Identification of biomolecule mass transport and binding rate parameters in living cells by inverse modeling

BACKGROUND: Quantification of in-vivo biomolecule mass transport and reaction rate parameters from experimental data obtained by Fluorescence Recovery after Photobleaching (FRAP) is becoming more important. METHODS AND RESULTS: The Osborne-Moré extended version of the Levenberg-Marquardt optimization algorithm was coupled with the experimental data obtained by the Fluorescence Recovery after Photobleaching (FRAP) protocol, and the numerical solution of a set of two partial differential equations governing macromolecule mass transport and reaction in living cells, to inversely estimate optimized values of the molecular diffusion coefficient and binding rate parameters of GFP-tagged glucocorticoid receptor. The results indicate that the FRAP protocol provides enough information to estimate one parameter uniquely using a nonlinear optimization technique. Coupling FRAP experimental data with the inverse modeling strategy, one can also uniquely estimate the individual values of the binding rate coefficients if the molecular diffusion coefficient is known. One can also simultaneously estimate the dissociation rate parameter and molecular diffusion coefficient given the pseudo-association rate parameter is known. However, the protocol provides insufficient information for unique simultaneous estimation of three parameters (diffusion coefficient and binding rate parameters) owing to the high intercorrelation between the molecular diffusion coefficient and pseudo-association rate parameter. Attempts to estimate macromolecule mass transport and binding rate parameters simultaneously from FRAP data result in misleading conclusions regarding concentrations of free macromolecule and bound complex inside the cell, average binding time per vacant site, average time for diffusion of macromolecules from one site to the next, and slow or rapid mobility of biomolecules in cells. CONCLUSION: To obtain unique values for molecular diffusion coefficient and binding rate parameters from FRAP data, we propose conducting two FRAP experiments on the same class of macromolecule and cell. One experiment should be used to measure the molecular diffusion coefficient independently of binding in an effective diffusion regime and the other should be conducted in a reaction dominant or reaction-diffusion regime to quantify binding rate parameters. The method described in this paper is likely to be widely used to estimate in-vivo biomolecule mass transport and binding rate parameters

Mechanical Strain Stabilizes Reconstituted Collagen Fibrils against Enzymatic Degradation by Mammalian Collagenase Matrix Metalloproteinase 8 (MMP-8)

Collagen, a triple-helical, self-organizing protein, is the predominant structural protein in mammals. It is found in bone, ligament, tendon, cartilage, intervertebral disc, skin, blood vessel, and cornea. We have recently postulated that fibrillar collagens (and their complementary enzymes) comprise the basis of a smart structural system which appears to support the retention of molecules in fibrils which are under tensile mechanical strain. The theory suggests that the mechanisms which drive the preferential accumulation of collagen in loaded tissue operate at the molecular level and are not solely cell-driven. The concept reduces control of matrix morphology to an interaction between molecules and the most relevant, physical, and persistent signal: mechanical strain.The investigation was carried out in an environmentally-controlled microbioreactor in which reconstituted type I collagen micronetworks were gently strained between micropipettes. The strained micronetworks were exposed to active matrix metalloproteinase 8 (MMP-8) and relative degradation rates for loaded and unloaded fibrils were tracked simultaneously using label-free differential interference contrast (DIC) imaging. It was found that applied tensile mechanical strain significantly increased degradation time of loaded fibrils compared to unloaded, paired controls. In many cases, strained fibrils were detectable long after unstrained fibrils were degraded.In this investigation we demonstrate for the first time that applied mechanical strain preferentially preserves collagen fibrils in the presence of a physiologically-important mammalian enzyme: MMP-8. These results have the potential to contribute to our understanding of many collagen matrix phenomena including development, adaptation, remodeling and disease. Additionally, tissue engineering could benefit from the ability to sculpt desired structures from physiologically compatible and mutable collagen

Calcium-dependent molecular fMRI using a magnetic nanosensor

Calcium ions are ubiquitous signalling molecules in all multicellular organisms, where they mediate diverse aspects of intracellular and extracellular communication over widely varying temporal and spatial scales1. Though techniques to map calcium-related activity at a high resolution by optical means are well established, there is currently no reliable method to measure calcium dynamics over large volumes in intact tissue2. Here, we address this need by introducing a family of magnetic calcium-responsive nanoparticles (MaCaReNas) that can be detected by magnetic resonance imaging (MRI). MaCaReNas respond within seconds to [Ca2+] changes in the 0.1-1.0 mM range, suitable for monitoring extracellular calcium signalling processes in the brain. We show that the probes permit the repeated detection of brain activation in response to diverse stimuli in vivo. MaCaReNas thus provide a tool for calcium-activity mapping in deep tissue and offer a precedent for the development of further nanoparticle-based sensors for dynamic molecular imaging with MRI.National Institutes of Health (U.S.) (Grant R01-DA038642)National Institutes of Health (U.S.) (Grant DP2-OD2114)National Institutes of Health (U.S.) (Grant U01-NS090451)National Institutes of Health (U.S.) (Grant R01-EY007023)National Science Foundation (U.S.) (Grant 0070319)National Institutes of Health (U.S.) (Grant S10-OD016326