Research Overview

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

Reconstructed 23 Human 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).

Publication

FISH-Hi-C Paradox

Genomic Folding Landscape

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.

Publication

Resources

Code

Copolymer Chromosome Model

folding process of 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.

Publication

Multi-motor System

multiple molecular motors share a cargo

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.