Mathematics and 21st Century Biology (2005) / Chapter Skim
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3 Understanding Molecules
3 Understanding Molecules
Pages 38-50
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From page 38... ...
In between are a wide variety of organic molecules necessary for life, including sugars and lipids, vitamins and other enzyme cofactors, and the nucleic acid and amino acid monomers required for DNA, RNA, and protein synthesis. The molecules interact in many ways and are capable of recognizing one another; some are active in the form of larger complexes.
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From page 39... ...
From the analysis of sequences to techniques for determining the three-dimensional structures of molecules to studies of the dynamics of entities ranging from individual molecules up to entire networks, mathematical techniques and computational algorithms are critical. Because of the rapid advances in the technology for DNA sequencing, DNA sequences are now easily obtained, and protein sequences can be inferred with reasonably high accuracy and completeness.
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From page 40... ...
The structure of a protein provides strong clues about its biochemical function -- for example, the mechanism for action by an enzyme -- but at the moment, there have been only a few successes in predicting biological function from sequence. The structures of these macromolecules are also important for other research purposes -- for example, they are the starting point for predicting biochemical action or for modeling the dynamics of the macromolecules, for suggesting ways to inhibit the action of undesired proteins, for predicting potential chemical inhibitors or activators of a given protein, or for altering a protein's functionality through its environment or through reengineering its sequence and, consequently, its structure.
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From page 41... ...
Using those data to inform dynamical models of the cell is critical to advancing our understanding of biology and is likely to tax existing mathematical techniques, opening up new areas of mathematical and biological research. AREAS OF MATHEMATICAL APPLICATIONS FOR MOLECULES Sequence Analysis The central role of sequences in mathematics is unquestioned.
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From page 42... ...
For the distance matrix approach, a distance is defined between each pair of sequences based, for instance, on pairwise sequence alignment scores from DP or from a position-by-position score relating a pair of sequences sampled from a full multiple alignment. Can a tree generated this way have the property that the distance between any two sequences is the same as the sum of distances through the vertices that connect those sequences?
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From page 43... ...
A typical protein structure must be inferred from enormous amounts of information that indirectly reveal the relative locations of key atoms in a biomolecular structure. The mapping from structure to data is straightforward, but the inverse problem, going from data to structure, is quite complex.
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From page 44... ...
Until recently, the energy functions used to simulate the folding process, built up from the interactions of fragments of protein, were too rugged to yield correctly folded structures. Instead, depending on the fine details of the optimization process, many unrelated structures were predicted to represent the global free energy minimum.
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From page 45... ...
The difficulty of making accurate predictions is undoubtedly due to some combination of the following facts: There is an enormous number of possible structures with nearly equal predicted energies; available thermodynamic parameters have limited accuracies; many RNAs require cofactors, such as magnesium, in the medium in order to fold properly; and efficient algorithms eliminate some possible structures, such as pseudoknots, that may be necessary to obtain the correct folding. As with proteins, RNAs can be folded most accurately by using information from homologous RNAs with known structure.
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From page 46... ...
While the atoms in proteins carry out the bulk of their motions in less than a picosecond, the fastest characteristic response time for a cell is in the millisecond range. Evolution has tuned and selected molecular properties to deliver results on the latter timescale.
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From page 47... ...
Statistical methods for predicting DNA target sites for specific proteins, given previous examples of similar sites, can be useful for discovering new regulatory interactions. What is needed is a recognition code that maps from the protein sequence (and utilizes the known structures of the transcription factor families)
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From page 48... ...
All mathematical descriptions that adequately model the diverse components at suitable resolution while also capturing the stochastic character of intermolecular partnership and the complexity of individual biomolecular dynamics remain a distant goal but one that the community of mathematical and physical scientists is beginning to tackle. FUTURE DIRECTIONS There are many daunting mathematical challenges to understanding and modeling the molecular aspects of biology.
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From page 49... ...
1990. Basic local alignment search tool.
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From page 50... ...
1995. Introduction to Computational Biology: Sequences, Maps and Genomes.
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