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.

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.

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>

scholarly journals Thermodynamically reversible paths of the first fusion intermediate reveal an important role for membrane anchors of fusion proteins

2019 ◽  
Vol 116 (7) ◽  
pp. 2571-2576 ◽  
Author(s):  
Yuliya G. Smirnova ◽  
Herre Jelger Risselada ◽  
Marcus Müller
Keyword(s):  
Free Energy ◽  
Fusion Proteins ◽  
Biological Membrane ◽  
Fusion Reaction ◽  
Molecular Shape ◽  
Minimum Free Energy ◽  
Spontaneous Curvature ◽  
Free Energy Barrier ◽  
Lipid Species ◽  
Dynamics Simulations

Biological membrane fusion proceeds via an essential topological transition of the two membranes involved. Known players such as certain lipid species and fusion proteins are generally believed to alter the free energy and thus the rate of the fusion reaction. Quantifying these effects by theory poses a major challenge since the essential reaction intermediates are collective, diffusive and of a molecular length scale. We conducted molecular dynamics simulations in conjunction with a state-of-the-art string method to resolve the minimum free-energy path of the first fusion intermediate state, the so-called stalk. We demonstrate that the isolated transmembrane domains (TMDs) of fusion proteins such as SNARE molecules drastically lower the free energy of both the stalk barrier and metastable stalk, which is not trivially explained by molecular shape arguments. We relate this effect to the local thinning of the membrane (negative hydrophobic mismatch) imposed by the TMDs which favors the nearby presence of the highly bent stalk structure or prestalk dimple. The distance between the membranes is the most crucial determinant of the free energy of the stalk, whereas the free-energy barrier changes only slightly. Surprisingly, fusion enhancing lipids, i.e., lipids with a negative spontaneous curvature, such as PE lipids have little effect on the free energy of the stalk barrier, likely because of its single molecular nature. In contrast, the lipid shape plays a crucial role in overcoming the hydration repulsion between two membranes and thus rather lowers the total work required to form a stalk.

Displacement of carbonates in Ca2UO2(CO3)3 by amidoxime-based ligands from free-energy simulations

2018 ◽  
Vol 47 (5) ◽  
pp. 1604-1613 ◽  
Author(s):  
Bo Li ◽  
Chad Priest ◽  
De-en Jiang
Keyword(s):  
Molecular Dynamics ◽  
Free Energy ◽  
Molecular Dynamics Simulations ◽  
Umbrella Sampling ◽  
Nacl Solution ◽  
Classical Molecular Dynamics ◽  
Energy Profiles ◽  
Energy Simulations ◽  
Dynamics Simulations ◽  
Free Energy Profiles

Classical molecular dynamics simulations coupled with umbrella sampling reveal the atomistic processes and free-energy profiles of the displacement of carbonate groups in the Ca2UO2(CO3)3 complex by amidoxime-based ligands in a 0.5 M NaCl solution.

scholarly journals Electrostatic Interactions with Choline and Phosphate Groups Regulate Cisplatin Permeation through a Dioleoylphosphocholine Bilayer

2020 ◽  
Author(s):  
Lorena Ruano ◽  
Gustavo Cárdenas ◽  
Juan Jose Nogueira
Keyword(s):  
Free Energy ◽  
Lipid Bilayers ◽  
Long Range ◽  
Electrostatic Interactions ◽  
Umbrella Sampling ◽  
Energy Minimum ◽  
Free Energy Minimum ◽  
Dynamics Simulations ◽  
First Moment ◽  
Phosphate Groups

The investigation of the intermolecular interactions between platinum-based anticancer drugs and lipid bilayers is of special relevance to unveil the mechanisms involved in different steps of the mode of action of these drugs. We have simulated the permeation of cisplatin through a model membrane composed of 1,2-dioleoyl-sn-glycero-3-phosphocholine lipids by means of umbrella sampling classical molecular dynamics simulations. The initial physisorption of cisplatin in the polar region of the membrane is controlled, in a first moment, by long-range electrostatic interactions with the choline groups, which trap the drug in a shallow free-energy minimum. Then, cisplatin is driven to a deeper free-energy minimum by long-range electrostatic interactions with the phosphate groups. From this minimum to the middle of the bilayer the electrostatic repulsion between cisplatin and the choline groups partially cancels out the electrostatic attraction between cisplatin and the phosphate groups, inducing a general drop of the total interaction with the polar heads. In addition, the attractive interactions with the non-polar tails, which are dominated by van der Waals contributions, gain significance. The large energy barrier found when going from the global minimum to the middle of the membrane indicates that the non-electrostatic interactions between the drug and the non-polar tails are badly reproduced by the fixed point-charge force field used here, and that the introduction of polarization effects are likely necessary.

scholarly journals Structural and energetic analysis of metastable intermediate states in the E1P–E2P transition of Ca2+-ATPase

2021 ◽  
Vol 118 (40) ◽  
pp. e2105507118
Author(s):  
Chigusa Kobayashi ◽  
Yasuhiro Matsunaga ◽  
Jaewoon Jung ◽  
Yuji Sugita
Keyword(s):  
Free Energy ◽  
Structural Changes ◽  
Umbrella Sampling ◽  
X Ray Crystallography ◽  
Atomic Structures ◽  
Energy Profiles ◽  
Intermediate States ◽  
Before And After ◽  
Energetic Analysis ◽  
Dynamics Simulations

