Program Director/Principal Investigator (Liang, Jie):
PROJECT SUMMARY/ABSTRACT
We will continue our study of biopolymers and their interactions at two levels. At the molecular
network level, we will study the A) probability landscape of stochastic networks of molecular
reactions. We will develop efficient computational tools to construct exact probability landscapes in
high-dimension, quantify probability discrete fluxes, and characterize their exact topology. These
powerful tools will be applied to gain mechanistic understanding of stochastic control of network
phenotypes in a number of important biological problems. At the (sub)cellular level, we will study B)
biophysics of 3D chromatin folding. We will develop algorithms to identify driver interactiomes that
can generate large ensembles of accurate models of single-cell 3D chromatin conformations
consistent with Hi-C and single-cell experimental data. Our methods will be applied to study
foundational problems of 3D genome to gain understanding of principles of genome organization.
In A), we will study stochastic reaction networks of molecules to gain mechanistic understanding of
their behavior. Many important cellular processes involve a small copy number of molecules of
transcription factors, enzymes, and signaling molecules. Stochasticity and rare events arising from
such low copy number reactions are important for processes such as embryonic development, stem
cell differentiation, and nongenetic heterogeneity. Our approach will be based on the fundamental
framework of the stochastic kinetic processes and the discrete chemical master equation (dCME).
The central tasks are: 1) constructing the probability landscape of the network, and from which to 2)
gain analytical insight into mechanism of network behavior. For 1), we have developed the ACME
method that can construct the exact probability landscapes of a large class of complex stochastic
reaction networks and will make further improvement. For 2), we will develop landscape analysis
tools using persistent homology that can compute the exact topology of the high-dimensional
probability landscape. We have also developed the concept of discrete fluxes and methods for its
computation. We will further formulate and generalize the concept of discrete rotational flux to higher
dimension. These developments will enable global and mechanistic understanding of the behavior of
stochastic networks through accurately constructed probability landscape and exactly computed
topological structures. Our work will open up new frontiers for investigations, many of which are
currently not computationally feasible. Specifically, we will construct probability landscapes of
networks, study how global flux maps evolve and how phenotype switching occur. We will generalize
the discovery of stochastic oscillation and investigate higher-order oscillatory behavior of networks,
where probability mass may be transferred through higher-dimensional k-channels. In addition, we
will carry-out in-depth analysis on a selected set of important biological problems, including stochastic
control of mRNA splicing/transcription at single-cell level, initiation of protein fibril aggregation,
network architectures for multi-stability and maintenance of epigenetic states, and switching of
cellular phenotypes.
In B), we will study the biophysical principles of 3D genome organization. We will develop
computational tools to generate thoroughly sampled large ensembles of coarse-grained polymer
models of 3D chromatin structures based on experimental Hi-C and other data. We will develop
strategies to study a number of fundamental problems: We will determine and uncover the minimal
sets of critical driver interactions sufficient to determine folding of chromatin at specific loci and at
whole chromosome level. We will further investigate how chromatin-nuclear envelope interactions,
along with chromatin driver interactome, nuclear bodies, and speckles, orchestrate the overall 3D
genome organization. We will decipher the persistent driver interactomes at different genomic loci,
which are preserved across different tissues and are responsible for the formation of common
genomic structural scaffolds and folding landscapes. We will also identify adaptive interactomes that
differ among tissues and inferring how they evolve and rewire during development. We will further
infer how these temporally evolving structural interactomes spatially arrange genomic elements and
how they may influence structural gene accessibility at genome scale.
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