Molecular Dynamics Simulations of High-Performance, Dissipationless Desalination across Self-Assembled Amyloid Beta Nanotubes.

Climate change is causing droughts and water shortages. Membrane desalination is one of the most widely employed conventional methods of creating a source of clean water, but is a very energy-intensive process. Membrane separation requires high salt selectivity across nano-channels, yet traditional techniques remain inefficient in this regard. Herein, a bioinspired, chemically robust, amyloid-fibril-based nanotube is designed, exhibiting water permeability and salt rejection properties capable of providing highly efficient desalination. Molecular dynamics simulations show that nano-dewetting facilitates the unidirectional motion of water molecules on the surface of amyloid beta (Aß) sheets owing to the ratchet structure of the underlying potential surface and the broken detailed balance. The water inside the self-assembled Aß nanotube (ABNT) overflows, while the passage of salts can be blocked using amphiphilic peptides. The designed nanofilter ABNT shows 100% desalination efficiency with perfect NaCl rejection. The production of ≈2.5 tons of pure water per day without any energy input, which corresponds to a water flux up to 200 times higher than those of existing commercial methods, is assessed by this simulation method. These results provide a detailed fundamental understanding of potential high-performance nanotechnologies for water treatment.

Insights into the free energy landscape and salt-controlled mechanism of the conformational conversions between human telomeric G-quadruplex structures.

G-quadruplexes have become attractive drug targets in cancer therapy. However, due to the polymorphism of G-quadruplex structures, it is difficult to experimentally verify the relevant structures of multiple intermediates and transition states in dynamic equilibrium. Hence, understanding the mechanism by which structural conversions of G-quadruplexes occur is still challenging. We conducted targeted molecular dynamics simulation with umbrella sampling to investigate how salt affects the conformational conversion of human telomeric G-quadruplex. Our results explore a unique view into the structures and energy barrier of the intermediates and transition states in the interconversion process. The pathway of G-quadruplex conformational interconversion was mapped out by a free energy landscape, consisting of branched parallel pathways with multiple energy basins. We propose a salt-controlled mechanism that as the salt concentration increases, the conformational conversion mechanism switches from multi-pathway folding to sequential folding pathways. The hybrid-I and hybrid-II structures are intermediates in the basket-propeller transformation. In high-salt solutions, the conformational conversion upon K+ binding is more feasible than upon Na+ binding. The free energy barrier for conformational conversions ranges from 1.6 to 4.6 kcal/mol. Our work will be beneficial in developing anticancer agents.

Surface Topography Effects of Globular Biomolecules on Hydration Water.

Hydration water serves as a microscopic manifestation of structural stability and functions of biomolecules. To develop bio-nanomaterials in applications, it is important to study how the surface topography and heterogeneity of biomolecules result in their diversity of the hydration dynamics and energetics. We here performed molecular dynamics simulations combined with the steered molecular dynamics and umbrella sampling to investigate the dynamics and escape process associated with the free energy change of water molecules close to a globular biomolecule, i.e., hemoglobin (Hb) and G-quadruplex DNA (GDNA). The residence time, power of long-time tail, and dipole relaxation time were found to display drastic changes within the averaged hydration shell of 3.0-5.0 Å. Compared with bulk water, in the inner hydration shell, the water dipole moment displays a slower relaxation process and is more oriented toward GDNA than toward Hb, forming a hedgehog-like structure when it surrounds GDNA. In particular, a spine water structure is observed in the GDNA narrow groove. The water isotope effect not only prolongs the dynamic time scales of libration motion in the inner hydration shell and the dipole relaxation processes in the bulk but also strengthens the DNA spine water structure. The potential of the mean force profile reflects the integrity of the hydration shell structure and enables us to obtain detailed insights into the structures formed by water, such as the caged H-bond network and the edge bridge structures; it also reveals that local hydration shell free energy (LHSFE) depends on H-bond rupture processes and ranges from 0.2 to 4.2 kcal/mol. Our results demonstrate that the surface topography of a biomolecule influences the integrity of the hydration shell structure and LHSFE. Our studies are able to identify various further applications in the areas of microfluid devices and nano-dewetting on bioinspired surfaces.

Directed motion from particle size oscillations inside an asymmetric channel.

The motion of a spherical Brownian particle in an asymmetric periodic channel is considered. Under an external periodic stimulus, the particle switches between two states with different particle radius, every half-period. Using Brownian dynamics simulations, we show that the particle size oscillation, combined with the asymmetry of the channel, induces a drift along the channel axis, directed towards the steeper wall of the channel. The oscillation of the particle size is accompanied by a time variation of the space accessible to the particle and by an oscillation of its diffusion coefficient. The former underlies the drift inducing mechanism of purely entropic nature. The latter, combined with the former, leads to a significant amplification of the effect. The drift velocity vanishes when interconversion between the states occurs either very slow or very fast, having a maximum in between. The position and magnitude of the maximum are discussed by providing an analytical approach based on intuitively appealing assumptions.

