In vivo, the human genome folds into a characteristic ensemble of 3D structures. The mechanism driving the folding process remains unknown. A theoretical model for chromatin (the minimal chromatin model) explains the folding of interphase chromosomes and generates chromosome conformations consistent with experimental data is presented. The energy landscape of the model was derived by using the maximum entropy principle and relies on two experimentally derived inputs: a classification of loci into chromatin types and a catalog of the positions of chromatin loops. This model was generalized by utilizing a neural network to infer these chromatin types using epigenetic marks present at a locus, as assayed by ChIP-Seq. The ensemble of structures resulting from these simulations completely agree with HI-C data and exhibits unknotted chromosomes, phase separation of chromatin types, and a tendency for open chromatin to lie at the periphery of chromosome territories. Although this theoretical methodology was trained in one cell line, the human GM12878 lymphoblastoid cells, it has successfully predicted the structural ensembles of multiple human cell lines. Finally, going beyond Hi-C, our predicted structures are also consistent with microscopy measurements. Analysis of both structures from simulation and microscopy reveals that short segments of chromatin make two-state transitions between closed conformations and open dumbbell conformations. For gene active segments, the vast majority of genes appear clustered in the linker region of the chromatin segment, allowing us to speculate possible mechanisms by which chromatin structure and dynamics may be involved in controlling gene expression. * Supported by the NSF

Rigidity is the ability of a system to resist imposed stresses before ultimately undergoing failure. However, disordered materials often contain both rigid and floppy subregions that complicate the utility of taking system-wide averages. I will talk about 3 frameworks capable of connecting the internal structure of disordered materials to their rigidity and/or failure under loading, and describe how my collaborators and I have applied these frameworks to laboratory data on laser-cut lattices and idealized granular materials. These are, in order of increasing physics content: (1) centrality within an adjacency matrix describing its connectivity, (2) Maxwell constraint counting on the full network of frictional contact forces, and (3) the vibrational modes of a synthetic dynamical matrix (Hessian). The first two rely primarily on topology, and the second two contrast the utility of considering interparticle forces (Coulomb failure) vs. the energy landscape. All three methods, while successfully elucidating the origins of rigidity and brittle vs. ductile failure, also provide interesting counterpoints regarding how much information is enough to make predictions.

Evidence regarding protein structure and function manifest the imperative role that dynamics play in proteins, underlining reconsideration of the unanimated sequence-to-structure-to-function paradigm. Structural dynamics portray a heterogeneous energy landscape described by conformational ensembles where each structural representation can be responsible for unique functions or enable macromolecular assemblies. Using the human p27/Cdk2/Cyclin A ternary complex as an example, we highlight the vital role of intra- and intermolecular dynamics for target recognition, binding, and inhibition as a critical modulator of cell division. Rapidly sampling configurations is critical for the population of different conformational ensembles encoding functional roles. To garner this knowledge, we present how the integration of (sub)ensemble and single-molecule fluorescence spectroscopy with molecular dynamic simulations can characterize structural dynamics linking the heterogeneous ensembles to function. The incorporation of dynamics into the sequence-to-structure-to-function paradigm promises to assist in tackling various challenges, including understanding the formation and regulation of mesoscale assemblies inside cells.