487 research outputs found
Identification of drug resistance mutations in HIV from constraints on natural evolution
Human immunodeficiency virus (HIV) evolves with extraordinary rapidity.
However, its evolution is constrained by interactions between mutations in its
fitness landscape. Here we show that an Ising model describing these
interactions, inferred from sequence data obtained prior to the use of
antiretroviral drugs, can be used to identify clinically significant sites of
resistance mutations. Successful predictions of the resistance sites indicate
progress in the development of successful models of real viral evolution at the
single residue level, and suggest that our approach may be applied to help
design new therapies that are less prone to failure even where resistance data
is not yet available.Comment: 5 pages, 3 figure
Melting of persistent double-stranded polymers
Motivated by recent DNA-pulling experiments, we revisit the Poland-Scheraga
model of melting a double-stranded polymer. We include distinct bending
rigidities for both the double-stranded segments, and the single-stranded
segments forming a bubble. There is also bending stiffness at the branch points
between the two segment types. The transfer matrix technique for single
persistent chains is generalized to describe the branching bubbles. Properties
of spherical harmonics are then exploited in truncating and numerically solving
the resulting transfer matrix. This allows efficient computation of phase
diagrams and force-extension curves (isotherms). While the main focus is on
exposition of the transfer matrix technique, we provide general arguments for a
reentrant melting transition in stiff double strands. Our theoretical approach
can also be extended to study polymers with bubbles of any number of strands,
with potential applications to molecules such as collagen.Comment: 9 pages, 7 figure
Positive Feedback Regulation Results in Spatial Clustering and Fast Spreading of Active Signaling Molecules on a Cell Membrane
Positive feedback regulation is ubiquitous in cell signaling networks, often
leading to binary outcomes in response to graded stimuli. However, the role of
such feedbacks in clustering, and in spatial spreading of activated molecules,
has come to be appreciated only recently. We focus on the latter, using a
simple model developed in the context of Ras activation with competing negative
and positive feedback mechanisms. We find that positive feedback, in the
presence of slow diffusion, results in clustering of activated molecules on the
plasma membrane, and rapid spatial spreading as the front of the cluster
propagates with a constant velocity (dependent on the feedback strength). The
advancing fronts of the clusters of the activated species are rough, with
scaling consistent with the Kardar-Parisi-Zhang (KPZ) equation in one
dimension. Our minimal model is general enough to describe signal transduction
in a wide variety of biological networks where activity in the
membrane-proximal region is subject to feedback regulation.Comment: 37 pages, 8 figures. Journal of Chemical Physics (in press
How nonuniform contact profiles of T cell receptors modulate thymic selection outcomes
T cell receptors (TCRs) bind foreign or self-peptides attached to major
histocompatibility complex (MHC) molecules, and the strength of this
interaction determines T cell activation. Optimizing the ability of T cells to
recognize a diversity of foreign peptides yet be tolerant of self-peptides is
crucial for the adaptive immune system to properly function. This is achieved
by selection of T cells in the thymus, where immature T cells expressing
unique, stochastically generated TCRs interact with a large number of
self-peptide-MHC; if a TCR does not bind strongly enough to any
self-peptide-MHC, or too strongly with at least one self-peptide-MHC, the T
cell dies. Past theoretical work cast thymic selection as an extreme value
problem, and characterized the statistical enrichment or depletion of amino
acids in the post-selection TCR repertoire, showing how T cells are selected to
be able to specifically recognize peptides derived from diverse pathogens, yet
have limited self-reactivity. Here, we investigate how the degree of enrichment
is modified by nonuniform contacts that a TCR makes with peptide-MHC.
Specifically, we were motivated by recent experiments showing that amino acids
at certain positions of a TCR sequence have large effects on thymic selection
outcomes, and crystal structure data that reveal a nonuniform contact profile
between a TCR and its peptide-MHC ligand. Using a representative TCR contact
profile as an illustration, we show via simulations that the degree of
enrichment now varies by position according to the contact profile, and,
importantly, it depends on the implementation of nonuniform contacts during
thymic selection. We explain these nontrivial results analytically. Our study
has implications for understanding the selection forces that shape the
functionality of the post-selection TCR repertoire.Comment: 10 pages, 4 figures, submitted to Phys. Rev.
