Free vibration of rectangular plates of arbitrary thickness

Free vibration of thick rectangular plates is investigated by using the “method of initial functions” proposed by Vlasov. The governing equations are derived from the three-dimensional elastodynamic equations. They are obtained in the form of series and theories of any desired order can be constructed by deleting higher terms in the infinite order differential equations. The numerical results are compared with those of classical, Mindlin, and Lee and Reismann solutions.

Evolution of Grain-Boundary Microstructure and Texture in Interstitial-Free Steel Processed by Equal-Channel Angular Extrusion

The equal-channel angular extrusion (ECAE) of Ti-bearing interstitial-free (IF) steel was performed following two different routes, up to four passes, at a temperature of 300 degrees C. The ECAE led to a grain refinement to submicron size. After the second pass, the grain size attained saturation thereafter. The microstructural analysis indicated the presence of coincident-site lattice (CSL) boundaries in significant fraction, in addition to a high volume fraction of high-angle random boundaries and some low-angle boundaries after the deformation. Among the special boundaries, Sigma 3 and Sigma 13 were the most prominent ones and their fraction depended on the processing route followed. A deviation in the misorientation angle distribution from the Mackenzie distribution was noticed. The crystallographic texture after the first pass resembled that of simple shear, with the {112}, {110}, and {123} aligned to the macroscopic shear plane.

Free energy calculations of glycosaminoglycan - Protein interactions

Glycosaminoglycans (GAGs) are complex highly charged linear polysaccharides that have a variety of roles in biological processes. We report the first use of molecular dynamics (MD) free energy calculations using the MM/PBSA method to investigate the binding of GAGs to protein molecules, namely the platelet endothelial cell adhesion molecule 1 (PECAM-1) and annexin A2. Calculations of the free energy of the binding of heparin fragments of different sizes reveal the existence of a region of low GAG-binding affinity in domains 5-6 of PECAM-1 and a region of high affinity in domains 2-3, consistent with experimental data and ligand-protein docking studies. A conformational hinge movement between domains 2 and 3 was observed, which allows the binding of heparin fragments of increasing size (pentasaccharides to octasaccharides) with an increasingly higher binding affinity. Similar simulations of the binding of a heparin fragment to annexin A2 reveal the optimization of electrostatic and hydrogen bonding interactions with the protein and protein-bound calcium ions. In general, these free energy calculations reveal that the binding of heparin to protein surfaces is dominated by strong electrostatic interactions for longer fragments, with equally important contributions from van der Waals interactions and vibrational entropy changes, against a large unfavorable desolvation penalty due to the high charge density of these molecules.

Free energy calculations of the interactions of c-Jun-based synthetic peptides with the c-Fos protein

The c-Fos–c-Jun complex forms the activator protein 1 transcription factor, a therapeutic target in the treatment of cancer. Various synthetic peptides have been designed to try to selectively disrupt the interaction between c-Fos and c-Jun at its leucine zipper domain. To evaluate the binding affinity between these synthetic peptides and c-Fos, polarizable and nonpolarizable molecular dynamics (MD) simulations were conducted, and the resulting conformations were analyzed using the molecular mechanics generalized Born surface area (MM/GBSA) method to compute free energies of binding. In contrast to empirical and semiempirical approaches, the estimation of free energies of binding using a combination of MD simulations and the MM/GBSA approach takes into account dynamical properties such as conformational changes, as well as solvation effects and hydrophobic and hydrophilic interactions. The predicted binding affinities of the series of c-Jun-based peptides targeting the c-Fos peptide show good correlation with experimental melting temperatures. This provides the basis for the rational design of peptides based on internal, van der Waals, and electrostatic interactions.

