33 research outputs found
Molecular Dynamics of the Proline Switch and Its Role in Crk Signaling
The Crk adaptor proteins play a central
role as a molecular timer
for the formation of protein complexes including various growth and
differentiation factors. The loss of regulation of Crk results in
many kinds of cancers. A self-regulatory mechanism for Crk was recently
proposed, which involves domainâdomain rearrangement. It is
initiated by a cisâtrans isomerization of a specific proline
residue (Pro238 in chicken Crk II) and can be accelerated by Cyclophilin
A. To understand how the proline switch controls the autoinhibition
at the molecular level, we performed large-scale molecular dynamics
and metadynamics simulations in the context of short peptides and
multidomain constructs of chicken Crk II. We found that the equilibrium
and kinetic properties of the macrostates are regulated not only by
the local environments of specified prolines but also by the global
organization of multiple domains. We observe the two macrostates (cis
closed/autoinhibited and trans open/uninhibited) consistent with NMR
experiments and predict barriers. We also propose an intermediate
state, the trans closed state, which interestingly was reported to
be a prevalent state in human Crk II. The existence of this macrostate
suggests that the rate of switching off the autoinhibition by Cyp
A may be limited by the relaxation rate of this intermediate state
Improving Prediction Accuracy of Binding Free Energies and Poses of HIV Integrase Complexes Using the Binding Energy Distribution Analysis Method with Flattening Potentials
To accelerate conformation
sampling of slow dynamics from receptor
or ligand, we introduced flattening potentials on selected bonded
and nonbonded intramolecular interactions to the binding energy distribution
analysis method (BEDAM) for calculating absolute binding free energies
of proteinâligand complexes using an implicit solvent model
and implemented flattening BEDAM using the asynchronous replica exchange
(AsyncRE) framework for performing large scale replica exchange molecular
dynamics (REMD) simulations. The advantage of using the flattening
feature to reduce high energy barriers was exhibited first by the <i>p</i>-xylene-T4 lysozyme complex, where the intramolecular interactions
of a protein side chain on the binding site were flattened to accelerate
the conformational transition of the side chain from the <i>trans</i> to the <i>gauche</i> state when the <i>p</i>-xylene ligand is present in the binding site. Much more extensive
flattening BEDAM simulations were performed for 53 experimental binders
and 248 nonbinders of HIV-1 integrase which formed the SAMPL4 challenge,
with the total simulation time of 24.3 Îźs. We demonstrated that
the flattening BEDAM simulations not only substantially increase the
number of true positives (and reduce false negatives) but also improve
the prediction accuracy of binding poses of experimental binders.
Furthermore, the values of area under the curve (AUC) of receiver
operating characteristic (ROC) and the enrichment factors at 20% cutoff
calculated from the flattening BEDAM simulations were improved significantly
in comparison with that of simulations without flattening as we previously
reported for the whole SAMPL4 database. Detailed analysis found that
the improved ability to discriminate the binding free energies between
the binders and nonbinders is due to the fact that the flattening
simulations reduce the reorganization free energy penalties of binders
and decrease the overlap of binding free energy distributions of binders
relative to that of nonbinders. This happens because the conformational
ensemble distributions for both the ligand and protein in solution
match those at the fully coupled (complex) state more closely when
the systems are more fully sampled after the flattening potentials
are applied to the intermediate states
How Kinetics within the Unfolded State Affects Protein Folding: An Analysis Based on Markov State Models and an Ultra-Long MD Trajectory
Understanding
how kinetics in the unfolded state affects protein folding is a fundamentally
important yet less well-understood issue. Here we employ three different
models to analyze the unfolded landscape and folding kinetics of the
miniprotein Trp-cage. The first is a 208 Îźs explicit solvent
molecular dynamics (MD) simulation from D. E. Shaw Research containing
tens of folding events. The second is a Markov state model (MSM-MD)
constructed from the same ultralong MD simulation; MSM-MD can be used
to generate thousands of folding events. The third is a Markov state
model built from temperature replica exchange MD simulations in implicit
solvent (MSM-REMD). All the models exhibit multiple folding pathways,
and there is a good correspondence between the folding pathways from
direct MD and those computed from the MSMs. The unfolded populations
interconvert rapidly between extended and collapsed conformations
on time scales â¤40 ns, compared with the folding time of âź5
Îźs. The folding rates are independent of where the folding is
initiated from within the unfolded ensemble. About 90% of the unfolded
states are sampled within the first 40 Îźs of the ultralong MD
