Appendix 3

Training Computational and Mathematical Biologists


1. Introduction

It has been estimated that in mid-1990, there were approximately 4000 professional level scientists identi_able as computational or mathematical biologists. These scientists were found in a wide variety of institutions and in a wide range of positions within those institutions.

The pattern of distribution of these individuals among and within different institutions appears to be related to their academic training. For example, mathematicians and computer scientists who have primarily followed an interest in the biological sciences generally work as biologists and _nd themselves in nonacademic research positions in industry, government or private research institutes, or quasi-academic research centers (e.g., supercomputer centers). A small minority are in biology departments. In contrast, mathematicians who have continued to pursue research activities in mathematics, choosing biologically related problems or examples, or collaborating with biologists, tend to remain in departments of mathematics or applied mathematics in academic institutions. Computer scientists follow a similar pattern. Statisticians may be found in statistics departments, biostatistics groups or departments, or even in biological sciences departments, depending on the extent of their involvement with biological problems, and the local structure of the institutions within which they work.

Biologists who rely on computational and mathematical tools in their research activities are found in many institutions. A large number have moved into industry where they play a role in the analysis of macro-molecules in biotechnology and pharmaceutical companies. Another major source of employment is in government and private research institutes, which tend to focus on problem-oriented research and directly utilize their computational biology skills. In the academic environment, computational biologists pursuing accepted biological problems are found in a variety of departments of biology (including departments of related name such as genetics, ecology and evolutionary biology, molecular biology, and microbiology), chemistry, and biochemistry.

The character of the institutional acceptance of these interdisciplinary activities depends on two factors: the need of the institution for problem-oriented work, and the traditional academic expectations on the performance of the individual. For example, biology departments place their emphasis on disciplinary achievements, and computational and mathematical approaches are secondary to the disciplinary results. Therefore, the infusion of mathematical and computational tools is dependent on the con_dence of the researcher that they can afford to invest the time and effort to enable them to use this approach, let alone develop new tools. Thus in many cases, computational and mathematical biology makes a backdoor entrance into the academic world. In contrast, these approaches are embraced more directly by industry and research institutes whose problem-oriented programs utilize a broader range of approaches, including direct application of mathematical and computational techniques.

The workshop participants' assessment is that in the immediate future, this situation will not undergo a substantial change. Therefore, scientists expecting to enter the academic research world will continue to need a strong disciplinary grounding for their cross disciplinary work. Employment opportunities in industry and research institutes appear to be stable, or growing slowly. Such centers will continue to be major sites for the development of computational techniques and applications in biology.

Because of their frequently strong mathematical and computational environments, and the less frequent presence of rigid departmental structures, one possible source of future growth for computational biology is the four-year college. Mathematical and computational approaches _t well within the research environments found in these institutions, and they are likely to _nd effective implementation in the teaching programs. In this context, faculty in these institutions may be expected to employ mathematical and computational techniques in both research and the development of teaching aids that will eventually _nd their way into research institutions. However, here again, strong disciplinary training will be essential as the basis for the research approach.

2. Pro_les of Computational and Mathematical Biologists

In the past, most of the migration of scientists into computational biology has been from disciplines outside of biology (e.g., math, physics, chemistry, computer science, etc.). Physicists become biologists, but not the reverse. This migration and its asymmetry has been prompted by successful applications of domain-speci_c technology to solving biological problems.

Many early successes in computational biology were obtained by scientists who were primarily biologists with marginal skills in computer science and mathematics (programming skills and some algorithmics), while many others were the result of work by scientists with extensive mathematical and computational backgrounds. However, as the problems under investigation become more complex, training which provides great depth in quantitative analysis will be essential.

Current interest and excitement in computational and mathematical biology is driven in large part by neurobiology, global change, and genomics. In all of these areas, vast amounts of information are accumulating at a rate that precludes human absorption and, hence, understanding. Biology needs tools for manipulating and analyzing information. In order for training environments to be maximally effective there must be a clear understanding of which professional pro_les are suitable for current and future researchers in computational and mathematical biology.

