A simplified approach for calculating the moments of action for linear reaction-diffusion equations

The mean action time is the mean of a probability density function that can be interpreted as a critical time, which is a finite estimate of the time taken for the transient solution of a reaction-diffusion equation to effectively reach steady state. For high-variance distributions, the mean action time under-approximates the critical time since it neglects to account for the spread about the mean. We can improve our estimate of the critical time by calculating the higher moments of the probability density function, called the moments of action, which provide additional information regarding the spread about the mean. Existing methods for calculating the nth moment of action require the solution of n nonhomogeneous boundary value problems which can be difficult and tedious to solve exactly. Here we present a simplified approach using Laplace transforms which allows us to calculate the nth moment of action without solving this family of boundary value problems and also without solving for the transient solution of the underlying reaction-diffusion problem. We demonstrate the generality of our method by calculating exact expressions for the moments of action for three problems from the biophysics literature. While the first problem we consider can be solved using existing methods, the second problem, which is readily solved using our approach, is intractable using previous techniques. The third problem illustrates how the Laplace transform approach can be used to study coupled linear reaction-diffusion equations.

Multiscale investigation of microfilament networks disruption in living cells

Actin is the most abundantly distributed protein in living cells which plays critical roles in the cell interior force generation and transmission. The fracture mechanism of microfilament networks, whose principle component is actin, would provide insights which can contribute to the understandings of self-protective characters of cytoskeleton. In this study, molecular simulations are conducted to investigate the molecular mechanisms of disruption of microfilament networks from the viewpoint of biophysics. By employing a coarse-grained (CG) model of actin filament networks, we focused on the ultimate strength and crack growth mode of microfilament networks that have dependency on the crack length. It can be found that, the fracture mechanism of microfilament network has dependency on the structural properties of microfilament networks. The structure flaws marginally change the strength of microfilament networks which would explain the self-protective characters of cytoskeleton.

Prospects for studying how high-intensity compression waves cause damage in human blast injuries

Since World War I, explosions have accounted for over 70% of all injuries in conflict. With the development of improved personnel protection of the torso, improved medical care and faster aeromedical evacuation, casualties are surviving with more severe injuries to the extremities. Understanding the processes involved in the transfer of blast-induced shock waves through biological tissues is essential for supporting efforts aimed at mitigating and treating blast injury. Given the inherent heterogeneities in the human body, we argue that studying these processes demands a highly integrated approach requiring expertise in shock physics, biomechanics and fundamental biological processes. This multidisciplinary systems approach enables one to develop the experimental framework for investigating the material properties of human tissues that are subjected to high compression waves in blast conditions and the fundamental cellular processes altered by this type of stimuli. Ultimately, we hope to use the information gained from these studies in translational research aimed at developing improved protection for those at risk and improved clinical outcomes for those who have been injured from a blast wave.

Molecular sliding filament model for muscular contraction based on multiscale investigation

A multiscale approach that bridges the biophysics of the actin molecules at nanoscale and the biomechanics of actin filament at microscale level is developed and used to evaluate the mechanical performances of actin filament bundles. In order to investigate the contractile properties of skeletal muscle which is induced by the protein motor of myosin, a molecular model is proposed in the prediction of the dynamic behaviors of skeletal muscle based on classic sliding filament model. Randomly distributed myosin motors are applied on a 2.2 μm long sarcomere, whose principal components include actin and myosin filaments. It can be found that, the more myosin motors on the sarcomere, the faster the sarcomere contracts. The result demonstrates that the sarcomere shortening speed cannot increase infinitely by the modulation of myosin, thus providing insight into the self-protective properties of skeletal muscles. This molecular filament sliding model provides a theoretical way to evaluate the properties of skeletal muscles, and contributes to the understandings of the molecular mechanisms in the physiological phenomenon of muscular contraction.

