Oscillations of a helical plasma crystal

Oscillations and the stability of the helical structures of likely charged particles undergoing Coulomb interactions and confined in an axisymmetric potential well are studied theoretically.     

Theoretical studies of the structure and molecular dynamics of a peptide crystal

Energy minimizations and molecular dynamics simulations have been performed on the cyclic peptide cyclo-(Ala-Pro-D-Phe)2 in both the isolated and crystal states. The results of these calculations have been analyzed, both to investigate our ability to reproduce experimental data (structure and vibrational and NMR spectra) and to investigate the effects of environment on the energy, structure, and dynamics of peptides. Comparison of the minimized and time-averaged crystal systems with the experimental peptide structure shows that the calculations have closely reproduced the experimental structure. Molecular dynamics of the isolated molecule has led to a new conformation, which is approximately equal to 8.5 kcal/mol more stable than the conformation that exists in the crystal, the latter conformation being stabilized by intermolecular (packing) forces. This illustrates the considerable effect that environment can have on the conformation of peptides. The crystal environment has also been shown to significantly reduce the dynamic conformational fluctuations seen for the isolated molecule. The behavior of the peptide during the isolated simulation also supports the experimental NMR observation of a symmetric structure that differs from the asymmetric, instantaneous structures which characterize the molecule during the dynamics. Calculations of vibrational frequencies of the peptide in the crystal and isolated states show the expected shifts in bond-stretching frequencies due to intermolecular interactions. Finally, we have calculated NMR coupling constants from the dynamics simulation of the isolated peptide and have compared these with the experimental values. This has led to a possible reinterpretation of the experimental data.     

The crystal and molecular structures of a cathepsin K:chondroitin sulfate complex

Cathepsin K is the major collagenolytic enzyme produced by bone-resorbing osteoclasts. We showed earlier that the unique triple-helical collagen-degrading activity of cathepsin K depends on the formation of complexes with bone-or cartilage-resident glycosaminoglycans, such as chondroitin 4-sulfate (C4-S). Here, we describe the crystal structure of a 1:n complex of cathepsin K:C4-S inhibited by E64 at a resolution of 1.8 Å. The overall structure reveals an unusual “beads-on-a-string”-like organization. Multiple cathepsin K molecules bind specifically to a single cosine curve-shaped strand of C4-S with each cathepsin K molecule interacting with three disaccharide residues of C4-S. One of the more important sets of interactions comes from a single turn of helix close to the N terminus of the proteinase containing a basic amino acid triplet (Arg8-Lys9-Lys10) that forms multiple hydrogen bonds either to the caboxylate or to the 4-sulfate groups of C4-S. Altogether, the binding sites with C4-S are located in the R-domain of cathepsin K and are distant from its active site. This explains why the general proteolytic activity of cathepsin K is not affected by the binding of chondroitin sulfate. Biochemical analyses of cathepsin K and C4-S mixtures support the presence of a 1:n complex in solution; a dissociation constant, K_d, of about 10 nM was determined for the interaction between cathepsin K and C4-S.     

Oscillations in a size-structured prey-predator model

This article introduces a predator–prey model with the prey structured by body size, based on reports in the literature that predation rates are prey-size specific. The model is built on the foundation of the one-species physiologically structured models studied earlier. Three types of equilibria are found: extinction, multiple prey-only equilibria and possibly multiple predator–prey coexistence equilibria. The stabilities of the equilibria are investigated. Comparison is made with the underlying ODE Lotka–Volterra model. It turns out that the ODE model can exhibit sustain oscillations if there is an Allee effect in the net reproduction rate, that is the net reproduction rate grows for some range of the prey’s population size. In contrast, it is shown that the structured PDE model can exhibit sustain oscillations even if the net reproductive rate is strictly declining with prey population size. We find that predation, even size-non-specific linear predation can destabilize a stable prey-only equilibrium, if reproduction is size specific and limited to individuals of large enough size. Furthermore, we show that size-specific predation can also destabilize the predator–prey equilibrium in the PDE model. We surmise that size-specific predation allows for temporary prey escape which is responsible for destabilization in the predator–prey dynamics.     

Oscillations in a refractory neural net

A functional differential equation that arises from the classic theory of neural networks is considered. As the length of the absolute refractory period is varied, there is, as shown here, a super-critical Hopf bifurcation. As the ratio of the refractory period to the time constant of the network increases, a novel relaxation oscillation occurs. Some approximations are made and the period of this oscillation is computed.     

