The long reach of DNA sequence heterogeneity in diffusive processes

Many biological processes involve one dimensional diffusion over a correlated inhomogeneous energy landscape with a correlation length $\xi_c$. Typical examples are specific protein target location on DNA, nucleosome repositioning, or DNA translocation through a nanopore, in all cases with $\xi_c\approx$ 10 nm. We investigate such transport processes by the mean first passage time (MFPT) formalism, and find diffusion times which exhibit strong sample to sample fluctuations. For a a displacement $N$, the average MFPT is diffusive, while its standard deviation over the ensemble of energy profiles scales as $N^{3/2}$ with a large prefactor. Fluctuations are thus dominant for displacements smaller than a characteristic $N_c \gg \xi_c$: typical values are much less than the mean, and governed by an anomalous diffusion rule. Potential biological consequences of such random walks, composed of rapid scans in the vicinity of favorable energy valleys and occasional jumps to further valleys, is discussed

The 3D Genome as Moderator of Chromosomal Communication

Proper expression of genes requires communication with their regulatory elements that can be located elsewhere along the chromosome. The physics of chromatin fibers imposes a range of constraints on such communication. The molecular and biophysical mechanisms by which chromosomal communication is established, or prevented, have become a topic of intense study, and important roles for the spatial organization of chromosomes are being discovered. Here we present a view of the interphase 3D genome characterized by extensive physical compartmentalization and insulation on the one hand and facilitated long-range interactions on the other. We propose the existence of topological machines dedicated to set up and to exploit a 3D genome organization to both promote and censor communication along and between chromosomes.National Human Genome Research Institute (U.S.) (Grant R01 HG003143)National Human Genome Research Institute (U.S.) (Grant U54 HG007010)National Human Genome Research Institute (U.S.) (Grant U01 HG007910)National Cancer Institute (U.S.) (Grant U54 CA193419)National Institutes of Health (U.S.) (Grant U54 DK107980)National Institutes of Health (U.S.) (Grant U01 DA 040588)National Institute of General Medical Sciences (U.S.) (Grant R01 GM 112720)National Institute of Allergy and Infectious Diseases (U.S.) (Grant U01 R01 AI 117839

Higher-order chromatin structure: bridging physics and biology

Advances in microscopy and genomic techniques have provided new insight into spatial chromatin organization inside of the nucleus. In particular, chromosome conformation capture data has highlighted the relevance of polymer physics for high-order chromatin organization. In this context, we review basic polymer states, discuss how an appropriate polymer model can be determined from experimental data, and examine the success and limitations of various polymer models of higher-order interphase chromatin organization. By taking into account topological constraints acting on the chromatin fiber, recently developed polymer models of interphase chromatin can reproduce the observed scaling of distances between genomic loci, chromosomal territories, and probabilities of contacts between loci measured by chromosome conformation capture methods. Polymer models provide a framework for the interpretation of experimental data as ensembles of conformations rather than collections of loops, and will be crucial for untangling functional implications of chromosomal organization.National Cancer Institute (U.S.). Physical Sciences-Oncology Center (MIT, (U54CA143874)

Using orthologous and paralogous proteins to identify specificity determining residues

Background: Concepts of orthology and paralogy are become increasingly important as whole-genome comparison allows their identification in complete genomes. Functional specificity of proteins is assumed to be conserved among orthologs and is different among paralogs. We used this assumption to identify residues which determine specificity of protein-DNA and protein-ligand recognition. Finding such residues is crucial for understanding mechanisms of molecular recognition and for rational protein and drug design. Results: Assuming conservation of specificity among orthologs and different specificity of paralogs, we identify residues which correlate with this grouping by specificity. The method is taking advantage of complete genomes to find multiple orthologs and paralogs. The central part of this method is a procedure to compute statistical significance of the predictions. The procedure is based on a simple statistical model of protein evolution. When applied to a large family of bacterial transcription factors, our method identified 12 residues that are presumed to determine the protein-DNA and protein-ligand recognition specificity. Structural analysis of the proteins and available experimental results strongly support our predictions. Our results suggest new experiments aimed at rational re-design of specificity in bacterial transcription factors by a minimal number of mutations. Conclusions: While sets of orthologous and paralogous proteins can be easily derived from complete genomic sequences, our method can identify putative specificity determinants in such proteins

