466 research outputs found
The shape of a flexible polymer in a cylindrical pore
We calculate the mean end-to-end distance R of a self-avoiding polymer encapsulated in an infinitely long cylinder with radius D. A self-consistent perturbation theory is used to calculate R as a function of D for impenetrable hard walls and soft walls. In both cases, R obeys the predicted scaling behavior in the limit of large and small D. The crossover from the three-dimensional behavior (Dββ) to the fully stretched one-dimensional case (Dβ0) is nonmonotonic. The minimum value of R is found at D βΌ 0.46RF, where RF is the Flory radius of R at Dββ. The results for soft walls map onto the hard wall case with a larger cylinder radius
Generalized Erdos Numbers for network analysis
In this paper we consider the concept of `closeness' between nodes in a
weighted network that can be defined topologically even in the absence of a
metric. The Generalized Erd\H{o}s Numbers (GENs) satisfy a number of desirable
properties as a measure of topological closeness when nodes share a finite
resource between nodes as they are real-valued and non-local, and can be used
to create an asymmetric matrix of connectivities. We show that they can be used
to define a personalized measure of the importance of nodes in a network with a
natural interpretation that leads to a new global measure of centrality and is
highly correlated with Page Rank. The relative asymmetry of the GENs (due to
their non-metric definition) is linked also to the asymmetry in the mean first
passage time between nodes in a random walk, and we use a linearized form of
the GENs to develop a continuum model for `closeness' in spatial networks. As
an example of their practicality, we deploy them to characterize the structure
of static networks and show how it relates to dynamics on networks in such
situations as the spread of an epidemic
Visualisation techniques for users and designers of layout algorithms
Visualisation systems consisting of a set of components through which data and interaction commands flow have been explored by a number of researchers. Such hybrid and multistage algorithms can be used to reduce overall computation time, and to provide views of the data that show intermediate results and the outputs of complementary algorithms. In this paper we present work on expanding the range and variety of such components, with two new techniques for analysing and controlling the performance of visualisation processes. While the techniques presented are quite different, they are unified within HIVE: a visualisation system based upon a data-flow model and visual programming. Embodied within this system is a framework for weaving together our visualisation components to better afford insight into data and also deepen understanding of the process of the data's visualisation. We describe the new components and offer short case studies of their application. We demonstrate that both analysts and visualisation designers can benefit from a rich set of components and integrated tools for profiling performance
Correlation functions for strongly confined wormlike chains
Polymer models describing the statistics of biomolecules under confinement
have applications to a wide range of single molecule experimental techniques
and give insight into biologically relevant processes in vivo. In this paper, I
determine the transverse position and bending correlation functions for a
wormlike chain confined within slits and cylinders (with one and two confined
dimensions, respectively) using a mean field approach that enforces rigid
constraints on average. I show the theoretical predictions accurately capture
the statistics of a wormlike chain from Configurational Bias Monte Carlo
simulations in both confining geometries for both weak and strong confinement.
I also show that the longitudinal correlation function is accurately computed
for a chain confined to a slit, and leverage the accuracy of the model to
suggest an experimental technique to infer the (often unobservable) transverse
statistics from the (directly observable) longitudinal end-to-end distance
Theoretical Perspectives on Protein Folding
Understanding how monomeric proteins fold under in vitro conditions is
crucial to describing their functions in the cellular context. Significant
advances both in theory and experiments have resulted in a conceptual framework
for describing the folding mechanisms of globular proteins. The experimental
data and theoretical methods have revealed the multifaceted character of
proteins. Proteins exhibit universal features that can be determined using only
the number of amino acid residues (N) and polymer concepts. The sizes of
proteins in the denatured and folded states, cooperativity of the folding
transition, dispersions in the melting temperatures at the residue level, and
time scales of folding are to a large extent determined by N. The consequences
of finite N especially on how individual residues order upon folding depends on
the topology of the folded states. Such intricate details can be predicted
using the Molecular Transfer Model that combines simulations with measured
transfer free energies of protein building blocks from water to the desired
concentration of the denaturant. By watching one molecule fold at a time, using
single molecule methods, the validity of the theoretically anticipated
heterogeneity in the folding routes, and the N-dependent time scales for the
three stages in the approach to the native state have been established. Despite
the successes of theory, of which only a few examples are documented here, we
conclude that much remains to be done to solve the "protein folding problem" in
the broadest sense.Comment: 48 pages, 9 figure
Kinetics of Loop Formation in Polymer Chains
We investigate the kinetics of loop formation in flexible ideal polymer
chains (Rouse model), and polymers in good and poor solvents. We show for the
Rouse model, using a modification of the theory of Szabo, Schulten, and
Schulten, that the time scale for cyclization is (where
is a microscopic time scale and is the number of monomers),
provided the coupling between the relaxation dynamics of the end-to-end vector
and the looping dynamics is taken into account. The resulting analytic
expression fits the simulation results accurately when , the capture radius
for contact formation, exceeds , the average distance between two connected
beads. Simulations also show that, when , ,
where in the range used in the simulations.
By using a diffusion coefficient that is dependent on the length scales and
(with ), which captures the two-stage mechanism by which looping
occurs when , we obtain an analytic expression for that fits
the simulation results well. The kinetics of contact formation between the ends
of the chain are profoundly affected when interactions between monomers are
taken into account. Remarkably, for the values of decrease
by more than two orders of magnitude when the solvent quality changes from good
to poor. Fits of the simulation data for to a power law in
() show that varies from about 2.4 in
a good solvent to about 1.0 in poor solvents. Loop formation in poor solvents,
in which the polymer adopts dense, compact globular conformations, occurs by a
reptation-like mechanism of the ends of the chain.Comment: 30 pages, 9 figures. Revised version includes a new figure (8) and
minor changes to the tex
Scaling regimes for wormlike chains confined to cylindrical surfaces under tension
We compute the free energy of confinement for a wormlike chain
(WLC), with persistence length , that is confined to the surface of a
cylinder of radius under an external tension using a mean field
variational approach. For long chains, we analytically determine the behavior
of the chain in a variety of regimes, which are demarcated by the interplay of
, the Odijk deflection length (), and the Pincus
length (, with being the thermal energy). The theory
accurately reproduces the Odijk scaling for strongly confined chains at ,
with . For moderate values of , the Odijk
scaling is discernible only when for strongly confined chains.
Confinement does not significantly alter the scaling of the mean extension for
sufficiently high tension. The theory is used to estimate unwrapping forces for
DNA from nucleosomes.Comment: 17 pages, 4 figure
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