Calculations of the free energy of interaction of the c-Fos−c-Jun coiled coil: Effects of the solvation model and the inclusion of polarization effects

The leucine zipper region of activator protein-1 (AP-1) comprises the c-Jun and c-Fos proteins and constitutes a well-known coiled coil protein−protein interaction motif. We have used molecular dynamics (MD) simulations in conjunction with the molecular mechanics/Poisson−Boltzmann generalized-Born surface area [MM/PB(GB)SA] methods to predict the free energy of interaction of these proteins. In particular, the influence of the choice of solvation model, protein force field, and water potential on the stability and dynamic properties of the c-Fos−c-Jun complex were investigated. Use of the AMBER polarizable force field ff02 in combination with the polarizable POL3 water potential was found to result in increased stability of the c-Fos−c-Jun complex. MM/PB(GB)SA calculations revealed that MD simulations using the POL3 water potential give the lowest predicted free energies of interaction compared to other nonpolarizable water potentials. In addition, the calculated absolute free energy of binding was predicted to be closest to the experimental value using the MM/GBSA method with independent MD simulation trajectories using the POL3 water potential and the polarizable ff02 force field, while all other binding affinities were overestimated.

Free vibration of rectangular plates of arbitrary thickness with one or more edges clamped

Frequencies of free vibration of rectangular plates of arbitrary thickness, with different support conditions, are calculated by using the Method of Initial Functions (MIF), proposed by Vlasov. Sixth and fourth order MIF theories are used for the solution. Numerical results are presented for three square plates for three thickness ratios. The support conditions considered are (i) three sides simply supported and one side clamped, (ii) two opposite sides simply supported and the other two sides clamped and (iii) all sides clamped. It is found that the results produced by the MIF method are in fair agreement with those obtained by using other methods. The classical theory gives overestimates of the frequencies and the departures from the MIF results increase for higher modes and larger thickness ratios.

Theoretical calculations of base-base interactions in nucleic acids: I Stacking interactions in free bases

Stacking interactions in free bases were computed on the basis of molecular association. The results of the calculations were compared with the stacking patterns observed in a few single crystals of nucleic acid components as examples. The following are the conclusions: (i) there can be two types of stacking pattern classified as normal and inverted types for any two interacting bases and both can be energetically favourable (ii) in both the types the stacking interaction is a combined effect of the overlap of the interacting bases and relative positions and orientations of the atomic centres of the two bases (iii) crystal symmetry and H-bonding interaction may influence stacking patterns.

Vitrification, relaxation and free volume in glycerol-water binary liquid mixture:Spin probe ESR studies

Glass transition and relaxation of the glycerol-water (G-W) binary mixture system have been studied over the glycerol concentration range of 5-85 mol% by using the highly sensitive technique of electron spin resonance (ESR). For the water rich mixture the glass transition,sensed by the dissolved spin probe, arises from the vitrified mesoscopic portion of the binary system. The concentration dependence of the glass transition temperature manifests a closely related molecular level cooperativity in the system. A drastic change in the mesoscopic structure of the system at the critical concentration of 40 mol is confirmed by an estimation of the spin probe effective volume in a temperature range where the tracer reorientation is strongly coupled to the system dynamics.

Microneurovascular free muscle transfer with cross-over nerve grafts in facial reanimation

