The investigation of the effects of counterions in protein dynamics simulations.

Molecular simulations able to exactly represent solvated charged proteins are helpful in understanding protein dynamics, structure and function. In the present study we have used two different starting structures of papain (a typical, stable, globular protein of intermediate net charge) and different modeling procedures to evaluate some effects of counterions in simulations. A number of configurations have been generated and relaxed for each system by various combinations of constrained simulated annealing and molecular dynamics procedures, using the AMBER force field. The analysis of trajectories shows that the simulations of solvated proteins are moderately sensitive to the presence of counterions. However, this sensitivity is highly dependent on the starting model and different procedures of equilibration used. The neutralized systems tend to evince smaller root mean square deviations regardless of the system investigated and the simulation procedure used. The results of parameterized fitting of the simulated structures to the crystallographic data, giving quantitative measure of the total charge influence on the stability of various elements of the secondary structure, revealed a clear scatter of different reactions of various systems' secondary structures to counterions addition: some systems apparently were stabilized when neutralized, while the others were not. Thus, one cannot unequivocally state, despite consideration of specific simulation conditions, whether protein secondary structures are more stable when they have neutralized charges. This suggests that caution should be taken when claiming the stabilizing effect of counterions in simulations other than those involving small, unstable polypeptides or highly charged proteins.     

Dependence of DNA condensation on the correlation distance between condensed counterions

Based on the ground state of counterions condensed on a DNA molecule, a model has been developed to successfully detect the process of DNA condensation. Through further investigation, the process of DNA condensation strongly depends on the correlation distance between condensed counterions on DNA molecules. Generally, there are two routes. The process of DNA condensation with the correlation distance between condensed counterions being 2 nm or 4 nm is different from the one with the correlation distance between condensed counterions being 3 nm or 5 nm. Effects of ionic strength on the diameter of toroidal condensates originate from the increase of correlation distance between condensed counterions.     

Clustering of macroions in solutions of highly asymmetric electrolytes

In this paper, we present results of computer simulations for a primitive model of asymmetric electrolyte solutions containing macroions, counterions and in a few cases, also co-ions. The results show that the valency of counterions plays an important role in shaping the net interaction between the macroions. For solutions with monovalent counterions, the macroions are distributed at larger distances, and in solutions with divalent counterions, the macroions come closer to each other and share a layer of counterions, whereas, in solutions with trivalent counterions, the macroions form clusters. These clusters dissolve upon dilution or addition of a simple electrolyte. These findings suggest a mechanism whereby the nonuniform distribution of macroions observed experimentally in charged systems may occur.     

DNA condensation by multivalent cations

In the presence of multivalent cations, high molecular weight DNA undergoes a dramatic condensation to a compact, usually highly ordered toroidal structure. This review begins with an overview of DNA condensation : condensing agents, morphology, kinetics, and reversibility, and the minimum size required to form orderly condensates. It then summarizes the statistical mechanics of the collapse of stiff polymers, which shows why DNA condensation is abrupt and why toroids are favored structures. Various ways to estimate or measure intermolecular forces in DNA condensation are discussed, all of them agreeing that the free energy change per base pair is very small, on the order of 1% of thermal energy. Experimental evidence is surveyed showing that DNA condensation occurs when about 90% of its charge is neutralized by counterions. The various intermolecular forces whose interplay gives rise to DNA condensation are then reviewed. The entropy loss upon collapse of the expanded wormlike coil costs free energy, and stiffness sets limits on tight curvature. However, the dominant contributions seem to come from ions and water. Electrostatic repulsions must be overcome by high salt concentrations or by the correlated fluctuations of territorially bound multivalent cations. Hydration must be adjusted to allow a cooperative accommodation of the water structure surrounding surface groups on the DNA helices as they approach. Undulations of the DNA in its confined surroundings extend the range of the electrostatic forces. The condensing ions may also subtly modify the local structure of the double helix. © 1998 John Wiley & Sons, Inc. Biopoly 44: 269–282, 1997     

Electron microscope studies of glycogen synthase

Summary Glycogen synthase from rabbit muscle was examined with the electron microscope. In preparations of the completely converted glucose-6-phosphate dependent form (GSD) and the independent form (GSI) three structures were observed: toroids, hexagons and stacks of four elements which appear to be aggregates of four toroids. Toroids can be formed from hexagons by radial inward movement of subunits which form the vertices of the hexagons. Analysis of the dimensions of these structures and comparison of the known chemistry of the enzyme to the subunits as inferred from electron microscopy suggests a model for the structure of glycogen synthase. The model allows predictions of types of subunits in the enzyme, their relation to phosphorylatable and -SH sites and the possibilities of control by small effector molecules.     

