14 research outputs found
Mechanistic Models of Chemical Exchange Induced Relaxation in Protein NMR
Long-lived conformational states
and their interconversion rates
critically determine protein function and regulation. When these states
have distinct chemical shifts, the measurement of relaxation by NMR
may provide us with useful information about their structure, kinetics,
and thermodynamics at atomic resolution. However, as these experimental
data are sensitive to many structural and dynamic effects, their interpretation
with phenomenological models is challenging, even if only a few metastable
states are involved. Consequently, approximations and simplifications
must often be used which increase the risk of missing important microscopic
features hidden in the data. Here, we show how molecular dynamics
simulations analyzed through Markov state models and the related hidden
Markov state models may be used to establish mechanistic models that
provide a microscopic interpretation of NMR relaxation data. Using
ubiquitin and BPTI as examples, we demonstrate how the approach allows
us to dissect experimental data into a number of dynamic processes
between metastable states. Such a microscopic view may greatly facilitate
the mechanistic interpretation of experimental data and serve as a
next-generation method for the validation of molecular mechanics force
fields and chemical shift prediction algorithms
Hierarchical Time-Lagged Independent Component Analysis: Computing Slow Modes and Reaction Coordinates for Large Molecular Systems
Analysis
of molecular dynamics, for example using Markov models, often requires
the identification of order parameters that are good indicators of
the rare events, i.e. good reaction coordinates. Recently, it has
been shown that the time-lagged independent component analysis (TICA)
finds the linear combinations of input coordinates that optimally
represent the slow kinetic modes and may serve in order to define
reaction coordinates between the metastable states of the molecular
system. A limitation of the method is that both computing time and
memory requirements scale with the square of the number of input features.
For large protein systems, this exacerbates the use of extensive feature
sets such as the distances between all pairs of residues or even heavy
atoms. Here we derive a hierarchical TICA (hTICA) method that approximates
the full TICA solution by a hierarchical, divide-and-conquer calculation.
By using hTICA on distances between heavy atoms we identify previously
unknown relaxation processes in the bovine pancreatic trypsin inhibitor
Identifying Conformational-Selection and Induced-Fit Aspects in the Binding-Induced Folding of PMI from Markov State Modeling of Atomistic Simulations
Unstructured
proteins and peptides typically fold during binding
to ligand proteins. A challenging problem is to identify the mechanism
and kinetics of these binding-induced folding processes in experiments
and atomistic simulations. In this Article, we present a detailed
picture for the folding of the inhibitor peptide PMI into a helix
during binding to the oncoprotein fragment <sup>25â109</sup>Mdm2 obtained from atomistic, explicit-water simulations and Markov
state modeling. We find that binding-induced folding of PMI is highly
parallel and can occur along a multitude of pathways. Some pathways
are induced-fit-like with binding occurring prior to PMI helix formation,
while other pathways are conformational-selection-like with binding
after helix formation. On the majority of pathways, however, binding
is intricately coupled to folding, without clear temporal ordering.
A central feature of these pathways is PMI motion on the Mdm2 surface,
along the binding groove of Mdm2 or over the rim of this groove. The
native binding groove of Mdm2 thus appears as an asymmetric funnel
for PMI binding. Overall, binding-induced folding of PMI does not
fit into the classical picture of induced fit or conformational selection
that implies a clear temporal ordering of binding and folding events.
