James Keener : Flexing your Protein muscles: How to Pull with a Burning Rope
- Mathematical Biology ( 727 Views )The segregation of chromosomes during cell division is accomplished by kinetochore machinery that uses depolymerizing microtubules to pull the chromosomes to opposite poles of the dividing cell. While much is known about molecular motors that pull by walking or push by polymerizing, the mechanism of how a pulling force can be achieved by depolymerization is still unresolved. In this talk, I will describe a new model for the depolymerization motor that is used by eukaryotic cells to segregate chromosomes during mitosis. In the process we will explore the use of Huxley-type models (population models) of protein binding and unbinding to study load-velocity curves of several different motor-like proteins.
Seth Sullivant : Statistically-Consistent k-mer Methods for Phylogenetic Tree Reconstruction
- Mathematical Biology ( 166 Views )Frequencies of k-mers in sequences are sometimes used as a basis for inferring phylogenetic trees without first obtaining a multiple sequence alignment. We show that a standard approach of using the squared-Euclidean distance between k-mer vectors to approximate a tree metric can be statistically inconsistent. To remedy this, we derive model-based distance corrections for orthologous sequences without gaps, which lead to consistent tree inference. The identifiability of model parameters from k-mer frequencies is also studied. Finally, we report simulations showing the corrected distance out-performs many other k-mer methods, even when sequences are generated with an insertion and deletion process. These results have implications for multiple sequence alignment as well, since k-mer methods are usually the first step in constructing a guide tree for such algorithms. This is joint work with Elizabeth Allman and John Rhodes.
Guillaume Lajoie : Artificially-induced synaptic plasticity in motor cortex: a theoretical model of a bidirectional brain-computer interface
- Mathematical Biology ( 132 Views )Experiments on macaque monkeys show that spike-triggered stimulation performed by a Bidirectional Brain-Computer-Interfaces (BBCI) can artificially strengthen synaptic connections between distant neural sites in Motor Cortex (MC) and even between MC and spinal cord, with changes that last several days. Here, a neural implant records from some neurons in MC and electrically stimulates others after set delays. The working hypothesis is that this stimulation procedure, which interacts with the very fast spiking activity of cortical circuits (on the order of milliseconds), induces changes mediated by synaptic plasticity mechanisms on much longer timescales (hours and days). The field of online, closed-loop BBCI's is rapidly evolving, with applications ranging from a science-oriented tool to clinical treatments of motor injuries. However, with the enhanced capability of novel devices that can record and stimulate an ever-growing number of neural sites comes growing complexity. It is therefore crucial to develop a theoretical understanding of the effects of closed-loop artificial stimulation in the highly recurrent neural circuits found in cortex, and how such protocols affect functional cotex-to-muscle mappings across a range of timescales. In parallel with ongoing experiments, we are developing a mathematical model of recurrent MC networks with probabilistic spiking mechanisms and spike-time-dependent plastic synapses (STDP) capable of capturing both neural and synaptic activity statistics relevant to BBCI protocols. This model successfully reproduces key experimental results and we use analytical derivations to predict optimal operational regimes for BBCIs. We make experimental predictions concerning the efficacy of spike-triggered stimulation in different regimes of cortical activity such as awake behaving states or sleep. Importantly, this work provides a first step toward a theoretical framework aimed at the design and development of next-generations applications of BBCI's.
Linda Petzold : The Emerging Roles and Computational Challenges of Stochasticity in Biological Systems
- Mathematical Biology ( 103 Views )
In recent years it has become increasingly clear that
stochasticity plays
an important role in many biological processes. Examples
include bistable
genetic switches, noise enhanced robustness of oscillations,
and fluctuation
enhanced sensitivity or "stochastic focusing." Numerous
cellular systems
rely on spatial stochastic noise for robust performance. We
examine the
need for stochastic models, report on the state of the art of
algorithms and
software for modeling and simulation of stochastic biochemical
systems, and
identify some computational challenges.