240 research outputs found
Maximum entropy models for antibody diversity
Recognition of pathogens relies on families of proteins showing great
diversity. Here we construct maximum entropy models of the sequence repertoire,
building on recent experiments that provide a nearly exhaustive sampling of the
IgM sequences in zebrafish. These models are based solely on pairwise
correlations between residue positions, but correctly capture the higher order
statistical properties of the repertoire. Exploiting the interpretation of
these models as statistical physics problems, we make several predictions for
the collective properties of the sequence ensemble: the distribution of
sequences obeys Zipf's law, the repertoire decomposes into several clusters,
and there is a massive restriction of diversity due to the correlations. These
predictions are completely inconsistent with models in which amino acid
substitutions are made independently at each site, and are in good agreement
with the data. Our results suggest that antibody diversity is not limited by
the sequences encoded in the genome, and may reflect rapid adaptation to
antigenic challenges. This approach should be applicable to the study of the
global properties of other protein families
Dynamics of magnetization coupled to a thermal bath of elastic modes
We study the dynamics of magnetization coupled to a thermal bath of elastic
modes using a system plus reservoir approach with realistic magnetoelastic
coupling. After integrating out the elastic modes we obtain a self-contained
equation for the dynamics of the magnetization.
We find explicit expressions for the memory friction kernel and hence, {\em
via} the Fluctuation-Dissipation
Theorem, for the spectral density of the magnetization thermal fluctuations.
For magnetic samples in which the single domain approximation is valid, we
derive an equation for the dynamics of the uniform mode.
Finally we apply this equation to study the dynamics of the uniform
magnetization mode in insulating ferromagnetic thin films.
As experimental consequences we find that the fluctuation correlation time is
of the order of the ratio between the film thickness, , and the speed of
sound in the magnet and that the line-width of the ferromagnetic resonance peak
should scale as where is the magnetoelastic coupling constant.Comment: Revised version as appeared in print. 12 pages 9 figure
Time evolution towards q-Gaussian stationary states through unified Ito-Stratonovich stochastic equation
We consider a class of single-particle one-dimensional stochastic equations
which include external field, additive and multiplicative noises. We use a
parameter which enables the unification of the traditional
It\^o and Stratonovich approaches, now recovered respectively as the
and particular cases to derive the associated Fokker-Planck
equation (FPE). These FPE is a {\it linear} one, and its stationary state is
given by a -Gaussian distribution with , where characterizes the
strength of the confining external field, and is the (normalized)
amplitude of the multiplicative noise. We also calculate the standard kurtosis
and the -generalized kurtosis (i.e., the standard
kurtosis but using the escort distribution instead of the direct one). Through
these two quantities we numerically follow the time evolution of the
distributions. Finally, we exhibit how these quantities can be used as
convenient calibrations for determining the index from numerical data
obtained through experiments, observations or numerical computations.Comment: 9 pages, 2 figure
Conformational Dependence of a Protein Kinase Phosphate Transfer Reaction
Atomic motions and energetics for a phosphate transfer reaction catalyzed by
the cAMP-dependent protein kinase (PKA) are calculated by plane-wave density
functional theory, starting from structures of proteins crystallized in both
the reactant conformation (RC) and the transition-state conformation (TC). In
the TC, we calculate that the reactants and products are nearly isoenergetic
with a 0.2 eV barrier; while phosphate transfer is unfavorable by over 1.2 eV
in the RC, with an even higher barrier. With the protein in the TC, the motions
involved in reaction are small, with only P and the catalytic proton
moving more than 0.5 \AA. Examination of the structures reveals that in the RC
the active site cleft is not completely closed and there is insufficient space
for the phosphorylated serine residue in the product state. Together, these
observations imply that the phosphate transfer reaction occurs rapidly and
reversibly in a particular conformation of the protein, and that the reaction
can be gated by changes of a few tenths of an \AA in the catalytic site.Comment: revtex4, 7 pages, 4 figures, to be submitted to Scienc
Thermal conductivity of one-dimensional lattices with self-consistent heat baths: a heuristic derivation
We derive the thermal conductivities of one-dimensional harmonic and
anharmonic lattices with self-consistent heat baths (BRV lattice) from the
Single-Mode Relaxation Time (SMRT) approximation. For harmonic lattice, we
obtain the same result as previous works. However, our approach is heuristic