Sarcoplasmic reticulum (SR) Ca2+-ATPase transports two Ca2+ ions from the cytoplasm to the SR lumen against a large concentration gradient. X-ray crystallography has revealed the atomic structures of the protein before and after the dissociation of Ca2+, while biochemical studies have suggested the existence of intermediate states in the transition between E1P⋅ADP⋅2Ca2+ and E2P. Here, we explore the pathway and free energy profile of the transition using atomistic molecular dynamics simulations with the mean-force string method and umbrella sampling. The simulations suggest that a series of structural changes accompany the ordered dissociation of ADP, the A-domain rotation, and the rearrangement of the transmembrane (TM) helices. The luminal gate then opens to release Ca2+ ions toward the SR lumen. Intermediate structures on the pathway are stabilized by transient sidechain interactions between the A- and P-domains. Lipid molecules between TM helices play a key role in the stabilization. Free energy profiles of the transition assuming different protonation states suggest rapid exchanges between Ca2+ ions and protons when the Ca2+ ions are released toward the SR lumen.

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>

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 How Does the Novel Coronavirus Interact with the Human ACE2 Enzyme? A Thermodynamic Answer

2020 ◽  
Author(s):  
Jones de Andrade ◽  
Paulo Fernando Bruno Gonçalves ◽  
Paulo Augusto Netz
Keyword(s):  
Free Energy ◽  
Protein Complexes ◽  
Minimum Free Energy ◽  
New Drugs ◽  
Host Cells ◽  
Spike Protein ◽  
Health Concern ◽  
Novel Coronavirus ◽  
Dynamics Simulations ◽  
Free Energy Of Binding

<p>The SARS-CoV-2 coronavirus pandemic is certainly the most important public health concern today. Until now there are no vaccines or treatments available, despite intensive international efforts. One of the targets for new drugs is the Coronavirus Spike Protein, responsible for its binding and entry into the host cells. The Receptor Binding Domain (RBD) found at the Spike Protein recognizes the human angiotensin-converting enzyme 2 (hACE2). The present in silico study discuss structural and thermodynamic aspects of the protein complexes involving the RBD’s from the 2002 SARS-CoV and 2019 SARS-CoV-2 with the hACE2. Molecular docking and molecular dynamics simulations of the complexes and isolated proteins were performed, providing insights on their detailed pattern of interactions, and estimating the free energy of binding. The obtained results support previous studies indicating that the chemical affinity of the new SARS-CoV-2 for the hACE2 enzyme virus is much higher than the 2002 SARS-CoV. The herein calculated Gibbs free energy of binding to the hACE2 enzyme is, depending on the technique, from 5.11 kcal/mol to 8.39 kcal/mol more negative in the case of the new coronavirus’ RBD. In addition, within each employed technique, this free energy is consistently 61±2% stronger for SARS-CoV-2 than for SARS-CoV. This work presents a chemical reason for the difficulty in treating the SARS-CoV-2 virus using drugs targeting its Spike Protein, as well as helps to explain its infectivity, while defining a minimum free energy of binding for new drugs to be designed against this disease.<br></p>

scholarly journals Molecular Dynamics Simulations of the “Breathing” Phase Transformation of MOF Nanocrystallites

2019 ◽  
Author(s):  
Julian Keupp ◽  
Rochus Schmid
Keyword(s):  
Free Energy ◽  
Phase Transformation ◽  
Surface Effect ◽  
Umbrella Sampling ◽  
Distance Restraint ◽  
Free Energy Barrier ◽  
The One ◽  
Dynamics Simulations ◽  
The Impact ◽  
Closed Pore

One of the intriguing features of certain metal-organic frameworks (MOFs) is the large volume change upon external stimuli like pressure or guest molecule adsorption, referred to as “breathing”. This displacive phase transformation from an open to a closed pore has been investigated intensively by theoretical simulations within periodic boundary conditions (PBC). However, the actual free energy barriers for the transformation under real conditions and the impact of surface effects on it can only be studied beyond PBC for nanocrystallites. In this work, we used the first-principles parameterized forcefield MOF-FF to investigate the thermal- and pressure induced transformations for nanocrystallites of the pillared-layer DMOF-1 (Zn<math> <mrow> <msub><mrow></mrow> <mrow><mn>2</mn> </mrow> </msub> </mrow></math>(bdc)<math> <mrow> <msub><mrow></mrow> <mrow><mn>2</mn> </mrow> </msub> </mrow></math>(dabco); bdc: 1,4-benzenedicarboxylate; dabco: 1,4-diazabicyclo[2.2.2]octane) as a model system. By heating of prepared closed pore nanocrystallites of different size, a spontaneous opening is observed within a few tenth of picoseconds with an interface between the closed and open pore phase moving with a velocity of several 100 m/s<math><mrow><mrow><mi></mi> </mrow><mrow><mi></mi> </mrow> </mrow></math> through the system. The critical nucleation temperature for the opening transition raises with size. On the other hand, by forcing the closing transition with a distance restraint between paddle-wheel units placed on opposite edges of the crystallite, the free energy barrier can be determined by umbrella sampling. As expected, this barrier is substantially lower than the one determined for a concerted process under PBC. Interestingly, the barrier reduces with the size of the crystallite, indicating a hindering surface effect. The results demonstrate the need consider domain boundaries and surfaces, for example by simulations that go beyond PBC and to large system sizes in order to properly predict and describe first order phase transitions in MOFs.<div> </div>

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