scholarly journals Thermodynamic and Kinetic Characterization of Protein Conformational Dynamics within a Riemannian Framework

2021 ◽  
Author(s):  
Curtis Goolsby ◽  
Ashkan Fakharzadeh ◽  
Mahmoud Moradi
Keyword(s):  
Free Energy ◽  
Transition Rate ◽  
Conformational Dynamics ◽  
Diffusion Constant ◽  
Minimum Free Energy ◽  
Umbrella Sampling ◽  
Potential Of Mean Force ◽  
Collective Variable ◽  
Bayesian Estimator ◽  
Riemannian Framework

AbstractWe have formulated a Riemannian framework for describing the geometry of collective variable spaces of biomolecules within the context of molecular dynamics (MD) simulations. The formalism provides a theoretical framework to develop enhanced sampling techniques, path-finding algorithms, and transition rate estimators consistent with a Riemannian treatment of the collective variable space, where the quantities of interest such as the potential of mean force (PMF) and minimum free energy path (MFEP) remain invariant under coordinate transformation. Specific algorithms within this framework are discussed such as the Riemannian umbrella sampling, the Riemannian string method, and a Riemannian-Bayesian estimator of free energy and diffusion constant, which can be used to estimate the transition rate along an MFEP.

scholarly journals Thermodynamic and Kinetic Characterization of Protein Conformational Dynamics within a Riemannian Diffusion Formalism

2019 ◽  
Author(s):  
Curtis Goolsby ◽  
Ashkan Fakharzadeh ◽  
Mahmoud Moradi
Keyword(s):  
Free Energy ◽  
Transition Rate ◽  
Conformational Dynamics ◽  
Diffusion Constant ◽  
Minimum Free Energy ◽  
Umbrella Sampling ◽  
Collective Variable ◽  
Bayesian Estimator ◽  
Variable Space ◽  
Dynamics Simulations

AbstractWe have formulated a Riemannian framework for describing the geometry of collective variable spaces of biomolecules within the context of collective variable based molecular dynamics simulations. The formalism provides a theoretical framework to develop enhanced sampling techniques, path-finding algorithms, and transition rate estimators consistent with a Riemannian treatment of the collective variable space, where the quantities of interest such as the potential of the mean force, minimum free energy path, the diffusion constant, and the transition rate remain invariant under coordinate transformation due to the Riemannian treatment of the collective variable space. Specific algorithms within this framework are discussed such as the Riemannian umbrella sampling, the Riemannian string method, and a Riemannian-Bayesian estimator of free energy and diffusion constant, which can be used to estimate the transition rate along a minimum free energy path.

Computational Investigation on the MDM2-Idasanutlin Interaction using the Potential of Mean Force method

2021 ◽  
Vol 15 ◽  
Author(s):  
Pundarikaksha Das ◽  
Venkata Satish Kumar Mattaparthi
Keyword(s):  
Free Energy ◽  
Binding Free Energy ◽  
Conformational Dynamics ◽  
Umbrella Sampling ◽  
Potential Of Mean Force ◽  
Negative Regulator ◽  
Energy Profile ◽  
Significant Information ◽  
Free Energy Profile ◽  
Binding Characteristics

Background: The Murine Double Minute 2 (MDM2) protein is a well-studied primary negative regulator of the tumor suppressor p53 molecule. Therefore, nowadays, many research studies have focused on the inhibition of MDM2 with potent inhibitors. Idasanutlin (RG7388) is a well-studied small molecule, the antagonist of MDM2 with potential antineoplastic activity. Nevertheless, the highly significant information about the free energy profile, intermediates, and the association of receptor and ligand components in the MDM2-idasanutlin complex remains unclear. Objective: To study the free energy profile of the MDM2-idasanutlin complex in terms of the Potential of Mean Force (PMF) method. Method: We have used the PMF method coupled with umbrella sampling simulations to generate the free energy profile for the association of N-Terminal Domain (NTD) of MDM2 and idasanutlin and a specific reaction coordinate for identifying transition states, intermediates as well as the relative stabilities of the endpoints. We have also determined the binding characteristics and interacting residues at the interface of the MDM2-idasanutlin complex from the Binding Free Energy (BFE) and Per Residue Energy Decomposition (PRED) analyses. Results: The PMF minima for the MDM2-idasanutlin complex was observed at a center of mass (CoM) distance of separation of 11 Å with dissociation energy of 17.5 kcal mol-1. As a function of the distance of separation of MDM2 from idasanutlin. We also studied the conformational dynamics and stability of the NTD of MDM2. We found a high binding affinity between MDM2 and idasanutlin (∆Grinding = -3.19 kcal mol-1). We found that in MDM2, the residues MET54, VAL67, and LEU58 provide the highest energy input for the interaction between MDM2 and idasanutlin. Conclusion: Our results in this study illustrate the significant structural and binding features of the MDM2-idasanutlin complex that may be useful in developing potent inhibitors of MDM2.

