Lowest Free Energy State Research Articles

Unraveling the conformational dynamics of glycerol 3-phosphate dehydrogenase, a nicotinamide adenine dinucleotide-dependent enzyme of Leishmania mexicana

Allosteric changes modulate the enzymatic activity, leading to activation or inhibition of the molecular target. Understanding the induced fit accommodation mechanism of a ligand in its lowest-free energy state and the subsequent conformational changes induced in the protein are important questions for drug design. In the present study, molecular dynamics (MD) simulations, binding free energy calculations, and principal component analysis (PCA) were applied to analyze the glycerol-3-phosphate dehydrogenase of Leishmania mexicana (LmGPDH) conformational changes induced by its cofactor and substrate binding. GPDH is a nicotinamide adenine dinucleotide (NAD)-dependent enzyme, which has been reported as an interesting target for drug discovery and development against leishmaniasis. Despite its relevance for glycolysis and pentose phosphate pathways, the structural flexibility and conformational motions of LmGPDH in complex with NADH and dihydroxyacetone phosphate (DHAP) remain unexplored. Here, we analyzed the conformational dynamics of the enzyme-NADH complex (cofactor), and the enzyme-NADH-DHAP complex (adduct), mapped the hydrogen-bond interactions for the complexes and pointed some structural determinants of the enzyme that emerge from these contacts to NADH and DHAP. Finally, we proposed a consistent mechanism for the conformational changes on the first step of the reversible redox conversion of dihydroxyacetone phosphate to glycerol 3-phosphate, indicating key residues and interactions that could be further explored in drug discovery.

Microstructure of Sodium Montmorillonite Gels with Long Aging Time Scale.

Purified sodium montmorillonite (SWy-2) gels of a few percent solids displayed pronounced time-dependent rheological or aging behavior with a long time scale. The aging behavior was characterized by an increasing yield stress with rest time. This increase continued even after a week of rest. An open sponge-like cellular microstructure of the aged gels was captured by cryo-SEM with samples prepared at high pressure. The size of the openings of the cellular structure is small, generally less than 1 μm formed by thin flexible platelet with curling edges. This structure was formed by strong attractive and repulsive forces. The rapid yield stress increase in the early stage of aging is due to rapid bond formation occurring between network platelets and free individual platelet, isolated aggregates, and platelet particles in network with free edges. Over time, all platelets are bonded in the network. During aging, the platelets in the structure would have to adjust continually in response to a net force acting on it by its neighbors. The high concentration of platelets responding to this force imbalance is the cause of the long aging time scale. The operation of the attractive and repulsive forces, and the shape and charge properties of the platelets are responsible for the cellular structure being built. At complete structural recovery, the structure should attain the state of lowest free energy. The repulsive force regulates the development of the microstructure. The aging data of the 3.3 wt % gel were fitted by different aging models.

Binding of Starch Fragments to the Starch Branching Enzyme: Implications for Developing Slower-Digesting Starch.

Molecular weight distributions of starch branches affect functional properties, which can be controlled by engineering starch branching enzymes (SBEs). Molecular dynamics and docking approaches are used to examine interactions between SBE and starch fragments. In the native protein, three residues formed stable interactions with starch fragments in the central binding region; these residues may play key roles in substrate recognition. Fragments containing 5-12 glucose units interacted more tightly with SBE than smaller fragments, suggesting a minimal functional fragment size of 5, agreeing with experiment. Effects of three different point mutations on interactions with maltopentaose in the central binding region correlated well with experiment. Simulations indicate that SBE may template formation of the crystalline lamellae characteristic of native starch, consistent with the observation that crystalline lamellae formed by starch in a plant, are not necessarily the state of lowest free energy. The methodology will help develop starches with optimized functional properties.

Effect of pH on the Aggregation of α-syn12 Dimer in Explicit Water by Replica-Exchange Molecular Dynamics Simulation.

The dimeric structure of the N-terminal 12 residues drives the interaction of α-synuclein protein with membranes. Moreover, experimental studies indicated that the aggregation of α-synuclein is faster at low pH than neutral pH. Nevertheless, the effects of different pH on the structural characteristics of the α-syn12 dimer remain poorly understood. We performed 500 ns temperature replica exchange molecular dynamics (T-REMD) simulations of two α-syn12 peptides in explicit solvent. The free energy surfaces contain ten highly populated regions at physiological pH, while there are only three highly populated regions contained at acidic pH. The anti-parallel β-sheet conformations were found as the lowest free energy state. Additionally, these states are nearly flat with a very small barrier which indicates that these states can easily transit between themselves. The dimer undergoes a disorder to order transition from physiological pH to acidic pH and the α-syn12 dimer at acidic pH involves a faster dimerization process. Further, the Lys6–Asp2 contact may prevent the dimerization.