The crystal and molecular structure of 9-alpha-D-arabinofuranosyladenine.

The glycosyl torsional angles in two crystallographically-independent molecules of alpha-araA are -73 and -64 degrees, both of which are in the "anti" region. The sugar conformations are C(3')-endo and C(2')-exo-C(3')-endo.     

Oscillations in a patchy environment disease model

For a single patch SIRS model with a period of immunity of fixed length, recruitment-death demographics, disease related deaths and mass action incidence, the basic reproduction number R(0) is identified. It is shown that the disease-free equilibrium is globally asymptotically stable if R(0)<1. For R(0)>1, local stability of the endemic equilibrium and Hopf bifurcation analysis about this equilibrium are carried out. Moreover, a practical numerical approach to locate the bifurcation values for a characteristic equation with delay-dependent coefficients is provided. For a two patch SIRS model with travel, it is shown that there are several threshold quantities determining its dynamic behavior and that travel can reduce oscillations in both patches; travel may enhance oscillations in both patches; or travel can switch oscillations from one patch to another.     

Oscillations in a system with material cycling

We study a system of two integrodifierential equations which models the evolution of a biotic species feeding on an abiotic resource. We also consider nutrient recycling with time delay. By Hopf bifurcation theory we prove the existence of stable oscillations for a range of values of the input of nutrients.Work performed within the activity of the research group Evolution Equations and Physico-Mathematical Applications, M.P.I. (Italy), and under the auspices of G.N.F.M., C.N.R. (Italy)     

Calcium Oscillations

Calcium signaling results from a complex interplay between activation and inactivation of intracellular and extracellular calcium permeable channels. This complexity is obvious from the pattern of calcium signals observed with modest, physiological concentrations of calcium-mobilizing agonists, which typically present as sequential regenerative discharges of stored calcium, a process referred to as calcium oscillations. In this review, we discuss recent advances in understanding the underlying mechanism of calcium oscillations through the power of mathematical modeling. We also summarize recent findings on the role of calcium entry through store-operated channels in sustaining calcium oscillations and in the mechanism by which calcium oscillations couple to downstream effectors.Calcium ions participate in a multiplicity of physiological and pathological functions. Among the most intensely studied, and the major focus of this article, is the role of Ca²⁺ as a cellular signal. Elevations in cytoplasmic Ca²⁺ mediate a plethora of cellular responses, ranging from extremely rapid events (muscle contraction, neurosecretion), to slower more subtle responses (cell division, differentiation, apoptosis). In contrast to most cellular signals, it is a relatively simple matter to observe changes in cytoplasmic Ca²⁺ in real time in living cells. As a result, the truly complex nature of Ca²⁺ signaling pathways has been revealed. The challenge is to understand what regulates these signals and what the biological significance of their complexity is.In the majority of laboratory experiments examining effects of various stimulants on Ca²⁺ signaling, supramaximal concentrations of activating agonists are employed resulting in rapid, robust, and often sustained increases in cytoplasmic Ca²⁺. It has long been appreciated that these signals result from a coordinated release of intracellular stores and increased Ca²⁺ influx across the plasma membrane (Bohr, 1973; Putney et al. 1981). The intracellular release of Ca²⁺ most commonly results from the Ca²⁺ releasing action of the phospholipase C-derived second messenger, inositol 1,4,5-trisphosphate (InsP₃) (Streb et al. 1983), whereas the entry of Ca²⁺ is because of the activation of store-operated channels in the plasma membrane (Putney 1986). However, it is becoming increasingly clear that these large sustained elevations seldom occur with physiological levels of stimulants. Rather the more common pattern of Ca²⁺ signaling, in both excitable and nonexcitable cells is a pattern of periodic discharges and/or entry of Ca²⁺. In excitable cells, such as the heart for example, these may be comprised of, or initiated by regenerative all-or-none plasma membrane channel activation, the Ca²⁺ action potential (Tsien et al. 1986) with amplification by intracellular Ca²⁺ release (Fabiato 1983). In nonexcitable cells, these spikes of cytoplasmic Ca²⁺ arise from regenerative discharge of stored Ca²⁺, a process generally termed Ca²⁺ oscillations (Prince and Berridge 1973; Woods et al. 1986). Like Ca²⁺ action potentials, these all-or-none discharges of Ca²⁺ represent a form of excitable behavior of the intracellular Ca²⁺ release signaling mechanism. However, because it is not possible to easily monitor and control the transmembrane chemical and biophysical parameters, as is the case for excitable plasma membrane behavior, it has been more difficult to fully understand the basic mechanisms by which these Ca²⁺ oscillations arise. Thus, although the question has been exhaustively studied for well over twenty years, there is still uncertainty and controversy over the underlying processes that give rise to Ca²⁺ oscillations. A number of reviews have discussed these issues at some length (Berridge and Galione 1988; Rink and Jacob 1989; Berridge 1990; Petersen and Wakui 1990; Berridge 1991; Cuthbertson and Cobbold 1991; Meyer and Stryer 1991; Hellman et al. 1992; Tepikin and Petersen 1992; Thomas et al. 1992; Dupont and Goldbeter 1993; Keizer 1993; Sneyd et al. 1994; Li et al. 1995; Thomas et al. 1996; Shuttleworth 1999; Lewis 2003; Dupont et al. 2007). In the current treatment, we have chosen to focus on two important aspects of Ca²⁺ oscillations. First, we review the available evidence for various computational models of Ca²⁺ oscillations that employ a quantitative approach to validate or repudiate specific mechanisms. Second, we consider the interrelationship between Ca²⁺ oscillations and plasma membrane Ca²⁺ influx mechanisms, with the view that we may learn more of the physiological function that these intracellular discharges of Ca²⁺ provide.     