First order wetting of rough substrates and quantum unbinding
Replica and functional renormalization group methods show that, with short
range substrate forces or in strong fluctuation regimes, wetting of a
self-affine rough wall in 2D turns first-order as soon as the wall roughness
exponent exceeds the anisotropy index of bulk interface fluctuations. Different
thresholds apply with long range forces in mean field regimes. For
bond-disordered bulk, fixed point stability suggests similar results, which
ultimately rely on basic properties of quantum bound states with asymptotically
power-law repulsive potentials.Comment: 11 pages, 1 figur
Patterns in the Kardar-Parisi-Zhang equation
We review a recent asymptotic weak noise approach to the Kardar-Parisi-Zhang
equation for the kinetic growth of an interface in higher dimensions. The weak
noise approach provides a many body picture of a growing interface in terms of
a network of localized growth modes. Scaling in 1d is associated with a gapless
domain wall mode. The method also provides an independent argument for the
existence of an upper critical dimension.Comment: 8 pages revtex, 4 eps figure
Apex Exponents for Polymer--Probe Interactions
We consider self-avoiding polymers attached to the tip of an impenetrable
probe. The scaling exponents and , characterizing the
number of configurations for the attachment of the polymer by one end, or at
its midpoint, vary continuously with the tip's angle. These apex exponents are
calculated analytically by -expansion, and numerically by simulations
in three dimensions. We find that when the polymer can move through the
attachment point, it typically slides to one end; the apex exponents quantify
the entropic barrier to threading the eye of the probe
Scaling laws describe memories of host–pathogen riposte in the HIV population
The enormous genetic diversity and mutability of HIV has prevented effective control of this virus by natural immune responses or vaccination. Evolution of the circulating HIV population has thus occurred in response to diverse, ultimately ineffective, immune selection pressures that randomly change from host to host. We show that the interplay between the diversity of human immune responses and the ways that HIV mutates to evade them results in distinct sets of sequences defined by similar collectively coupled mutations. Scaling laws that relate these sets of sequences resemble those observed in linguistics and other branches of inquiry, and dynamics reminiscent of neural networks are observed. Like neural networks that store memories of past stimulation, the circulating HIV population stores memories of host–pathogen combat won by the virus. We describe an exactly solvable model that captures the main qualitative features of the sets of sequences and a simple mechanistic model for the origin of the observed scaling laws. Our results define collective mutational pathways used by HIV to evade human immune responses, which could guide vaccine design.Ragon Institute of MGH, MIT and Harvar
Energy Barriers to Motion of Flux Lines in Random Media
We propose algorithms for determining both lower and upper bounds for the
energy barriers encountered by a flux line in moving through a two-dimensional
random potential. Analytical arguments, supported by numerical simulations,
suggest that these bounds scale with the length of the line as
and , respectively. This provides the first confirmation
of the hypothesis that barriers have the same scaling as the fluctuation in the
free energy. \pacs{PACS numbers: 74.60.Ge, 05.70.Ln, 05.40.+j}Comment: 4 pages Revtex, 2 figures, to appear in PRL 75, 1170 (1995
Isobar of an ideal Bose gas within the grand canonical ensemble
We investigate the isobar of an ideal Bose gas confined in a cubic box within
the grand canonical ensemble, for a large yet finite number of particles, N.
After solving the equation of the spinodal curve, we derive precise formulae
for the supercooling and the superheating temperatures which reveal an N^{-1/3}
or N^{-1/4} power correction to the known Bose-Einstein condensation
temperature in the thermodynamic limit. Numerical computations confirm the
accuracy of our analytical approximation, and further show that the isobar
zigzags on the temperature-volume plane if N is greater than or equal to 14393.
In particular, for the Avogadro's number of particles, the volume expands
discretely about 10^5 times. Our results quantitatively agree with a previous
study on the canonical ensemble within 0.1% error.Comment: 6 pages, 2 figures; Reference added. Accepted for publication in
Phys. Rev.
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