Cytoskeletal strains in modeled optohydrodynamically stressed healthy and diseased biological cells.

Controlled external chemomechanical stimuli have been shown to influence cellular and tissue regeneration/degeneration, especially with regards to distinct disease sequelae or health maintenance. Recently, a unique three-dimensional stress state was mathematically derived to describe the experimental stresses applied to isolated living cells suspended in an optohydrodynamic trap (optical tweezers combined with microfluidics). These formulae were previously developed in two and three dimensions from the fundamental equations describing creeping flows past a suspended sphere. The objective of the current study is to determine the full-field cellular strain response due to the applied three-dimensional stress environment through a multiphysics computational simulation. In this investigation, the multiscale cytoskeletal structures are modeled as homogeneous, isotropic, and linearly elastic. The resulting computational biophysics can be directly compared with experimental strain measurements, other modeling interpretations of cellular mechanics including the liquid drop theory, and biokinetic models of biomolecule dynamics. The described multiphysics computational framework will facilitate more realistic cytoskeletal model interpretations, whose intracellular structures can be distinctly defined, including the cellular membrane substructures, nucleus, and organelles.

A cell-matrix model of anabolic and catabolic dynamics during cartilage biomolecule regulation.

Physiologic regulation of extracellular matrix (ECM) in articular cartilage tissue is controlled by cellular and molecular mechanisms which are not fully understood. It has been observed that the synthesis of the ECM structural molecules, glycosaminoglycan and collagen are promoted by growth factors such as IGF-1 and TGF-ß. Concomitant ECM degradation is promoted by a variety of cytokines such as IL-1. The clinical need for reparative therapies of articular cartilage is linked with its poor intrinsic healing capacity. The following modelling approach was applied to engineered cartilage as a platform for exploring cartilage biology and to introduce a predictive tool as a bioinformatic support system supporting regenerative therapies. Systems biology was adapted through a mathematical framework producing a computational intelligence paradigm to explore a controlled phasic regulatory influence of the inhibition and production of ECM biomolecules. Model outcomes describe a steady synthesis of ECM as a dependence on a cyclic influence of the catabolic action of proteases and anabolic action of growth factors. This relationship is shown quantitatively in a governing harmonic equation representing the simplified biological mechanisms of biomolecule homeostasis.

Ultrasonic wave propagation assessment of native cartilage explants and hydrogel scaffolds for tissue engineering.

Non-destructive techniques characterising the mechanical properties of cells, tissues, and biomaterials provide baseline metrics for tissue engineering design. Ultrasonic wave propagation and attenuation has previously demonstrated the dynamics of extracellular matrix synthesis in chondrocyte-seeded hydrogel constructs. In this paper, we describe an ultrasonic method to analyse two of the construct elements used to engineer articular cartilage in real-time, native cartilage explants and an agarose biomaterial. Results indicated a similarity in wave propagation velocity ranges for both longitudinal (1500-1745 m/s) and transverse (350-950 m/s) waveforms. Future work will apply an acoustoelastic analysis to distinguish between the fluid and solid properties including the cell and matrix biokinetics as a validation of previous mathematical models.

Biokinetic Mechanisms Linked With Musculoskeletal Health Disparities: Stochastic Models Applying Tikhonov's Theorem to Biomolecule Homeostasis.

Multiscale technology and advanced mathematical models have been developed to control and characterize physicochemical interactions, respectively, enhancing cellular and molecular engineering progress. Ongoing tissue engineering development studies have provided experimental input for biokinetic models examining the influence of static or dynamic mechanical stimuli (Saha, A. K., and Kohles, S. S., 2010, "A Distinct Catabolic to Anabolic Threshold Due to Single-Cell Nanomechanical Stimulation in a Cartilage Biokinetics Model," J. Nanotechnol. Eng. Med., 1(3) p. 031005; 2010, "Periodic Nanomechanical Stimulation in a Biokinetics Model Identifying Anabolic and Catabolic Pathways Associated With Cartilage Matrix Homeostasis," J. Nanotechnol. Eng. Med., 1(4), p. 041001). In the current study, molecular regulatory thresholds associated with specific disease disparities are further examined through applications of stochastic mechanical stimuli. The results indicate that chondrocyte bioregulation initiates the catabolic pathway as a secondary response to control anabolic processes. In addition, high magnitude loading produced as a result of stochastic input creates a destabilized balance in homeostasis. This latter modeled result may be reflective of an injurious state or disease progression. These mathematical constructs provide a framework for single-cell mechanotransduction and may characterize transitions between healthy and disease states.