The effect of HNS on the reinforcement of TNT crystal: a molecular simulation study

The effect of crystal modifier 2,2’,4,4’,6,6’-hexanitrostillbene(HNS) on the reinforcement of crystalline 1,3,5-trinitrotoluene (TNT) was investigated by molecular simulation. The intermolecular interactions between HNS and TNT were revealed by quantum chemistry calculations in detail, strong attractive forces were found between HNS and TNT. The solid interface models of TNT/HNS along three crystalline directions were studied, the distance between HNS molecule and TNT system was narrowed after optimization; the mechanical properties were calculated, showing the mechanism of the reinforcement.     

A redox-controlled molecular switch revealed by the crystal structure of a bacterial heme PAS sensor

PAS domains, which have been identified in over 1100 proteins from all three kingdoms of life, convert various input stimuli into signals that propagate to downstream components by modifying protein-protein interactions. One such protein is the Escherichia coli redox sensor, Ec DOS, a phosphodiesterase that degrades cyclic adenosine monophosphate in a redox-dependent manner. Here we report the crystal structures of the heme PAS domain of Ec DOS in both inactive Fe(3+) and active Fe(2+) forms at 1.32 and 1.9 A resolution, respectively. The protein folds into a characteristic PAS domain structure and forms a homodimer. In the Fe(3+) form, the heme iron is ligated to a His-77 side chain and a water molecule. Heme iron reduction is accompanied by heme-ligand switching from the water molecule to a side chain of Met-95 from the FG loop. Concomitantly, the flexible FG loop is significantly rigidified, along with a change in the hydrogen bonding pattern and rotation of subunits relative to each other. The present data led us to propose a novel redox-regulated molecular switch in which local heme-ligand switching may trigger a global "scissor-type" subunit movement that facilitates catalytic control.     

KcsA crystal structure as framework for a molecular model of the Na(+) channel pore

The crystal structure of the pore-forming part of the KcsA bacterial K(+)-selective channel suggests a possible motif for related voltage-gated channels. We examined the hypothesis that the spacial orientation of the KcsA M1 and M2 alpha-helices also predicts the backbone location of S5 and S6 helices of the voltage-gated Na(+) channel. That channel's P region structure is expected to be different because selectivity is determined by side-chain interactions rather than by main-chain carbonyls, and its outer vestibule accommodates relatively large toxin molecules, tetrodotoxin (TTX) and saxitoxin (STX), which interact with selectivity ring residues. The Na(+) channel P loop was well-modeled by the alpha-helix-turn-beta-strand motif, which preserves the relationships for toxin interaction with the Na(+) channel found experimentally. This outer vestibule was docked into the extracellular part of the inverted teepee structure formed by the S5 and S6 helices that were spacially located by coordinates of the KcsA M1 and M2 helix main chains [Doyle et al. (1998) Science 280, 69-74], but populated with side chains of the respective S5 and S6 structures. van der Waals contacts were optimized with minimal adjustment of the S5, S6, and P loop structures, forming a densely packed pore structure. Nonregular external S5-P and P-S6 segments were not modeled here, except the P-S6 segment of domain II. The resulting selectivity region structure is consistent with Na(+) channel permeation properties, offering suggestions for the molecular processes involved in selectivity. The ability to construct a Na(+) channel pore model consistent with most of the available biophysical and mutational information suggests that the KcsA structural framework may be conserved in voltage-gated channels.     