trajectory, which on average explores âź27% of the unfolded
state ensemble between consecutive folding events. We clustered the
folding pathways according to structural similarity into âtubesâ,
and kinetically partitioned the unfolded state into populations that
fold along different tubes. From our analysis of the simulations and
a simple kinetic model, we find that, when the mixing within the unfolded
state is comparable to or faster than folding, the folding waiting
times for all the folding tubes are similar and the folding kinetics
is essentially single exponential despite the presence of heterogeneous
folding paths with nonuniform barriers. When the mixing is much slower
than folding, different unfolded populations fold independently, leading
to nonexponential kinetics. A kinetic partition of the Trp-cage unfolded
state is constructed which reveals that different unfolded populations
have almost the same probability to fold along any of the multiple
folding paths. We are investigating whether the results for the kinetics
in the unfolded state of the 20-residue Trp-cage is representative
of larger single domain proteins
Contingency and Entrenchment of Drug-Resistance Mutations in HIV Viral Proteins
The
ability of HIV-1 to rapidly mutate leads to antiretroviral
therapy (ART) failure among infected patients. Drug-resistance mutations
(DRMs), which cause a fitness penalty to intrinsic viral fitness,
are compensated by accessory mutations with favorable epistatic interactions
which cause an evolutionary trapping effect, but the kinetics of this
overall process has not been well characterized. Here, using a Potts
Hamiltonian model describing epistasis combined with kinetic Monte
Carlo simulations of evolutionary trajectories, we explore how epistasis
modulates the evolutionary dynamics of HIV DRMs. We show how the occurrence
of a drug-resistance mutation is contingent on favorable epistatic
interactions with many other residues of the sequence background and
that subsequent mutations entrench DRMs. We measure the time-autocorrelation
of fluctuations in the likelihood of DRMs due to epistatic coupling
with the sequence background, which reveals the presence of two evolutionary
processes controlling DRM kinetics with two distinct time scales.
Further analysis of waiting times for the evolutionary trapping effect
to reverse reveals that the sequences which entrench (trap) a DRM
are responsible for the slower time scale. We also quantify the overall
strength of epistatic effects on the evolutionary kinetics for different
mutations and show these are much larger for DRM positions than polymorphic
positions, and we also show that trapping of a DRM is often caused
by the collective effect of many accessory mutations, rather than
a few strongly coupled ones, suggesting the importance of multiresidue
sequence variations in HIV evolution. The analysis presented here
provides a framework to explore the kinetic pathways through which
viral proteins like HIV evolve under drug-selection pressure
NMR Relaxation in Proteins with Fast Internal Motions and Slow Conformational Exchange: Model-Free Framework and Markov State Simulations
Calculating
NMR relaxation effects for proteins with dynamics on
multiple time scales generally requires very long trajectories based
on conventional molecular dynamics simulations. In this report, we
have built Markov state models from multiple MD trajectories and used
the resulting MSM to capture the very fast internal motions of the
protein within a free energy basin on a time scale up to hundreds
of picoseconds and the more than 3 orders of magnitude slower conformational
exchange between macrostates. To interpret the relaxation data, we
derive new equations using the model-free framework which includes
two slowly exchanging macrostates, each of which also exhibits fast
local motions. Using simulations of HIV-1 protease as an example,
we show how the populations of slowly exchanging conformational states
as well as order parameters for the different states can be determined
from the NMR relaxation data
Contingency and Entrenchment of Drug-Resistance Mutations in HIV Viral Proteins
The
ability of HIV-1 to rapidly mutate leads to antiretroviral
therapy (ART) failure among infected patients. Drug-resistance mutations
(DRMs), which cause a fitness penalty to intrinsic viral fitness,
are compensated by accessory mutations with favorable epistatic interactions
which cause an evolutionary trapping effect, but the kinetics of this
overall process has not been well characterized. Here, using a Potts
Hamiltonian model describing epistasis combined with kinetic Monte
Carlo simulations of evolutionary trajectories, we explore how epistasis
modulates the evolutionary dynamics of HIV DRMs. We show how the occurrence
of a drug-resistance mutation is contingent on favorable epistatic
interactions with many other residues of the sequence background and
that subsequent mutations entrench DRMs. We measure the time-autocorrelation
of fluctuations in the likelihood of DRMs due to epistatic coupling
with the sequence background, which reveals the presence of two evolutionary
processes controlling DRM kinetics with two distinct time scales.