Three-Dimensional Culture of Cells and Matrix Biomolecules for Engineered Tissue Development and Biokinetics Model Validation.

There has been considerable progress in cellular and molecular engineering due to recent advances in multiscale technology. Such technologies allow controlled manipulation of physiochemical interactions among cells in tissue culture. In particular, a novel chemomechanical bioreactor has recently been designed for the study of bone and cartilage tissue development, with particular focus on extracellular matrix formation. The bioreactor is equally significant as a tool for validation of mathematical models that explore biokinetic regulatory thresholds (Saha, A. K., and Kohles, S. S., 2010, "A Distinct Catabolic to Anabolic Threshold Due to Single-Cell Nanomechanical Stimulation in a Cartilage Biokinetics Model," J. Nanotechnol. Eng. Med., 1(3), p. 031005; 2010, "Periodic Nanomechanical Stimulation in a Biokinetics Model Identifying Anabolic and Catabolic Pathways Associated With Cartilage Matrix Homeostasis," J. Nanotechnol. Eng. Med., 1(4), p. 041001). In the current study, three-dimensional culture protocols are described for maintaining the cellular and biomolecular constituents within defined parameters. Preliminary validation of the bioreactor's form and function, expected bioassays of the resulting matrix components, and application to biokinetic models are described. This approach provides a framework for future detailed explorations combining multiscale experimental and mathematical analyses, at nanoscale sensitivity, to describe cell and biomolecule dynamics in different environmental regimes.

Volumetric stress-strain analysis of optohydrodynamically suspended biological cells.

Ongoing investigations are exploring the biomechanical properties of isolated and suspended biological cells in pursuit of understanding single-cell mechanobiology. An optical tweezer with minimal applied laser power has positioned biologic cells at the geometric center of a microfluidic cross-junction, creating a novel optohydrodynamic trap. The resulting fluid flow environment facilitates unique multiaxial loading of single cells with site-specific normal and shear stresses resulting in a physical albeit extensional state. A recent two-dimensional analysis has explored the cytoskeletal strain response due to these fluid-induced stresses [Wilson and Kohles, 2010, "Two-Dimensional Modeling of Nanomechanical Stresses-Strains in Healthy and Diseased Single-Cells During Microfluidic Manipulation," J Nanotechnol Eng Med, 1(2), p. 021005]. Results described a microfluidic environment having controlled nanometer and piconewton resolution. In this present study, computational fluid dynamics combined with multiphysics modeling has further characterized the applied fluid stress environment and the solid cellular strain response in three dimensions to accompany experimental cell stimulation. A volumetric stress-strain analysis was applied to representative living cell biomechanical data. The presented normal and shear stress surface maps will guide future microfluidic experiments as well as provide a framework for characterizing cytoskeletal structure influencing the stress to strain response.

A Distinct Catabolic to Anabolic Threshold Due to Single-Cell Static Nanomechanical Stimulation in a Cartilage Biokinetics Model.

Understanding physicochemical interactions during biokinetic regulation will be critical for the creation of relevant nanotechnology supporting cellular and molecular engineering. The impact of nanoscale influences in medicine and biology can be explored in detail through mathematical models as an in silico testbed. In a recent single-cell biomechanical analysis, the cytoskeletal strain response due to fluid-induced stresses was characterized (Wilson, Z. D., and Kohles, S. S., 2010, "Two-Dimensional Modeling of Nanomechanical Strains in Healthy and Diseased Single-Cells During Microfluidic Stress Applications," J. Nanotech. Eng. Med., 1(2), p. 021005). Results described a microfluidic environment having controlled nanometer and piconewton resolution for explorations of multiscale mechanobiology. In the present study, we constructed a mathematical model exploring the nanoscale biomolecular response to that controlled microenvironment. We introduce mechanical stimuli and scaling factor terms as specific input values for regulating a cartilage molecule synthesis. Iterative model results for this initial multiscale static load application have identified a transition threshold load level from which the mechanical input causes a shift from a catabolic state to an anabolic state. Modeled molecule homeostatic levels appear to be dependent upon the mechanical stimulus as reflected experimentally. This work provides a specific mathematical framework from which to explore biokinetic regulation. Further incorporation of nanomechanical stresses and strains into biokinetic models will ultimately lead to refined mechanotransduction relationships at the cellular and molecular levels.