The pro_les which follow are dependent upon the nature of the position. Academicians tend to reside within traditional departmental units; whereas, in industrial settings and research institutes there is a wider range in the mixtures of disciplines in working groups. The following lists of specialities within computer science, mathematics and biology are those in which there is substantial research activity today and where there is likely to remain some research focus in the future.

Computer Scientists:

Most computer scientists retain their primary professional identi_cation with computer science. They tend to view biological applications as a source of computer science problems. Biological applications are new to computer scientists, and the traditions across the interface are developing at a moderate pace. The tendency is to cross the line as a senior scientist by developing collaborations. There are some successful scientists in this _eld whose _rst exposure to biology was at the graduate level. Examples of the areas of computer science in which such collaborations take place are:

Arti_cial Neural Networks (AI)


Database design and theory

Visualization (Graphics)


Biologists working on computational problems come from a plethora of backgrounds: computer science, mathematics, statistics, engineering, physics and chemistry as well as biological disciplines. The biological sciences are themselves diverse and different areas of biology draw upon very different quantitative skills. Those biologists who have crossed the boundaries between biology and other disciplines have often done so to address speci_c biological problems. Their acceptance by the biological community has been out of necessity since many biological problems require technology that has been driven by insight and intuition from other disciplines. This report is motivated by the assumption that this trend will accelerate in the near future in areas such genomics, neurobiology, imaging, structural biology and issues of global climate change. Many of these developments have been initiated by scientists whose initial training was outside biology (e.g., mathematics, chemistry and physics). The current technological advances will require a new range of quantitative skills beyond the norm of current curricula in the biological sciences. Biological Sciences that currently draw substantially from the computational and mathematical sciences include:

Population Biology, including Ecology and Genetics

Molecular Biology

Molecular Genetics

Cellular Biology


Biophysics and Structural Biology

Ecosystem Ecology




There is a long tradition of mathematicians and statisticians working on biological problems. Indeed, the _eld of statistics grew largely out of biological origins, and there is a substantial portion of the statistics community working on problems of biometry and biostatistics. There is also a small but stable community of mathematical biologists working within departments of pure and applied mathematics. Some members of this community migrate to biological departments during the course of their careers while others remain in mathematical science departments. Those who do remain within mathematical science departments either establish a career based upon collaborations with biologists, or focus upon mathematical questions driven by biological problems. In some cases, threads of mathematical research initiated by biological problems take on a life of their own as interesting areas of mathematics per se. Areas of mathematics making substantial contributions to biology include:

Applied Mathematics (Differential Equation Models, Image

Processing and Analysis)

Probability (Sequence Analysis, Interacting Particle Systems)


Discrete Mathematics

Topology and Differential Geometry

2.1. Summary of the Current Status

With regard to the current panorama of activity, we perceive that several dif_culties exist. First, computer scientists are not suf_ciently involved in computational biology. Their work is frequently on problems so abstracted from the application as to make them less than fully effective as collaborators. Another limitation is that biologists tend to view the work of computational scientists as service, and not original research, which tends to alienate this community. Mathematicians are caught between mathematical peers who evaluate their work on the basis of its mathematical depth and elegance, and biologists who have little appreciation for theory that does not have a direct bearing on the interpretation of experimental data. Finally, those biologists who have invested in cross-training are frequently misunderstood and undervalued by their colleagues, most of whom do not understand how to evaluate their work.

Computer science is a new discipline that is rapidly maturing. As the _eld develops, a tradition of interdisciplinary work will evolve much as it has for mathematics, especially statistics. This will, in part, alleviate the problem of computer scientists' involvement. A greater emphasis on the early grounding in scienti_c disciplines while at the undergraduate level should also help to cultivate computer scientists with a stronger interdisciplinary focus. As the needs for computation in the various areas described above becomes clearer, the biological community must become increasingly more tolerant and accepting of computational biologists within their midst. As a result of this and other factors, such as heavy dependence on physical measurement, the training of biologists at all levels must become increasingly more quantitative in nature.

