6,480 research outputs found
Detailed balance has a counterpart in non-equilibrium steady states
When modelling driven steady states of matter, it is common practice either
to choose transition rates arbitrarily, or to assume that the principle of
detailed balance remains valid away from equilibrium. Neither of those
practices is theoretically well founded. Hypothesising ergodicity constrains
the transition rates in driven steady states to respect relations analogous to,
but different from the equilibrium principle of detailed balance. The
constraints arise from demanding that the design of any model system contains
no information extraneous to the microscopic laws of motion and the macroscopic
observables. This prevents over-description of the non-equilibrium reservoir,
and implies that not all stochastic equations of motion are equally valid. The
resulting recipe for transition rates has many features in common with
equilibrium statistical mechanics.Comment: Replaced with minor revisions to introduction and conclusions.
Accepted for publication in Journal of Physics
Exploring the Free Energy Landscape: From Dynamics to Networks and Back
The knowledge of the Free Energy Landscape topology is the essential key to
understand many biochemical processes. The determination of the conformers of a
protein and their basins of attraction takes a central role for studying
molecular isomerization reactions. In this work, we present a novel framework
to unveil the features of a Free Energy Landscape answering questions such as
how many meta-stable conformers are, how the hierarchical relationship among
them is, or what the structure and kinetics of the transition paths are.
Exploring the landscape by molecular dynamics simulations, the microscopic data
of the trajectory are encoded into a Conformational Markov Network. The
structure of this graph reveals the regions of the conformational space
corresponding to the basins of attraction. In addition, handling the
Conformational Markov Network, relevant kinetic magnitudes as dwell times or
rate constants, and the hierarchical relationship among basins, complete the
global picture of the landscape. We show the power of the analysis studying a
toy model of a funnel-like potential and computing efficiently the conformers
of a short peptide, the dialanine, paving the way to a systematic study of the
Free Energy Landscape in large peptides.Comment: PLoS Computational Biology (in press
MSM/RD: Coupling Markov state models of molecular kinetics with reaction-diffusion simulations
Molecular dynamics (MD) simulations can model the interactions between
macromolecules with high spatiotemporal resolution but at a high computational
cost. By combining high-throughput MD with Markov state models (MSMs), it is
now possible to obtain long-timescale behavior of small to intermediate
biomolecules and complexes. To model the interactions of many molecules at
large lengthscales, particle-based reaction-diffusion (RD) simulations are more
suitable but lack molecular detail. Thus, coupling MSMs and RD simulations
(MSM/RD) would be highly desirable, as they could efficiently produce
simulations at large time- and lengthscales, while still conserving the
characteristic features of the interactions observed at atomic detail. While
such a coupling seems straightforward, fundamental questions are still open:
Which definition of MSM states is suitable? Which protocol to merge and split
RD particles in an association/dissociation reaction will conserve the correct
bimolecular kinetics and thermodynamics? In this paper, we make the first step
towards MSM/RD by laying out a general theory of coupling and proposing a first
implementation for association/dissociation of a protein with a small ligand (A
+ B C). Applications on a toy model and CO diffusion into the heme cavity
of myoglobin are reported
Path Similarity Analysis: a Method for Quantifying Macromolecular Pathways
Diverse classes of proteins function through large-scale conformational
changes; sophisticated enhanced sampling methods have been proposed to generate
these macromolecular transition paths. As such paths are curves in a
high-dimensional space, they have been difficult to compare quantitatively, a
prerequisite to, for instance, assess the quality of different sampling
algorithms. The Path Similarity Analysis (PSA) approach alleviates these
difficulties by utilizing the full information in 3N-dimensional trajectories
in configuration space. PSA employs the Hausdorff or Fr\'echet path
metrics---adopted from computational geometry---enabling us to quantify path
(dis)similarity, while the new concept of a Hausdorff-pair map permits the
extraction of atomic-scale determinants responsible for path differences.
Combined with clustering techniques, PSA facilitates the comparison of many
paths, including collections of transition ensembles. We use the closed-to-open
transition of the enzyme adenylate kinase (AdK)---a commonly used testbed for
the assessment enhanced sampling algorithms---to examine multiple microsecond
equilibrium molecular dynamics (MD) transitions of AdK in its substrate-free
form alongside transition ensembles from the MD-based dynamic importance
sampling (DIMS-MD) and targeted MD (TMD) methods, and a geometrical targeting
algorithm (FRODA). A Hausdorff pairs analysis of these ensembles revealed, for
instance, that differences in DIMS-MD and FRODA paths were mediated by a set of
conserved salt bridges whose charge-charge interactions are fully modeled in
DIMS-MD but not in FRODA. We also demonstrate how existing trajectory analysis
methods relying on pre-defined collective variables, such as native contacts or
geometric quantities, can be used synergistically with PSA, as well as the
application of PSA to more complex systems such as membrane transporter
proteins.Comment: 9 figures, 3 tables in the main manuscript; supplementary information
includes 7 texts (S1 Text - S7 Text) and 11 figures (S1 Fig - S11 Fig) (also
available from journal site
Weak ergodicity breaking of receptor motion in living cells stemming from random diffusivity
Molecular transport in living systems regulates numerous processes underlying
biological function. Although many cellular components exhibit anomalous
diffusion, only recently has the subdiffusive motion been associated with
nonergodic behavior. These findings have stimulated new questions for their
implications in statistical mechanics and cell biology. Is nonergodicity a
common strategy shared by living systems? Which physical mechanisms generate
it? What are its implications for biological function? Here, we use single
particle tracking to demonstrate that the motion of DC-SIGN, a receptor with
unique pathogen recognition capabilities, reveals nonergodic subdiffusion on
living cell membranes. In contrast to previous studies, this behavior is
incompatible with transient immobilization and therefore it can not be
interpreted according to continuous time random walk theory. We show that the
receptor undergoes changes of diffusivity, consistent with the current view of
the cell membrane as a highly dynamic and diverse environment. Simulations
based on a model of ordinary random walk in complex media quantitatively
reproduce all our observations, pointing toward diffusion heterogeneity as the
cause of DC-SIGN behavior. By studying different receptor mutants, we further
correlate receptor motion to its molecular structure, thus establishing a
strong link between nonergodicity and biological function. These results
underscore the role of disorder in cell membranes and its connection with
function regulation. Due to its generality, our approach offers a framework to
interpret anomalous transport in other complex media where dynamic
heterogeneity might play a major role, such as those found, e.g., in soft
condensed matter, geology and ecology.Comment: 27 pages, 5 figure
Deep Self-Taught Learning for Handwritten Character Recognition
Recent theoretical and empirical work in statistical machine learning has
demonstrated the importance of learning algorithms for deep architectures,
i.e., function classes obtained by composing multiple non-linear
transformations. Self-taught learning (exploiting unlabeled examples or
examples from other distributions) has already been applied to deep learners,
but mostly to show the advantage of unlabeled examples. Here we explore the
advantage brought by {\em out-of-distribution examples}. For this purpose we
developed a powerful generator of stochastic variations and noise processes for
character images, including not only affine transformations but also slant,
local elastic deformations, changes in thickness, background images, grey level
changes, contrast, occlusion, and various types of noise. The
out-of-distribution examples are obtained from these highly distorted images or
by including examples of object classes different from those in the target test
set. We show that {\em deep learners benefit more from out-of-distribution
examples than a corresponding shallow learner}, at least in the area of
handwritten character recognition. In fact, we show that they beat previously
published results and reach human-level performance on both handwritten digit
classification and 62-class handwritten character recognition
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