202 research outputs found
ATP hydrolysis stimulates large length fluctuations in single actin filaments
Polymerization dynamics of single actin filaments is investigated
theoretically using a stochastic model that takes into account the hydrolysis
of ATP-actin subunits, the geometry of actin filament tips, the lateral
interactions between the monomers as well as the processes at both ends of the
polymer. Exact analytical expressions are obtained for a mean growth velocity
and for dispersion in length fluctuations. It is found that the ATP hydrolysis
has a strong effect on dynamic properties of single actin filaments. At high
concentrations of free actin monomers the mean size of unhydrolyzed ATP-cap is
very large, and the dynamics is governed by association/dissociation of
ATP-actin subunits. However, at low concentrations the size of the cap becomes
finite, and the dissociation of ADP-actin subunits makes a significant
contribution to overall dynamics. Actin filament length fluctuations reach the
maximum at the boundary between two dynamic regimes, and this boundary is
always larger than the critical concentration. Random and vectorial mechanisms
of hydrolysis are compared, and it is found that they predict qualitatively
similar dynamic properties. The possibility of attachment and detachment of
oligomers is also discussed. Our theoretical approach is successfully applied
to analyze the latest experiments on the growth and length fluctuations of
individual actin filaments.Comment: Submitted to Biophysical Journa
Simple Growth Models of Rigid Multifilament Biopolymers
The growth dynamics of rigid biopolymers, consisting of parallel
protofilaments, is investigated theoretically using simple approximate models.
In our approach, the structure of a polymer's growing end and lateral
interactions between protofilaments are explicitly taken into account, and it
is argued that only few conformations are important for biopolymer's growth. As
a result, exact analytic expressions for growth velocity and dispersion are
obtained for {\it any} number of protofilaments and arbitrary geometry of the
growing end of the biopolymer. Our theoretical predictions are compared with a
full description of biopolymer growth dynamics for the simplest N=2 model. It
is found that the results from the approximate theory are approaching the exact
ones for large lateral interactions between the protofilaments. Our theory is
also applied to analyze the experimental data on the growth of microtubules.Comment: 18 pages, 6 figures, submitted to J. Chem. Phy
Transport of Single Molecules Along the Periodic Parallel Lattices with Coupling
General discrete one-dimensional stochastic models to describe the transport
of single molecules along coupled parallel lattices with period are
developed. Theoretical analysis that allows to calculate explicitly the
steady-state dynamic properties of single molecules, such as mean velocity
and dispersion , is presented for N=1 and N=2 models. For the systems with
exact analytic expressions for the large-time dynamic properties are
obtained in the limit of strong coupling between the lattices that leads to
dynamic equilibrium between two parallel kinetic pathways.Comment: Submitted to J. Chem. Phy
Coupling of Two Motor Proteins: a New Motor Can Move Faster
We study the effect of a coupling between two motor domains in
highly-processive motor protein complexes. A simple stochastic discrete model,
in which the two parts of the protein molecule interact through some energy
potential, is presented. The exact analytical solutions for the dynamic
properties of the combined motor species, such as the velocity and dispersion,
are derived in terms of the properties of free individual motor domains and the
interaction potential. It is shown that the coupling between the motor domains
can create a more efficient motor protein that can move faster than individual
particles. The results are applied to analyze the motion of helicase RecBCD
molecules
Self-Healing of Unentangled Polymer Networks with Reversible Bonds
Self-healing polymeric materials are systems that after damage can revert to their original state with full or partial recovery of mechanical strength. Using scaling theory we study a simple model of autonomic self-healing of unentangled polymer networks. In this model one of the two end monomers of each polymer chain is fixed in space mimicking dangling chains attachment to a polymer network, while the sticky monomer at the other end of each chain can form pairwise reversible bond with the sticky end of another chain. We study the reaction kinetics of reversible bonds in this simple model and analyze the different stages in the self-repair process. The formation of bridges and the recovery of the material strength across the fractured interface during the healing period occur appreciably faster after shorter waiting time, during which the fractured surfaces are kept apart. We observe the slowest formation of bridges for self-adhesion after bringing into contact two bare surfaces with equilibrium (very low) density of open stickers in comparison with self-healing. The primary role of anomalous diffusion in material self-repair for short waiting times is established, while at long waiting times the recovery of bonds across fractured interface is due to hopping diffusion of stickers between different bonded partners. Acceleration in bridge formation for self-healing compared to self-adhesion is due to excess non-equilibrium concentration of open stickers. Full recovery of reversible bonds across fractured interface (formation of bridges) occurs after appreciably longer time than the equilibration time of the concentration of reversible bonds in the bulk
