arXiv subjects

Aleksandra M. Walczak

Publications and source records attributed to Aleksandra M. Walczak.

95 records · Page 6Linked to original sources

arXiv2008

Gene-gene cooperativity in small networks

We show how to construct a reduced description of interacting genes in noisy, small regulatory networks using coupled binary "spin" variables. Treating both the protein number and gene expression state variables stochastically and on equal footing we propose a mapping which connects the molecular level description of networks to the binary representation. We construct a phase diagram indicating when genes can be considered to be independent and when the coupling between them cannot be neglected leading to synchrony or correlations. We find that an appropriately mapped boolean description reproduces the probabilities of gene expression states of the full stochastic system very well and can be transfered to examples of self-regulatory systems with a larger number of gene copies.

q-bio.MN↗

arXiv2008

Constructing explicit magnetic analogies for the dynamics of glass forming liquids

By defining a spatially varying replica overlap parameter for a supercooled liquid referenced to an ensemble of fiducial liquid state configurations we explicitly construct a constrained replica free energy functional that maps directly onto an Ising Hamiltonian with both random fields and random interactions whose statistics depend on liquid structure. Renormalization group results for random magnets when combined with these statistics for the Lennard-Jones glass suggest that discontinuous replica symmetry breaking would occur if a liquid with short range interactions could be equilibrated at a sufficiently low temperature where its mean field configurational entropy would vanish, even though the system strictly retains a finite configurational entropy.

cond-mat.soft↗

arXiv2005

Absolute Rate Theories of Epigenetic Stability

Spontaneous switching events in most characterized genetic switches are rare, resulting in extremely stable epigenetic properties. We show how simple arguments lead to theories of the rate of such events much like the absolute rate theory of chemical reactions corrected by a transmission factor. Both the probability of the rare cellular states that allow epigenetic escape, and the transmission factor, depend on the rates of DNA binding and unbinding events and on the rates of protein synthesis and degradation. Different mechanisms of escape from the stable attractors occur in the nonadiabatic, weakly adiabatic and strictly adiabatic regimes, characterized by the relative values of those input rates.

q-bio.MN↗

arXiv2005

Exotic quantum phases and phase transitions in correlated matter

We present a pedagogical overview of recent theoretical work on unconventional quantum phases and quantum phase transitions in condensed matter systems. Strong correlations between electrons can lead to a breakdown of two traditional paradigms of solid state physics: Landau's theories of Fermi liquids and phase transitions. We discuss two resulting "exotic" states of matter: topological and critical spin liquids. These two quantum phases do not display any long-range order even at zero temperature. In each case, we show how a gauge theory description is useful to describe the new concepts of topological order, fractionalization and deconfinement of excitations which can be present in such spin liquids. We make brief connections, when possible, to experiments in which the corresponding physics can be probed. Finally, we review recent work on deconfined quantum critical points. The tone of these lecture notes is expository: focus is on gaining a physical picture and understanding, with technical details kept to a minimum.

cond-mat.str-el↗

arXiv2004

Self consistent proteomic field theory of stochastic gene switches

We present a self-consistent field approximation to the problem of the genetic switch composed of two mutually repressing/activating genes. The protein and DNA state dynamics are treated stochastically and on equal footing. In this approach the mean influence of the proteomic cloud created by one gene on the action of another is self-consistently computed. Within this approximation a broad range of stochastic genetic switches may be solved exactly in terms of finding the probability distribution and its moments. A much larger class of problems, such as genetic networks and cascades also remain exactly solvable with this approximation. We discuss in depth certain specific types of basic switches, which are used by biological systems and compare their behavior to the expectation for a deterministic switch.

q-bio.MN↗