How Does the First Molar Root Location Affect the Critical Stress Pattern in the Periodontium? A Finite Element Analysis.

Statement of the Problem: The first molar root location plays a pivotal role in neutralization of forces applied to the teeth to prevent injury. Purpose: This study aimed to assess the effect of maxillary and mandibular first molar root location on biomechanical behavior of the periodontium under vertical and oblique loadings. Materials and Method: In this three-dimensional (3D) finite element analysis (FEA), the maxillary and mandibular first molars and their periodontium were modeled. The Young's modulus and the Poisson's ratio for the enamel, dentin, dental pulp, periodontal ligament (PDL), and cortical and cancellous bones were adopted from previous studies. The changes in maximum von Misses stress (MVMS) values of each component were analyzed. Results: The MVMS values were the highest in the enamel followed by dentin, cortical bone, cancellous bone, and PDL. The maxillary and mandibular first molars with different root locations and their periodontium showed different biomechanical behaviors under the applied loads. Conclusion: An interesting finding was that the stress concentration point in the path of load degeneration changed from the cervical third in dentin to the apical third in the cancellous bone, which can greatly help in detection of susceptible areas over time.

Design optimization procedure for an orthopedic insole having a continuously variable stiffness/shape to reduce the plantar pressure in the foot of a diabetic patient.

Foot ulcers and lower-limb amputations are among the major problems in diabetic patients. Orthopedic insoles can reduce the risk of diabetic foot ulcers in patients through pressure redistribution on the bottom of the foot. The purpose of this study was to propose an optimization method to design the dedicated insoles for diabetic patients in order to decrease the maximum plantar pressure. At first, a three-dimensional finite element model of bones, ligaments and soft tissue of a diabetic patient's foot was created using CT scan images. Then, the foot plantar pressure was calculated by means of a finite element software. Next, the stiffness and shape of a simple flat insole were separately modified to reduce the maximum foot plantar pressure. The optimization method resulted in a dedicated insole design with a continuously variable stiffness/shape within its area that creates a smooth pressure distribution for the patient comfort. The results showed a 40% reduction in the maximum foot pressure, which we attribute to the modification of insole stiffness. In addition, the optimal shape of the proposed insole decreased the maximum plantar pressure by 25% compared to the flat insole.

A Study on the Bending Stiffness of a New DNA Origami Nano-Joint.

The present article aims to investigate the mechanical properties of a new DNA origami nano-joint using the steered molecular dynamics (SMD) simulation. Since the analysis of mechanical properties is of great importance in bending conditions for a nano-joint, the forces are selected to achieve angular changes in the joint by the resultant torque. In this study, the nano-joint is considered as a beam in order to use mechanical equations to extract the mechanical properties of the designed nano-joint. In addition, the bending stiffness of the beam is investigated in different modes of deflection using the Euler-Bernoulli beam theory. The results revealed that the value of bending stiffness increases with increasing deflection, and the changes in the bending stiffness relative to the deflection is linear. The proposed DNA origami nano-joint can be used as a joint in nanorobots and can be effectively applied in nanorobotic systems to move different components.

The effect of functionally graded materials on bone remodeling around osseointegrated trans-femoral prostheses.

Osseointegrated trans-femoral fixations have been used as alternatives for conventional sockets in recent years. Despite numerous advantages, the dissimilarity of the mechanical properties between bone and implant has led to issues in periprosthetic bone adaptation. This study aims to address these issues by proposing fixations made of functionally graded materials (FGMs). The computational study of bone remodeling was performed by linking a bone remodeling algorithm to the finite element analysis. The 3D model of the femur was created by computerized tomography (CT) scan images, and a Titanium fixture, along with nine Titanium/Hydroxyapatite FGM fixtures, were modeled. The analyses revealed evident advantages for the FGM fixtures over the conventionally used Titanium fixtures. Furthermore, it was shown that the gradation direction considerably affects the bone adaptation procedure. The results showed that using a radial FGM with low-stiffness material in the outer layer and less metal composition significantly improves the bone remodeling behavior.