Simulating the chromatin-mediated phase separation of model proteins with multiple domains

We perform simulations of a system containing simple model proteins and a polymer representing chromatin. We study the interplay between protein-protein and protein-chromatin interactions, and the resulting condensates that arise due to liquid-liquid phase separation, or a via a “bridging-induced attraction” mechanism. For proteins that interact multivalently, we obtain a phase diagram which includes liquid-like droplets, droplets with absorbed polymer, and coated polymer regimes. Of particular interest is a regime where protein droplets only form due to interaction with the polymer; here, unlike a standard phase separating system, droplet density rather than size varies with the overall protein concentration. We also observe that protein dynamics within droplets slow down as chromatin is absorbed. If the protein-protein interactions have a strictly limited valence, fractal or gel-like condensates are instead observed. A specific example that inspired our model is heterochromatin protein 1, or HP1. Recent in vivo experiments have shown that HP1 exhibits similar droplet size buffering behavior as our simulations. Overall, our results provide biologically relevant insights into the general nature of protein-chromatin condensates in living cells.     

Influence of charged surfaces on the morphology of DNA condensed with multivalent ions

DNA in solution can be condensed into dense aggregates by multivalent counterions. Here we investigate the effect of a nearby surface on the morphology of DNA condensates. We show that, contrary to what has often been assumed, interactions between DNA condensates and the surface can strongly influence the observed morphology. This limits the usefulness of surface probes such as atomic force microscopy for studying the morphology of condensates in bulk solution. Surprisingly, we find that the most negatively charged surface disturbs the condensate morphology most, suggesting that the microscopic mechanism resulting in DNA condensation is also responsible for the attractive force between DNA and the surface.     

Molecular dynamics of a DNA Holliday junction: the inverted repeat sequence d(CCGGTACCGG)₄

All-atom molecular dynamics (MD) computer simulations have been applied successfully to duplex DNA structures in solution for some years and found to give close accord with observed results. However, the MD force fields have generally not been parameterized against unusual DNA structures, and their use to obtain dynamical models for this class of systems needs to be independently validated. The four-way junction (4WJ), or Holliday junction, is a dynamic DNA structure involved in central cellular processes of homologous replication and double strand break repair. Two conformations are observed in solution: a planar open-X form (OPN) with a mobile center and four duplex arms, and an immobile stacked-X (STX) form with two continuous strands and two crossover strands, stabilized by high salt conditions. To characterize the accuracy of MD modeling on 4WJ, we report a set of explicit solvent MD simulations of ～100 ns on the repeat sequence d(CCGGTACCGG)₄ starting from the STX structure (PDB code 1dcw), and an OPN structure built for the same sequence. All 4WJ MD simulations converged to a stable STX structure in close accord with the crystal structure. Our MD beginning in the OPN form converts to the STX form spontaneously at both high and low salt conditions, providing a model for the conformational transition. Thus, these simulations provide a successful account of the dynamical structure of the STX form of d(CCGGTACCGG)₄ in solution, and provide new, to our knowledge, information on the conformational stability of the junction and distribution of counterions in the junction interior.     

Effect of the reaction field electrostatic term on the molecular dynamics simulation of the activation domain of procarboxypeptidase B

Molecular dynamics simulations of the activation domain of porcine procarboxypeptidase B (ADBp) were performed in order to examine the effects of the inclusion of a reaction field (RF) term into the calculation of electrostatics forces for highly charged proteins. Two simulations were performed with the GROMOS96 package, studying the influence of counterions on the final results. Comparison with previous results without the inclusion of the RF term (Martí-Renom, M.A., Mas,J.M., Oliva,B., Querol,E. and Avilés,F.X., Protein Engng, 1998, 11, 101-110) shows that the structure is well maintained when the RF term is included. Moreover, the analysis of the trajectories shows that simulations of solvated highly-charged proteins are sensitive to the presence of counterions, the secondary structures being more stable when their charges are neutralized.     