scholarly journals Adaptive free energy sampling in multidimensional collective variable space using boxed molecular dynamics

2016 ◽  
Vol 195 ◽  
pp. 395-419 ◽  
Author(s):  
Mike O'Connor ◽  
Emanuele Paci ◽  
Simon McIntosh-Smith ◽  
David R. Glowacki
Keyword(s):  
Molecular Dynamics ◽  
Free Energy ◽  
Rare Event ◽  
Potential Of Mean Force ◽  
Good Evidence ◽  
Collective Variable ◽  
Rigid Body Dynamics ◽  
Free Energy Surface ◽  
Molecular Configuration ◽  
Free Energy Sampling

The past decade has seen the development of a new class of rare event methods in which molecular configuration space is divided into a set of boundaries/interfaces, and then short trajectories are run between boundaries. For all these methods, an important concern is how to generate boundaries. In this paper, we outline an algorithm for adaptively generating boundaries along a free energy surface in multi-dimensional collective variable (CV) space, building on the boxed molecular dynamics (BXD) rare event algorithm. BXD is a simple technique for accelerating the simulation of rare events and free energy sampling which has proven useful for calculating kinetics and free energy profiles in reactive and non-reactive molecular dynamics (MD) simulations across a range of systems, in both NVT and NVE ensembles. Two key developments outlined in this paper make it possible to automate BXD, and to adaptively map free energy and kinetics in complex systems. First, we have generalized BXD to multidimensional CV space. Using strategies from rigid-body dynamics, we have derived a simple and general velocity-reflection procedure that conserves energy for arbitrary collective variable definitions in multiple dimensions, and show that it is straightforward to apply BXD to sampling in multidimensional CV space so long as the Cartesian gradients ∇CV are available. Second, we have modified BXD to undertake on-the-fly statistical analysis during a trajectory, harnessing the information content latent in the dynamics to automatically determine boundary locations. Such automation not only makes BXD considerably easier to use; it also guarantees optimal boundaries, speeding up convergence. We have tested the multidimensional adaptive BXD procedure by calculating the potential of mean force for a chemical reaction recently investigated using both experimental and computational approaches – i.e., F + CD3CN → DF + D2CN in both the gas phase and a strongly coupled explicit CD3CN solvent. The results obtained using multidimensional adaptive BXD agree well with previously published experimental and computational results, providing good evidence for its reliability.

MOLECULAR DYNAMICS SIMULATIONS OF DNA DIMERS BASED ON REPLICA-EXCHANGE UMBRELLA SAMPLING II: FREE ENERGY ANALYSIS

2005 ◽  
Vol 04 (02) ◽  
pp. 433-448 ◽  
Author(s):  
KATSUMI MURATA ◽  
YUJI SUGITA ◽  
YUKO OKAMOTO
Keyword(s):  
Free Energy ◽  
Energy Analysis ◽  
Umbrella Sampling ◽  
Potential Of Mean Force ◽  
Sequence Dependence ◽  
Reaction Coordinates ◽  
Energy Profiles ◽  
Dynamics Simulations ◽  
Free Energy Analysis ◽  
Good Agreement

The free energy change of the stacking process of DNA dimers has been investigated by potential of mean force (PMF) calculations. Two reaction coordinates were considered. One is the distance R between the glycosidic nitrogen atoms of the bases. The other is the pseudo dihedral angle X (N–Cl′–Cl′–N) . All 16 possible DNA dimers composed of the adenine, cytosine, guanine, or thymine bases in 5′ and 3′ positions were considered. From the free energy profiles, we observed good stacking for all DNA dimers and sequence-dependent stacking stability. This sequence dependence of the stacking free energy is in good agreement with the experimental results. We also observed that the PMF is the lowest at R = 4.0~4.4 Å and X = 20~40° for all the DNA dimers except for the dGpdA dimer. These values are close to those of the canonical B-DNA (4.4 Å and 29°).