The effect of the degradation pattern of biodegradable bone plates on the healing process using a biphasic mechano-regulation theory.

Bone plates are used to treat bone fractures by stabilizing the fracture site and allowing treatments to take place. Mechanical properties of the applied bone plate determine the stability of the fracture site and affect the endochondral ossification process and the healing performance. In recent years, biodegradable bone plates have been used in demand for the elimination of a second surgery to remove the plate. The degradation of these plates into the body environment is commonly accompanied by alterations in the mechanical properties of the bone plate and a shift in the healing performance of the bone. In the present study, the effects of using biodegradable plates with various elastic moduli and degradation patterns, including linear and nonlinear, on the healing process are investigated. A three-dimensional finite element model of the radius bone along with a mechano-regulation theory was used to study the healing performance. Two mechanical stimuli of octahedral shear strain and interstitial fluid flow are considered as the propelling factors of healing. The results of this study indicated that increasing the bone plate's initial elastic modulus accelerates the healing process. However, by increasing the initial Young's modulus of the plate more than 100 GPa, no noticeable alteration is observed. The degradation time period of the plate was seen to be directly related to the speed of the healing process. It is shown, however, that by increasing the degradation time period to more than 8 weeks, the healing performance remains almost unchanged. The results of this work showed that the application of plates with a high enough initial elastic modulus and degradation period can prevent the healing process from decelerating.

Comparative analysis of the viscoelastic properties of collagen-like proteins by virtual creep test.

Viscoelasticity of collagen is essential for the integrity of connective tissue and its aberrancy may result in collagen dysfunction and the emergence of connective tissue diseases. Precise identification of viscoelastic properties of collagens, and affecting factors are necessary to understand collagen behavior in the extracellular matrix as well as the mechanism of collagen-related diseases. The aim of this study is to investigate the mechanical and viscoelastic properties and time-lapse changes of protein-protein and protein-solvent hydrogen bonds of proline-rich and hydroxyproline-rich collagens by molecular dynamics simulation applying a virtual creep test. To this end, ten different collagen-like protein structures including [(Gly-Pro-Ala)7]3, [(Gly-Pro-Arg)7]3, [(Gly-Pro-Asp)7]3, [(Gly-Pro-Lys)7]3, [(Gly-Pro-Ser)7]3, [(Gly-Pro-Hyp)7]3, [(Gly-Ala-Hyp)7]3, [(Gly-Glu-Hyp)7]3, [(Gly-Leu-Hyp)7]3 and [(Gly-Val-Hyp)7]3 were virtually built and the viscoelastic properties of the structures were determined by virtual creep test according to Kelvin-Voigt model with various constant pulling forces. Different pulling forces ranged from 500 piconewton (pN) to 5000 pN were applied. As a result, Young's modulus of the collagens was found positively correlated with the pulling force. The viscosity values and relaxation times were negatively correlated. Results also revealed a decreased number of intramolecular hydrogen bonds in hydroxyproline-rich collagens (but not in proline-rich collagens) and an increased number of protein-solvent hydrogen bonds in response to the increasing pulling force. Our results also confirmed that proline and hydroxyproline are the most critical amino acids in determining the collagen viscoelasticity. We suggest that collagen length and mechanical force may be additional important factors for biomechanical properties and behavior of collagen in the extracellular matrix.Communicated by Ramaswamy H. Sarma.

Design and Simulation of a DNA Origami Nanopore for Large Cargoes.

