Active and thermal fluctuations in multi-scale polymer structure and dynamics

Motorized chain models of the ideal chromosome

An array of motor proteins consumes chemical energy in setting up the architectures of chromosomes. Here, we explore how the structure of ideal polymer chains is influenced by two classes of motors. The first class which we call "swimming motors" acts to propel the chromatin fiber through three-dimensional space. They represent a caricature of motors such as RNA polymerases. Previously, they have often been described by adding a persistent flow onto Brownian diffusion of the chain. The second class of motors, which we call "grappling motors" caricatures the loop extrusion processes in which segments of chromatin fibers some distance apart are brought together. We analyze these models using a self-consistent variational phonon approximation to a many-body Master equation incorporating motor activities. We show that whether the swimming motors lead to contraction or expansion depends on the susceptibility of the motors, that is, how their activity depends on the forces they must exert. Grappling motors in contrast to swimming motors lead to long-ranged correlations that resemble those first suggested for fractal globules and that are consistent with the effective interactions inferred by energy landscape analyses of Hi-C data on the interphase chromosome.

Attractive crowding effect on passive and active polymer looping kinetics

Loop formation in complex environments is crucially important to many biological processes in life. In the present work, we adopt three-dimensional Langevin dynamics simulations to investigate passive and active polymer looping kinetics in crowded media featuring polymer-crowder attraction. We find polymers undergo a remarkable coil-globule-coil transition, highlighted by a marked change in the Flory scaling exponent of the gyration radius. Meanwhile, looping time as a function of the crowder's volume fraction demonstrates an apparent non-monotonic alteration. A small number of crowders induce a compact structure, which largely facilitates the looping process. While a large number of crowders heavily impede end-to-end diffusion, looping kinetics is greatly inhibited. For a self-propelled chain, we find that the attractive crowding triggers an unusual activity effect on looping kinetics. Once a globular state is formed, activity takes an effort to open the chain from the compact structure, leading to an unexpected activity-induced inhibition of looping. If the chain maintains a coil state, the dominant role of activity is to enhance diffusivity and, thus, speed up looping kinetics. The novel conformational change and looping kinetics of both passive and active polymers in the presence of attractive crowding highlight a rather distinct scenario that has no analogy in a repulsive crowding counterpart. The underlying mechanism enriches our understanding of the crucial role of attractive interactions in modulating polymer structure and dynamics.

Transcription-induced active forces suppress chromatin motion

The organization of interphase chromosomes in a number of species is starting to emerge thanks to advances in a variety of experimental techniques. However, much less is known about the dynamics, especially in the functional states of chromatin. Some experiments have shown that the motility of individual loci in human interphase chromosome decreases during transcription and increases upon inhibiting transcription. This is a counterintuitive finding because it is thought that the active mechanical force (F) on the order of ten piconewtons, generated by RNA polymerase II (RNAPII) that is presumably transmitted to the gene-rich region of the chromatin, would render it more open, thus enhancing the mobility. We developed a minimal active copolymer model for interphase chromosomes to investigate how F affects the dynamical properties of chromatin. The movements of the loci in the gene-rich region are suppressed in an intermediate range of F and are enhanced at small F values, which has also been observed in experiments. In the intermediate F, the bond length between consecutive loci increases, becoming commensurate with the distance at the minimum of the attractive interaction between nonbonded loci. This results in a transient disorder-to-order transition, leading to a decreased mobility during transcription. Strikingly, the F-dependent change in the locus dynamics preserves the organization of the chromosome at [Formula: see text]. Transient ordering of the loci, which is not found in the polymers with random epigenetic profiles, in the gene-rich region might be a plausible mechanism for nucleating a dynamic network involving transcription factors, RNAPII, and chromatin.

Effect of local active fluctuations on structure and dynamics of flexible biopolymers

Active fluctuations play a significant role in the structure and dynamics of biopolymers (e.g. chromatin and cytoskeletal proteins) that are instrumental in the functioning of living cells. For a large range of experimentally accessible length and time scales, these polymers can be represented as flexible chains that are subjected to spatially and temporally varying fluctuating forces. In this work, we introduce a mathematical framework that correlates the spatial and temporal patterns of the fluctuations to different observables that describe the dynamics and conformations of the polymer. We demonstrate the power of this approach by analyzing the case of a point fluctuation on the polymer with an exponential decay of correlation in time with a finite time constant. Specifically, we identify the length and time scale over which the behavior of the polymer exhibits a significant departure from the behavior of a Rouse chain and the range of impact of the fluctuation along the chain. Furthermore, we show that the conformation of the polymer retains the memory of the active fluctuation from earlier times. Altogether, this work sets the basis for understanding and interpreting the role of spatio-temporal patterns of fluctuations in the dynamics, conformation, and functionality of biopolymers in living cells.

