Left ventricular wall stress compendium

Left ventricular (LV) wall stress has intrigued scientists and cardiologists since the time of Lame and Laplace in 1800s. The left ventricle is an intriguing organ structure, whose intrinsic design enables it to fill and contract. The development of wall stress is intriguing to cardiologists and biomedical engineers. The role of left ventricle wall stress in cardiac perfusion and pumping as well as in cardiac pathophysiology is a relatively unexplored phenomenon. But even for us to assess this role, we first need accurate determination of in vivo wall stress. However, at this point, 150 years after Lame estimated left ventricle wall stress using the elasticity theory, we are still in the exploratory stage of (i) developing left ventricle models that properly represent left ventricle anatomy and physiology and (ii) obtaining data on left ventricle dynamics. In this paper, we are responding to the need for a comprehensive survey of left ventricle wall stress models, their mechanics, stress computation and results. We have provided herein a compendium of major type of wall stress models: thin-wall models based on the Laplace law, thick-wall shell models, elasticity theory model, thick-wall large deformation models and finite element models. We have compared the mean stress values of these models as well as the variation of stress across the wall. All of the thin-wall and thick-wall shell models are based on idealised ellipsoidal and spherical geometries. However, the elasticity model's shape can vary through the cycle, to simulate the more ellipsoidal shape of the left ventricle in the systolic phase. The finite element models have more representative geometries, but are generally based on animal data, which limits their medical relevance. This paper can enable readers to obtain a comprehensive perspective of left ventricle wall stress models, of how to employ them to determine wall stresses, and be cognizant of the assumptions involved in the use of specific models.     

Effect of membrane stiffness and cytoskeletal element density on mechanical stimuli within cells: an analysis of the consequences of ageing in cells

A finite element model of a single cell was created and used to compute the biophysical stimuli generated within a cell under mechanical loading. Major cellular components were incorporated in the model: the membrane, cytoplasm, nucleus, microtubules, actin filaments, intermediate filaments, nuclear lamina and chromatin. The model used multiple sets of tensegrity structures. Viscoelastic properties were assigned to the continuum components. To corroborate the model, a simulation of atomic force microscopy indentation was performed and results showed a force/indentation simulation with the range of experimental results. A parametric analysis of both increasing membrane stiffness (thereby modelling membrane peroxidation with age) and decreasing density of cytoskeletal elements (thereby modelling reduced actin density with age) was performed. Comparing normal and aged cells under indentation predicts that aged cells have a lower membrane area subjected to high strain as compared with young cells, but the difference, surprisingly, is very small and may not be measurable experimentally. Ageing is predicted to have a more significant effect on strain deep in the nucleus. These results show that computation of biophysical stimuli within cells are achievable with single-cell computational models; correspondence between computed and measured force/displacement behaviours provides a high-level validation of the model. Regarding the effect of ageing, the models suggest only small, although possibly physiologically significant, differences in internal biophysical stimuli between normal and aged cells.     

The investigation of the G-quadruplex aptamer selectivity to Pb2+ ion: a joint molecular dynamics simulation and density functional theory study

Abstract

The aptamers with the ability to form a G-quadruplex structure can be stable in the presence of some ions. Hence, study of the interactions between such aptamers and ions can be beneficial to determine the highest selective aptamer toward an ion. In this article, molecular dynamics (MD) simulations and quantum mechanics (QM) calculations have been applied to investigate the selectivity of the T30695 aptamer toward Pb²⁺ in comparison with some ions. The Free Energy Landscape (FEL) analysis indicates that Pb²⁺ has remained inside the aptamer during the MD simulation, while the other ions have left it. The Molecular Mechanics Poisson-Boltzmann Surface Area (MM-PBSA) binding energies prove that the conformational stability of the aptamer is the highest in the presence of Pb²⁺. According to the compaction parameters, the greatest compressed ion-aptamer complex, and hence, the highest ion-aptamer interaction have been induced in the presence of Pb²⁺. The contact maps clarify the closer contacts between the nucleotides of the aptamer in the presence of Pb²⁺. The density functional theory (DFT) results show that Pb²⁺ forms the most stable complex with the aptamer, which is consistent with the MD results. The QM calculations reveal that the N-H bonds and the O…H distances are the longest and the shortest, respectively, in the presence of Pb²⁺. The obtained results verify that the strongest hydrogen bonds (HBs), and hence, the most compressed aptamer structure are induced by Pb²⁺. Besides, atoms in molecules (AIM) and natural bond orbital (NBO) analyses confirm the results.