The illusive search for the lowest free energy state of globular proteins and RNAs.

As a consequence of the one-dimensional storage and transfer of genetic information, DNA→RNA→protein, the process by which globular proteins and RNAs achieve their three-dimensional structure involves folding of a linear chain. The folding process itself could create massive activation barriers that prevent the attainment of many stable protein and RNA structures. We consider several kinds of energy barriers inherent in folding that might serve as kinetic constraints to achieving the lowest energy state. Alternative approaches to forming 3D structure, where a substantial number of weak interactions would be created prior to the formation of all the peptide (or phosphodiester) bonds, might not be subjected to such high barriers. This could lead to unique 3D conformational states, potentially more stable than "native" proteins and RNAs, with new functionalities.

A virtual-system coupled multicanonical molecular dynamics simulation: Principles and applications to free-energy landscape of protein–protein interaction with an all-atom model in explicit solvent

We propose a novel generalized ensemble method, a virtual-system coupled multicanonical molecular dynamics (V-McMD), to enhance conformational sampling of biomolecules expressed by an all-atom model in an explicit solvent. In this method, a virtual system, of which physical quantities can be set arbitrarily, is coupled with the biomolecular system, which is the target to be studied. This method was applied to a system of an Endothelin-1 derivative, KR-CSH-ET1, known to form an antisymmetric homodimer at room temperature. V-McMD was performed starting from a configuration in which two KR-CSH-ET1 molecules were mutually distant in an explicit solvent. The lowest free-energy state (the most thermally stable state) at room temperature coincides with the experimentally determined native complex structure. This state was separated to other non-native minor clusters by a free-energy barrier, although the barrier disappeared with elevated temperature. V-McMD produced a canonical ensemble faster than a conventional McMD method.

Boundary-layer method for the analytical calculation of stable textures of bent-core liquid crystal fibers

We study the equilibrium textures of molecular orientation inside cylindrical fibers made of coaxial layers of bent-core smectics. We propose a free-energy model taking into account surface-like and bulk contributions--including layer-compression and electrostatic terms among others--with constant values of the material parameters. We follow the usual variational procedure of minimization of the free energy with respect to the tilt-angle profile θ(r) and obtain an Euler-Lagrange equation and its boundary condition. We solve the variational equations for the equilibrium configurations using a boundary-layer approximation and find multiple solutions. Since the equilibrium tilt profiles are found to be radially inhomogeneous, we select those with minimum distortions in order to find the lowest free-energy state. We minimize further the free energy of the system with respect to the fiber radius and find wider intervals of stability than those previously reported, depending on the balance of the material's spontaneous polarization, elastic and electric divergence-of-polarization constants, and surface-tension coefficients. The bulk and surface-layer structures thus found could be used to calculate the allowed modes of propagation of electromagnetic waves inside the fiber.

Effects of pH and Temperature on the Structural and Thermodynamic Character of a-syn12 Peptide in Aqueous Solution

The structural and thermodynamic characters of α-syn12 peptide in aqueous solution at different pH and temperatures have been investigated through temperature replica exchange molecular dynamics (T-REMD) simulations with GROMOS 43A1 force field. The two independent T-REMD simulations were completed at pH = 7.0 and 10.0, respectively. Each replica was run for 300 ns. The structural and thermodynamic characters of α-syn12 peptide were studied based on the distributions of backbone dihedral angles, the free energy surface, and the stability of different type structure and the favorite conformations of the peptide. The results showed that the simulation at pH = 10.0 produced more sampling in α region than the simulation at pH = 7.0. The temperature changes from 283 K to 308 K result in negligible effects on the distributions of backbone dihedral angle. The β hairpin conformation with Turn9-6 and four hydrogen bonds (HB4-11, HB6-9, HB9-6 and HB11-4) is the lowest free energy state in the simulation at pH = 7.0. However, for the simulation at pH = 10.0, the lowest free energy state corresponds to a structure with Turn9-6 and two hydrogen bonds (HB6-10 and HB10-6) induced by an overly strong residue-residue interaction effect between lysine residues. For the simulation at pH = 7.0, the free energy change of the α-syn12 peptide from the unfolded state to the β hairpin state was in good agreement with the experiments and molecular dynamics simulation results for the other β-peptides, the β hairpin state of the α-syn12 peptide included the conformations that not only the Turn9-6 is formed, but also the terminus are closed together in space. However, the subtle balances between lysine-lysine interactions and lysine-solvent interaction are disrupted in the simulation at pH = 10.0, which induced the assembly of lysine residues, the β hairpin conformation is destabilized by the deprotonation of the Lys side chain. This study can help us to understand the conformation changes and the thermodynamic character of α-syn12 peptide at atomic level induced by changing pH and temperature, which is propitious to reveal the nosogenesis of Parkinson disease. In our knowledge, this is the first report to study the influence of pH and temperature on isolated α-syn12 peptide in water by T-REMD.