We argue that this holds in general for binding-induced folding processes
because binding and folding events in these processes likely occur
on similar time scales and do exhibit the time-scale separation required
for temporal ordering
Journal officiel de la République française. Lois et décrets
05 avril 18861886/04/05 (A18,N94).Appartient Ă lâensemble documentaire : MAEDIGen0Appartient Ă lâensemble documentaire : MAEDI008Appartient Ă lâensemble documentaire : MAEDI012Appartient Ă lâensemble documentaire : MAEDI006Appartient Ă lâensemble documentaire : MAEDI00
Identifying Conformational-Selection and Induced-Fit Aspects in the Binding-Induced Folding of PMI from Markov State Modeling of Atomistic Simulations
Unstructured
proteins and peptides typically fold during binding
to ligand proteins. A challenging problem is to identify the mechanism
and kinetics of these binding-induced folding processes in experiments
and atomistic simulations. In this Article, we present a detailed
picture for the folding of the inhibitor peptide PMI into a helix
during binding to the oncoprotein fragment <sup>25â109</sup>Mdm2 obtained from atomistic, explicit-water simulations and Markov
state modeling. We find that binding-induced folding of PMI is highly
parallel and can occur along a multitude of pathways. Some pathways
are induced-fit-like with binding occurring prior to PMI helix formation,
while other pathways are conformational-selection-like with binding
after helix formation. On the majority of pathways, however, binding
is intricately coupled to folding, without clear temporal ordering.
A central feature of these pathways is PMI motion on the Mdm2 surface,
along the binding groove of Mdm2 or over the rim of this groove. The
native binding groove of Mdm2 thus appears as an asymmetric funnel
for PMI binding. Overall, binding-induced folding of PMI does not
fit into the classical picture of induced fit or conformational selection
that implies a clear temporal ordering of binding and folding events.
We argue that this holds in general for binding-induced folding processes
because binding and folding events in these processes likely occur
on similar time scales and do exhibit the time-scale separation required
for temporal ordering
Identifying Conformational-Selection and Induced-Fit Aspects in the Binding-Induced Folding of PMI from Markov State Modeling of Atomistic Simulations
Unstructured
proteins and peptides typically fold during binding
to ligand proteins. A challenging problem is to identify the mechanism
and kinetics of these binding-induced folding processes in experiments
and atomistic simulations. In this Article, we present a detailed
picture for the folding of the inhibitor peptide PMI into a helix
during binding to the oncoprotein fragment <sup>25â109</sup>Mdm2 obtained from atomistic, explicit-water simulations and Markov
state modeling. We find that binding-induced folding of PMI is highly
parallel and can occur along a multitude of pathways. Some pathways
are induced-fit-like with binding occurring prior to PMI helix formation,
while other pathways are conformational-selection-like with binding
after helix formation. On the majority of pathways, however, binding
is intricately coupled to folding, without clear temporal ordering.
A central feature of these pathways is PMI motion on the Mdm2 surface,
along the binding groove of Mdm2 or over the rim of this groove. The
native binding groove of Mdm2 thus appears as an asymmetric funnel
for PMI binding. Overall, binding-induced folding of PMI does not
fit into the classical picture of induced fit or conformational selection
that implies a clear temporal ordering of binding and folding events.
We argue that this holds in general for binding-induced folding processes
because binding and folding events in these processes likely occur
on similar time scales and do exhibit the time-scale separation required
for temporal ordering
Identifying Conformational-Selection and Induced-Fit Aspects in the Binding-Induced Folding of PMI from Markov State Modeling of Atomistic Simulations
Unstructured
proteins and peptides typically fold during binding
to ligand proteins. A challenging problem is to identify the mechanism
and kinetics of these binding-induced folding processes in experiments
and atomistic simulations. In this Article, we present a detailed
picture for the folding of the inhibitor peptide PMI into a helix
during binding to the oncoprotein fragment <sup>25â109</sup>Mdm2 obtained from atomistic, explicit-water simulations and Markov
state modeling. We find that binding-induced folding of PMI is highly
parallel and can occur along a multitude of pathways. Some pathways
are induced-fit-like with binding occurring prior to PMI helix formation,
while other pathways are conformational-selection-like with binding
after helix formation. On the majority of pathways, however, binding
is intricately coupled to folding, without clear temporal ordering.
A central feature of these pathways is PMI motion on the Mdm2 surface,
along the binding groove of Mdm2 or over the rim of this groove. The
native binding groove of Mdm2 thus appears as an asymmetric funnel
for PMI binding. Overall, binding-induced folding of PMI does not
fit into the classical picture of induced fit or conformational selection
that implies a clear temporal ordering of binding and folding events.