Leveraging polymer modeling to reconstruct chromatin connectivity from live images

Chromosomal dynamics plays a central role in a number of critical biological processes, such as transcriptional regulation, genetic recombination, and DNA replication. However, visualization of chromatin is generally limited to live imaging of a few fluorescently labeled chromosomal loci or high-resolution reconstruction of multiple loci from a single time frame. To aid in mapping the underlying chromosomal structure based on parsimonious experimental measurements, we present an exact analytical expression for the evolution of the polymer configuration based on a flexible-polymer model, and we propose an algorithm that tracks the polymer configuration from live images of chromatin marked with several fluorescent marks. Our theory identifies the resolution of microscopy needed to achieve high-accuracy tracking for a given spacing of markers, establishing the statistical confidence in the assignment of genome identity to the visualized marks. We then leverage experimental data of locus-tracking measurements to demonstrate the validity of our modeling approach and to establish a basis for the design of experiments with a desired resolution. Altogether, this work provides a computational approach founded on polymer physics that vastly improves the interpretation of in vivo measurements of biopolymer dynamics.

Effects of inertia on conformation and dynamics of tangentially driven active filaments

Active filamentlike systems propelling along their backbone exist across scales ranging from motor-driven biofilaments to worms and robotic chains. In macroscopic active filaments such as a chain of robots, in contrast to their microscopic counterparts, inertial effects on their motion cannot be ignored. Nonetheless, the consequences of the interplay between inertia and flexibility on the shape and dynamics of active filaments remain unexplored. Here we examine inertial effects on a flexible tangentially driven active polymer model pertinent to the above examples and we determine the conditions under which inertia becomes important. Performing Langevin dynamics simulations of active polymers with underdamped and overdamped dynamics for a wide range of contour lengths and activities, we uncover striking inertial effects on conformation and dynamics for high levels of activities. Inertial collisions increase the persistence length of active polymers and remarkably alter their scaling behavior. In stark contrast to passive polymers, inertia leaves its fingerprint at long times by an enhanced diffusion of the center of mass. We rationalize inertia-induced enhanced dynamics by analytical calculations of center-of-mass velocity correlations, applicable to any active polymer model, which reveal significant contributions from active force fluctuations convoluted by inertial relaxation.

Parameter Determination of the 2S2P1D Model and Havriliak-Negami Model Based on the Genetic Algorithm and Levenberg-Marquardt Optimization Algorithm

This study utilizes the genetic algorithm (GA) and Levenberg-Marquardt (L-M) algorithm to optimize the parameter acquisition process for two commonly used viscoelastic models: 2S2P1D and Havriliak-Negami (H-N). The effects of the various combinations of the optimization algorithms on the accuracy of the parameter acquisition in these two constitutive equations are investigated. Furthermore, the applicability of the GA among different viscoelastic constitutive models is analyzed and summarized. The results indicate that the GA can ensure a correlation coefficient of 0.99 between the fitting result and the experimental data of the 2S2P1D model parameters, and it is further proved that the fitting accuracy can be achieved through the secondary optimization via the L-M algorithm. Since the H-N model involves fractional power functions, high-precision fitting by directly fitting the parameters to experimental data is challenging. This study proposes an improved semi-analytical method that first fits the Cole-Cole curve of the H-N model, followed by optimizing the parameters of the H-N model using the GA. The correlation coefficient of the fitting result can be improved to over 0.98. This study also reveals a close relationship between the optimization of the H-N model and the discreteness and overlap of experimental data, which may be attributed to the inclusion of fractional power functions in the H-N model.

Polymer folding through active processes recreates features of genome organization

From proteins to chromosomes, polymers fold into specific conformations that control their biological function. Polymer folding has long been studied with equilibrium thermodynamics, yet intracellular organization and regulation involve energy-consuming, active processes. Signatures of activity have been measured in the context of chromatin motion, which shows spatial correlations and enhanced subdiffusion only in the presence of adenosine triphosphate. Moreover, chromatin motion varies with genomic coordinate, pointing toward a heterogeneous pattern of active processes along the sequence. How do such patterns of activity affect the conformation of a polymer such as chromatin? We address this question by combining analytical theory and simulations to study a polymer subjected to sequence-dependent correlated active forces. Our analysis shows that a local increase in activity (larger active forces) can cause the polymer backbone to bend and expand, while less active segments straighten out and condense. Our simulations further predict that modest activity differences can drive compartmentalization of the polymer consistent with the patterns observed in chromosome conformation capture experiments. Moreover, segments of the polymer that show correlated active (sub)diffusion attract each other through effective long-ranged harmonic interactions, whereas anticorrelations lead to effective repulsions. Thus, our theory offers nonequilibrium mechanisms for forming genomic compartments, which cannot be distinguished from affinity-based folding using structural data alone. As a first step toward exploring whether active mechanisms contribute to shaping genome conformations, we discuss a data-driven approach.