Bridging the Resolution Gap in Structural Modeling of 3D Genome Organization

Over the last decade, and especially after the advent of fluorescent in situ hybridization imaging and chromosome conformation capture methods, the availability of experimental data on genome three-dimensional organization has dramatically increased. We now have access to unprecedented details of how genomes organize within the interphase nucleus. Development of new computational approaches to leverage this data has already resulted in the first three-dimensional structures of genomic domains and genomes. Such approaches expand our knowledge of the chromatin folding principles, which has been classically studied using polymer physics and molecular simulations. Our outlook describes computational approaches for integrating experimental data with polymer physics, thereby bridging the resolution gap for structural determination of genomes and genomic domains.Spain. Ministerio de Ciencia e Innovación (BFU2010-19310)National Cancer Institute (U.S.)David H. Koch Institute for Integrative Cancer Research at MI

Modeling chromosomes: Beyond pretty pictures

Recently, Chromosome Conformation Capture (3C) based experiments have highlighted the importance of computational models for the study of chromosome organization. In this review, we propose that current computational models can be grouped into roughly four classes, with two classes of data-driven models: consensus structures and data-driven ensembles, and two classes of de novo models: structural ensembles and mechanistic ensembles. Finally, we highlight specific questions mechanistic ensembles can address.National Institutes of Health (U.S.) (Grant R01HG003143)National Institutes of Health (U.S.) (Grant R01 GM114190

Chromosome Compaction by Active Loop Extrusion

During cell division, chromosomes are compacted in length by more than a 100-fold. A wide range of experiments demonstrated that in their compacted state, mammalian chromosomes form arrays of closely stacked consecutive ∼100 kb loops. The mechanism underlying the active process of chromosome compaction into a stack of loops is unknown. Here we test the hypothesis that chromosomes are compacted by enzymatic machines that actively extrude chromatin loops. When such loop-extruding factors (LEF) bind to chromosomes, they p rogressively bridge sites that are further away along the chromosome, thus extruding a loop. We demonstrate that collective action of LEFs leads to formation of a dynamic array of consecutive loops. Simulations and an analytically solved model identify two distinct steady states: a sparse state, where loops are highly dynamic but provide little compaction; and a dense state, where there are more stable loops and dramatic chromosome compaction. We find that human chromosomes operate at the border of the dense steady state. Our analysis also shows how the macroscopic characteristics of the loop array are determined by the microscopic properties of LEFs and their abundance. When the number of LEFs are used that match experimentally based estimates, the model can quantitatively reproduce the average loop length, the degree of compaction, and the general loop-array morphology of compact human chromosomes. Our study demonstrates that efficient chromosome compaction can be achieved solely by an active loop-extrusion process.National Institutes of Health (U.S.) (Grant GM114190)National Institutes of Health (U.S.) (Grant R01HG003143

Exploring the three-dimensional organization of genomes: interpreting chromatin interaction data

How DNA is organized in three dimensions inside the cell nucleus and how this affects the ways in which cells access, read and interpret genetic information are among the longest standing questions in cell biology. Using newly developed molecular, genomic and computational approaches based on the chromosome conformation capture technology (such as 3C, 4C, 5C and Hi-C), the spatial organization of genomes is being explored at unprecedented resolution. Interpreting the increasingly large chromatin interaction data sets is now posing novel challenges. Here we describe several types of statistical and computational approaches that have recently been developed to analyse chromatin interaction data.National Institutes of Health (U.S.)National Human Genome Research Institute (U.S.) (HG003143)National Human Genome Research Institute (U.S.) (HG003143-06S1)W. M. Keck FoundationSpain. Ministerio de Ciencia e Innovación (BFU2010-19310/BMC)Human Frontier Science Program (Strasbourg, France) (RGP0044/2011)European Union (BLUEPRINT project (EU FP7 grant agreement 282510))National Cancer Institute (U.S.) (Physical Sciences Oncology Center at MIT, U54CA143874

Protein knot server: detection of knots in protein structures

KNOTS (http://knots.mit.edu) is a web server that detects knots in protein structures. Several protein structures have been reported to contain intricate knots. The physiological role of knots and their effect on folding and evolution is an area of active research. The user submits a PDB id or uploads a 3D protein structure in PDB or mmCIF format. The current implementation of the server uses the Alexander polynomial to detect knots. The results of the analysis that are presented to the user are the location of the knot in the structure, the type of the knot and an interactive visualization of the knot. The results can also be downloaded and viewed offline. The server also maintains a regularly updated list of known knots in protein structures