Interfacial water effect on cooperativity and signal communication in Scapharca dimeric hemoglobin.

Cooperativity is important in controlling the biological functions of allosteric proteins. Understanding the detailed mechanisms of cooperativity and allosteric regulation in such proteins is essential to understanding their function; however, the mechanism by which allosteric proteins undergo conformational transitions to aid the ligand escape process and its relevance to interfacial water molecules is not well understood. Here, we perform molecular dynamics simulations to examine these issues in Scapharca dimeric hemoglobin. The effects of interfacial water on dimeric motion, ligand escape probability, gate function, and cross-correlation are considered. The results reveal that interfacial water exhibits an unbalanced stress distribution in the interface region, leading to a bias helix bundle motion that not only can expedite the escape of the first ligand but also can increase the interval between the escape of both ligands. Correspondingly, the gate function follows the same time scale as the F-helix movement, and the gate opening is non-stochastic; moreover, the inconsistent motion between the gate parts resembles cooperative behavior. An explicit analysis of the intersubunit communication map provides at least 14 signal transduction pathways. Our results significantly aid in understanding the role of interfacial water in manipulating cooperativity and will lead to further applications involving molecular machines.

Mechanically Controlled Electron Transfer in a Single-Polypeptide Transistor.

Proteins are of interest in nano-bio electronic devices due to their versatile structures, exquisite functionality and specificity. However, quantum transport measurements produce conflicting results due to technical limitations whereby it is difficult to precisely determine molecular orientation, the nature of the moieties, the presence of the surroundings and the temperature; in such circumstances a better understanding of the protein electron transfer (ET) pathway and the mechanism remains a considerable challenge. Here, we report an approach to mechanically drive polypeptide flip-flop motion to achieve a logic gate with ON and OFF states during protein ET. We have calculated the transmission spectra of the peptide-based molecular junctions and observed the hallmarks of electrical current and conductance. The results indicate that peptide ET follows an NC asymmetric process and depends on the amino acid chirality and α-helical handedness. Electron transmission decreases as the number of water molecules increases, and the ET efficiency and its pathway depend on the type of water-bridged H-bonds. Our results provide a rational mechanism for peptide ET and new perspectives on polypeptides as potential candidates in logic nano devices.

High-temperature ratchets with sawtooth potentials.

The concept of the effective potential is suggested as an efficient instrument to get a uniform analytical description of stochastic high-temperature on-off flashing and rocking ratchets. The analytical representation for the average particle velocity, obtained within this technique, allows description of ratchets with sharp potentials (and potentials with jumps in particular). For sawtooth potentials, the explicit analytical expressions for the average velocity of on-off flashing and rocking ratchets valid for arbitrary frequencies of potential energy fluctuations are derived; the difference in their high-frequency asymptotics is explored for the smooth and cusped profiles, and profiles with jumps. The origin of the difference as well as the appearance of the jump behavior in ratchet characteristics are interpreted in terms of self-similar universal solutions which give the continuous description of the effect. It is shown how the jump behavior in motor characteristics arises from the competition between the characteristic times of the system.

A model for ultra-fast charge transport in membrane proteins.

Isolated proteins have recently been observed to transport charge and reactivity over very long distances with extraordinary rates and near perfect efficiencies in spite of their site. This is not the case if the peptide is in water, where the efficiency of charge hopping to the next site is reduced to approximately 2%. Here, water is not an ideal solvent for charge transport. The issue at hand is how to explain such enormous charge transfer quenching in water compared to another typical medium, namely lipid. We performed molecular dynamics simulations to computationally substantiate the novel long-distance charge transfer yield of the polypeptides in lipids. This is characterized by the charge transfer persistent-distance decay constant and not by the rate, which is seldom, if ever, measured and hence not directly addressed here. This model can encompass an extremely wide range of yields over very long distances in peptides in various media. The calculations here demonstrate the good charge transport efficiency in lipids in contrast to the poor efficiency in water. The protein charge transport also exhibits a very strong anisotropic effect in lipids. The peptide secondary structure effect of charge transfer in membranes is analyzed in contrast to that in water. These results suggest that this model can be useful for the prediction of charge transfer efficiency in various environments of interest and indicate that the charge transfer is highly efficient in membrane proteins.