Synthesis and crystal and molecular structure of a methyl N,N-diethylcarbamylmethylenephosphonato dysprosium thiocyanate complex

Bis-Methyl N,N-diethylcarbamylmethylenephosphonato dysprosium thiocyanate, Dy[O₂P(OCH₃)CH₂C(O)N(C₂H₅)₂]₂(NCS) was prepared from the combination of ethanolic solutions of Dy(NCS)₃·xH₂O and (CH₃O)₂P(O)CH₂C(O)N(C₂H₅)₂. The complex was characterized by infrared and NMR spectroscopy, and single crystal X-ray diffraction methods. The crystal structure was determined at 25 °C from 3727 independent reflections by using a standard automated diffractometer. The complex was found to crystallize in the monoclinic space group P2₁/c with a = 13.282(4) Å, b = 19.168(5) Å, c = 9.648(2) Å, β = 90.09(2)°, Z = 4, V = 2456.4 ų and ?_cald = 1.72 g cm^?3. The structure was solved by standard heavy atom techniques, and blocked least-squares refinement converged with R_f = 4.7% and R_wF = 4.9%. The Dy atom is seven coordinate and bonded in a bidentate fashion to two anionic phosphonate ligands [O₂P(OCH₃)CH₂C(O)N(C₂H₅)₂^?] through the carbonyl oxygen atoms and one of two phosphonate oxygen atoms. In addition, each Dy atom is coordinated to two phosphonate oxygen atoms from two neighboring complexes and to the nitrogen atom of a thiocyanate ion. This coordination scheme gives rise to a two-dimensional polymeric structure. Some important bond distances include DyNCS 2.433(8) Å, DyO(carbonyl)_avg 2.39(2) Å, DyO(equat. phosphoryl)_avg 2.303(8) Å, DyO(axial phosphoryl)_avg 2.25(2), PO(phosphoryl)_avg 1.493(3) Å and CO(carbonyl)_avg 1.25(1) Å.     

Electrophoresis in protein crystal: nonequilibrium molecular dynamics simulations

Electrophoresis of a mixture of NaCl and CaCl₂ in a lysozyme crystal is investigated using nonequilibrium molecular dynamics (MD) simulations. Upon exposure to an electric field, the stability of lysozyme is found to decrease slightly. This finding is demonstrated by increases in the root mean-square deviations of the heavy atoms of lysozyme, in the solvent-accessible surface area of hydrophobic residues, and in the number of hydrogen bonds between lysozyme and water. The solvent-accessible surface area of hydrophilic residues changes marginally, and the number of hydrogen bonds between lysozyme molecules decreases. Water molecules tend to align preferentially parallel to the electric field, and the dipole moment along the pore axis increases linearly with increasing field strength. Two pronounced layered structures are observed for Na⁺ and Ca²⁺ in the vicinity of protein surface, but only one enriched layer is observed for Cl⁻. The number distributions of all ions are nearly independent of the electric field. The water coordination numbers of all ions are smaller in the crystal than in aqueous bulk solution; however, the reverse is found for the Cl⁻ coordination numbers of cations. Both the water and the Cl⁻ coordination numbers are insensitive to the electric field. Ion diffusivities in the crystal are ∼2 orders of magnitude smaller than those in aqueous bulk solution. The drift velocities of ions increase proportionally to the electric field, particularly at high strengths, and depend on ionic charge and coordination with oppositely charged ions. Electrical current exhibits a linear relationship with the field strength. The zero-field electrical conductivity is estimated to be 0.56 S/m, which is very close to 0.61 S/m as predicted by the Nernst-Einstein equation.     

Synthesis, crystal structure and molecular conformation of N-Ac-dehydro-Phe-L-Val-OH.