Asymmetric synthesis of (S)-3-chloro-1-phenyl-1-propanol using Saccharomyces cerevisiae reductase with high enantioselectivity

3-Chloro-1-phenyl-1-propanol is used as a chiral intermediate in the synthesis of antidepressant drugs. Various microbial reductases were expressed in Escherichia coli, and their activities toward 3-chloro-1-phenyl-1-propanone were evaluated. The yeast reductase YOL151W (GenBank locus tag) exhibited the highest level of activity and exclusively generated the (S)-alcohol. Recombinant YOL151W was purified by Ni-nitrilotriacetic acid (Ni-NTA) and desalting column chromatography. It displayed an optimal temperature and pH of 40 degrees C and 7.5-8.0, respectively. The glucose dehydrogenase coupling reaction was introduced as an NADPH regeneration system. NaOH solution was occasionally added to maintain the reaction solution pH within the range of 7.0-7.5. By using this reaction system, the substrate (30 mM) could be completely converted to the (S)-alcohol product with an enantiomeric excess value of 100%. A homology model of YOL151W was constructed based on the structure of Sporobolomyces salmonicolor carbonyl reductase (Protein Data Bank ID: 1Y1P). A docking model of YOL151W with NADPH and 3-chloro-1-phenyl-1-propanone was then constructed, which showed that the cofactor and substrate bound tightly to the active site of the enzyme in the lowest free energy state and explained how the (S)-alcohol was produced exclusively in the reduction process.

Phonon softening in triangular lattice

We have numerically studied the phonon softening in a triangular lattice system with Su–Schrieffer–Heeger's (SSH) type interaction and with a three-quarter-filled electronic band. When the temperature is lowered, the simultaneous softening of multiple phonon modes is observed at a critical temperature. These softened modes have momenta parallel to the vectors connecting neighboring vertices of the hexagonal structure of the Fermi surface, being irrelevant to nesting vectors. Therefore, this phenomenon that occurs when the temperature is lowered is not a conventional Peierls transition. It is found that the Fermi surface composed of straight lines is a necessary condition for the simultaneous phonon softening. Multi-mode states are realized below the critical temperature. However, all of the softened modes are not necessarily condensed at the lowest free-energy state.

Orientational Landscapes of Peptides in Membranes: Prediction of 2H NMR Couplings in a Dynamic Context

Unlike soluble proteins, membrane polypeptides face an anisotropic milieu. This imposes restraints on their orientation and provides a reference that makes structure prediction tractable by minimalistic thermodynamic models. Here we use this framework to build orientational distributions of monomeric membrane-bound peptides and to predict their expected solid-state (2)H NMR quadrupolar couplings when labeled at specific side chain positions. Using a complete rigid-body sampling of configurations relative to an implicit lipid membrane, peptide free energy landscapes are calculated. This allows us to obtain probability distributions of the peptide tilt, azimuthal rotation, and depth of membrane insertion. The orientational distributions are broad and originate from an interplay among the three relevant rigid-body degrees of freedom, which allows population of multiple states in shallow free energy minima. Remarkably, only when the orientational distributions are taken into account do we obtain a close correlation between predicted (2)H NMR splittings and values measured in experiments. Such a good correlation is not seen with splittings calculated from single configurations, being either the averaged or the lowest free energy state, showing there are distributions, rather than single structures, that best define the peptide-membrane systems. Moreover, we propose that these distributions contribute to the understanding of the rigid-body dynamics of the system.