scholarly journals Evaluating the accuracy of the umbrella sampling plots with different dissociation paths, conformational changes, and structure preparation

2017 ◽  
Author(s):  
Wanli You ◽  
Zhiye Tang ◽  
Chia-en A. Chang
Keyword(s):  
Molecular Dynamics ◽  
Free Energy ◽  
Conformational Changes ◽  
Umbrella Sampling ◽  
Potential Of Mean Force ◽  
Conformational Space ◽  
Drug Candidate ◽  
Energy Calculation ◽  
Dissociation Pathway ◽  
Collective Variables

AbstractThe kinetics of ligand dissociation has been found to be crucial for a good drug candidate. Therefore, examining the underlying free energy profile of the dissociation that governs the kinetics becomes important. Umbrella sampling (US), a widely used free energy calculation method, has long been used to explore the dissociation process of ligand-receptor systems. The potential of mean force (PMF) computed from US seems to always produce binding affinity and energy barriers that more or less agree with experiments. However, such PMFs are influenced by many practical aspects, like the method used to generate the initial dissociation pathway, collective variables (CVs) that used to describe the reaction coordinate (RC), and how intensive the sampling is in the conformational space restrained by the CVs. These critical factors were rarely studied. Here we applied US to study the dissociation processes of β-cyclodextrin (β-CD) and p38α complex systems. For β-CD, we used three different β-CD conformations to generate the dissociation path manually. For p38α, we generated the dissociation pathway using accelerated molecular dynamics (AMD) followed by conformational relaxing with short conventional molecular dynamics (MD), steered molecular dynamics (SMD) and manual pulling. We found that even for small β-CD complexes, different β-CD conformations will alter the height of the PMF and different dissociation directions result in appearance/disappearance of local minima. SMD poorly samples the residue sidechain movement, leading to overestimated height of PMF. On the other hand, the AMD pathway relaxed by short conventional MD sampled more accurate structures, resulting in reasonable PMF.

Determination of Base Flipping Free Energy Landscapes from Nonequilibrium Stratification

2019 ◽  
Author(s):  
Xiaohui Wang ◽  
Zhaoxi Sun
Keyword(s):  
Free Energy ◽  
Energy Landscape ◽  
Sampling Technique ◽  
Umbrella Sampling ◽  
Energy Simulation ◽  
Nonlinear Dependence ◽  
Free Energy Landscape ◽  
Convergence Criterion ◽  
Base Flipping ◽  
Convergence Behavior

<p>Correct calculation of the variation of free energy upon base flipping is crucial in understanding the dynamics of DNA systems. The free energy landscape along the flipping pathway gives the thermodynamic stability and the flexibility of base-paired states. Although numerous free energy simulations are performed in the base flipping cases, no theoretically rigorous nonequilibrium techniques are devised and employed to investigate the thermodynamics of base flipping. In the current work, we report a general nonequilibrium stratification scheme for efficient calculation of the free energy landscape of base flipping in DNA duplex. We carefully monitor the convergence behavior of the equilibrium sampling based free energy simulation and the nonequilibrium stratification and determine the empirical length of time blocks required for converged sampling. Comparison between the performances of equilibrium umbrella sampling and nonequilibrium stratification is given. The results show that nonequilibrium free energy simulation is able to give similar accuracy and efficiency compared with the equilibrium enhanced sampling technique in the base flipping cases. We further test a convergence criterion we previously proposed and it comes out that the convergence behavior determined by this criterion agrees with those given by the time-invariant behavior of PMF and the nonlinear dependence of standard deviation on the sample size. </p>

Molecular Basis of Glucose Transport Mechanism in Plants

2019 ◽  
Author(s):  
Balaji Selvam ◽  
Ya-Chi Yu ◽  
Liqing Chen ◽  
Diwakar Shukla
Keyword(s):  
Molecular Dynamics ◽  
Free Energy ◽  
Molecular Dynamics Simulations ◽  
Conformational Changes ◽  
Transport Mechanism ◽  
Conformational Dynamics ◽  
Site Directed Mutagenesis ◽  
Free Energy Barrier ◽  
Transport Cycle ◽  
Dynamics Simulations

