Growth Cone Pathfinding: a competition between deterministic and stochastic events

BACKGROUND: Growth cone migratory patterns show evidence of both deterministic and stochastic search modes. RESULTS: We quantitatively examine how these two different migration modes affect the growth cone's pathfinding response, by simulating growth cone contact with a repulsive cue and measuring the resultant turn angle. We develop a dimensionless number, we call the determinism ratio Ψ, to define the ratio of deterministic to stochastic influences driving the growth cone's migration in response to an external guidance cue. We find that the growth cone can exhibit three distinct types of turning behaviors depending on the magnitude of Ψ. CONCLUSIONS: We conclude, within the context of these in silico studies, that only when deterministic and stochastic migration factors are in balance (i.e. Ψ ~ 1) can the growth cone respond constructively to guidance cues

An in vitro assay of collagen fiber alignment by acupuncture needle rotation

BACKGROUND: During traditional acupuncture therapy, soft tissues attach to and wind around the acupuncture needle. To study this phenomenon in a controlled and quantitative setting, we performed acupuncture needling in vitro. METHODS: Acupuncture was simulated in vitro in three-dimensional, type I collagen gels prepared at 1.5 mg/ml, 2.0 mg/ml, and 2.5 mg/ml collagen, and either crosslinked with formalin or left untreated. Acupuncture needles were inserted into the gels and rotated via a computer-controlled motor at 0.3 rev/sec for up to 10 revolutions while capturing the evolution of birefringence under cross-polarization. RESULTS: Simulated acupuncture produced circumferential alignment of collagen fibers close to the needle that evolved into radial alignment as the distance from the needle increased, which generally matched observations from published tissue explant studies. All gels failed prior to 10 revolutions, and the location of failure was near the transition between circumferential and radial alignment. Crosslinked collagen failed at a significantly lower number of revolutions than untreated collagen, whereas collagen concentration had no effect on gel failure. The strength of the alignment field increased with increasing collagen concentration and decreased with crosslinking. Separate studies were performed in which the gel thickness and depth of needle insertion were varied. As gel thickness increased, gels failed at fewer needle revolutions. For the same depth of insertion, alignment was greater in thinner gels. Alignment increased as the depth of insertion increased. CONCLUSION: These results indicate that the mechanostructural properties of soft connective tissues may affect their response to acupuncture therapy. The in vitro model provides a platform to study mechanotransduction during acupuncture in a highly controlled and quantitative setting

Mitochondrial physiology

As the knowledge base and importance of mitochondrial physiology to evolution, health and disease expands, the necessity for harmonizing the terminology concerning mitochondrial respiratory states and rates has become increasingly apparent. The chemiosmotic theory establishes the mechanism of energy transformation and coupling in oxidative phosphorylation. The unifying concept of the protonmotive force provides the framework for developing a consistent theoretical foundation of mitochondrial physiology and bioenergetics. We follow the latest SI guidelines and those of the International Union of Pure and Applied Chemistry (IUPAC) on terminology in physical chemistry, extended by considerations of open systems and thermodynamics of irreversible processes. The concept-driven constructive terminology incorporates the meaning of each quantity and aligns concepts and symbols with the nomenclature of classical bioenergetics. We endeavour to provide a balanced view of mitochondrial respiratory control and a critical discussion on reporting data of mitochondrial respiration in terms of metabolic flows and fluxes. Uniform standards for evaluation of respiratory states and rates will ultimately contribute to reproducibility between laboratories and thus support the development of data repositories of mitochondrial respiratory function in species, tissues, and cells. Clarity of concept and consistency of nomenclature facilitate effective transdisciplinary communication, education, and ultimately further discovery

Mitochondrial physiology

As the knowledge base and importance of mitochondrial physiology to evolution, health and disease expands, the necessity for harmonizing the terminology concerning mitochondrial respiratory states and rates has become increasingly apparent. The chemiosmotic theory establishes the mechanism of energy transformation and coupling in oxidative phosphorylation. The unifying concept of the protonmotive force provides the framework for developing a consistent theoretical foundation of mitochondrial physiology and bioenergetics. We follow the latest SI guidelines and those of the International Union of Pure and Applied Chemistry (IUPAC) on terminology in physical chemistry, extended by considerations of open systems and thermodynamics of irreversible processes. The concept-driven constructive terminology incorporates the meaning of each quantity and aligns concepts and symbols with the nomenclature of classical bioenergetics. We endeavour to provide a balanced view of mitochondrial respiratory control and a critical discussion on reporting data of mitochondrial respiration in terms of metabolic flows and fluxes. Uniform standards for evaluation of respiratory states and rates will ultimately contribute to reproducibility between laboratories and thus support the development of data repositories of mitochondrial respiratory function in species, tissues, and cells. Clarity of concept and consistency of nomenclature facilitate effective transdisciplinary communication, education, and ultimately further discovery

Autocorrelation function and power spectrum of two-state random processes used in neurite guidance

During development neurons extend and retract cytoskeletal structures, chiefly microtubules and filopodia, to process informational cues from the extracellular environment and thereby guide growth cone migration toward an appropriate synaptic partner. This cytoskeleton-based exploration is achieved by stochastic switching, with microtubules and filopodia alternating between growing and shortening phases apparently at random. If stabilizing signals are not detected during the growth phase, then the structures switch to a shortening state, from which they can again return to a growth phase, and so forth. A useful means of characterizing these stochastic processes in a model-independent way is by autocorrelation and spectral analysis. Previously, we compared experiment to theory by performing Monte Carlo simulations and computing the autocorrelation function and power spectrum from the simulated dynamics, an approach that is computationally intensive and requires recalculation whenever model parameters are changed. Here we present analytical expressions for the autocorrelation function and power spectrum, which compactly characterize microtubule and filopodial dynamics based on the stochastic, two-state model. The model assumes that the phase times are of variable duration and gamma-distributed, consistent with experimental evidence for microtubules assembled in vitro from purified tubulin. The analytical expressions permit the precise quantitative characterization of changes in microtubule and filopodial searching behavior corresponding to changes in the shape of the gamma distribution

Monte Carlo calculation of effective diffusivities in two- and three-dimensional heterogeneous materials of variable structure

A Monte Carlo technique that simulates tracer diffusion in multiphase materials of arbitrary complexity has been developed. Effective diffusivities are calculated for structures consisting of either overlapping or nonoverlapping inclusions with diffusivity Dc, distributed in a continuous phase with diffusivity D0\u3eDc. Two-dimensional simulations for various values of D0/Dc generate normalized diffusivities that correspond closely to their three-dimensional counterparts; they nearly collapse to a common curve when a simple scaling relation is applied