5,950 research outputs found
Anomalous transport in the crowded world of biological cells
A ubiquitous observation in cell biology is that diffusion of macromolecules
and organelles is anomalous, and a description simply based on the conventional
diffusion equation with diffusion constants measured in dilute solution fails.
This is commonly attributed to macromolecular crowding in the interior of cells
and in cellular membranes, summarising their densely packed and heterogeneous
structures. The most familiar phenomenon is a power-law increase of the MSD,
but there are other manifestations like strongly reduced and time-dependent
diffusion coefficients, persistent correlations, non-gaussian distributions of
the displacements, heterogeneous diffusion, and immobile particles. After a
general introduction to the statistical description of slow, anomalous
transport, we summarise some widely used theoretical models: gaussian models
like FBM and Langevin equations for visco-elastic media, the CTRW model, and
the Lorentz model describing obstructed transport in a heterogeneous
environment. Emphasis is put on the spatio-temporal properties of the transport
in terms of 2-point correlation functions, dynamic scaling behaviour, and how
the models are distinguished by their propagators even for identical MSDs.
Then, we review the theory underlying common experimental techniques in the
presence of anomalous transport: single-particle tracking, FCS, and FRAP. We
report on the large body of recent experimental evidence for anomalous
transport in crowded biological media: in cyto- and nucleoplasm as well as in
cellular membranes, complemented by in vitro experiments where model systems
mimic physiological crowding conditions. Finally, computer simulations play an
important role in testing the theoretical models and corroborating the
experimental findings. The review is completed by a synthesis of the
theoretical and experimental progress identifying open questions for future
investigation.Comment: review article, to appear in Rep. Prog. Phy
Field-Theoretic Simulations of Polyelectrolyte Complexation
We briefly discuss our recent field-theoretic study of polyelectrolyte
complexation, which occurs in solutions of two oppositely charged
polyelectrolytes. Charged systems require theoretical methods beyond the
mean-field (or self-consistent field) approximation; indeed, mean-field theory
is qualitatively incorrect for such polyelectrolyte solutions. Both analytical
(one-loop) and numerical (complex Langevin) methods to account for charge
correlations are discussed. In particular, the first application of
field-theoretic simulations to polyelectrolyte systems is reported. The
polyelectrolyte charge-charge correlation length and a phase diagram are
provided; effects of charge redistribution are qualitatively explored.Comment: 7 pages, 3 figures, 3 equations, LaTeX; accepted to Journal of
Polymer Science B: Polymer Physics; v2: a revised and expanded version, 6
paragraphs of text and about 20 references adde
Quasi-Chemical Theory and Implicit Solvent Models for Simulations
A statistical thermodynamic development is given of a new implicit solvent
model that avoids the traditional system size limitations of computer
simulation of macromolecular solutions with periodic boundary conditions. This
implicit solvent model is based upon the quasi-chemical approach, distinct from
the common integral equation trunk of the theory of liquid solutions. The
physical content of this theory is the hypothesis that a small set of solvent
molecules are decisive for these solvation problems. A detailed derivation of
the quasi-chemical theory escorts the development of this proposal. The
numerical application of the quasi-chemical treatment to Li ion hydration
in liquid water is used to motivate and exemplify the quasi-chemical theory.
Those results underscore the fact that the quasi-chemical approach refines the
path for utilization of ion-water cluster results for the statistical
thermodynamics of solutions.Comment: 30 pages, contribution to Santa Fe Workshop on Treatment of
Electrostatic Interactions in Computer Simulation of Condensed Medi
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
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