arXiv subjects

Leonid Mirny

Publications and source records attributed to Leonid Mirny.

6 recordsLinked to original sources

arXiv2014

Effects of topological constraints on globular polymers

Topological constraints can affect both equilibrium and dynamic properties of polymer systems, and can play a role in the organization of chromosomes. Despite many theoretical studies, the effects of topological constraints on the equilibrium state of a single compact polymer have not been systematically studied. Here we use simulations to address this longstanding problem. We find that sufficiently long unknotted polymers differ from knotted ones in the spatial and topological states of their subchains. The unknotted globule has subchains that are mostly unknotted and form asymptotically compact $R_G(s) \sim s^{1/3}$ crumples. However, crumples display high fractal dimension of the surface $d_b = 2.8$, forming excessive contacts and interpenetrating each other. We conclude that this topologically constrained equilibrium state resembles a conjectured crumpled globule [Grosberg et al., Journal de Physique, 1988, 49, 2095], but differs from its idealized hierarchy of self-similar, isolated and compact crumples.

cond-mat.soft↗

arXiv2014

A tug-of-war between driver and passenger mutations in cancer and other adaptive processes

Cancer progression is an example of a rapid adaptive process where evolving new traits is essential for survival and requires a high mutation rate. Precancerous cells acquire a few key mutations that drive rapid population growth and carcinogenesis. Cancer genomics demonstrates that these few 'driver' mutations occur alongside thousands of random 'passenger' mutations-a natural consequence of cancer's elevated mutation rate. Some passengers can be deleterious to cancer cells, yet have been largely ignored in cancer research. In population genetics, however, the accumulation of mildly deleterious mutations has been shown to cause population meltdown. Here we develop a stochastic population model where beneficial drivers engage in a tug-of-war with frequent mildly deleterious passengers. These passengers present a barrier to cancer progression that is described by a critical population size, below which most lesions fail to progress, and a critical mutation rate, above which cancers meltdown. We find support for the model in cancer age-incidence and cancer genomics data that also allow us to estimate the fitness advantage of drivers and fitness costs of passengers. We identify two regimes of adaptive evolutionary dynamics and use these regimes to rationalize successes and failures of different treatment strategies. We find that a tumor's load of deleterious passengers can explain previously paradoxical treatment outcomes and suggest that it could potentially serve as a biomarker of response to mutagenic therapies. Collective deleterious effect of passengers is currently an unexploited therapeutic target. We discuss how their effects might be exacerbated by both current and future therapies.

q-bio.PE↗

arXiv2012

The impact of deleterious passenger mutations on cancer progression

Cancer progression is driven by a small number of genetic alterations accumulating in a neoplasm. These few driver alterations reside in a cancer genome alongside tens of thousands of other mutations that are widely believed to have no role in cancer and termed passengers. Many passengers, however, fall within protein coding genes and other functional elements and can possibly have deleterious effects on cancer cells. Here we investigate a potential of mildly deleterious passengers to accumulate and alter the course of neoplastic progression. Our approach combines evolutionary simulations of cancer progression with the analysis of cancer sequencing data. In our simulations, individual cells stochastically divide, acquire advantageous driver and deleterious passenger mutations, or die. Surprisingly, despite selection against them, passengers accumulate and largely evade selection during progression. Although individually weak, the collective burden of passengers alters the course of progression leading to several phenomena observed in oncology that cannot be explained by a traditional driver-centric view. We tested predictions of the model using cancer genomic data. We find that many passenger mutations are likely to be damaging and that, in agreement with the model, they have largely evaded purifying selection. Finally, we used our model to explore cancer treatments that exploit the load of passengers by either 1) increasing the mutation rate; or 2) exacerbating their deleterious effects. While both approaches lead to cancer regression, the later leads to less frequent relapse. Our results suggest a new framework for understanding cancer progression as a balance of driver and passenger mutations.

q-bio.PE↗

arXiv2011

High-order chromatin architecture determines the landscape of chromosomal alterations in cancer

The rapid growth of cancer genome structural information provides an opportunity for a better understanding of the mutational mechanisms of genomic alterations in cancer and the forces of selection that act upon them. Here we test the evidence for two major forces, spatial chromosome structure and purifying (or negative) selection, that shape the landscape of somatic copy-number alterations (SCNAs) in cancer1. Using a maximum likelihood framework we compare SCNA maps and three-dimensional genome architecture as determined by genome-wide chromosome conformation capture (HiC) and described by the proposed fractal-globule (FG) model2. This analysis provides evidence that the distribution of chromosomal alterations in cancer is spatially related to three-dimensional genomic architecture and additionally suggests that purifying selection as well as positive selection shapes the landscape of SCNAs during somatic evolution of cancer cells.

q-bio.GN↗

arXiv2003

Virus shapes and buckling transitions in spherical shells

We show that the icosahedral packings of protein capsomeres proposed by Caspar and Klug for spherical viruses become unstable to faceting for sufficiently large virus size, in analogy with the buckling instability of disclinations in two-dimensional crystals. Our model, based on the nonlinear physics of thin elastic shells, produces excellent one parameter fits in real space to the full three-dimensional shape of large spherical viruses. The faceted shape depends only on the dimensionless Foppl-von Karman number γ=YR^2/κ, where Y is the two-dimensional Young's modulus of the protein shell, κis its bending rigidity and R is the mean virus radius. The shape can be parameterized more quantitatively in terms of a spherical harmonic expansion. We also investigate elastic shell theory for extremely large γ, 10^3 < γ< 10^8, and find results applicable to icosahedral shapes of large vesicles studied with freeze fracture and electron microscopy.

cond-mat.soft↗

arXiv2000

Evolutionary conservation of the folding nucleus

In this Communication we present statistical analysis of conservation profiles in families of homologous sequences for nine proteins whose folding nucleus was determined by protein engineering methods. We show that in all but one protein (AcP) folding nucleus residues are significantly more conserved than the rest of the protein. Two aspects of our study are especially important: 1) grouping of amino acids into classes according to their physical-chemical properties and 2) proper normalization of amino acid probabilities that reflects the fact that evolutionary pressure to conserve some amino acid types may itself affect concentration of various amino acid types in protein families. Neglect of any of those two factors may make physical and biological ``signals'' from conservation profiles disappear.

physics.bio-ph↗