scholarly journals Allostery in oligomeric receptor models

2018 ◽  
Author(s):  
Gregory Douglas Conradi Smith
Keyword(s):  
Spanning Tree ◽  
Polynomial Functions ◽  
Allosteric Coupling ◽  
Receptor Models ◽  
Equilibrium Binding ◽  
Rational Polynomial ◽  
Tree Construction ◽  
Binding Curves

We show how equilibrium binding curves of receptor heterodimers and homodimers can be expressed as rational polynomial functions of the equilibrium binding curves of the constituent monomers, without approximation and without assuming independence of receptor monomers. Using a distinguished spanning tree construction for reduced graph powers, the method properly accounts for thermodynamic constraints and allosteric coupling between receptor monomers.

scholarly journals Allostery in oligomeric receptor models

2019 ◽  
Vol 37 (3) ◽  
pp. 313-333
Author(s):  
Gregory Douglas Conradi Smith
Keyword(s):  
Algebraic Expression ◽  
Transition Diagram ◽  
Guanine Nucleotide Binding Protein ◽  
Allosteric Interactions ◽  
Equilibrium Binding ◽  
Rational Polynomial ◽  
Tree Construction ◽  
Guanine Nucleotide Binding ◽  
Receptor Dimers ◽  
Binding Curves

Abstract We show how equilibrium binding curves of receptor homodimers can be expressed as rational polynomial functions of the equilibrium binding curves of the constituent monomers, without approximation and without assuming independence of receptor monomers. Using a distinguished spanning tree construction for reduced graph powers, the method properly accounts for thermodynamic constraints and allosteric interactions between receptor monomers (i.e. conformational coupling). The method is completely general; it begins with an arbitrary undirected graph representing the topology of a monomer state-transition diagram and ends with an algebraic expression for the equilibrium binding curve of a receptor oligomer composed of two or more identical and indistinguishable monomers. Several specific examples are analysed, including guanine nucleotide-binding protein-coupled receptor dimers and tetramers composed of multiple ‘ternary complex’ monomers.

scholarly journals Algorithms for the power-p Steiner tree problem in the Euclidean plane

2018 ◽  
Vol 25 (4) ◽  
pp. 28
Author(s):  
Christina Burt ◽  
Alysson Costa ◽  
Charl Ras
Keyword(s):  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Valid Inequalities ◽  
Minimum Cost ◽  
Performance Ratio ◽  
Mixed Integer ◽  
Steiner Tree Problem ◽  
Steiner Points ◽  
Tree Construction ◽  
The Cost

We study the problem of constructing minimum power-$p$ Euclidean $k$-Steiner trees in the plane. The problem is to find a tree of minimum cost spanning a set of given terminals where, as opposed to the minimum spanning tree problem, at most $k$ additional nodes (Steiner points) may be introduced anywhere in the plane. The cost of an edge is its length to the power of $p$ (where $p\geq 1$), and the cost of a network is the sum of all edge costs. We propose two heuristics: a ``beaded" minimum spanning tree heuristic; and a heuristic which alternates between minimum spanning tree construction and a local fixed topology minimisation procedure for locating the Steiner points. We show that the performance ratio $\kappa$ of the beaded-MST heuristic satisfies $\sqrt{3}^{p-1}(1+2^{1-p})\leq \kappa\leq 3(2^{p-1})$. We then provide two mixed-integer nonlinear programming formulations for the problem, and extend several important geometric properties into valid inequalities. Finally, we combine the valid inequalities with warm-starting and preprocessing to obtain computational improvements for the $p=2$ case.

scholarly journals Fast Self-stabilizing Minimum Spanning Tree Construction

2010 ◽  
pp. 480-494 ◽  
Author(s):  
Lélia Blin ◽  
Shlomi Dolev ◽  
Maria Gradinariu Potop-Butucaru ◽  
Stephane Rovedakis
Keyword(s):  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Tree Construction

Technical Note: Rational Polynomial Functions for Modeling E. coli and Bromide Breakthrough

2012 ◽  
Vol 55 (5) ◽  
pp. 1821-1826 ◽  
Author(s):  
D. W. Meek ◽  
C. K. Hoang ◽  
R. W. Malone ◽  
R. S. Kanwar ◽  
G. A. Fox ◽  
...  
Keyword(s):  
Technical Note ◽  
Polynomial Functions ◽  
E Coli ◽  
Rational Polynomial

scholarly journals Random minimal directed spanning trees and Dickman-type distributions

2004 ◽  
Vol 36 (03) ◽  
pp. 691-714 ◽  
Author(s):  
Mathew D. Penrose ◽  
Andrew R. Wade
Keyword(s):  
Spanning Tree ◽  
Spanning Trees ◽  
Dirichlet Distribution ◽  
Maximal Length ◽  
Directed Path ◽  
Limiting Distributions ◽  
Limit Distributions ◽  
Tree Construction ◽  
Directed Spanning Tree ◽  
Westerly Direction

In Bhatt and Roy's minimal directed spanning tree construction fornrandom points in the unit square, all edges must be in a south-westerly direction and there must be a directed path from each vertex to the root placed at the origin. We identify the limiting distributions (for largen) for the total length of rooted edges, and also for the maximal length of all edges in the tree. These limit distributions have been seen previously in analysis of the Poisson-Dirichlet distribution and elsewhere; they are expressed in terms of Dickman's function, and their properties are discussed in some detail.

scholarly journals Using Rational Polynomial Functions for rectification of GeoEye-1 imagery

2013 ◽  
Vol 1 (6) ◽  
pp. 12-17 ◽  
Author(s):  
Pasquale Maglione ◽  
◽  
Claudio Parente ◽  
Andrea Vallario
Keyword(s):  
Polynomial Functions ◽  
Rational Polynomial

scholarly journals Random minimal directed spanning trees and Dickman-type distributions

2004 ◽  
Vol 36 (3) ◽  
pp. 691-714 ◽  
Author(s):  
Mathew D. Penrose ◽  
Andrew R. Wade
Keyword(s):  
Spanning Tree ◽  
Spanning Trees ◽  
Dirichlet Distribution ◽  
Maximal Length ◽  
Directed Path ◽  
Limiting Distributions ◽  
Limit Distributions ◽  
Tree Construction ◽  
Directed Spanning Tree ◽  
Westerly Direction

In Bhatt and Roy's minimal directed spanning tree construction for n random points in the unit square, all edges must be in a south-westerly direction and there must be a directed path from each vertex to the root placed at the origin. We identify the limiting distributions (for large n) for the total length of rooted edges, and also for the maximal length of all edges in the tree. These limit distributions have been seen previously in analysis of the Poisson-Dirichlet distribution and elsewhere; they are expressed in terms of Dickman's function, and their properties are discussed in some detail.

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