Mathematics and 21st Century Biology (2005) / Chapter Skim
Currently Skimming:
1 The Nature of the Field
1 The Nature of the Field
Pages 12-28
The Chapter Skim interface presents what we've algorithmically identified as the most significant single chunk of text within every page in the chapter.
Select key terms on the right to highlight them within pages of the chapter.
From page 12... ...
1 The Nature of the Field INTRODUCTION Biology is in dramatic flux due to a surge of new sources of data, access to high-performance computing, increasing reliance on quantitative research methods, and an internally driven need to produce more quantitative and predictive models of biological processes. The growing infusion of mathematical tools and reasoning into biology may therefore be expected to further transform the life sciences during the decades ahead.
|
From page 13... ...
Molecular biology focuses on the chemical components of life and their interactions. These components differ greatly in size and complexity, ranging from atoms and simple ions, through the basic molecular building blocks of life such as nucleic and amino acids, sugars, and fats, to polymers and homogeneous and heterogeneous aggregates of the more basic units, forming macromolecular assemblies and supermolecular structures that carry out many of the fundamental processes in the life of a cell.
|
From page 14... ...
Other models may be formulated mathematically even though they are primarily intended for heuristic use rather than for data analysis: Simple differential equations describing idealized predator-prey interactions are in this category. Finally, sophisticated models designed to capture subtle features of large, real data sets are also diverse.
|
From page 15... ...
New techniques in protein chemistry, as well as new radiation sources for structural analyses, are accelerating the rate at which proteins can be detected in complex biological samples, purified, and characterized structurally at atomic resolution. · On the cellular scale, new methods of cellular imaging are making it possible to track subcellular processes and to trace the propagation of signals at millisecond timescales.
|
From page 16... ...
The analysis of spatial data poses particular challenges due to the correlations that are inherent in spatial processes and due to local interactions and stochastic effects. As an example, a method widely used for detecting anomalies in space is the spatial-scan statistic.
|
From page 17... ...
However, as experimental genomic science advances, options are becoming increasingly available. In the future, experimental design considerations must be tightly coupled to the mathematical representations to be used to model the system and the computational and statistical methods to be used for model identification and parameter estimation.
|
From page 18... ...
That is, we need to consider the output of a computational model as a testable hypothesis and then design biological experiments that try to disprove the hypothesis by collecting appropriate data or exploring whether qualitative features of the computer output exist in real systems. In order for such approaches to contribute significantly to progress in understanding biology, the experimental com
|
From page 19... ...
WHAT MAKES COMPUTATIONAL BIOLOGY PROBLEMS HARD? While the challenges posed by rapidly increasing amounts of data cut across all the sciences, those challenges posed by increased amounts of data in biology are uniquely difficult.
|
From page 20... ...
FACTORS COMMON TO SUCCESSFUL INTERACTIONS BETWEEN THE MATHEMATICAL SCIENCES AND THE BIOSCIENCES As the committee examined the historical record and contemporary experience in applying mathematics to biology, a few simple observations that commonly underlie successful interactions came to the fore: · The biological problem has always been primary. Successful applications of mathematics to biology are driven by a deep understanding of the relevant biology.
|
From page 21... ...
Rigorous prioritization will support a structural change in the biological sciences that encourages the use of quantitative approaches of all categories. More generally, success stories based on such considerations will be readily exported to other biological research problems and will serve to validate the role of mathematicians in biology qua mathematicians rather than just as technical contributors and to validate, for experimental biologists, the role of mathematics itself in understanding biology.2 · As the committee discusses in more detail below, cultural and linguistic barriers create a potentially large divide between mathematicians and biologists.
|
From page 22... ...
This process is also a critical test of whether the biologists and mathematicians working together on a problem have actually arrived at a common language. · Even though many biological problems have been solved using simple mathematics, a sophisticated and experienced mathematical scientist has often been required to find the solution.
|
From page 23... ...
(The primary model in the mind of the committee is mathematical scientists contributing to biology research teams, not, for the most part, biologists learning all the necessary mathematics and statistics.) Interestingly, some of the most successful practitioners at the interface have come out of the physical and mathematical sciences, bringing a deep understanding of quantitative methods as well as biology, but neither to the exclusion of the other.
|
From page 24... ...
The goal should be to foster effective collaboration between mathematical scientists and bioscientists by working to eliminate barriers posed by in adequate communication, disparate timescales for achieving research objectives, inequitable recognition of contributors to interdisciplinary projects, and cultural divisions within univer sities, research institutes, and national laboratories. In spite of the committee's belief that most problems in biology can initially be addressed with fairly standard mathematics or statistics, there are occasions where exceptionally innovative researchers may be driven by the particularities of a problem to break out of traditional mathematics paradigms and develop truly novel methods.
|
From page 25... ...
Recommendation: Funding agencies supporting mathematical research related to the life sciences should support the refine ment of general-purpose tools whose broad biological utility has already been established. Such research might require spe cialized review criteria, particularly when the focus is on tool enhancement rather than breakthrough research.
|
From page 26... ...
More specifically, the plans for generalized tool development will need similar careful review and a mandate provided through the call for proposals. Recommendation: Funding agencies supporting mathematical research related to the life sciences should give priority to re
|
From page 27... ...
Specifying a priori the tools to be developed inverts that goal. However, it is clear that if DOE's applied mathematics program is to contribute to computational biology, it should focus on research that is linked to the intrinsic characteristics of biological systems that reappear at many levels of biological organization: high dimensionality, heterogeneity, robustness, and the existence of multiple spatial and temporal scales.
|
From page 28... ...
2004. Integrating remote sensing and ecosystem process models for landscape- to regional-scale analysis of the carbon cycle.
|
Key Terms
This material may be derived from roughly machine-read images, and so is provided only to facilitate research.
More
information on Chapter Skim is available.