Microneurovascular free muscle transfer with cross-over nerve grafts in facial reanimation Loss of facial symmetry and mimetic function as seen in facial paralysis has an enormous impact on the psychosocial conditions of the patients. Patients with severe long-term facial paralysis are often reanimated with a two-stage procedure combining cross-facial nerve grafting, and 6 to 8 months later with microneurovascular (MNV) muscle transfer. In this thesis, we recorded the long-term results of MNV surgery in facial paralysis and observed the possible contributing factors to final functional and aesthetic outcome after this procedure. Twenty-seven out of forty patients operated on were interviewed, and the functional outcome was graded. Magnetic resonance imaging (MRI) of MNV muscle flaps was done, and nerve graft samples (n=37) were obtained in second stage of the operation and muscle biopsies (n=18) were taken during secondary operations.. The structure of MNV muscles and nerve grafts was evaluated using histological and immunohistochemical methods ( Ki-67, anti-myosin fast, S-100, NF-200, CD-31, p75NGFR, VEGF, Flt-1, Flk-1). Statistical analysis was performed. In our studies, we found that almost two-thirds of the patients achieved good result in facial reanimation. The longer the follow-up time after muscle transfer the weaker was the muscle function. A majority of the patients (78%) defined their quality of life improved after surgery. In MRI study, the free MNV flaps were significantly smaller than originally. A correlation was found between good functional outcome and normal muscle structure in MRI. In muscle biopsies, the mean muscle fiber diameter was diminished to 40% compared to control values. Proliferative activity of satellite cells was seen in 60% of the samples and it tended to decline with an increase of follow-up time. All samples showed intramuscular innervation. Severe muscle atrophy correlated with prolonged intraoperative ischaemia. The good long-term functional outcome correlated with dominance of fast fibers in muscle grafts. In nerve grafts, the mean number of viable axons amounted to 38% of that in control samples. The grafted nerves characterized by fibrosis and regenerated axons were thinner than in control samples although they were well vascularized. A longer time between cross facial nerve grafting and biopsy sampling correlated with a higher number of viable axons. P75Nerve Growth Factor Receptor (p75NGFR) was expressed in every nerve graft sample. The expression of p75NGFR was lower in older than in younger patients. A high expression of p75NGFR was often seen with better function of the transplanted muscle. In grafted nerve Vascular Endothelial Growth Factor (VEGF) and its receptors were expressed in nervous tissue. In conclusion, most of the patients achieved good result in facial reanimation and were satisfied with the functional outcome. The mimic function was poorer in patients with longer follow-up time. MRI can be used to evaluate the structure of the microneurovascular muscle flaps. Regeneration of the muscle flaps was still going on many years after the transplantation and reinnervation was seen in all muscle samples. Grafted nerves were characterized by fibrosis and fewer, thinner axons compared to control nerves although they were well vascularized. P75NGFR and VEGF were expressed in human nerve grafts with higher intensity than in control nerves which is described for the first time.

Functional Outcome after Free Flap Reconstructions in Oral and Pharyngeal Cancer

Oral cancer ranks among the 10 most common cancers worldwide. Since it is commonly diagnosed at locally advanced stage, curing the cancer demands extensive tissue resection. The emergent defect is reconstructed generally with a free flap transfer. Repair of the upper aerodigestive track with maintenance of its multiform activities is challenging. The aim of the study was to extract comprehensive treatment outcomes for patients having undergone microvascular free flap transfer because of large oral cavity or pharyngeal cancer. Ninety-four patients were analyzed for postoperative survival and complications. Forty-four patients were followed-up and analyzed for functional outcome, which was determined in terms of quality of life, speech, swallowing, and intraoral sensation. Quality of life was assessed using the University of Washington Head and Neck Questionnaire. Speech was analyzed for aerodynamic parameters and for nasal acoustic energy, as well as perceptually for articulatory proficiency, voice quality, and intelligibility. Videofluorography was performed to determine the swallowing ability. Intraoral sensation was measured by moving 2-point discrimination. The 3-year overall survival was over 40%. The 1-year disease-free survival was 43%. Postoperative complications arose in over half of the patients. Flap success rate was high. Perioperative mortality varied between 2% and 11%. Unemployment and heavy drinking were the strongest predictors of survival. Sociodemographic factors were found to associate with quality of life. The global quality of life score deteriorated and did not return to the preoperative level. Significant reduction was detectable in the domains measuring chewing and speech, and in appearance and shoulder function. The basic elements necessary for normal speech were maintained. Speech intelligibility reduced and was related to the misarticulations of the /r/ and /s/ phonemes. Deviant /r/ and /s/ persisted in most patients. Hoarseness and hypernasality occurred infrequently. One year postoperatively, 98% of the patients had achieved oral nutrition and half of them were on a regular masticated diet. Overt and silent aspiration was encountered throughout the follow-up. At 12-month swallow test, 44% of the patients aspirated, 70% of whom silently. Of these patients, 15% presented with pulmonary changes referring to aspiration. Intraoral sensation weakened but was unrelated to oral functions. The results provide new data for oral reconstructions and highlight the importance of the functional outcome of the treatment for an oral cancer patient. The mouth and the pharynx encompass a unit of utmost functional complexity. Surgery should continue to make progress in this area, and methods that lead to good function should be developed. Operational outcome should always be evaluated in terms of function.