3. Encouraging Interactions

The most effective way to encourage interactions between mathematicians and computer scientists on the one hand, and biologists on the other, is through direct co-involvement with a particular problem. This applies at all levels from undergraduate through senior scientist. The ways in which this interaction may be encouraged depend on the level and direction of movement (math/CS to biol or biol to math/cs). At present, the pattern is generally unidirectional, with movement from mathematics or computer science into biology as the dominant paradigm. Significant changes in this state of affairs are likely to require substantial curricular changes based upon effective means of overcoming the apprehension of most biology students towards mathematics.

Interaction can be improved through a strengthening of mechanisms that already exist. However, one area deserves much greater emphasis than is now the case, and that is support of small research groups with a genuine interdisciplinary focus: within this, substantial support is needed for post-doctoral scientists. Support of small group research will develop critical mass in important areas, will help to foster and sustain collaborative research, and provide a crucial home for individuals who are in the early stages of (what is now) a cross-disciplinary research career.

The most effective mechanisms for stimulating these _elds vary by the level of a scientist's career stage as outlined below.

(a) Senior researchers (tenured and above)

(CS, Math -> Biol) Support for sabbaticals and, later, research in biology.

(Biol -> Math/CS) Support for visits to math research groups to learn/update new technical areas.

(b) Pre-tenure

Most mathematics and statistics PhD students will start in untenured positions. Changing _elds (or, at least becoming more interdisciplinary) at such an early stage is a very risky career move, particularly by individuals approaching a tenure decision. One way to ameliorate this situation is through a new focus on PYI-level type support (National Science Foundation Presidential Young Investigator) for promising people (prestigious competitive awards).

(c) Postdoctoral

Support for postdoctoral training within existing grants is essential. Postdocs are an important educational component of existing research groups, and are very scienti_cally pro_table in the short term. These should support a given individual for multiple years, and not be speci_cally tied to a particular investigator within the group. This mechanism allows quick response to changing areas of interest, while providing enough time for a postdoctoral fellow to develop a useful independent research focus.

Another aid to young investigators is the computational research associates program at the NSF sponsored Supercomputing Centers. This program is of great value to the biological sciences and the _eld would bene_t from its continued existence. However, to be maximally effective these investigators must be part of an active and focused research program and not "generalists" in applied computer science.

The concepts behind these training programs are not based on the assumption that all people passing through them will eventually obtain tenure track positions in universities.

(d) Graduate students

An important source of mathematical biologists comes from mathematically trained undergraduates who change _elds early in their postgraduate education. Such students are then main-stream biologists, with the requisite quantitative background to enter the _elds of mathematical or computational biology. The educational challenge for students with this background is the continuation of the quantitative approach to biology in a supportive environment. This requires an appropriate mentor and an appropriate departmental or graduate group environment so that the student's background is valued and prior training reinforced. Given the many opportunities available to an undergraduate with computer science or mathematical training, it is essential that graduate student support be provided to entice these students to forego the immediate grati_cation of lucrative employment for the longer term prospects of graduate training and research careers in biology. To this end the continued and renewed support of training grants or traineeships (for example in the research groups described above) are of central and continuing importance.

Furthermore, educational institutions must be encouraged to recognize the need for training students in these areas as a means of dealing with the future of biological research. To this end institutional and departmental support of fellowships and RA (Research Assistant) positions are of supreme signi_cance. Cross-training students at the graduate level will lengthen an educational process that already can be inordinately long. Freeing a student from the demands of a teaching assistantship or a research assistantship with responsibilities to further the work of a principal investigator will help make such programs educationally feasible. It would be especially appealing to _nd a mechanism to support mathematical or computational biologists within the structure of departments of mathematics or computer science.

One of the most signi_cant factors in the training of graduate students is the role model of the major professor. This mentorship plays a greater role in the ultimate aspirations of a student than is generally acknowledged. The successes, failures, and frustrations of a student's mentor plays a profound role in the expectations and aspirations of a student. In this context the small group research environment is a highly signi_cant environment in which to train students for the future of the biological sciences.

