Steiner Trees and 3-D Macromolecular Conformation

Stanton, Courtney; Smith, J. MacGregor

doi:10.1287/ijoc.1040.0101

Cited by 10 publications

(4 citation statements)

References 19 publications

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“…The length of the tree SMT has the simple formula If the forces at the vertices are not uniform, then the SMT acts only as a lower bound. This was discussed in detail in a previous paper 16. Notice that in Maxwell's Theorem the function is separable in the force components.…”

Section: Methodsmentioning

confidence: 91%

Steiner minimal trees, twist angles, and the protein folding problem

2007

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The Steiner Minimal Tree (SMT) problem determines the minimal length network for connecting a given set of vertices in three-dimensional space. SMTs have been shown to be useful in the geometric modeling and characterization of proteins. Even though the SMT problem is an NP-Hard Optimization problem, one can define planes within the amino acids that have a surprising regularity property for the twist angles of the planes. This angular property is quantified for all amino acids through the Steiner tree topology structure. The twist angle properties and other associated geometric properties unique for the remaining amino acids are documented in this paper. We also examine the relationship between the Steiner ratio rho and the torsion energy in amino acids with respect to the side chain torsion angle chi(1). The rho value is shown to be inversely proportional to the torsion energy. Hence, it should be a useful approximation to the potential energy function. Finally, the Steiner ratio is used to evaluate folded and misfolded protein structures. We examine all the native proteins and their decoys at http://dd.stanford.edu. and compare their Steiner ratio values. Because these decoy structures have been delicately misfolded, they look even more favorable than the native proteins from the potential energy viewpoint. However, the rho value of a decoy folded protein is shown to be much closer to the average value of an empirical Steiner ratio for each residue involved than that of the corresponding native one, so that we recognize the native folded structure more easily. The inverse relationship between the Steiner ratio and the energy level in the protein is shown to be a significant measure to distinguish native and decoy structures. These properties should be ultimately useful in the ab initio protein folding prediction.

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Section: Methodsmentioning

confidence: 91%

Steiner minimal trees, twist angles, and the protein folding problem

2007

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“…This is important because the structure of a protein greatly influences its function. This knowledge is useful to help determine the chemical structure of drugs needed to counter protein malfunctions also known as "targeted therapy" Stanton and MacGregor Smith [91], have shown that the native state of a protein seems to be close to the geometry of a Steiner tree and prove that the Steiner tree provides a lower bound on the protein's energy. The study of protein energy is valuable because it relates to the forces that drive the protein folding.…”

Section: Computational Biology and Biomedicinementioning

confidence: 99%

Operations research

Pierskalla¹

2009

Information Knowledge Systems Management

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Prologue:In Evita, Andrew Lloyd Webber and Tim Rice wrote: Politics, the Art of the Possible. To those of us in the operations research community, we postulate: Operations Research, the Science of Better -(i.e. better processes, better systems and better decisions). Using our own and other scientific, engineering, mathematical, and social sciences methodologies, operations researchers help decision makers make better decisions; decisions leading to improvements: greater quality, lower costs, greater revenues, better access, better scheduling, lower risks, more satisfaction -with the goal of always striving for the best or optimal decisions.1389-1995/09/$17.00  2009 -IOS Press and the authors. All rights reserved 242 W.P. Pierskalla / Operations research sectors, health-care sectors, and virtually every other sector in which strategic or operational decisions must be made to improve planning, performance and outcomes.Most operations research applications involve analyzing complex situations. The approach taken begins by looking at the complex situation from a systems perspective. Inside the system, processes are diagrammed and analyzed and a model is constructed based on the flows of people, products, services, technologies and information. Using this structure, the approach models the objectives desired to be achieved, the fixed and variable constraints on the system, all available options for decisions, evaluation of all possible outcomes, estimation of risks and bringing to bear the latest tools and techniques leading to improved or optimal decisions on system operation and outcomes. In most applications, it is frequently the case that multiple objectives such as to improve quality, lower costs, improve access and improve satisfaction are simultaneously achieved. In some cases, multiple objectives trade-off against one another and the decision maker has to weigh these objectives and choose among them. In this latter situation, operations research also provides decision analytic methodologies for optimally weighing and choosing among competing objectives.Because this book is about "Engineering the Health Care System", this chapter will be devoted to operations research applications in health care delivery with mentions of theory and methodologies as appropriate. We have space to cover only some of the applications from the thousands available but hope to do so with enough breadth of topic and depth of description to give a flavor for the capabilities of operations research in developing better or best solutions for many complex health care issues. If one wishes to have a brief introduction to the theory and methodologies mentioned in this chapter see Gass and Harris [35] and the website Wikipedia, http://en.wikipedia.org/wiki/Main Page.Operations research has been used in the development of theories and methodologies and in applications in many areas of health services delivery. Some of these areas are strategic in decision making and others are operational. Some examples are:1. Health care and health care syst...

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“…It has nevertheless several applications. To cite a few, phylogenetics (see Cavalli‐Sforza and Edwards, 1967; Montenegro et al., 2003; Brazil et al., 2009) and structure and folding proteins (see Stanton and Smith, 2004; Smith et al., 2007).…”

Section: Introductionmentioning

confidence: 99%

A new second‐order conic optimization model for the Euclidean Steiner tree problem in Rd$\mathbb {R}^d$

Ouzia

Pinto

Maculan

2023

Int Trans Operational Res

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In this work, a new second‐order conic optimization model for the Euclidean Steiner tree problem in d‐space, where the dimension d is at least three, will be presented. Also, two strategies for eliminating isomorphic trees will be developed. Computational results highlighting the efficiency of this model compared to existing models for the Euclidean Steiner tree problem will be discussed. Finally, enforcing the proposed model with any of the isomorphic tree elimination strategies permits us to compute for the first time, to the best of our knowledge, the minimum Steiner tree for the cube in double-struckR3$ \mathbb {R}^{3}$.

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Steiner Trees and 3-D Macromolecular Conformation

Cited by 10 publications

References 19 publications

Steiner minimal trees, twist angles, and the protein folding problem

Steiner minimal trees, twist angles, and the protein folding problem

Operations research

A new second‐order conic optimization model for the Euclidean Steiner tree problem in Rd$\mathbb {R}^d$

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