(443c) Active Fluctuations Control Biopolymer Dynamics*

One of the fundamental difficulties in biological physics is to establish a predictive time-dependent statistical mechanical theory of the out of equilibrium processes that maintain and control virtually every biological process. We develop a theoretical statistical mechanical framework based on the path integral formulation of Brownian dynamics for predicting the combined influence of active and thermal forces on the dynamics of a single particle in presence of harmonic trap. This provides the time evolution of joint probability distribution function of the particle as well as position correlation functions. An active Brownian polymer obeying Rouse dynamics can be effectively decomposed to an infinite set of active particles (using normal mode transformation) of various length scales in presence of harmonic potentials of varying strength. In this talk, we will present our theoretical model, with a focus on the structural and dynamic behavior of polymers at various length and time scales. The active forces exhibit a temporal correlation in their statistical behavior, capturing the processivity associated with the characteristic time scale of biological fluctuations such as ATP hydrolysis or enzymatic activity. Based on the same path-integral formalism, we demonstrate that the non-equilibrium fluctuations can be mapped onto an effective time-dependent temperature that depends on the active-force decorrelation rate. In the long-time steady state this suggests presence of a higher effective temperature and a quasi-equilibrium like scenario where steady state probability distribution follows Boltzmann statistics (albeit a higher effective temperature). This theoretical picture also indicates a hierarchy of behaviors, where local conformational fluctuations are unaffected by the presence of active forces however, large length-scale conformational dynamics is significantly altered. Conformational fluctuations suggest a large-scale swelling behavior of the active Brownian polymer. These results suggest that active fluctuations have a varying impact on biological processes based on the time and length scale on which these events occur. The theory has been extended to understand spontaneous dynamic events of the polymer chain. The resultant of the competing effects of (i) large scale swelling (structural effect) and (ii) faster sampling of space due to active forces (dynamic effect) is shown to determine polymer rate process such as end-to-end loop formation. Overall, the theoretical analysis and conceptualization of a time-dependent temperature provides a roadmap for the interpretation of in-vivo measurements across the spectrum of time scales.

*Funding for this work is provided by the Human Frontier Science Program, HFSP/REF RGP0019/20.