Algebra and Geometry Seminar

Semirings and schemes in tropical geometry
 
The tropicalization of a variety is usually considered as a polyhedral set inside Euclidean space, but people often think of it heuristically as an algebraic set defined over the idempotent semiring of real numbers with the (max,+) structure.  I'll explain how to give this heuristic picture teeth: it turns out that the tropicalization trop(X) is actually the solution set to a system of (max,+) polynomial equations canonically associated with X.   This leads to tropical Hilbert polynomials and several other interesting things.

 

Date:
-
Location:
POT 745

Chemistry Department Seminar

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Dr. David Sept will be presenting a seminar titled Structure/Function Studies on Ion Channels and New Models for Ions. Refreshments will be provided at this event.

Abstract: Voltage and Ca2+ activated BK channels modulate neuronal activities. Previous studies found that the Ca2+ binding sites and the activation gate are spatially separated, but exactly how Ca2+ binding couples to gate opening is not clear. We address this question by studying how a mutation in BK channels, which is associated with generalized epilepsy and paroxysmal dyskinesia, enhances Ca2+ sensitivity. This epilepsy mutation is located in a structural domain (the AC region) that is close to a putative Ca2+ binding site, and mutagenesis studies show that the AC region is important in the coupling between Ca2+ binding and gate opening.  Through a combination of experimental and computational studies, we find the epilepsy mutation enhances Ca2+ sensitivity by an allosteric mechanism affecting the coupling between Ca2+ binding and gate opening. 

Our efforts to determine the details of the Ca2+-bound structure of the AC region took an unexpected turn that required us to develop a new model for divalent cations.  Current ion models in molecular mechanics are simple spheres, and their interactions are solely determined from the radius of the sphere and the total charge. This set of parameters is chosen to closely reproduce the hydration free energy for the ion, but this exercise uses all the available degrees of freedom and our ability to reproduce the binding free energy to a protein or other thermodynamic quantities is therefore limited.  In our new model we distribute the total charge of the ion into n-dummy centers that are placed in the direction of the coordinating atoms. We have parameterized this model for two divalent cations, Ca2+ and Mg2+, and have tested the model’s accuracy in a variety of simulations.  With this model we are not only able to correctly predict the free energy and selectivity for cation binding sites in both proteins and nucleic acids, but we achieve better coordination geometries and can capture more subtle effects such as the exchange of inner shell waters.  One further advantage of this model is that it does not use higher-order electrostatics and thus can be easily used with standard force fields.

 

Faculty Host: Dr. Pete Kekenes-Huskey

 

 

Date:
-
Location:
CP-114A/B

SIAM Meeting

We are having a meeting on Tuesday, March 30 at 5:15pm to discuss the details of our invited speaker for the semester.

 

If you have further questions please contact one of the following people.

George Lytle

Chase Russell

Fouche Smith

Date:
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Location:
745 Patterson Office Tower

Applied Math Seminar

Title: Optimality of the Neighbor Joining Algorithm and Faces of the Balanced Minimum Evolution Polytope



Abstract:  Balanced minimum evolution (BME) is a statistically consistent distance-based method to reconstruct a phylogenetic tree from an alignment of molecular data. In 2008, Eickmeyer, Huggins, Pachter, and myself developed a notion of the BME polytope, the convex hull of the BME vectors obtained from Pauplin's formula applied to all binary trees. We also showed that the BME can be formulated as a linear programming problem over the BME polytope.  The BME is related to the Neighbor Joining (NJ) algorithm, now known to be a greedy optimization of the BME principle. Further, the NJ and BME algorithms have been studied previously to understand when the NJ algorithm returns a BME tree for small numbers of taxa. In this talk we aim to elucidate the structure of the BME polytope and strengthen knowledge of the connection between the BME method and NJ algorithm. We first show that any subtree-prune-regraft move from a binary tree to another binary tree corresponds to an edge of the BME polytope. Moreover, we describe an entire family of faces parametrized by disjoint clades. We show that these clade-faces are smaller-dimensional BME polytopes themselves. Finally, we show that for any order of joining nodes to form a tree, there exists an associated distance matrix (i.e., dissimilarity map) for which the NJ algorithm returns the BME tree. More strongly, we show that the BME cone and every NJ cone associated to a tree T have an intersection of positive measure.  We end this talk with the current and future projects on phylogenomics with biologists in University of Kentucky and Eastern Kentucky University.  This work is supported by NIH.



 

Date:
-
Location:
245 Patterson Office Tower
Event Series:
APPLIED MATHEMATICS SEMINAR

A Conversation with Dr. James May Jr.

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Dr. James W. May Jr (Chemistry '65) will be available to talk with students about several topics, including: his path to becoming a surgeon, the value of a science degree, how to get into medical school, and a career in medicine at a major research institution.

All interested students are welcome.  Refreshments will be served at this event.

Co-sponsored by the College of Arts & Sciences and the Department of Chemistry

 

 

Date:
-
Location:
CP-114A/B
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