Communicated by Ramaswamy H. Sarma     

Computationally guided identification of Akt-3, a serine/threonine kinase inhibitors: Insights from homology modelling,structure-based screening,molecular dynamics and quantum mechanical calculations

Abstract

Chemical entities targeting kinase signalling pathways serve as a potential strategy to combat malignancies. Protein Kinase B or Akt is a validated target for various malignancies and Akt3 remains the least explored isoform among all its isoforms. Initially, homology modelling technique was used for generating protein structure and further validation was performed using molecular dynamics simulation and Ramachandran plot. The validated protein structure was then subjected for active site analysis which led to identification of active site residues based on metrics provided by site score. The important residues in binding site were identified as Thr81, Asp271 and Asp289 for binding energetics and inhibition. Subsequently, virtual screening methodologies were used for identification of novel hits for inhibition of Protein Kinase B or Akt3. This led to the identification of two hits, i.e. thiophene derivative and thieno-pyridine derivative which were selected on the basis of their binding affinity and drug likeliness. These identified hits were subjected for molecular dynamics simulations, quantum mechanical and synthetic accessibility studies. The role of crucial residues in binding site stood validated as suggested by molecular dynamics simulations studies.

Communicated by Ramaswamy H. Sarma     

Ligand binding and dynamics of the monomeric epidermal growth factor receptor ectodomain

The ectodomain of the human epidermal growth factor receptor (hEGFR) controls input to several cell signalling networks via binding with extracellular growth factors. To gain insight into the dynamics and ligand binding of the ectodomain, the hEGFR monomer was subjected to molecular dynamics simulation. The monomer was found to be substantially more flexible than the ectodomain dimer studied previously. Simulations where the endogeneous ligand EGF binds to either Subdomain I or Subdomain III, or where hEGFR is unbound, show significant differences in dynamics. The molecular mechanics Poisson–Boltzmann surface area method has been used to derive relative free energies of ligand binding, and we find that the ligand is capable of binding either subdomain with a slight preference for III. Alanine‐scanning calculations for the effect of selected ligand mutants on binding reproduce the trends of affinity measurements. Taken together, these results emphasize the possible role of the ectodomain monomer in the initial step of ligand binding, and add details to the static picture obtained from crystal structures. Proteins 2013; 81:1931–1943. © 2013 The Authors. Proteins published by Wiley Periodicals, Inc.     

Basic statistics and variational concepts behind the reverse Monte Carlo technique

We revise the statistical foundations of the reverse Monte Carlo (RMC) technique by constructing the associated functional of a variational principle which incorporates, without any ad hoc assumptions, the inherent errors accompanying the simulation and the experimental data. We propose a Bayesian criteria for acceptance/rejection of configurations, in terms of the variations of the functional. The loss function and variational functional minimization approaches are compared.     

Configurational Temperature for Brownian Dynamics

Abstract

Expressions for the configurational temperature are evaluated in Brownian dynamics simulations of a Lennard-Jones fluid and compared with the input temperature which is used to generate the random displacements. It is found that the two temperatures agree in the limit of large numbers of particles, and even for moderate system sizes the configurational temperature is a useful check on the correctness of the simulation algorithm. Investigation of the autocorrelation functions shows that for Lennard-Jones and power-law fluids, the correlation time of the configurational temperature is shorter than other typical thermodynamic quantities, and it generally increases with the range of the potential.     

Ab initio fragment molecular orbital calculations on the specific interactions between human,mouse and rat PPARα and GW409544

To elucidate the specific interactions between the peroxisome proliferator-activated receptor (PPARα) and ligand GW409544 (GW), we obtained the solvated structures of the PPARα+GW complexes for human, mouse and rat by classical molecular mechanics calculations, and investigated their electronic properties by ab initio fragment molecular orbital calculations. The results indicate that the positively charged amino acids (Lys and Arg) of PPARα make a major contribution to the binding between PPARα and GW. In addition, it was clarified that Ser280 and Tyr314 of human and rat PPARα have a large attractive interaction with GW, while Ser280, Tyr314 and His440 of mouse PPARα have large interaction. These results on the difference in specific interactions between human and mouse/rat PPARα will be useful for predicting the effects of new chemicals on the human body based on the biomedical studies for the experimental animals such as mouse and rat.     

Molecular Mechanics Studies of Molybdenum Disulphide Catalysts Parameterisation of Molybdenum and Sulphur

Abstract

A method for the parameterisation of molybdenum disulphide is presented which reproduces the crystal structure accurately. The method involves calculating parameters such that there is no net force contribution from any individual term of the potential on any atom. Ideal bond lengths and bond angles are taken from the X-ray crystal structure; stretching and bending force constants are calculated from a combination of spectroscopic data and quantum mechanics calculations, whereby the energy function with bond length or bond angle is calculated and fitted with an harmonic potential. For the non-bonded Lennard-Jones parameters, the dispersion coefficient C was calculated by an interpolation of existing published parameters using a multiple regression and then the crystal energy was minimised with respect to the van der Waals radius r₀ using a fixed crystal fragment.

These parameters were tested for various models of the hexagonal and rhombohedral forms of MoS₂. RMS fits between structures minimised with molecular mechanics and experimental models ranged from 0.006 Å to 0.012 Å.