The molecular mechanism of ligand unbinding from the human telomeric G-quadruplex by steered molecular dynamics and umbrella sampling simulations.

G-quadruplexes are attractive drug targets in cancer therapy. Understanding the mechanisms of the binding-unbinding processes involving biomolecules and molecular recognition is essential for designing new drugs of G-quadruplexes. We performed steered molecular dynamics and umbrella sampling simulations to investigate the molecular mechanism and kinetics of ligand unbinding processes of the basket, propeller and hybrid G-quadruplex structures. Our studies of the ligand charge effect showed that Coulomb interaction plays a significant role in stabilizing the G-quadruplex structure in the unbinding process. The free energy profiles were carried out and the free energy changes associated with the unbinding process were computed quantitatively, whereas these results could help to identify accessible binding sites and transient interactions. The dynamics of the hydration shell water molecules around the G-quadruplex exhibits an abnormal Brownian motion, and the thickness and free energy of the hydration shell were estimated. A two-step relaxation scheme was theoretically developed to describe the kinetic reaction of BMVC and G-quadruplex interactions. Our computed results fall in a reasonable range of experimental data. The present investigation could be helpful in the structure-based drug design.

Diffusion of a massive particle in a periodic potential: Application to adiabatic ratchets.

We generalize a theory of diffusion of a massive particle by the way in which transport characteristics are described by analytical expressions that formally coincide with those for the overdamped massless case but contain a factor comprising the particle mass which can be calculated in terms of Risken's matrix continued fraction method (MCFM). Using this generalization, we aim to elucidate how large gradients of a periodic potential affect the current in a tilted periodic potential and the average current of adiabatically driven on-off flashing ratchets. For this reason, we perform calculations for a sawtooth potential of the period L with an arbitrary sawtooth length (l

Inertial effects in adiabatically driven flashing ratchets.

We study analytically the effect of a small inertial correction on the properties of adiabatically driven flashing ratchets. Parrondo's lemma [J. M. R. Parrondo, Phys. Rev. E 57, 7297 (1998)] is generalized to include the inertial term so as to establish the symmetry conditions allowing directed motion (other than in the overdamped massless case) and to obtain a high-temperature expansion of the motion velocity for arbitrary potential profiles. The inertial correction is thus shown to enhance the ratchet effect at all temperatures for sawtooth potentials and at high temperatures for simple potentials described by the first two harmonics. With the special choice of potentials represented by at least the first three harmonics, the correction gives rise to the motion reversal in the high-temperature region. In the low-temperature region, inertia weakens the ratchet effect, with the exception of the on-off model, where diffusion is important. The directed motion adiabatically driven by potential sign fluctuations, though forbidden in the overdamped limit, becomes possible due to purely inertial effects in neither symmetric nor antisymmetric potentials, i.e., not for commonly used sawtooth and two-sinusoid profiles.

Fluctuation-induced transport of two coupled particles: effect of the interparticle interaction.

We consider a system of two coupled particles fluctuating between two states, with different interparticle interaction potentials and particle friction coefficients. An external action drives the interstate transitions that induces reciprocating motion along the internal coordinate x (the interparticle distance). The system moves unidirectionally due to rectification of the internal motion by asymmetric friction fluctuations and thus operates as a dimeric motor that converts input energy into net movement. We focus on how the law of interaction between the particles affects the dimer transport and, in particular, the role of thermal noise in the motion inducing mechanism. It is argued that if the interaction potential behaves at large distances as x(α), depending on the value of the exponent α, the thermal noise plays a constructive (α > 2), neutral (α = 2), or destructive (α < 2) role. In the case of α = 1, corresponding piecewise linear potential profiles, an exact solution is obtained and discussed in detail.

Relative stability of G-quadruplex structures: Interactions between the human Bcl2 promoter region and derivatives of carbazole and diphenylamine.

The bcl2 promoter region forms a G-quadruplex structure, which is a crucial target for anticancer drug development. In this study, we provide theoretical predictions of the stability of different G-quadruplex folds of the 23-mer bcl2 promoter region and G-quadruplex ligand. We take into account the whole G-quadruplex structure, including bound-cations and solvent effects, in order to compute the ligand binding free energy using molecular dynamics simulation. Two series of the carbazole and diphenylamine derivatives are used to screen for the most potent drug in terms of stabilization. The energy analysis identifies the predominant energy components affecting the stability of the various different G-quadruplex folds. The energy associated with the stability of the G-quadruplex-K(+) structures obtained displays good correlation with experimental Tm measurements. We found that loop orientation has an intrinsic influence on G-quadruplex stability and that the basket structure is the most stable. Furthermore, parallel loops are the most effective drug binding site. Our studies also demonstrate that rigidity and planarity are the key structural elements of a drug that stabilizes the G-quadruplex structure. BMVC-4 is the most potential G-quadruplex ligand. This approach demonstrates significant promise and should benefit drug design.

