99 research outputs found
Protein secondary structure: Entropy, correlations and prediction
Is protein secondary structure primarily determined by local interactions
between residues closely spaced along the amino acid backbone, or by non-local
tertiary interactions? To answer this question we have measured the entropy
densities of primary structure and secondary structure sequences, and the local
inter-sequence mutual information density. We find that the important
inter-sequence interactions are short ranged, that correlations between
neighboring amino acids are essentially uninformative, and that only 1/4 of the
total information needed to determine the secondary structure is available from
local inter-sequence correlations. Since the remaining information must come
from non-local interactions, this observation supports the view that the
majority of most proteins fold via a cooperative process where secondary and
tertiary structure form concurrently. To provide a more direct comparison to
existing secondary structure prediction methods, we construct a simple hidden
Markov model (HMM) of the sequences. This HMM achieves a prediction accuracy
comparable to other single sequence secondary structure prediction algorithms,
and can extract almost all of the inter-sequence mutual information. This
suggests that these algorithms are almost optimal, and that we should not
expect a dramatic improvement in prediction accuracy. However, local
correlations between secondary and primary structure are probably of
under-appreciated importance in many tertiary structure prediction methods,
such as threading.Comment: 8 pages, 5 figure
Time step rescaling recovers continuous-time dynamical properties for discrete-time Langevin integration of nonequilibrium systems
When simulating molecular systems using deterministic equations of motion
(e.g., Newtonian dynamics), such equations are generally numerically integrated
according to a well-developed set of algorithms that share commonly agreed-upon
desirable properties. However, for stochastic equations of motion (e.g.,
Langevin dynamics), there is still broad disagreement over which integration
algorithms are most appropriate. While multiple desiderata have been proposed
throughout the literature, consensus on which criteria are important is absent,
and no published integration scheme satisfies all desiderata simultaneously.
Additional nontrivial complications stem from simulating systems driven out of
equilibrium using existing stochastic integration schemes in conjunction with
recently-developed nonequilibrium fluctuation theorems. Here, we examine a
family of discrete time integration schemes for Langevin dynamics, assessing
how each member satisfies a variety of desiderata that have been enumerated in
prior efforts to construct suitable Langevin integrators. We show that the
incorporation of a novel time step rescaling in the deterministic updates of
position and velocity can correct a number of dynamical defects in these
integrators. Finally, we identify a particular splitting that has essentially
universally appropriate properties for the simulation of Langevin dynamics for
molecular systems in equilibrium, nonequilibrium, and path sampling contexts.Comment: 15 pages, 2 figures, and 2 table
Bayesian estimates of free energies from nonequilibrium work data in the presence of instrument noise
The Jarzynski equality and the fluctuation theorem relate equilibrium free
energy differences to non-equilibrium measurements of the work. These relations
extend to single-molecule experiments that have probed the finite-time
thermodynamics of proteins and nucleic acids. The effects of experimental error
and instrument noise have not previously been considered. Here, we present a
Bayesian formalism for estimating free-energy changes from non-equilibrium work
measurements that compensates for instrument noise and combines data from
multiple driving protocols. We reanalyze a recent set of experiments in which a
single RNA hairpin is unfolded and refolded using optical tweezers at three
different rates. Interestingly, the fastest and farthest-from-equilibrium
measurements contain the least instrumental noise, and therefore provide a more
accurate estimate of the free energies than a few slow, more noisy,
near-equilibrium measurements. The methods we propose here will extend the
scope of single-molecule experiments; they can be used in the analysis of data
from measurements with AFM, optical, and magnetic tweezers.Comment: 8 page
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