Chromosomes, which are extremely long complexes formed by DNA and proteins, are essential components of heredity. Cellular functions, such as transcription, are determined by the three-dimensional organization of chromosomes and the associated dynamics. Recent exper- imental advances have given impetus to create models that could quantitatively describe the physics of chromosome architecture. With chromosome’s polymeric nature being a potential determinant of its biophysical property, theoretical and computational models for chromosomes have provided many insights into genome organization. Most of my research work focuses on developing new polymer-physics based theoretical and computational models to investigate the genome organization and dynamics.
Apart from my work on chromosomes, I also studied molecular motors with the eventual of describing how certain motors are dynamically involved in the structures of chromosomes. Molecular motors are proteins, which consume ATP (fuel) to ferry cargo in the cell. They play important roles in many biological processes, such as RNA polymerase that translocate along DNA to transcribe gene, Kinesins or Dyneins in carrying a vesicle along the microtube, Myosin in generating a muscle contraction. I developed a network model for studying multi-motor systems.
These theories and computational models explain experimental results and make predictions on the outcome of future measurements.
3D Reconstruction of Chromosomes
How to go from measured contact map to three-dimensional structure of a chromosome is an unsolved problem. Solving such an inverse problem is hard because there is no direct mapping between the contact map and 3D structure due to the heterogeneity of cell populations.
In this work, based on the theory proposed in our recent study, we proved that there exists a theoretical lower bound connecting both the quantities by a simple power-law relation. Hence, the inverse problem - inferring spatial organization from genomic contact map - can be solved approximately even in the presence of conformational heterogeneity. Using simulations, we showed that constructing the distance maps from contact maps could capture the overall organization, justifying the use of the lower bound. Finally, by applying the method combined with various manifold embedding methods to experimental Hi-C data, we were able to visualize the averaged global 3D organization of single chromosome, and also local structures such as Topological Associated Domains (TADs).
Hi-C experiments infer the contact probabilities between loci separated by varying genome lengths. Contact probability should decrease as the spatial distance between two loci increases. However, studies comparing Hi-C and FISH data show that in some cases the distance between one pair of loci, with larger Hi-C readout, is paradoxically larger compared to another pair with a smaller value of the contact probability.
We proposed a theoretical framework based on Generalized Rouse Model to solve the FISH-Hi-C paradox, which revealed the heterogeneity of genome organization. The FISH-Hi-C paradox arises because the cell population is highly heterogeneous, which means that a given contact is present in only a fraction of cells. Using an exactly solvable model I constructed a theory, without any adjustable parameters, to extract the distribution of subpopulations from the FISH data, which quantitatively reproduces the Hi-C data.
We applied the theory to the latest experimental measurements and found that the heterogeneity is pervasive in genome organization at all length scales, reﬂecting large cell-to-cell variations.
Copolymer Chromosome Model
Fingerprints of the three-dimensional organization of genomes have emerged using advances in Hi-C and imaging techniques (see the review). However, genome dynamics is poorly understood. We created the chromosome copolymer model by representing chromosomes as a copolymer with two epigenetic loci types corresponding to euchromatin (active) and heterochromatin (inactive). Using novel clustering techniques, we established quantitatively that the simulated contact maps and topologically associating domains (TADs) for chromosomes 5 and 10 and those inferred from Hi-C experiments are in excellent agreement.
Using CCM, we predicted that chromatin exhibits glassy dynamics with coherent motion on micron scale. The broad distribution of the diffusion exponents of the individual loci, which quantitatively agrees with experiments, is suggestive of highly heterogeneous dynamics. This is also reﬂected in the cell-to-cell variations in the contact maps. Finally, the folding process of chromosomes reveals that their organization is hierarchical, involving the formation of chro- mosome droplets (CDs) on genomic scale, coinciding with the TAD size, followed by coalescence of the CDs, reminiscent of Ostwald ripening.
Motors in vivo often work in tandem - multiple motors share cargo of the same kind or even different kind. It is unclear multiple motors work as a team and conﬂicting results of the velocity of the multi-motor system have been reported.
We developed a kinetic model for the coupled a motor system. The chemical kinetic scheme for a single motor is a one-state model, allowing an analytical solution. The simplicity of the model allowed me to investigate the effects of mechanical coupling between multiple motors on the velocity and force-velocity behavior. Reduction of velocity is predicted for coupled motor system especially when the coupling strength is strong. In addition, we found that multi-motors system is more efﬁcient in transporting large cargo but less efﬁcient in transporting small cargo compared to the single motor. The model is general and could be extended to study cooperation and tug-of-war between motors.