<p>The SWEET family belongs to a class of transporters in plants that undergoes large conformational changes to facilitate transport of sugar molecules across the cell membrane. However, the structures of their functionally relevant conformational states in the transport cycle have not been reported. In this study, we have characterized the conformational dynamics and complete transport cycle of glucose in OsSWEET2b transporter using extensive molecular dynamics simulations. Using Markov state models, we estimated the free energy barrier associated with different states as well as 1 for the glucose the transport mechanism. SWEETs undergoes structural transition to outward-facing (OF), Occluded (OC) and inward-facing (IF) and strongly support alternate access transport mechanism. The glucose diffuses freely from outside to inside the cell without causing major conformational changes which means that the conformations of glucose unbound and bound snapshots are exactly same for OF, OC and IF states. We identified a network of hydrophobic core residues at the center of the transporter that restricts the glucose entry to the cytoplasmic side and act as an intracellular hydrophobic gate. The mechanistic predictions from molecular dynamics simulations are validated using site-directed mutagenesis experiments. Our simulation also revealed hourglass like intermediate states making the pore radius narrower at the center. This work provides new fundamental insights into how substrate-transporter interactions actively change the free energy landscape of the transport cycle to facilitate enhanced transport activity.</p>

Minimum free energy coding for DNA storage

2021 ◽  
pp. 1-1
Author(s):  
Ben Cao ◽  
Xiaokang Zhang ◽  
Jieqiong Wu ◽  
Bin Wang ◽  
Qiang Zhang ◽  
...  
Keyword(s):  
Free Energy ◽  
Minimum Free Energy ◽  
Dna Storage ◽  
Energy Coding

scholarly journals Spontaneous and frequent conformational dynamics induced by A…A mismatch in d(CAA)·d(TAG) duplex

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Yogeeshwar Ajjugal ◽  
Kripi Tomar ◽  
D. Krishna Rao ◽  
Thenmalarchelvi Rathinavelan
Keyword(s):  
Mismatch Repair ◽  
Conformational Dynamics ◽  
Md Simulations ◽  
Umbrella Sampling ◽  
Base Flipping ◽  
Base Pairs ◽  
2D Noesy ◽  
Junction Formation ◽  
Nmr Techniques ◽  
Transient Events

AbstractBase pair mismatches in DNA can erroneously be incorporated during replication, recombination, etc. Here, the influence of A…A mismatch in the context of 5′CAA·5′TAG sequence is explored using molecular dynamics (MD) simulation, umbrella sampling MD, circular dichroism (CD), microscale thermophoresis (MST) and NMR techniques. MD simulations reveal that the A…A mismatch experiences several transient events such as base flipping, base extrusion, etc. facilitating B–Z junction formation. A…A mismatch may assume such conformational transitions to circumvent the effect of nonisostericity with the flanking canonical base pairs so as to get accommodated in the DNA. CD and 1D proton NMR experiments further reveal that the extent of B–Z junction increases when the number of A…A mismatch in d(CAA)·d(T(A/T)G) increases (1–5). CD titration studies of d(CAA)·d(TAG)n=5 with the hZαADAR1 show the passive binding between the two, wherein, the binding of protein commences with B–Z junction recognition. Umbrella sampling simulation indicates that the mismatch samples anti…+ syn/+ syn…anti, anti…anti & + syn…+ syn glycosyl conformations. The concomitant spontaneous transitions are: a variety of hydrogen bonding patterns, stacking and minor or major groove extrahelical movements (with and without the engagement of hydrogen bonds) involving the mismatch adenines. These transitions frequently happen in anti…anti conformational region compared with the other three regions as revealed from the lifetime of these states. Further, 2D-NOESY experiments indicate that the number of cross-peaks diminishes with the increasing number of A…A mismatches implicating its dynamic nature. The spontaneous extrahelical movement seen in A…A mismatch may be a key pre-trapping event in the mismatch repair due to the accessibility of the base(s) to the sophisticated mismatch repair machinery.

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