We argue that this holds in general for binding-induced folding processes
because binding and folding events in these processes likely occur
on similar time scales and do exhibit the time-scale separation required
for temporal ordering
Skipping the Replica Exchange Ladder with Normalizing Flows
We combine replica exchange (parallel tempering) with
normalizing
flows, a class of deep generative models. These two sampling strategies
complement each other, resulting in an efficient method for sampling
molecular systems characterized by rare events, which we call learned
replica exchange (LREX). In LREX, a normalizing flow is trained to
map the configurations of the fastest-mixing replica into configurations
belonging to the target distribution, allowing direct exchanges between
the two without the need to simulate intermediate replicas. This can
significantly reduce the computational cost compared to standard replica
exchange. The proposed method also offers several advantages with
respect to Boltzmann generators that directly use normalizing flows
to sample the target distribution. We apply LREX to some prototypical
molecular dynamics systems, highlighting the improvements over previous
methods
Skipping the Replica Exchange Ladder with Normalizing Flows
We combine replica exchange (parallel tempering) with
normalizing
flows, a class of deep generative models. These two sampling strategies
complement each other, resulting in an efficient method for sampling
molecular systems characterized by rare events, which we call learned
replica exchange (LREX). In LREX, a normalizing flow is trained to
map the configurations of the fastest-mixing replica into configurations
belonging to the target distribution, allowing direct exchanges between
the two without the need to simulate intermediate replicas. This can
significantly reduce the computational cost compared to standard replica
exchange. The proposed method also offers several advantages with
respect to Boltzmann generators that directly use normalizing flows
to sample the target distribution. We apply LREX to some prototypical
molecular dynamics systems, highlighting the improvements over previous
methods
Modulation of a Ligandâs Energy Landscape and Kinetics by the Chemical Environment
Understanding how the chemical environment modulates
the predominant
conformations and kinetics of flexible molecules is a core interest
of biochemistry and a prerequisite for the rational design of synthetic
catalysts. This study combines molecular dynamics simulation and Markov
state models (MSMs) to a systematic computational strategy for investigating
the effect of the chemical environment of a molecule on its conformations
and kinetics. MSMs allow quantities to be computed that are otherwise
difficult to access, such as the metastable sets, their free energies,
and the relaxation time scales related to the rare transitions between
metastable states. Additionally, MSMs are useful to identify observables
that may act as sensors for the conformational or binding state of
the molecule, thus guiding the design of experiments. In the present
study, the conformation dynamics of UDP-GlcNAc are studied in vacuum,
water, water + Mg<sup>2+</sup>, and in the protein UDP-GlcNAc 2-epimerase.
It is found that addition of Mg<sup>2+</sup> significantly affects
the conformational stability, thermodynamics, and kinetics of UDP-GlcNAc.
In particular, the slowest structural process, puckering of the GlcNAc
sugar, depends on the overall conformation of UDP-GlcNAc and may thus
act as a sensor of whether Mg<sup>2+</sup> is bound or not. Interestingly,
transferring the molecule from vacuum to water makes the protein-binding
conformations UDP-GlcNAc first accessible, while adding Mg<sup>2+</sup> further stabilizes them by specifically associating to binding-competent
conformations. While Mg<sup>2+</sup> is not cocrystallized in the
UDP-GlcNAc 2-epimerase complex, the selectively stabilized Mg<sup>2+</sup>/UDP-GlcNAc complex may be a template for the bound state,
and Mg<sup>2+</sup> may accompany the binding-competent ligand conformation
to the binding pocket. This serves as a possible explanation of the
enhanced epimerization rate in the presence of Mg<sup>2+</sup>. This
role of Mg<sup>2+</sup> has previously not been described and opens
the question whether âbinding co-factorsâ may be a concept
of general relevance for proteinâligand binding