Amyotrophic lateral sclerosis (ALS) is the most common Motor Neuron Disease. It is a progressive neurodegenerative disease that affects motor neurons in the brain and the spinal cord. The progressive degeneration of motor neurons in the spinal cord causes patients to lose their ability to control their muscle movement. As the disease progresses they lose the ability to move their limbs, speak, eat, and eventually breath, leading to death. It is the most lethal of the common neurodegenerative disorders, and has thus far been refractory to all treatments. Recent hypotheses of ALS progression have posited a point-source origin of motor neuron death with neuroanatomic propagation either contiguously to adjacent regions, or along networks via axonal and synaptic connections. Although the molecular mechanisms of propagation are unknown, one leading hypothesis is a "prion-like" spread of misfolded and aggregated proteins.

To better understand this devastating disease, we are developing a cellular and molecular scale computational model of the spread of ALS within the spinal cord. We parametrized our stochastic reaction-­diffusion SIR style model by reconstructing human spinal cord from high­-resolution magnetic resonance (MR) images and known gross and histological neuroanatomy. Our model appears to realistically recapitulate the clinical and pathological spread of ALS in human spinal cord. We are using the model combined with clinical assessment data to quantify and characterize the cellular and molecular spread of ALS, predict the relative contributions of network and contiguous spread, and attempt to explain the differential cellular vulnerability to the disease.

Discrete stochastic simulation has become an important and widely-used tool for modeling of biological systems at the molecular scale. At the same time, there is no single place where one can go to develop a discrete stochastic model with increasing levels of complexity: from the early stages, where it may begin as an ODE model, to a well-mixed (spatially homogeneous) discrete stochastic model, to a spatially inhomogeneous stochastic model with complex geometry and multiple internal surfaces, and finally to a spatially inhomogeneous stochastic model where single molecules at a microscopic level may interact with molecules modeled mesoscopically. The focus of the StochSS project is to build such a place: an integrated development environment featuring state of the art algorithms as well as a means for the community to add new algorithms and capabilities, supported on a wide range of hardware from desktop workstations to high-performance clusters in the cloud.