The peptide N-Ac-dehydro-Phe-L-Val-OH (C16H20N2O4) was synthesized by the usual workup procedure. The peptide crystallizes from its solution in acetonitrile at 4 degrees in hexagonal space group P6(5) with a = b = 11.874(2)A, c = 21.856(9) A, V = 2668(1) A3, Z = 6, dm = 1.151(3) g cm-3, dc = 1.136(4) g cm-3, CuK alpha = 1.5418 A, mu = 0.641 mm-1, F(000) = 972, T = 293 K. The structure was solved by direct methods and refined by least-squares procedure to an R value of 0.074 for 1922 observed reflections. In the dehydro-residue, the C1 alpha-C1 beta distance is 1.35(1) A while the bond angle C1 alpha-C1 beta-C1 gamma is 131.2(9) degrees. The backbone torsion angles are: omega 0 = 172(1) degrees, phi 1 = -60(2) degrees, psi 1 = -31(2) degrees, omega 1 = -179(1) degrees, phi 2 = 59(2) degrees. These values suggest that the peptide tends to adopt an alternating right-handed and left-handed helical conformation. The side chain torsion angles are: chi 1(1) = -6(2) degrees, chi 1(2.1) = -1(2) degrees, chi 1(2.2) = -178(2) degrees, chi 2(1.1) = 63(2) degrees and chi 2(1.2) = -173(1) degrees. These values show that the side chain of dehydro-Phe is planar whereas the valyl side chain adopts a sterically most preferred conformation. The molecules, linked by intermolecular hydrogen bonds and van der Waals forces, are arranged in helices along the c-axis. The helices are held side-by-side by van der Waals contacts.     

The crystal and molecular structures of cellulose I and II

The paper describes molecular dynamics (MD) simulations on the crystal structures of the Iβ and II phases of cellulose. Structural proposals for each of these were made in the 1970s on the basis of X-ray diffraction data. However, due to the limited resolution of these data some controversies remained and details on hydrogen bonding could not be directly obtained. In contrast to structure factor amplitudes in X-ray diffraction, energies, as obtained from MD simulations, are very sensitive to the positions of the hydroxyl hydrogen atoms. Therefore the latter technique is very suitable for obtaining such structural details. MD simulations of the Iβ phase clearly shows preference for one of the two possible models in which the chains are packed in a parallel orientation. Only the parallel-down mode (in the definition of Gardner and Blackwell (1974) J Biopolym 13: 1975-2001) presents a stable structure. The hydrogen bonding consists of two intramolecular hydrogen bonds parallel to the glycosidic linkage for both chains, and two intralayer hydrogen bonds. The layers are packed hydrophobically. All hydroxymethyl group are positioned in the tg conformation. For the cellulose II form it was found that, in contrast to what seemed to emerge from the X-ray fibre diffraction data, both independent chains had the gt conformation. This idea already existed because of elastic moduli calculations and 13C-solid state NMR data. Recently, the structure of cellotetraose was determined. There appear to be a striking similarity between the structure obtained from the MD simulations and this cellotetraose structure in terms of packing of the two independent molecules, the hydrogen bonding network and the conformations of the hydroxymethyl group, which were also gt for both molecules. The structure forms a 3D hydrogen bonded network, and the contribution from electrostatics to the packing is more pronounced than in case of the Iβ structure. In contrast to what is expected, in view of the irreversible transition of the cellulose I to II form, the energies of the Iβ form is found to be lower than that of II by 1 kcal mol-1 per cellobiose. This revised version was published online in November 2006 with corrections to the Cover Date.     

Modeling crystal and molecular deformation in regenerated cellulose fibers

Experimental deformation micromechanics of regenerated cellulose fibers using Raman spectroscopy have been widely reported. Here we report on computer modeling simulations of Raman band shifts in modes close to the experimentally observed 1095 cm(-1) band, which has previously been shown to shift toward a lower wavenumber upon application of external fiber deformation. A molecular mechanics approach is employed using a previously published model structure of cellulose II. Changing the equilibrium c-spacing of this structure and then performing a minimization routine mimics tensile deformation. Normal-mode analysis is then performed on the minimized structure to predict the Raman-intensive vibrations. By using a dot-product analysis on the predicted eigenvectors it is shown that some Raman active modes close to the 1095 cm(-1) band interchange at certain strain levels. Nevertheless, when this is taken into account it is shown that it is possible to find reasonable agreement between theory and experiment. The effect of the experimentally observed broadening of the Raman bands is discussed in terms of crystalline and amorphous regions of cellulose, and this is compared to the lack of X-ray broadening to explain why discrepancies between theory and experiment are present. A hybrid model structure with a series-parallel arrangement of amorphous and misaligned amorphous-crystalline domains is proposed which is shown to agree with what is observed experimentally. Finally, the theoretical crystal modulus for cellulose II is reported as 98 GPa, which is shown to be in agreement with other studies and with an experimental measurement using synchrotron X-ray diffraction.