Counterions which favour the C form of DNA.

Recently the relationship between the B and C forms of DNA has been questioned. We have found some amino acids and related amines which form complexes with DNA and favour the C form. We have studied such complexes by X-ray diffraction. With some of these counterions the transition between the B and C forms occurs smoothly, whereas in other cases there is a discontinuous transition. We conclude that the C form is a well-defined variant of the B form favoured by some counterions under low humidity conditions.     

Molecular Dynamics Simulations of Double-Stranded DNA in an Explicit Solvent Model with the Zero-Dipole Summation Method

Molecular dynamics (MD) simulations of a double-stranded DNA with explicit water and small ions were performed with the zero-dipole summation (ZD) method, which was recently developed as one of the non-Ewald methods. Double-stranded DNA is highly charged and polar, with phosphate groups in its backbone and their counterions, and thus precise treatment for the long-range electrostatic interactions is always required to maintain the stable and native double-stranded form. A simple truncation method deforms it profoundly. On the contrary, the ZD method, which considers the neutralities of charges and dipoles in a truncated subset, well reproduced the electrostatic energies of the DNA system calculated by the Ewald method. The MD simulations using the ZD method provided a stable DNA system, with similar structures and dynamic properties to those produced by the conventional Particle mesh Ewald method.     

Condensation of DNA by trivalent cations. 2. Effects of cation structure

Electron microscopy is employed to examine DNA aggregates produced by three tripositively charged condensing agents. Spermidine, hexammine cobalt (III), and me8spermidine (in which the amine groups of spermidine are exhaustively methylated) all produce condensates. The predominant form of condensate observed is toroidal; however, me8spermidine produces a large fraction of rodlike condensates. Distributions of toroidal radii and estimated volumes suggest that the size of condensates depends on the condensing agent employed, its concentration, and the time elapsed after addition of condensing agent. While ligand charge seems to be the major factor in predicting condensing power, ligand structure influences the morphology and dimensions of the particles produced. The ability to form hydrogen bonds is not required to promote condensation, since me8spermidine has no NHs. There may be a kinetic barrier to condensation at low me8spermidine concentrations. The relative proportions of toroids and rods may depend on the energetic compensation between bending and binding in cyclic structures, or on rate-limiting formation of sharply bent or kinked regions in rods.     

Molecular dynamics simulations of rubredoxin from Clostridium pasteurianum: Changes in structure and electrostatic potential duringredox reactions

Molecular dynamics simulations of Clostridium pasteurianum rubredoxin in the oxidized and reduced forms have been performed. Good agreement between both forms and crystal data has been obtained (rms deviation of backbone atoms of 1.06 and 1.42 Å, respectively), which was due in part to the use of explicit solvent and counterions. The reduced form exhibits an unexpected structural change: the redox site becomes much more solvent-accessible, so that water enters a channel between the surface and the site, but with little actual structural rearrangement (the rms deviation of backbone atoms between the oxidized and reduced is 0.77 Å). The increase in solvent accessibility is also seen, although to a much lesser extent, between the oxidized and reduced crystal structures of Pyrococcus furiosus rubredoxin, but no high resolution crystal or nuclear magnetic resonance solution data exist for reduced C. pasteurianum rubredoxin. The electrostatic potential at the iron site and fluctuations in the potential, which contribute to both the redox and electron transfer properties, have also been evaluated for both the oxidized and the reduced simulations. These results show that the backbone plays a significant role (62–70 kcall/mol/e) and the polar sidechains contribute relatively little (0–4 kcal/mol/e) to the absolute electrostatic potential at the iron of rubredoxin for both forms. However, both groups contribute significantly to the change in redox state by becoming more polarized and more densely packed around the redox site upon reduction. Furthermore, these results show that the solvent becomes much more polarized in the reduced form than in the oxidized form, even excluding the penetrating water. Finally, the simulation indicates that the contribution of the charged side chains to the electrostatic potential is largely canceled by that of the counterions. © 1995 Wiley-Liss, Inc.     