Since less than a decade ago, the DNA origami technique has become an important tool in nanopore fabrication. DNA origami nanopores are highly efficient because of their compatibility with biomolecules and the possibility to precisely engineer their dimensions and designs. However, accurate comprehension of their molecular behavior under various conditions is still unsatisfactory. In this study, a thin plate DNA origami nanopore is designed and investigated using molecular dynamics simulation. The thin plate is designed using caDNAno software along with the square lattice method and the molecular dynamics simulation is performed using GROMACS software. The model is simulated in a wide temperature range and its stability is investigated. The shape and dimensions of the nanopore are also compared at these temperatures. The results indicate that the designed nanopore exhibits decent stability at these temperatures and no breakdown was observed despite some distortions in the structure at high temperatures. In addition, the effect of the number of staple strands on the structure, stability, and deformation of the DNA origami plate is investigated and it is found that addition of staple strands have a significant positive effect on the stability of nanopore's shape. By the results of analyzing the shape of the nanopore, it suggests that the proposed nanopore can be used to pass a wide range of molecules, macromolecules, and drug cargoes.

The effect of calcium binding on the unfolding force of mutated and healthy titin I10 domain: A steered molecular dynamics simulation study.

Titin plays an important role in eccentric contraction by creating elastic property in the sarcomere. It can restore muscle to its rest length by stretching and increasing its length. Titin's structure is made of 244 domains. Due to its position, the I10 domain can be subjected to a mutation which leads to Arrhythmogenic cardiomyopathy. Furthermore, the calcium ion has an important role in muscle contractions by binding to some domains like I10 in titin and accordingly creating changes in the unfolding force of these domains. The purpose of this study was to investigate the effect of calcium binding on the unfolding force of the I10 domain for the normal and mutated states. For this reason, the steered molecular dynamics simulation was performed in different states with various pulling rates. According to the results, calcium binding leads to a rising in the unfolding force of the I10 domain. In addition, mutation decreases the unfolding force of the domain, but the presence of calcium compensates for this effect by raising the unfolding force. Results also indicate that by increasing the pulling rates, the unfolding force would increase considerably.

Three-dimensional structural optimization of a cementless hip stem using a bi-directional evolutionary method.

A correct choice of stem geometry can increase the lifetime of hip implant in a total hip arthroplasty. This study presents a numerical methodology for structural optimization of stem geometry using a bi-directional evolutionary structural optimization method. The optimization problem was formulated with the objective of minimizing the stresses in the bone-stem interface. Finite element analysis was used to obtain stress distributions by three-dimensional simulation of the implant and the surrounding bone under normal walking conditions. To compare the initial and the optimal stems, the von Mises stress distribution in the bone-implant interface was investigated. Results showed that the optimization procedure leads to a decrease in the stress concentration in the implant and a reduction in stress shielding of the surrounding bone. Furthermore, periprosthetic bone adaptation was analyzed numerically using an adaptive bone remodeling procedure. The remodeling results showed that the bone mass loss could be reduced by 16% in the optimal implant compared to the initial one.

Mechanical elasticity of proline-rich and hydroxyproline-rich collagen-like triple-helices studied using steered molecular dynamics.

Identity of the amino acids in Gly-X-Y repetitive motives governs biomechanical features of collagen such as elasticity in the extracellular matrix. Proline and hydroxyproline are the most abundant residues at the X and Y sites of collagen repetitive motives, respectively. However, their effects on the elasticity of collagen have not been identified. Here, we investigated the molecular mechanics of five different proline-rich collagens with Gly-Pro-Y repetitive motives, four hydroxyproline-rich collagens with Gly-X-Hyp repetitive motives as well as a collagen with Gly-Pro-Hyp repetitive motif, focusing on molecular stiffness and elasticity. The proteins were virtually built and stiffness, Young's modulus, cross-sectional radius, intermolecular and protein-solvent hydrogen bonds of the collagens were investigated using steered molecular dynamic simulation. Results showed a higher stiffness and Young's moduli of the proline-rich collagens compared to the hydroxyproline-rich collagens. Young's modulus of the proline-rich collagens was negatively correlated with the cross-sectional radius. There was no significant difference between the proline-rich and the hydroxyproline-rich collagen from the point of view of intermolecular and protein-water hydrogen bonds. However, a decreased and an increased number of protein-water hydrogen bonds in response to stretching was found for the proline-rich and the hydroxyproline-rich collagens respectively. Interestingly, the collagen with Gly-Pro-Hyp repetitive motif showed an intermediate stiffness, Young's moduli and cross-sectional radius. The collagen also had a lower number of intermolecular and protein -water hydrogen bonds when compared to the proline-rich and hydroxproline-rich collagens. These results suggest that the presence of proline in the structure of collagen reduces elasticity and increases stiffness, whereas presence of hydroxyproline increases elasticity of the collagen. We conclude that any codon substitution in the collagen genes causing alteration of proline and/or hydroxyproline residues may result in drastic collagen deficiency.

