KOBRA: a fluctuating elastic rod model for slender biological macromolecules

Computational Biophysics lies at the intersection between biology, physics, applied mathematics and software engineering. Some of the most burning questions in molecular biology are concerned with biomechanical systems, the dynamics of which are driven by chemistry and physics. Unfortunately, we have extremely limited means to observe these dynamics experimentally. In the past, this problem has been solved with the use of molecular dynamics, sometimes referred to as a `computational microscope'. Studying biomolecules in silico can provide a wealth of new information at temporal and spatial resolutions far beyond any current imaging modality. But molecular dynamics algorithms are limited by current computing power, and by the assumptions used to construct them. The kinetochore, a supramolecular structure crucial to the process of cell division, operates on time and length scales outside the reach of atomistic molecular dynamics with current computing power. To overcome this limitation, we propose a new, coarse-grained algorithm, which allows for a more computationally inexpensive representation of the biomolecules that comprise the kinetochore. This algorithm, KOBRA (KirchOff Biological Rod Algorithm) is designed to perform dynamical simulations of elongated biomolecules such as those containing alpha-helices and coiled-coils. It represents these as coarsely-discretised Kirchoff rods, with linear elements that can stretch, bend and twist independently. These rods can have anisotropic and inhomogeneous parameters and bent or twisted equilibrium structures, allowing for a coarse-grained parameterisation of complex biological structures. Each element is non-inertial and subject to thermal fluctuations. This coarse-grained representation allows for simulations of extremely large, long-lived systems at the biological mesoscale. KOBRA has been extended with a parameterisation scheme that allows for rod parameters (in terms of stretching, bending and twisting constants) to be extracted from all-atom simulation trajectories. An all-atom representation of Ndc80C - a sub-unit of the kinetochore - was constructed, and the KOBRA parameters for the molecule were extracted from its trajectory. The KOBRA algorithm is validated against both the physics of elastic rods and the biology of Ndc80C and the kinetochore. A partial kinetochore system was constructed and simulated using KOBRA and FFEA (Fluctuating Finite Element Analysis). The resulting trajectories were analysed and used to investigate the microtubule-binding ability of Ndc80C in a variety of configurations. A C++ implementation of KOBRA is available under the GNU GPLv3 free software licence, and can http://ffea.bitbucket.io.