Liquid-liquid phase separation as a common organizing principle of intracellular space and biomembranes providing dynamic adaptive responses

This work is devoted to the phenomenon of liquid-liquid phase separation (LLPS), which has come to be recognized as fundamental organizing principle of living cells. We distinguish separation processes with different dimensions. Well-known 3D-condensation occurs in aqueous solution and leads to membraneless organelle (MLOs) formation. 2D-films may be formed near membrane surfaces and lateral phase separation (membrane rafts) occurs within the membranes themselves. LLPS may also occur on 1D structures like DNA and the cyto- and nucleoskeleton. Phase separation provides efficient transport and sorting of proteins and metabolites, accelerates the assembly of metabolic and signaling complexes, and mediates stress responses. In this work, we propose a model in which the processes of polymerization (1D structures), phase separation in membranes (2D structures), and LLPS in the volume (3D structures) influence each other. Disordered proteins and whole condensates may provide membrane raft separation or polymerization of specific proteins. On the other hand, 1D and 2D structures with special composition or embedded IDRs can nucleate condensates. We hypothesized that environmental change may trigger a LLPS which can propagate within the cell interior moving along the cytoskeleton or as an autowave. New phase propagation quickly and using a low amount of energy adjusts cell signaling and metabolic systems to new demands. Cumulatively, the interconnected phase separation phenomena in different dimensions represent a previously unexplored system of intracellular communication and regulation which cannot be ignored when considering both physiological and pathological cell processes.     

Hydrogen bonding in helical polypeptides from molecular dynamics simulations and amide hydrogen exchange analysis: alamethicin and melittin in methanol.

Molecular dynamics simulations of ion channel peptides alamethicin and melittin, solvated in methanol at 27 degrees C, were run with either regular alpha-helical starting structures (alamethicin, 1 ns; melittin 500 ps either with or without chloride counterions), or with the x-ray crystal coordinates of alamethicin as a starting structure (1 ns). The hydrogen bond patterns and stabilities were characterized by analysis of the dynamics trajectories with specified hydrogen bond angle and distance criteria, and were compared with hydrogen bond patterns and stabilities previously determined from high-resolution NMR structural analysis and amide hydrogen exchange measurements in methanol. The two alamethicin simulations rapidly converged to a persistent hydrogen bond pattern with a high level of 3(10) hydrogen bonding involving the amide NH's of residues 3, 4, 9, 15, and 18. The 3(10) hydrogen bonds stabilizing amide NH's of residues C-terminal to P2 and P14 were previously proposed to explain their high amide exchange stabilities. The absence, or low levels of 3(10) hydrogen bonds at the N-terminus or for A15 NH, respectively, in the melittin simulations, is also consistent with interpretations from amide exchange analysis. Perturbation of helical hydrogen bonding in the residues before P14 (Aib10-P14, alamethicin; T11-P14, melittin) was characterized in both peptides by variable hydrogen bond patterns that included pi and gamma hydrogen bonds. The general agreement in hydrogen bond patterns determined in the simulations and from spectroscopic analysis indicates that with suitable conditions (including solvent composition and counterions where required), local hydrogen-bonded secondary structure in helical peptides may be predicted from dynamics simulations from alpha-helical starting structures. Each peptide, particularly alamethicin, underwent some large amplitude structural fluctuations in which several hydrogen bonds were cooperatively broken. The recovery of the persistent hydrogen bonding patterns after these fluctuations demonstrates the stability of intramolecular hydrogen-bonded secondary structure in methanol (consistent with spectroscopic observations), and is promising for simulations on extended timescales to characterize the nature of the backbone fluctuations that underlie amide exchange from isolated helical polypeptides.     

