotherme [9] sind die Oberflächen-spannung durch eine Linienspannung t und der Gibbssche Grenzflächenüberschuss pro Fläche durch einen Linienüber-schuss pro Länge, G, ersetzt. Für ein einzelnes Polymer unter Einwirkung einer konstanten mechanischen Kraft F Des ist die Beziehung zwischen G und t durch Gleichung (1) gegeben.…”