Title: Long-range periodicity and an unusual DNA packaging mechanism

We describe DNA-surface interactions in activated C. elegans oocytes that are revealed through the activity of an endogenous nuclease. Our analysis began with an unexpected observation that a majority of DNA from C. elegans oocytes is recovered in fragments of < 500 base pairs, cleaved at regular intervals (10-11nt) along the DNA helix. In some areas of the genome, cleavage patterns in the endoreduplicated oocytes were consistent from cell-to-cell, indicating coherent rotational positioning of the DNA in chromatin. Particularly striking in this analysis were arrays of sensitive sites with a periodicity of ~10bp that persisted through extended segments of the C. elegans genome that were longer than a single nucleosome core (up to several hundred base pairs). Genomic regions with a strong bias toward 10-nt periodic occurrence of A(n)/T(n) exhibited a high degree of rotational constraint in endo-cleavage phasing, with a strong tendency for the periodic A(n)/T(n) sites to remain on the face of the helix protected from nuclease digestion. The relationships between DNA sequence and accessibility revealed from this analysis evidence an ultra structure in which DNA and underlying protein structures are coherently linked.

Title: Mathematical Ideas in the Life Sciences: Modeling Cellular Clocks

Clocks run continuously in our cells and their function (and malfunction) has enormous effect on our lives. Circadian clocks control our response to the environment, the cell division cycle controls how our cells duplicate themselves, cell metabolic cycles control the physiological and biochemical properties of a cell, and developmental clocks help lay down patterns like vertebrae and lateral roots.

There are many interesting clinical observations that suggest that these clocks are coupling together in interesting ways. Individuals with poor sleep patterns may be more likely to develop cancer, does this suggest a coupling of the circadian clock with the cell clock? Cancer cells have different metabolism. How do these clocks work together? Root growth of these clocks appears more and more to be a pathway to understanding clinical observations. Are individuals with poor sleep patterns more likely to develop cancer? (I.e. is the circadian clock coupled with the cell-cycle clock?) There is some evidence that there is a circadian rhythm in root growth. Again, are these clocks coupled?

One way to get at these questions is to look for the regulatory networks that control these processes. In this talk we will discuss the construction and modeling of gene regulatory networks that control periodic processes. This is an exciting area where biology, mathematics and statistics come together.

Title: Biophysical models of chromatin

In eukaryotic cells, genomic DNA is packaged into a complex multi-scale structure called chromatin. The fundamental building block of chromatin is the nucleosome, a protein-DNA complex in which a 147 bp-long DNA segment is wrapped around the surface of a histone octamer. In vitro, arrays of nucleosomes are positioned along DNA according to their sequence preferences and steric exclusion between neighboring particles. Nucleosomal arrays are folded into higher-order chromatin fibers whose structure and physical properties are poorly understood. We have developed a framework for predicting sequence-specific histone-DNA interactions and the effective two-body potential responsible for ordering nucleosomes into 3D fibers. We have derived surprisingly simple rules which allow us to predict nucleosome occupancy genome-wide.

We find these rules to be universal for chromatin assembled in vitro on genomic DNA from baker's yeast and from the nematode worm C. elegans. However, positioning rules in live C. elegans cells are strikingly different, reflecting a substantial role of chromatin remodelers in shaping functional chromosomes. One striking consequence of this genome-wide remodeling is pronounced depletion of nucleosomal sequence reads in arms relative to central regions, leading to the establishment of distinct Mbp-scale chromatin domains.

Title: Cellular simulations of morphogenesis

In this talk, I will describe discrete element simulations of cellular dynamics applied to several archetypal problems in development and disease. These problems include the development of building block structures in in vitro experiments, the formation of folds in normal development, and the evolution of structures in ductal cancerous growth. I will conclude by outlining challenges to cell-based simulations, especially with regard to accurately modeling complex three-dimensional structures.

Title: Scale-invariant responses in adapting biological systems

An ubiquitous property of biological sensory systems is adaptation: a step increase in stimulus triggers an initial change in a biochemical or physiological response, followed by a more gradual relaxation toward a basal, pre-stimulus level. Adaptation helps maintain essential variables within acceptable bounds and allows organisms to readjust themselves to an optimum and non-saturating sensitivity range when faced with a prolonged change in their environment. It has been recently observed that some adapting systems, ranging from bacterial chemotaxis pathways to signal transduction mechanisms in eukaryotes, enjoy a remarkable additional feature: scale invariance, meaning that the initial, transient behavior remains approximately the same even when the background signal level is scaled. This talk will review this phenomenon and discuss a theoretical framework as well as predictions and ongoing experimetal validations.