A better prediction of conformational changes of proteins using minimally connected network models.

Elastic network models have recently been used for studying low-frequency collective motions of proteins. These models simplify the complexity that arises from normal mode analysis by considering a simplified potential involving a few parameters. Two common parameters in most of the elastic network models are cutoff radius and force constant. Although the latter has been studied extensively and even elaborate new models were introduced, for the former usually an ad-hoc cutoff radius is considered. Moreover, the quality of the network models is usually assessed by evaluating their prediction against experimental B-factors. In this work, we consider various common elastic network models with different cutoff radii and assess them by their ability to predict conformational changes of proteins in complexes from unbound to bound state. This prediction is performed by perturbing the unbound structure using a number of low-frequency normal modes of its network model to optimally fit the bound structure. We evaluated a dataset of 30 proteins with distinct unbound and bound structures using this criterion. The results showed that, opposed to the common calibration process based on B-factors, a meaningful relationship exists between the quality of the prediction and model parameters. It was shown that the cutoff radius has a major role in this prediction and minimally connected network models, which use the shortest cutoff radius for which the network is stable, give the best results. It was also shown that by considering the first ten normal modes, the conformational changes can be predicted by about 25 percent. Hence, the evaluation process was extended to the case of considering the contribution of all normal modes in the prediction. The results indicated that minimally connected network models are superior, despite their simplicity, when any number of modes are considered in the prediction.

Rigorous coarse-graining for the dynamics of linear systems with applications to relaxation dynamics in proteins.

Reduced-dimensionality, coarse-grained models are commonly employed to describe the structure and dynamics of large molecular systems. In those models, the dynamics is often described by Langevin equations of motion with phenomenological parameters. This paper presents a rigorous coarse-graining method for the dynamics of linear systems. In this method, as usual, the conformational space of the original atomistic system is divided into master and slave degrees of freedom. Under the assumption that the characteristic timescales of the masters are slower than those of the slaves, the method results in Langevin-type equations of motion governed by an effective potential of mean force. In addition, coarse-graining introduces hydrodynamic-like coupling among the masters as well as non-trivial inertial effects. Application of our method to the long-timescale part of the relaxation spectra of proteins shows that such dynamic coupling is essential for reproducing their relaxation rates and modes.

Critical evaluation of simple network models of protein dynamics and their comparison with crystallographic B-factors.

In recent years, elastic network models (ENM) have been widely used to describe low-frequency collective motions in proteins. These models are often validated and calibrated by fitting mean-square atomic displacements estimated from x-ray crystallography (B-factors). We show that a proper calibration procedure must account for the rigid-body motion and constraints imposed by the crystalline environment on the protein. These fundamental aspects of protein dynamics in crystals are often ignored in currently used ENMs, leading to potentially erroneous network parameters. Here we develop an ENM that properly takes the rigid-body motion and crystalline constraints into account. Its application to the crystallographic B-factors reveals that they are dominated by rigid-body motion and thus are poorly suited for the calibration of models for internal protein dynamics. Furthermore, the translation libration screw (TLS) model that treats proteins as rigid bodies is considerably more successful in interpreting the experimental B-factors than ENMs. This conclusion is reached on the basis of a comparative study of various models of protein dynamics. To evaluate their performance, we used a data set of 330 protein structures that combined the sets previously used in the literature to test and validate different models. We further propose an extended TLS model that treats the bulk of the protein as a rigid body while allowing for flexibility of chain ends. This model outperforms other simple models of protein dynamics in interpreting the crystallographic B-factors.