Dynamical Rigidity Percolation in Microtubule Bundles

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TECHNICAL SUMMARYThis award supports theoretical and computational research and education at the interface of the mathematical sciences and biology. The coupled microtubule-tau bundles of the neuronal axon are a remarkable active material, functionally stable over decades even as the component proteins are constantly renewed. Using mechanisms proposed for tau removal in late stages of Alzheimer's Disease, which are initiated by oligomerization of the a-beta peptide, the PIs will develop a coarse grained theory of the mechanical failure of this system as the tau proteins are depleted via: (i) tau fragmentation induced by a-beta oligomer triggered protease production; (ii) tau charging (phosphorylation) through a-beta triggered kinase production; (iii) aggregation which robs tau monomers from the bundles. The kinetics of these processes should produce different time courses for tau removal and hence allow insight into mechanical failure mechanisms. The taus will be modeled as springs. The PIs will carry out explicit molecular dynamics simulations on likely tau oligomer structures to determine the relevant spring forces. The compressed tau springs hold off mechanical collapse induced by at least two sources: (i) depletion forces between microtubules induced by intercalating molecules, which have a higher translational entropy when the microtubules collapse together; (ii) surface tension from the outer membrane/actin filament cytoskeleton. The PIs will develop force models for the taus and microtubule depletion forces, and input them to a 2-dimensional percolation model for the mechanical rigidity. The sequential "spring removal" can be mapped to the kinetics of the tau degradation to predict time courses for cell mechanics experiments conducted under exposure to a-beta oligomers. The PIs will also explore a fully three-dimensional model, which allows for tilting of the microtubules, which might be important for allowing the microtubules to experience the depletion attraction. Finally, the PIs will attempt to develop algorithms to scale the time behavior at high laboratory concentrations for the damaging A-beta oligomers of Alzheimer's disease to physiologically relevant concentrations. The use of mechanical approaches to the study of intracellular properties is relatively new, as experimental approaches are only recently catching up to theoretical potential. The PIs will support both graduate students and advanced undergraduates to work on these problems; they will receive interdisciplinary education in the physical and biological sciences, and will have access to state of the art GPU based computing facilities augmented by this award. NON-TECHNICAL SUMMARYThis award supports theoretical and computational research and education at the interface of the mathematical sciences and biology. The PIs will develop computer-based models for the mechanical properties of the proteins inside the long shafts, or axons, of nerve cells. Specifically, they will simulate the long protein filaments, known as microtubules, which are interlinked by protein springs, tau proteins, to find how the stiffness of the system is degraded when the tau proteins are removed. This happens in the time course of Alzheimer's disease, but the precise manner in which the tau removal occurs is a matter of ongoing investigation. By developing simulations of the mechanical properties of these protein bundles, which include the dynamical behavior of the tau proteins and the microtubules, the PIs can account for the different paths by which tau proteins can be degraded in Alzheimer's disease. Including forces driving microtubules together due to other molecules inside the nerve cells and the "balloon skin" of the nerve cell external membrane, the PIs hope to provide experimentally testable predictions to identify the key processes of nerve cell degradation and death in Alzheimer's disease. Tau proteins are interesting systems in their own right: unlike proteins such as hemoglobin which adopt unique shapes in the human body, tau proteins are intrinsically unstructured yet clearly important to nerve cell function. As an input to larger scale mechanical models, the PIs will simulate the mechanical properties of individual and paired tau proteins. The insights gained may provide inspiration for new approaches to active, self-healing composite materials outside of living systems. Since the microtubule/tau bundles remain mechanically stable and functional over decades of time in healthy, disease free individuals, they are remarkable model systems for such smart, active materials.