Allostery and conformational free energy changes in human tryptophanyl-tRNA synthetase from essential dynamics and structure networks

The interdependence of the concept of allostery and enzymatic catalysis, and they being guided by conformational mobility is gaining increased prominence. However, to gain a molecular level understanding of llostery and hence of enzymatic catalysis, it is of utter importance that the networks of amino acids participating in allostery be deciphered. Our lab has been exploring the methods of network analysis combined with molecular dynamics simulations to understand allostery at molecular level. Earlier we had outlined methods to obtain communication paths and then to map the rigid/flexible regions of proteins through network parameters like the shortest correlated paths, cliques, and communities. In this article, we advance the methodology to estimate the conformational populations in terms of cliques/communities formed by interactions including the side-chains and then to compute the ligand-induced population shift. Finally, we obtain the free-energy landscape of the protein in equilibrium, characterizing the free-energy minima accessed by the protein complexes. We have chosen human tryptophanyl-tRNA synthetase (hTrpRS), a protein esponsible for charging tryptophan to its cognate tRNA during protein biosynthesis for this investigation. This is a multidomain protein exhibiting excellent allosteric communication. Our approach has provided valuable structural as well as functional insights into the protein. The methodology adopted here is highly generalized to illuminate the linkage between protein structure networks and conformational mobility involved in the allosteric mechanism in any protein with known structure.

Free and ATP-bound structures of Ap(4)A hydrolase from Aquifex aeolicus V5

Asymmetric diadenosine tetraphosphate (Ap(4)A) hydrolases degrade the metabolite Ap(4)A back into ATP and AMP. The three-dimensional crystal structure of Ap(4)A hydrolase (16 kDa) from Aquifex aeolicus has been determined in free and ATP-bound forms at 1.8 and 1.95 angstrom resolution, respectively. The overall three-dimensional crystal structure of the enzyme shows an alpha beta alpha-sandwich architecture with a characteristic loop adjacent to the catalytic site of the protein molecule. The ATP molecule is bound in the primary active site and the adenine moiety of the nucleotide binds in a ring-stacking arrangement equivalent to that observed in the X-ray structure of Ap(4)A hydrolase from Caenorhabditis elegans. Binding of ATP in the active site induces local conformational changes which may have important implications in the mechanism of substrate recognition in this class of enzymes. Furthermore, two invariant water molecules have been identified and their possible structural and/or functional roles are discussed. In addition, modelling of the substrate molecule at the primary active site of the enzyme suggests a possible path for entry and/or exit of the substrate and/or product molecule.

Force-free equilibria of magnetized jets

Force-free equilibrium configurations of magnetic-pressure-dominated magnetized supersonic jets confined by slowly varying external pressure are investigated analytically. For the case where internal dissipation mechanisms are active, the lowest-energy field configuration is found to be the superposition of an axisymmetric mode and a helical mode with a wavelength equal to 5 times the jet radius, and the pressure below which the nonaxisymmetric mode becomes energetically favorable is given as 2700 times the product of the 4th power of the magnetic helicity per unit length and the -6th power of the magnetic flux. A model of the total and polarized emission of such a configuration is developed and applied to the extended well-collimated astronomically resolved jet NGC 6251. The model is shown to reproduce significant features such as transverse oscillations of the ridge line, width oscillations and emission knots, the projected magnetic-field configuration, oscillations of the degree of polarization, and the distribution of the Faraday rotation measure.

Magnetic energy dissipation in force-free jets

It is shown that a magnetic-pressure-dominated, supersonic jet which expands (or contracts) in response to variations in the confining external pressure can dissipate magnetic energy through field-line reconnection as it relaxes to a minimum-energy configuration. In order for a continuous dissipation to take place, the effective reconnection time must be a fraction ɛ ⪉ 1 of the expansion time. The amount of energy dissipation is calculated, and it is concluded that magnetic energy dissipation could, in principle, power the observed synchrotron emission in extragalactic radio jets such as NGC 6251. However, this mechanism is only viable if the reconnection time is substantially shorter than the nominal resistive tearing time in the jet.