Velocity and processivity of helicase unwinding of double-stranded nucleic acids
Helicases are molecular motors which unwind double-stranded nucleic acids
(dsNA) in cells. Many helicases move with directional bias on single-stranded
(ss) nucleic acids, and couple their directional translocation to strand
separation. A model of the coupling between translocation and unwinding uses an
interaction potential to represent passive and active helicase mechanisms. A
passive helicase must wait for thermal fluctuations to open dsNA base pairs
before it can advance and inhibit NA closing. An active helicase directly
destabilizes dsNA base pairs, accelerating the opening rate. Here we extend
this model to include helicase unbinding from the nucleic-acid strand. The
helicase processivity depends on the form of the interaction potential. A
passive helicase has a mean attachment time which does not change between ss
translocation and ds unwinding, while an active helicase in general shows a
decrease in attachment time during unwinding relative to ss translocation. In
addition, we describe how helicase unwinding velocity and processivity vary if
the base-pair binding free energy is changed.Comment: To appear in special issue on molecular motors, Journal of Physics -
Condensed Matte
Plasticization and antiplasticization of polymer melts diluted by low molar mass species
An analysis of glass formation for polymer melts that are diluted by
structured molecular additives is derived by using the generalized entropy
theory, which involves a combination of the Adam-Gibbs model and the direct
computation of the configurational entropy based on a lattice model of polymer
melts that includes monomer structural effects. Antiplasticization is
accompanied by a "toughening" of the glass mixture relative to the pure
polymer, and this effect is found to occur when the diluents are small species
with strongly attractive interactions with the polymer matrix. Plasticization
leads to a decreased glass transition temperature T_g and a "softening" of the
fragile host polymer in the glass state. Plasticization is prompted by small
additives with weakly attractive interactions with the polymer matrix. The
shifts in T_g of polystyrene diluted by fully flexible short oligomers are
evaluated from the computations, along with the relative changes in the
isothermal compressibility at T_g to characterize the extent to which the
additives act as antiplasticizers or plasticizers. The theory predicts that a
decreased fragility can accompany both antiplasticization and plasticization of
the glass by molecular additives. The general reduction in the T_g and
fragility of polymers by these molecular additives is rationalized by analyzing
the influence of the diluent's properties (cohesive energy, chain length, and
stiffness) on glass formation in diluted polymer melts. The description of
glass formation at fixed temperature that is induced upon change the fluid
composition directly implies the Angell equation for the structural relaxation
time as function of the polymer concentration, and the computed "zero mobility
concentration" scales linearly with the inverse polymerization index N.Comment: 12 pages, 15 figure
Understanding Mechanochemical Coupling in Kinesins Using First-Passage Time Processes
Kinesins are processive motor proteins that move along microtubules in a
stepwise manner, and their motion is powered by the hydrolysis of ATP. Recent
experiments have investigated the coupling between the individual steps of
single kinesin molecules and ATP hydrolysis, taking explicitly into account
forward steps, backward steps and detachments. A theoretical study of
mechanochemical coupling in kinesins, which extends the approach used
successfully to describe the dynamics of conventional motor proteins, is
presented. The possibility of irreversible detachments of kinesins from the
microtubules is also explicitly taken into account. Using the method of first-
passage times, experimental data on the mechanochemical coupling in kinesins
are fully described using the simplest two-state model. It is shown that the
dwell times for the kinesin to move one step forward or backward, or to
dissociate irreversibly are the same, although the probabilities of these
events are different. It is concluded that the current theoretical view, that
only the forward motion of the motor protein molecule is coupled to ATP
hydrolysis, is consistent with all available experimental observations for
kinesins.Comment: Submitted to Biophysical Journa
- …