MAS NMR measurements of intact articular bovine cartilage

Articular cartilage (AC), an avascular connective tissue lining articulating surfaces of the long bones, comprises extracellular biopolymers. In functionally compromised states such as osteoarthritis, thinned or lost AC causes reduced mobility and increased health-care costs. Understanding of the characteristics responsible for the load bearing efficiency of AC and the factors leading to its degradation are incomplete. DTI shows the structural alignment of collagen in AC [1] and T2 relaxation measurements suggest that the average director of reorientational motion of water molecules depends on the degree of alignment of collagen in AC [2]. Information on the nature of the chemical interactions involved in functional AC is lacking. The need for AC structural integrity makes solid state NMR an ideal tool to study this tissue. We examined the contribution of water in different functional ‘compartments’ using 1H-MAS, 13C-MAS and 13C-CPMAS NMR of bovine patellar cartilage incubated in D2O. 1H-MAS spectra signal intensity was reduced due to H/D exchange without a measureable redistribution of relative signal intensity. Chemical shift anisotropy was estimated by lineshape analysis of multiple peaks in the 1H-MAS spinning sidebands. These asymmetrical sidebands suggested the presence of multiple water species in AC. Therefore, water was added in small aliquots to D2O saturated AC and the influence of H2O and D2O on organic components was studied with 13C-MAS-NMR and 13C-CPMAS-NMR. Signal intensity in 13C-MAS spectra showed no change in relative signal intensity throughout the spectrum. In 13C-CPMAS spectra, displacement of water by D2O resulted in a loss of signal in the aliphatic region due to a reduction in proton availability for cross-polarization. These results complement dehydration studies of cartilage using osmotic manipulation [3] and demonstrate components of cartilage that are in contact with mobile water.

Production of biodegradable nano and micro particles via ultrasonic atomization for biopharmaceutical delivery

Biopharmaceuticals have been shown to have low delivery and transformation efficiencies. To over come this, larger doses are administered in order to obtain the desired response which may lead to toxicity and drug resistance. This paper reports upon a continuous particle production method utilizing surface acoustic wave atomization to reliably produce micro and nanoparticles with physical characteristics to facilitate the cellular uptake of biopharmaceuticals. By producing particles of an optimal size for cellular uptake, the efficacy and specificity of drug loaded nanoparticles will be increased. Better delivery methods will result in dosage reduction (hence lower costs per dose), reduced toxicity, and reduced problems associated with multidrug resistance due to over dosing.

Investigation of the effects of extracellular osmotic pressure on morphology and mechanical 1 properties of individual chondrocyte

It has been demonstrated that most cells of the body respond to osmotic pressure in a systematic manner. The disruption of the collagen network in the early stages of osteoarthritis causes an increase in water content of cartilage which leads to a reduction of pericellular osmolality in chondrocytes distributed within the extracellular environment. It is therefore arguable that an insight into the mechanical properties of chondrocytes under varying osmotic pressure would provide a better understanding of chondrocyte mechanotransduction and potentially contribute to knowledge on cartilage degeneration. In this present study, the chondrocyte cells were exposed to solutions with different osmolality. Changes in their dimensions and mechanical properties were measured over time. Atomic Force Microscopy (AFM) was used to apply load at various strain-rates and the force-time curves were logged. The thin-layer elastic model was used to extract the elastic stiffness of chondrocytes at different strain-rates and at different solution osmolality. In addition, the porohyperelastic (PHE) model was used to investigate the strain-rate dependent responses under the loading and osmotic pressure conditions. The results revealed that the hypo-osmotic external environment increased chondrocyte dimensions and reduced Young’s modulus of the cells at all strain-rates tested. In contrast, the hyper-osmotic external environment reduced dimensions and increased Young’s modulus. Moreover, by using the PHE model coupled with inverse FEA simulation, we established that the hydraulic permeability of chondrocytes increased with decreasing extracellular osmolality which is consistent with previous work in the literature. This could be due to a higher intracellular fluid volume fraction with lower osmolality.