and reveals phonon picture explicitly within the heat transport process. The
results for harmonic and anharmonic lattices are compared with numerical
calculations from Green-Kubo formula. The consistency between derivation and
simulation strongly supports that effective (renormalized) phonons are energy
carriers in anharmonic lattices although there exist some other excitations
such as solitons and breathers.Comment: 4 pages, 3 figures. accepted for publication in JPS
Dynamics of barrier penetration in thermal medium: exact result for inverted harmonic oscillator
Time evolution of quantum tunneling is studied when the tunneling system is
immersed in thermal medium. We analyze in detail the behavior of the system
after integrating out the environment. Exact result for the inverted harmonic
oscillator of the tunneling potential is derived and the barrier penetration
factor is explicitly worked out as a function of time. Quantum mechanical
formula without environment is modifed both by the potential renormalization
effect and by a dynamical factor which may appreciably differ from the
previously obtained one in the time range of 1/(curvature at the top of
potential barrier).Comment: 30 pages, LATEX file with 11 PS figure
Connected Network of Minima as a Model Glass: Long Time Dynamics
A simple model to investigate the long time dynamics of glass-formers is
presented and applied to study a Lennard-Jones system in supercooled and glassy
phases. According to our model, the point representing the system in the
configurational phase space performs harmonic vibrations around (and activated
jumps between) minima pertaining to a connected network. Exploiting the model,
in agreement with the experimental results, we find evidence for: i) stretched
relaxational dynamics; ii) a strong T-dependence of the stretching parameter;
iii) breakdown of the Stokes-Einstein law.Comment: 4 pages (Latex), 4 eps figure
Polarons as Nucleation Droplets in Non-Degenerate Polymers
We present a study of the nucleation mechanism that allows the decay of the
metastable phase (trans-cisoid) to the stable phase
(cis-transoid) in quasi one-dimensional non-degenerate polymers within the
continuum electron-phonon model. The electron-phonon configurations that lead
to the decay, i.e. the critical droplets (or transition state), are identified
as polarons of the metastable phase. We obtain an estimate for the decay rate
via thermal activation within a range of parameters consistent with
experimental values for the gap of the cis-configuration. It is pointed out
that, upon doping, the activation barriers of the excited states are quite
smaller and the decay rate is greatly enhanced. Typical activation energies for
electron or hole polarons are eV and the typical size for a
critical droplet (polaron) is about . Decay via quantum nucleation is
also studied and it is found that the crossover temperature between quantum
nucleation and thermal activation is of order . Metastable
configurations of non-degenerate polymers may provide examples for mesoscopic
quantum tunneling.Comment: REVTEX 3.0, 28 PAGES, 3 FIGURES AVAILABLE UPON REQUEST, PITT 94-0
Work and heat fluctuations in two-state systems: a trajectory thermodynamics formalism
Two-state models provide phenomenological descriptions of many different
systems, ranging from physics to chemistry and biology. We investigate work
fluctuations in an ensemble of two-state systems driven out of equilibrium
under the action of an external perturbation. We calculate the probability
density P(W) that a work equal to W is exerted upon the system along a given
non-equilibrium trajectory and introduce a trajectory thermodynamics formalism
to quantify work fluctuations in the large-size limit. We then define a
trajectory entropy S(W) that counts the number of non-equilibrium trajectories
P(W)=exp(S(W)/kT) with work equal to W. A trajectory free-energy F(W) can also
be defined, which has a minimum at a value of the work that has to be
efficiently sampled to quantitatively test the Jarzynski equality. Within this
formalism a Lagrange multiplier is also introduced, the inverse of which plays
the role of a trajectory temperature. Our solution for P(W) exactly satisfies
the fluctuation theorem by Crooks and allows us to investigate
heat-fluctuations for a protocol that is invariant under time reversal. The
heat distribution is then characterized by a Gaussian component (describing
small and frequent heat exchange events) and exponential tails (describing the
statistics of large deviations and rare events). For the latter, the width of
the exponential tails is related to the aforementioned trajectory temperature.
Finite-size effects to the large-N theory and the recovery of work
distributions for finite N are also discussed. Finally, we pay particular
attention to the case of magnetic nanoparticle systems under the action of a
magnetic field H where work and heat fluctuations are predicted to be
observable in ramping experiments in micro-SQUIDs.Comment: 28 pages, 14 figures (Latex
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