Periodic Nanomechanical Stimulation in a Biokinetics Model Identifying Anabolic and Catabolic Pathways Associated With Cartilage Matrix Homeostasis.

Enhancing the available nanotechnology to describe physicochemical interactions during biokinetic regulation will strongly support cellular and molecular engineering efforts. In a recent mathematical model developed to extend the applicability of a statically loaded, single-cell biomechanical analysis, a biokinetic regulatory threshold was presented (Saha and Kohles, 2010, "A Distinct Catabolic to Anabolic Threshold Due to Single-Cell Static Nanomechanical Stimulation in a Cartilage Biokinetics Model," J. Nanotechnol. Eng. Med., 1(3), p. 031005). Results described multiscale mechanobiology in terms of catabolic to anabolic pathways. In the present study, we expand the mathematical model to continue exploring the nanoscale biomolecular response within a controlled microenvironment. Here, we introduce a dynamic mechanical stimulus for regulating cartilage molecule synthesis. Model iterations indicate the identification of a biomathematical mechanism balancing the harmony between catabolic and anabolic states. Relative load limits were defined to distinguish between "healthy" and "injurious" biomolecule accumulations. The presented mathematical framework provides a specific algorithm from which to explore biokinetic regulation.

Moderate exercise and chronic stress produce counteractive effects on different areas of the brain by acting through various neurotransmitter receptor subtypes: a hypothesis.

BACKGROUND: Regular, "moderate", physical exercise is an established non-pharmacological form of treatment for depressive disorders. Brain lateralization has a significant role in the progress of depression. External stimuli such as various stressors or exercise influence the higher functions of the brain (cognition and affect). These effects often do not follow a linear course. Therefore, nonlinear dynamics seem best suited for modeling many of the phenomena, and putative global pathways in the brain, attributable to such external influences. HYPOTHESIS: The general hypothesis presented here considers only the nonlinear aspects of the effects produced by "moderate" exercise and "chronic" stressors, but does not preclude the possibility of linear responses. In reality, both linear and nonlinear mechanisms may be involved in the final outcomes. The well-known neurotransmitters serotonin (5-HT), dopamine (D) and norepinephrine (NE) all have various receptor subtypes. The article hypothesizes that 'Stress' increases the activity/concentration of some particular subtypes of receptors (designated nts) for each of the known (and unknown) neurotransmitters in the right anterior (RA) and left posterior (LP) regions (cortical and subcortical) of the brain, and has the converse effects on a different set of receptor subtypes (designated nth). In contrast, 'Exercise' increases nth activity/concentration and/or reduces nts activity/concentration in the LA and RP areas of the brain. These effects may be initiated by the activation of Brain Derived Neurotrophic Factor (BDNF) (among others) in exercise and its suppression in stress. CONCLUSION: On the basis of this hypothesis, a better understanding of brain neurodynamics might be achieved by considering the oscillations caused by single neurotransmitters acting on their different receptor subtypes, and the temporal pattern of recruitment of these subtypes. Further, appropriately designed and planned experiments will not only corroborate such theoretical models, but also shed more light on the underlying brain dynamics.

Prediction of growth factor effects on engineered cartilage composition using deterministic and stochastic modeling.

In the design of engineered tissues, guided balance of biomaterial degeneration with tissue synthesis offers refined control of construct development. The objective of this study was to develop a mathematical model that describes the steady state metabolism of extracellular matrix molecules (ECM: glycosaminoglycan and collagen) in an engineered cartilage construct taking into account localized environmental changes that may arise because of the application of growth factors. The variable effects of growth factors were incorporated in the form of random noise rather than the difference in rates of synthesis and catabolism. Thus, the frequency of ECM accumulation for each matrix molecule in the steady state under the random influence of growth factor was produced relative to the matrix carrying capacity. Published synthesis-rate time constants and steady state ECM conditions from chondrocyte-polymer scaffold composites provided both input and validation for the model. Although the presence of growth factors in the presented system dynamics were considered randomized, the results described a positive feedback or promotional ECM synthesis at low levels of growth factors. While a negative feedback or inhibition of ECM synthesis was characterized at higher levels of growth factors. This transition phenomenon is based on a comparison with the results of a steady state condition in the form of a deterministic model and supports previous reports of guided accumulation in musculoskeletal, connective, and neuronal tissues.