19 research outputs found
Stochasticity of gene products from transcriptional pulsing
Transcriptional pulsing has been observed in both prokaryotes and eukaryotes and plays a crucial role in cell-to-cell variability of protein and mRNA numbers. An important issue is how the time constants associated with episodes of transcriptional bursting and mRNA and protein degradation rates lead to different cellular mRNA and protein distributions, starting from the transient regime leading to the steady state. We address this by deriving and then investigating the exact time-dependent solution of the master equation for a transcriptional pulsing model of mRNA distributions. We find a plethora of results. We show that, among others, bimodal and long-tailed (power-law) distributions occur in the steady state as the rate constants are varied over biologically significant time scales. Since steady state may not be reached experimentally we present results for the time evolution of the distributions. Because cellular behavior is determined by proteins, we also investigate the effect of the different mRNA distributions on the corresponding protein distributions using numerical simulations
Scaling laws governing stochastic growth and division of single bacterial cells
Uncovering the quantitative laws that govern the growth and division of
single cells remains a major challenge. Using a unique combination of
technologies that yields unprecedented statistical precision, we find that the
sizes of individual Caulobacter crescentus cells increase exponentially in
time. We also establish that they divide upon reaching a critical multiple
(1.8) of their initial sizes, rather than an absolute size. We show
that when the temperature is varied, the growth and division timescales scale
proportionally with each other over the physiological temperature range.
Strikingly, the cell-size and division-time distributions can both be rescaled
by their mean values such that the condition-specific distributions collapse to
universal curves. We account for these observations with a minimal stochastic
model that is based on an autocatalytic cycle. It predicts the scalings, as
well as specific functional forms for the universal curves. Our experimental
and theoretical analysis reveals a simple physical principle governing these
complex biological processes: a single temperature-dependent scale of cellular
time governs the stochastic dynamics of growth and division in balanced growth
conditions.Comment: Text+Supplementar
Gravitational Response of Topological Quantum States of Matter
Identifying novel topological properties of topological quantum states of
matter, such as exemplified by the quantized Hall conductance, is a valuable
step towards realizing materials with attractive topological attributes that
guarantee their imperviousness to realistic imperfections, disorder and
environmental disturbances. Is the gravitational coupling coefficient of
topological quantum states of matter a promising candidate? Substantially
building on well established results for quantum Hall states, using
disclinations as tools for controlled creation of pristine spatial curvature
free of undesirable artifacts such as would interfere with the electronic
motion of interest, herein we report that a large class of lattice topological
states of matter exhibit gravitational response, i.e., charge response to
intrinsic spatial curvature. This phenomenon is characterized by a
topologically quantized coupling constant. Remarkably, the charge-gravity
relationship remains linear in the curvature, up to the maximum curvature
achievable on the lattice, demonstrating absence of higher order nonlinear
response. Our findings facilitate articulating the physical principles
underlying the topological quantization of the gravitational coupling constant,
in analogy with the insights offered by the Chern number description of the
quantized Hall conductance