Not long ago we found a way to describe the large-scale statistical dynamics of neocortical neural activity in terms of (a) the equilibria of the mean-field Wilson-Cowan equations, and (b) the fluctuations about such equilibria due to intrinsic noise, as modeled by a stochastic version of such equations. Major results of this formulation include a role for critical branching, and the demonstration that there exists a nonequilibrium phase transition in the statistical dynamics which is in the same universality class as directed percolation (DP). Here we show how the mean-field dynamics of interacting excitatory and inhibitory neural populations is organized around a Bogdanov-Takens bifurcation, and how this property is related to the DP phase transition in the statistical dynamics. The resulting theory can be used to explain the origins and properties of random bursts of synchronous activity (avalanches), population oscillations(quasi-cycles), synchronous oscillations (limit-cycles)and fluctuation-driven spatial patterns (quasi-patterns). We will also show how such a system of interacting neural populations can be made to self-organize to a state near the Bogdanov-Takens bifurcation, if the coupling constants(synaptic weights) are activity-dependent, and follow approximately, a generalization of the Vogels et al. version of spike-time dependent synaptic plasticity (STDP).
As we move through an environment, we are constantly making assessments, judgments, and decisions about the things we encounter. Some are acted upon immediately, but many more become mental notes or fleeting impressions -- our implicit "labeling" of the world. In this talk I will describe our work using physiological correlates of this labeling to construct a hybrid brain-computer interface (hBCI) system for efficient navigation of a 3D environment. Specifically, we record electroencephalographic (EEG), saccadic, and pupillary data from subjects as they move through a small part of a 3D virtual city under free-viewing conditions. Using machine learning, we integrate the neural and ocular signals evoked by the objects they encounter to infer which ones are of subjective interest. These inferred labels are propagated through a large computer vision graph of objects in the city, using semi-supervised learning to identify other, unseen objects that are visually similar to those that are labelled. Finally, the system plots an efficient route so that subjects visit similar objects of interest. We show that by exploiting the subjects' implicit labeling, the median search precision is increased from 25% to 97%, and the median subject need only travel 40% of the distance to see 84% of the objects of interest. We also find that the neural and ocular signals contribute in a complementary fashion to the classifiers' inference of subjects' implicit labeling. In summary, we show that neural and ocular signals reflecting subjective assessment of objects in a 3D environment can be used to inform a graph-based learning model of that environment, resulting in an hBCI system that improves navigation and information delivery specific to the user's interests.
Soundscape Ecology and the concept of biophonies and geophonies in particular, form the basis of an emerging field that is only about dozen years old. While it is being defined to some extent in cultural, acoustic, and biological terms, translating these phenomena to numbers has been elusive and challenging. While my field of expertise is neither mathematics nor statistics — it is limited primarily to field recording, archiving and preliminary analysis of natural soundscapes — this discussion will provide some historical background and then focus on the ways in which biophonies and geophonies, in particular, might be framed through the lens of various statistical models and lay the groundwork for new ones.
Cells are highly ordered, and much of this organization is controlled by active molecular-motor based transport. At the single-molecule level, biophysical studies have been very effective at determining how motors work. However, in cells, motors do not function by themselves, but rather, act in groups. How these groups function is less well understood. In this talk I will discuss our experimental evidence underlying the statement that motors function in groups, and will then discuss how modeling can be used as a key tool to understand both how groups of motors function, and also which aspects of their single-molecule properties are particularly important for controlling this ensemble function.
Despite remarkable advances in protein structure prediction and design, an accurate predictive model of the thermodynamic effects of even point mutations remains elusive. The post-genomic era is a remarkable time to consider the problem of protein stability from a statistical perspective. How is information distributed in protein sequences? What protein properties are encoded by conserved and co-varying amino acids? And how can we use this information to engineer more stable proteins? We have been analyzing the effects of sequence conservation and correlation on enzyme function and physical properties, by engineering consensus and correlated mutations, or fully consensus variants, of the ubiquitous and well-studied metabolic enzymes triosephosphate isomerse (TIM) and adenylate kinase (ADK). We have established useful methods for calculating and visualizing conservation and correlation. From two consensus variants of TIM, we showed that correlated networks in weakly conserved positions can contribute strongly to protein biophysical properties. We also showed that consensus mutations are more likely to stabilize at more conserved positions, unless those positions strongly co-vary with other positions. I will review these results and discuss further efforts to refine our sequence-based algorithm for protein stabilization, and establish its generality. I will also briefly discuss experiments to explore the effects of correlated mutations directly, including through the use of a TIM-knockout based selection we pioneered in our lab.
Protein folding diseases occur when a specific protein fails to fold into its correct functional state as a consequence of mutation in the protein amino acid sequence. In this talk, I present a model of the folded and misfolded protein expression, processing and their interactions, which we have used to investigate how protein folding disease phenotypes develop from mutated genotypes. Modeling protein processing as a continuous flow reactor, we found that the pathogenesis of protein folding diseases can be modulated by a combination of the transition time of folded and misfolded proteins in the reactor, the ratio of folded and misfolded protein inflow rates in the reactor and a chemical interaction parameter between folded and misfolded proteins. Our analysis reveals therapeutic strategies targeting the modulation of protein folding diseases, which have been recently explored in cellular and animal models of Mutant INS-gene Induced Diabetes of Youth and Congenital Hypothyroidism with deficient thyroglobulin.