2D IR photon echo spectroscopy reveals hydrogen bond dynamics of aromatic nitriles

The CN vibrations of two aromatic nitriles, cinnamonitrile, PhCH CH–CN and benzonitrile, PhCN, representative of components of common enzyme inhibitors, are examined by two-dimensional infrared spectroscopy. In methanol, these spectra display cross peaks between the two CN components whose evolution exposes the few picosecond (4.5 ps for CIN and 5.3 ps for BN) equilibrium dynamics of hydrogen bond making and breaking. The main features of the 2D IR spectra are reproduced by simulations only when exchange is incorporated. The lowest free energy state is the non-hydrogen bonded form. Both alkyl and aryl nitriles have now shown this picosecond exchange process.

Folding of a DNA Hairpin Loop Structure in Explicit Solvent Using Replica-Exchange Molecular Dynamics Simulations

Hairpin loop structures are common motifs in folded nucleic acids. The 5′-GCGCAGC sequence in DNA forms a characteristic and stable trinucleotide hairpin loop flanked by a two basepair stem helix. To better understand the structure formation of this hairpin loop motif in atomic detail, we employed replica-exchange molecular dynamics (RexMD) simulations starting from a single-stranded DNA conformation. In two independent 36 ns RexMD simulations, conformations in very close agreement with the experimental hairpin structure were sampled as dominant conformations (lowest free energy state) during the final phase of the RexMDs (∼35% at the lowest temperature replica). Simultaneous compaction and accumulation of folded structures were observed. Comparison of the GCA trinucleotides from early stages of the simulations with the folded topology indicated a variety of central loop conformations, but arrangements close to experiment that are sampled before the fully folded structure also appeared. Most of these intermediates included a stacking of the C 2 and G 3 bases, which was further stabilized by hydrogen bonding to the A 5 base and a strongly bound water molecule bridging the C 2 and A 5 in the DNA minor groove. The simulations suggest a folding mechanism where these intermediates can rapidly proceed toward the fully folded hairpin and emphasize the importance of loop and stem nucleotide interactions for hairpin folding. In one simulation, a loop motif with G 3 in syn conformation (dihedral flip at N-glycosidic bond) accumulated, resulting in a misfolded hairpin. Such conformations may correspond to long-lived trapped states that have been postulated to account for the folding kinetics of nucleic acid hairpins that are slower than expected for a semiflexible polymer of the same size.

Can a physics‐based, all‐atom potential find a protein's native structure among misfolded structures? I. Large scale AMBER benchmarking

Recent work has shown that physics-based, all-atom energy functions (AMBER, CHARMM, OPLS-AA) and local minimization, when used in scoring, are able to discriminate among native and decoy structures. Yet, there have been only few instances reported of the successful use of physics based potentials in the actual refinement of protein models from a starting conformation to one that ends in structures, which are closer to the native state. An energy function that has a global minimum energy in the protein's native state and a good correlation between energy and native-likeness should be able to drive model structures closer to their native structure during a conformational search. Here, the possible reasons for the discrepancy between the scoring and refinement results for the case of AMBER potential are examined. When the conformational search via molecular dynamics is driven by the AMBER potential for a large set of 150 nonhomologous proteins and their associated decoys, often the native minimum does not appear to be the lowest free energy state. Ways of correcting the potential function in order to make it more suitable for protein model refinement are proposed.

Two-dimensional Peierls transition with multimode lattice distortions

Peierls transition in a square lattice electron–lattice system described by a two-dimensional version of Su, Schrieffer and Heeger's model with a half-filled electronic band is numerically analyzed. The Peierls phase accompanied by multimode distortions, where lattice distortions not only with the nesting vector Q=(π,π) but also with those wave vectors parallel to Q are coexisting, is found to be the lowest Free energy state even at finite temperatures. In contrast to the Peierls phase involving only the distortion with the nesting vector, there is no gapless region along the Fermi line.

Can a continuum solvent model reproduce the free energy landscape of a beta -hairpin folding in water?