Toroid formation in charge neutralized flexible or semi-flexible biopolymers: potential pathway for assembly of DNA carriers

BACKGROUND: The theoretical state diagram for semi-flexible macromolecules such as DNA predicts that a tightly wound toroid can be a stable structure. Experimentally, toroids roughly 100 nm in diameter are routinely observed for DNA in the presence of multivalent cations at low DNA concentration. Theory also predicts toroids can form between non-DNA semi-flexible polymers and multivalent counterions. This phenomenon provides a means to co-package DNA with functionalized anionic polymers to create gene delivery systems. METHODS AND RESULTS: We show using electron microscopy that non-DNA polymers (polylysine, polyglutamic acid, and dextran sulfate) form toroids when mixed with multi- or polyvalent ions of opposite charge. The non-DNA toroids are similar in diameter to ones made with DNA. The results using dextran sulfate, a semi-flexible polymer, are explained by current theory. However, theory predicts that high flexibility in polypeptides should discourage their incorporation into stable toroids. To explain these latter observations we propose that charge neutralization facilitates secondary structure formation, which confers stiffness, thereby allowing stable toroids for the polypeptides studied. We measured the secondary structure of the toroid-forming polypeptides using circular dichroism (CD). The CD spectrum indicates the polypeptides undergo transitions from non-ordered structures (random coil) to ordered secondary structures (either alpha-helix or beta-sheet) upon charge neutralization which supports the hypothesis. The type of secondary structure is dependent on the type of multivalent counterion used to form the toroids. Formation of the polypeptide toroids confers resistance to heat denaturation of the resulting polypeptide secondary structure. The CD spectrum of DNA in a toroid also is changed from that of uncomplexed DNA, but all of the counterions used to form DNA toroids created structures with similar CD spectra in the DNA region (250-290 nm). CONCLUSIONS: The toroid structure obtained using DNA is observed in other semi-flexible non-DNA polymers such as dextran sulfate, and also in flexible polymers such as polylysine and polyglutamic acid upon charge neutralization with multivalent counterions. In the flexible polymers we propose that this phenomenon is due to induction of secondary structure upon charge neutralization, which decreases polymer flexibility, i.e. increases polymer stiffness, to enable toroid formation. These results have significant implications for the co-assembly of non-DNA anionic polymers with DNA to create nanoscopic gene carriers.     

A 5-nanosecond molecular dynamics trajectory for B-DNA: analysis of structure, motions, and solvation.

We report the results of four new molecular dynamics (MD) simulations on the DNA duplex of sequence d(CGCGAATTCGCG)2, including explicit consideration of solvent water, and a sufficient number of Na+ counterions to provide electroneutrality to the system. Our simulations are configured particularly to characterize the latest MD models of DNA, and to provide a basis for examining the sensitivity of MD results to the treatment of boundary conditions, electrostatics, initial placement of solvent, and run lengths. The trajectories employ the AMBER 4.1 force field. The simulations use particle mesh Ewald summation for boundary conditions, and range in length from 500 ps to 5.0 ns. Analysis of the results is carried out by means of time series for conformationalm, helicoidal parameters, newly developed indices of DNA axis bending, and groove widths. The results support a dynamically stable model of B-DNA for d(CGCGAATTCGCG)2 over the entire length of the trajectory. The MD results are compared with corresponding crystallographic and NMR studies on the d(CGCGAATTCGCG)2 duplex, and placed in the context of observed behavior of B-DNA by comparisons with the complete crystallographic data base of B-form structures. The calculated distributions of mobile solvent molecules, both water and counterions, are displayed. The calculated solvent structure of the primary solvation shell is compared with the location of ordered solvent positions in the corresponding crystal structure. The results indicate that ordered solvent positions in crystals are roughly twice as structured as bulk water. Detailed analysis of the solvent dynamics reveals evidence of the incorporation of ions in the primary solvation of the minor groove B-form DNA. The idea of localized complexation of otherwise mobile counterions in electronegative pockets in the grooves of DNA helices introduces an additional source of sequence-dependent effects on local conformational, helicoidal, and morphological structure, and may have important implications for understanding the functional energetics and specificity of the interactions of DNA and RNA with regulatory proteins, pharmaceutical agents, and other ligands.     

Sequestration of cellular native factors by biomolecular assemblies: Physiological or pathological?

In addition to native-state structures, biomolecules often form condensed supramolecular assemblies or cellular membraneless organelles that are critical for cell life. These biomolecular assemblies, generally including liquid-like droplets (condensates) and amyloid-like aggregates, can sequester or recruit their interacting partners, so as to either modulate various cellular behaviors or even cause disorders. This review article summarizes recent advances in the sequestration of native factors by biomolecular assemblies and discusses their potential consequences on cellular function, homeostasis, and disease pathology.