Mario Nicodemi

Complexity of chromatin folding is captured by the strings and binders switch model

Chromatin has a complex spatial organization in the cell nucleus that serves vital functional purposes. A variety of chromatin folding conformations has been detected by single-cell imaging and chromosome conformation capture-based approaches. However, a unified quantitative framework describing spatial chromatin organization is still lacking. Here, we explore the “strings and binders switch” model to explain the origin and variety of chromatin behaviors that coexist and dynamically change within living cells. This simple polymer model recapitulates the scaling properties of chromatin folding reported experimentally in different cellular systems, the fractal state of chromatin, the processes of domain formation, and looping out. Additionally, the strings and binders switch model reproduces the recently proposed “fractal–globule” model, but only as one of many possible transient conformations.

Universal fluctuations in correlated systems

The probability density function (PDF) of a global measure in a large class of highly correlated systems has been suggested to be of the same functional form. Here, we identify the analytical form of the PDF of one such measure, the order parameter in the low temperature phase of the 2D XY model. We demonstrate that this function describes the fluctuations of global quantities in other correlated equilibrium and nonequilibrium systems. These include a coupled rotor model, Ising and percolation models, models of forest fires, sandpiles, avalanches, and granular media in a self-organized critical state. We discuss the relationship with both Gaussian and extremal statistics.

Hierarchical folding and reorganization of chromosomes are linked to transcriptional changes in cellular differentiation

Mammalian chromosomes fold into arrays of megabase‐sized topologically associating domains (TADs), which are arranged into compartments spanning multiple megabases of genomic DNA. TADs have internal substructures that are often cell type specific, but their higher‐order organization remains elusive. Here, we investigate TAD higher‐order interactions with Hi‐C through neuronal differentiation and show that they form a hierarchy of domains‐within‐domains (metaTADs) extending across genomic scales up to the range of entire chromosomes. We find that TAD interactions are well captured by tree‐like, hierarchical structures irrespective of cell type. metaTAD tree structures correlate with genetic, epigenomic and expression features, and structural tree rearrangements during differentiation are linked to transcriptional state changes. Using polymer modelling, we demonstrate that hierarchical folding promotes efficient chromatin packaging without the loss of contact specificity, highlighting a role far beyond the simple need for packing efficiency.

Complex multi-enhancer contacts captured by genome architecture mapping

The organization of the genome in the nucleus and the interactions of genes with their regulatory elements are key features of transcriptional control and their disruption can cause disease. Here we report a genome-wide method, genome architecture mapping (GAM), for measuring chromatin contacts and other features of three-dimensional chromatin topology on the basis of sequencing DNA from a large collection of thin nuclear sections. We apply GAM to mouse embryonic stem cells and identify enrichment for specific interactions between active genes and enhancers across very large genomic distances using a mathematical model termed SLICE (statistical inference of co-segregation). GAM also reveals an abundance of three-way contacts across the genome, especially between regions that are highly transcribed or contain super-enhancers, providing a level of insight into genome architecture that, owing to the technical limitations of current technologies, has previously remained unattainable. Furthermore, GAM highlights a role for gene-expression-specific contacts in organizing the genome in mammalian nuclei.

Universality in solar flare and earthquake occurrence

Earthquakes and solar flares are phenomena involving huge and rapid releases of energy characterized by complex temporal occurrence. By analyzing available experimental catalogs, we show that the stochastic processes underlying these apparently different phenomena have universal properties. Namely, both problems exhibit the same distributions of sizes, interoccurrence times, and the same temporal clustering: We find after flare sequences with power law temporal correlations as the Omori law for seismic sequences. The observed universality suggests a common approach to the interpretation of both phenomena in terms of the same driving physical mechanism.

Thermodynamic Pathways to Genome Spatial Organization in the Cell Nucleus

The architecture of the eukaryotic genome is characterized by a high degree of spatial organization. Chromosomes occupy preferred territories correlated to their state of activity and, yet, displace their genes to interact with remote sites in complex patterns requiring the orchestration of a huge number of DNA loci and molecular regulators. Far from random, this organization serves crucial functional purposes, but its governing principles remain elusive. By computer simulations of a statistical mechanics model, we show how architectural patterns spontaneously arise from the physical interaction between soluble binding molecules and chromosomes via collective thermodynamics mechanisms. Chromosomes colocalize, loops and territories form, and find their relative positions as stable thermodynamic states. These are selected by thermodynamic switches, which are regulated by concentrations/affinity of soluble mediators and by number/location of their attachment sites along chromosomes. Our thermodynamic switch model of nuclear architecture, thus, explains on quantitative grounds how well-known cell strategies of upregulation of DNA binding proteins or modification of chromatin structure can dynamically shape the organization of the nucleus.

Models of chromosome structure

Understanding the mechanisms that control chromosome folding in the nucleus of eukaryotes and their contribution to gene regulation is a key open issue in molecular biology. Microscopy and chromatin-capture techniques have shown that chromatin has a complex organization, which dynamically changes across organisms and cell types. The need to make sense of such a fascinating complexity has prompted the development of quantitative models from physics, to find the principles of chromosome folding, its origin and function. Here, we concisely review recent advances in chromosome modeling, focusing on a recently proposed framework, the Strings & Binders Switch (SBS) model, which recapitulates key features of chromosome organization in space and time.

A thermodynamic switch for chromosome colocalization

A general model for the early recognition and colocalization of homologous DNA sequences is proposed. We show, on thermodynamic grounds, how the distance between two homologous DNA sequences is spontaneously regulated by the concentration and affinity of diffusible mediators binding them, which act as a switch between two phases corresponding to independence or colocalization of pairing regions.

Polymer physics of chromosome large-scale 3D organisation

Chromosomes have a complex architecture in the cell nucleus, which serves vital functional purposes, yet its structure and folding mechanisms remain still incompletely understood. Here we show that genome-wide chromatin architecture data, as mapped by Hi-C methods across mammalian cell types and chromosomes, are well described by classical scaling concepts of polymer physics, from the sub-Mb to chromosomal scales. Chromatin is a complex mixture of different regions, folded in the conformational classes predicted by polymer thermodynamics. The contact matrix of the Sox9 locus, a region linked to severe human congenital diseases, is derived with high accuracy in mESCs and its molecular determinants identified by the theory; Sox9 self-assembles hierarchically in higher-order domains, involving abundant many-body contacts. Our approach is also applied to the Bmp7 locus. Finally, the model predictions on the effects of mutations on folding are tested against available data on a deletion in the Xist locus. Our results can help progressing new diagnostic tools for diseases linked to chromatin misfolding.

A statistical mechanics approach to the inherent states of granular media

We consider a Statistical Mechanics approach to granular systems by following the original ideas developed by Edwards. We use the concept of “inherent states”, defined as the stable configurations in the potential energy landscape, introduced in the context of glasses. Under simplifying assumptions, the equilibrium inherent states can be characterized by a configurational temperature, 1/β. We link β to Edwards’ compactivity and address the problem of its experimental measure. We also discuss the possibility to describe the time dependent distribution probability in the inherent states with an appropriate master equation.