The folding free energy landscape of the C-terminal beta-hairpin of protein G is explored using the surface-generalized Born (SGB) implicit solvent model, and the results are compared with the landscape from an earlier study with explicit solvent model. The OPLSAA force field is used for the beta-hairpin in both implicit and explicit solvent simulations, and the conformational space sampling is carried out with a highly parallel replica-exchange method. Surprisingly, we find from exhaustive conformation space sampling that the free energy landscape from the implicit solvent model is quite different from that of the explicit solvent model. In the implicit solvent model some nonnative states are heavily overweighted, and more importantly, the lowest free energy state is no longer the native beta-strand structure. An overly strong salt-bridge effect between charged residues (E42, D46, D47, E56, and K50) is found to be responsible for this behavior in the implicit solvent model. Despite this, we find that the OPLSAA/SGB energies of all the nonnative structures are higher than that of the native structure; thus the OPLSAA/SGB energy is still a good scoring function for structure prediction for this beta-hairpin. Furthermore, the beta-hairpin population at 282 K is found to be less than 40% from the implicit solvent model, which is much smaller than the 72% from the explicit solvent model and approximately equal 80% from experiment. On the other hand, both implicit and explicit solvent simulations with the OPLSAA force field exhibit no meaningful helical content during the folding process, which is in contrast to some very recent studies using other force fields.

Modified Thouless-Anderson-Palmer equations for the Sherrington-Kirkpatrick spin glass: Numerical solutions

For large but finite systems the static properties of the infinite-ranged Sherrington-Kirkpatrick model are numerically investigated in the entire glass regime. The approach is based on the modified Thouless-Anderson-Palmer equations in combination with a phenomenological relaxational dynamics used as a numerical tool. For all temperatures and all bond configurations, stable and metastable states are found. Following a discussion of the finite-size effects, the static properties of the state of lowest free energy are presented in the presence of a homogeneous magnetic field for all temperatures below the spin-glass temperature. Moreover some characteristic features of the metastable states are presented. These states exist in finite temperature intervals and disappear via local saddle-node bifurcations. Numerical evidence is found that the excess free energy of the metastable states remains finite in the thermodynamic limit. This implies a ``multivalley'' structure of the free energy on a subextensive scale.

Protein Folding and Assembly

One of the central dogmas in biochemistry is the view that the biologically active, three-dimensional structure of a protein is unique and exclusively determined by its amino acid sequence, and that the active conformation of a protein represents its state of lowest free energy in aqueous solution. Despite a large number of novel experiments supporting this view, including an exponentially increasing number of solved three-dimensional protein structures, it is still impossible to predict the tertiary structure of a protein from knowledge of its amino acid sequence alone.Towards the goal of identifying general principles underlying the mechanism of protein folding in vitro and in vivo, we are pursuing several projects that are briefly described in this article: (1) Circular permutation of proteins as a tool to study protein folding, (2) Catalysis of disulfide bond formation during protein folding, (3) Assembly of adhesive type 1 pili from Escherichia coli strains, and (4) Structure and folding of the mammalian prion protein.

Rapid acquisition of beta-sheet structure in the prion protein prior to multimer formation.

The N-terminally truncated form of the prion protein, PrP 27-30, and the corresponding recombinant protein, rPrP, were solubilized in 0.2% SDS, and the transitions induced by changing the conditions from 0.2% SDS to physiological conditions, i.e. removing SDS, were characterized with respect to solubility, resistance to proteolysis, secondary structure and multimerization. Circular dichroism, electron microscopy and fluorescence correlation spectroscopy were used to study the structural transitions of PrP. Within one minute the alpha-helical structure of PrP was transformed into one that was enriched in beta-sheets and consisted mainly of dimers. Larger oligomers were found after 20 minutes and larger multimers exhibiting resistance to proteolysis were found after several hours. It was concluded that the monomeric alpha-helical conformation was stable in SDS or when attached to the membrane; however, the state of lowest free energy in aqueous solution at neutral pH seems to be the multimeric, beta-sheet enriched conformation.

Bending rigidity of ionic surfactant interfaces with variable surface charge density: the salt-free case

The theoretical understanding of the electrostatic contribution to the bending constants of ionic surfactant interfaces has been extensively developed over the past decade. In this contribution, we deal with systems without added electrolyte, and allow for the interfacial charge density to vary with curvature, treating both an undulating sheet geometry and a spherical/cylindrical cell model. The rippled-plane case shows that the lowest free energy state is that for which the surface potential remains fixed, i.e. a conducting interface. Moreover, the deduced expression for the bending modulus agrees with that derived from the cell model, generalizing our previous result that the bending modulus is geometry-independent, even for systems without added salt, to cases where the surface charge is permitted to redistribute on bending.