Adiabatically driven Brownian pumps.

We investigate a Brownian pump which, being powered by a flashing ratchet mechanism, produces net particle transport through a membrane. The extension of the Parrondo's approach developed for reversible Brownian motors [Parrondo, Phys. Rev. E 57, 7297 (1998)] to adiabatically driven pumps is given. We demonstrate that the pumping mechanism becomes especially efficient when the time variation of the potential occurs adiabatically fast or adiabatically slow, in perfect analogy with adiabatically driven Brownian motors which exhibit high efficiency [Rozenbaum et al., Phys. Rev. E 85, 041116 (2012)]. At the same time, the efficiency of the pumping mechanism is shown to be less than that of Brownian motors due to fluctuations of the number of particles in the membrane.

Determination of protein surface hydration shell free energy of water motion: theoretical study and molecular dynamics simulation.

Water on protein surface plays a crucial role in the mechanistic aspects of biological processes; principally, this is characterized into two kinds of water molecules, biological water and bulk water. As compared to pure water, many aspects of the dynamics and structure of the surrounding water near the protein surface are much less understood. Evidence shows that those properties of the surrounding water induced by the presence of the biological systems differ from those of bulk water and that water has low mobility in the hydration shell. An intriguing question remains as to how to make a quantitative estimate of the hydration shell free energy when there is interaction between the protein and the hydration water. To explore this problem, we perform molecular dynamics simulation of the water motion in the hydration shell with respect to bulk water. A fractional Brownian motion theory combined with numerical simulation and a molecular dynamics simulation was developed. This theory was used to directly establish the connection between the dynamics of the protein surface water motion and the interaction between water and protein; this offers the possibility of determining the hydration shell free energy. In this study, we focused on water motion at the protein surface that is within a 4.4 Å layer, which is referred to as the hydration shell. We demonstrate that it actually follows a fractional Brownian motion. In this regime, a developed fractional Fokker-Planck equation, which is used to describe the dynamics of protein surface water motion, permits us to solve the mean first passage time of water molecules through the hydration shell. We then estimate the protein surface hydration shell free energy (HSFE), which depends on the barrier height of the hydration shell. For myoglobin, its HSFE is about 1.73 kcal/mol, and the accompanying activation entropy is 1.40R, where R is the gas constant. Corresponding reduced water mobility is observed for water surrounding myoglobin. In accord with the analysis of the radial distribution function, it is revealed that the effect of temperature on the HSFE is weak. The results show that the protein surface is wrapped by a shell of low mobility water motion and this hydration shell is dynamic rather than static.

Net transport due to noise-induced internal reciprocating motion.

We consider a system of two coupled Brownian particles fluctuating between two states. The fluctuations are produced by both equilibrium thermal and external nonthermal noise, the transition rates depending on the interparticle distance. An externally induced modulation of the transition rates acts on the internal degree of freedom (the interparticle distance) and generates reciprocating motion along this coordinate. The system moves unidirectionally due to rectification of the internal motion by asymmetric friction fluctuations and thus operates as a dimeric motor that converts input energy into net movement. The properties of the motor are primarily determined by the properties of the reciprocating engine, represented by the interparticle distance dynamics. Two main mechanisms are recognized by which the engine operates: energetic and informational. In the physically important cases where only one of the motion-inducing mechanisms is operative, exact solutions can be found for the model with linearly coupled particles. We focus on the informational mechanism, in which thermal noise is involved as a vital component and the reciprocating velocity exhibits a rich behavior as a function of the model parameters. An efficient rectification method for the reciprocating motion is also discussed.

Hydrogen bonds in membrane proteins.