Further analysis of waiting times for the evolutionary trapping effect
to reverse reveals that the sequences which entrench (trap) a DRM
are responsible for the slower time scale. We also quantify the overall
strength of epistatic effects on the evolutionary kinetics for different
mutations and show these are much larger for DRM positions than polymorphic
positions, and we also show that trapping of a DRM is often caused
by the collective effect of many accessory mutations, rather than
a few strongly coupled ones, suggesting the importance of multiresidue
sequence variations in HIV evolution. The analysis presented here
provides a framework to explore the kinetic pathways through which
viral proteins like HIV evolve under drug-selection pressure
Large Scale Affinity Calculations of Cyclodextrin HostâGuest Complexes: Understanding the Role of Reorganization in the Molecular Recognition Process
Hostâguest
inclusion complexes are useful models for understanding
the structural and energetic aspects of molecular recognition. Due
to their small size relative to much larger proteinâligand
complexes, converged results can be obtained rapidly for these systems
thus offering the opportunity to more reliably study fundamental aspects
of the thermodynamics of binding. In this work, we have performed
a large scale binding affinity survey of 57 β-cyclodextrin (CD)
hostâguest systems using the binding energy distribution analysis
method (BEDAM) with implicit solvation (OPLS-AA/AGBNP2). Converged
estimates of the standard binding free energies are obtained for these
systems by employing techniques such as parallel Hamiltonian replica
exchange molecular dynamics, conformational reservoirs, and multistate
free energy estimators. Good agreement with experimental measurements
is obtained in terms of both numerical accuracy and affinity rankings.
Overall, average effective binding energies reproduce affinity rank
ordering better than the calculated binding affinities, even though
calculated binding free energies, which account for effects such as
conformational strain and entropy loss upon binding, provide lower
root-mean-square errors when compared to measurements. Interestingly,
we find that binding free energies are superior rank order predictors
for a large subset containing the most flexible guests. The results
indicate that, while challenging, accurate modeling of reorganization
effects can lead to ligand design models of superior predictive power
for rank ordering relative to models based only on ligandâreceptor
interaction energies
A Stochastic Solution to the Unbinned WHAM Equations
The
weighted histogram analysis method (WHAM) and unbinned versions
such as the multistate Bennett acceptance ratio (MBAR) and unbinned
WHAM (UWHAM) are widely used to compute free energies and expectations
from data generated by independent or coupled parallel simulations.
Here we introduce a replica exchange-like algorithm (RE-SWHAM) that
can be used to solve the UWHAM equations stochastically. This method
is capable of analyzing large data sets generated by hundreds or even
thousands of parallel simulations that are too large to be âWHAMMEDâ
using standard methods. We illustrate the method by applying it to
obtain free energy weights for each of the 240 states in a simulation
of hostâguest ligand binding containing âź3.5 Ă
10<sup>7</sup> data elements collected from 16 parallel Hamiltonian
replica exchange simulations, performed at 15 temperatures. In addition
to using much less memory, RE-SWHAM showed a nearly 80-fold improvement
in computational time compared with UWHAM
Comparison of the sequence probabilities in the tail of the Lee database and the pair correlation model with the sequence probabilities in the Stanford database.
<p>The probabilities of sequences under the pair correlation model, , predicted using the Bethe approximation, are plotted as a function of the sequence probabilities from the Lee database, . Sequences with a probability of 0 in the Lee database, i.e. unobserved sequences, are plotted to the left of the abscissa break. Every sequence is shaded using a color gradient corresponding to , which represents the number of times the sequence occurs in the Stanford database, relative to its probability in the Lee database. Sequences that occur frequently in the Stanford database as compared to the Lee database have a higher ratio and are shaded red, while the sequences that do not occur as frequently in the Stanford database as compared to the Lee database have a lower ratio and are shaded blue. Sequences that are shaded green have equal probabilities in both databases. Sequences unobserved in the Lee database (leftmost row in the graph), but observed in the Stanford database have a ratio that is artificially set to equal 4, which corresponds to the color red. Unobserved Lee sequences that are also unobserved in the Stanford database are shaded green because . Sequences with probabilities are shaded according to the average value of for a window of 10 sequences around the sequence of interest. Sequences with probabilities or are not shown. The indices (0), (1), (2), etc mark the locations of sequences observed zero, once, twice (etc) in the Lee database. Each dot corresponds to a unique sequence.</p
Distance between like and unlike-charge pairs as a function of the statistical coupling parameter, .
<p>The statistical coupling parameter is a fitting parameter that describes the statistical interaction energy between pairs of states. Since the Bethe mean field pair correlation model is a good approximation for this data, a negative indicates that a pair of states is enhanced (positively correlated), while a positive indicates that a pair of states is suppressed (negatively correlated). Using simple electrostatics, we observe that like-charge patterns (blue) are mostly suppressed while unlike-charge patterns (red) are enhanced. The sign of is able to correctly predict the charge patterns for of the top 35 most significantly correlated charge pairs out of a total of 135 pairs. The p-value for the statistical significance of this result is . The reason there are 135 pairs is as follows: For each pair of residues, there are 4 possible sets of like and unlike charge combinations, resulting in a total of 612 like/unlike charge pair combinations. However, not all pairs exist in the database or are significantly correlated. Filtering results in 135 pairs with probability greater than 0.001%.</p