Hydrogen bonds are essential tie points inside protein structures. They undergo dynamic rupture and rebonding processes on the time scale of tens of picoseconds. Proteins can partially rearrange during such ruptures. In previous work, we performed molecular dynamics simulations of these fluctuating hydrogen bonds. This indicated long-range entropy and energy contributions extending far into the liquid environment. The results showed that the binding of a given hydrogen bond is much reduced as a result of these interactions in water, as is required for biological activity and in very good confirmation of known experimental results. The larger water environment directly interacts with the hydrogen bond essentially due to long-range molecular interactions. Such a substantial lowering of the energy of the hydrogen bond in water brings it into the range of activation by many biological processes ( Sheu et al. Chem. Phys. Lett. 2008 , 462 , 1 - 5 ). Thus, the water medium profoundly increases the rate. Furthermore, very large entropic changes are associated with the rupture of hydrogen bonds in water, whereas no such effects are seen for the isolated molecule. Interestingly, such an increase in rates in water is still accompanied by a large negative change in entropy in the extended solvent environment, and this reduces the rate by some 2 orders of magnitude. Recent molecular dynamics experiments in D(2)O substantiate this model and show a large solvent isotope effect. In this work, we used lipids as the environment for the hydrogen bond and discovered that the energy is also reduced from that found in the isolated molecule, but not as far as in water. On the other hand, we found that no entropy penalty exists for breaking the hydrogen bond in lipids, as seen for water. These two effects compensate, even though the energy is some 2 times larger. The entropic penalty is reduced such that the rate is higher than in water despite the higher energy. This is a significant result for understanding the reactivity and dynamics of proteins in lipids. It should be noted that these are very important solvent effects on entropies and free energies that are not usually reflected in statistical thermodynamic computations for reactants and products. The very long-range effect of the solvent makes substantial contributions to kinetic rate constants and is readily evaluated in this kinetic method. To ignore these long-range environmental effects on the entropy can lead to very spurious results when calculating rates of protein mobilities. Hence, the results not only agree very well with the known hydrogen-bond energies directly as a result of various environmental factors, but even correctly predict a phase transition in the lipid.

Molecular dynamics of hydrogen bonds in protein-D2O: the solvent isotope effect.

We suggest that the H-bond in proteins not only mirrors the motion of hydrogen in its own atomistic setting but also finds its origin in the collective environment of the hydrogen bond in a global lattice of surrounding H2O molecules. This water lattice is being perturbed in its optimal entropic configuration by the motion of the H-bond. Furthermore, bonding interaction with the lattice drop the H-bond energy from some 5 kcal/mol for the pure protein in the absence of H2O, to some 1.6 kcal/mol in the presence of the H2O medium. This low value here is determined in a computer experiment involving MD calculations and is a value close to the generally accepted value for biological systems. In accordance with these computer experiments under ambient conditions, the H-bond energy is seriously depressed, hence confirming the subtle effect of the H2O medium directly interacting with the H-bond and permitting a strong fluxional behavior. Furthermore, water produces a very large change in the entropy of activation due to the hydrogen bond breakage, which affects the rate by as much as 2 orders of magnitude. We also observe that there is an entire ensemble of H-bond structures, rather than a single transition state, all of which contribute to this H-bond. Here the model is tested by changing to D2O as the surrounding medium resulting in a substantial solvent isotope effect. This demonstrates the important influence of the environment on the individual hydrogen bond.

Interaction between human telomere and a carbazole derivative: a molecular dynamics simulation of a quadruplex stabilizer and telomerase inhibitor.

The mechanism of inhibition of telomerase by drugs is a key factor in an understanding of guanine-quadruplex complex stabilization during human cancer. This study describes a simulated annealing docking and molecular dynamics simulation to investigate a synthesized potent inhibitor, 3,6-bis(1-methyl-4-vinylpyridinium iodine) carbazole (BMVC), which stabilizes the quadruplex structure of the human telomeric DNA sequence d[AG3(T(2)AG(3))3] and inhibits telomerase activity. The compound was predicted to selectively interact with the quadruplex structure. During our simulation, the binding affinities were calculated and used to predict the best drug-binding sites as well as enhanced selectivity compared with other compounds. Our studies suggest that the simulation results quite coincide with the experimental results. In addition, molecular modeling shows that a 2:1 binding model involving the external binding of BMVC to both ends of the G-quartet of d[AG(3)(T(2)AG)3))3] is the most stable binding mode and this agrees with the absorbance titration results that show two binding sites. Of particular interest is that one pyridinium ring and carbazole moiety of the BMVC can stack well at the end of G-quartet. This implies that BMVC is a good human quadruplex stabilizer and also a good telomerase inhibitor.

Distal charge transport in peptides.

Biological systems often transport charges and reactive processes over substantial distances. Traditional models of chemical kinetics generally do not describe such extreme distal processes. In this Review, an atomistic model for a distal transport of information, which was specifically developed for peptides, is considered. Chemical reactivity is taken as the result of distal effects based on two-step bifunctional kinetics involving unique, very rapid motional properties of peptides in the subpicosecond regime. The bifunctional model suggests highly efficient transport of charge and reactivity in an isolated peptide over a substantial distance; conversely, a very low efficiency in a water environment was found. The model suggests ultrafast transport of charge and reactivity over substantial molecular distances in a peptide environment. Many such domains can be active in a protein.