(e) Undergraduate

In most institutions it is very common for the top biology students, especially those interested in eventual graduate study, to participate in undergraduate research projects, especially in their Junior and Senior years. this opportunity should not be con_ned to biology students, but should be expanded wherever possible to include interested students from mathematics and computer sciences whenever possible. The proper environment is essential to the nurturing of a student that might wish to commit to a career in the biological sciences, using this valuable undergraduate training. To this end the National Science Foundation REU (Research Experiences for Undergraduates) program provides an extraordinary opportunity in the Math/Biol area.

One area of extreme importance for the future development of a cadre of computational and mathematical biologists, and for the continued recruitment of students into biophysics and related disciplines is the development of better course materials devoted to the quantitative approach to biology. The workshop participants valued very highly the concept of "enculturation of quantitative thought" through the introduction of quantitative approaches in biology courses

(f) Pre-college

While there was considerable discussion during the workshop regarding the state of pre-college science education, no speci_c recommendations were developed. Many private and government agencies have focused great attention on this problem, and it remains a top national priority. There was general agreement that two issues posed particular concern to the participants. First, the need to involve more fully parents in the educational process. This is particularly important in groups which do not have a cultural history of educational achievement. The second concern was the current selection of the "ultimate underachiever" as the folk hero of the nation's children. We believe that this message is alarmingly inappropriate in the current context of rapid technological change and global competition. The participants hope that the leadership of the Education and Human Resources Directorate of the National Sciences Foundation will use its in_uence and insight to _nd a mechanism to reverse this trend.

(g) Summary Principles

(1) If time is limited for education, spend it in mathematics, not computer science.

(2) What we want is an attitude/consciousness change, so that people are aware of the input of the "other" type of science in their own area.

(3) While collaboration will enhance the science of the current generation, we are seeking to change the way that biology is done by changing the way biologists are educated for the next forty years.

4. Fundamental Educational Principles

(a) Undergraduate Education

(i) General Course Content

The cross-disciplinary aspects of modern science must be emphasized in all undergraduate science and mathematics courses. The role of computer science and mathematics, as well as technologies from physics and chemistry, need to be presented in biology courses. In contrast, the research areas that have used various tools of computer science and mathematics in the experimental sciences should be identi_ed throughout mathematics and cs courses.

(ii) Mathematics/Computer Science Majors

All mathematics and computer science majors should have required experimental science courses. We recommend a minimum of two years that can be concentrated in one area or spread over the basic sciences. The purpose of this is to provide the student with an understanding of the vocabulary and concepts and an experience of the ways in which mathematics or computer science have contributed to other disciplines.

(iii) Biological Sciences

In order to produce biological scientists who will be quali_ed to do modern research, we strongly recommend that the science curricula require four years of mathematics and/or computer science. Representative courses might include programming, theory of algorithms, probability and statistics, linear algebra, calculus, discrete mathematics, and numerical analysis.

(b) Consequences

Failure to implement these recommendations at a minimal level will foreclose the future for many undergraduates majoring in biological sciences. This originates in the types of problems that are coming into existence and that are consistently more and more dependent on quantitative skills for their solution. Secondarily, lack of training in these quantitative areas will limit the questions that can be asked by an investigator, and may come to threaten an individual's levels of funding. We must remember that we are addressing the education of persons who will be in the pool for the next forty years. If education changes are not implemented, much of biology will fail to thrive.

The broad education that we are proposing also permits people to change their minds and acquire additional course work in another _eld, even late in their studies, without having to start from the beginning.

Our recommendations should not be construed to support any concept that presupposes a gender-speci_c bias in the ability to perform. It may be that a type of math/cs anxiety will become apparent if our recommendations are instigated. In order to counter this, we propose that support groups, personal tutorials, study circles and other tools of encouragement and enhanced performance/esteem be supported so that they are readily available.

5. Additional Recommendations

Part of the dif_culty in implementing the course recommendations may be the prevalence of pre-med education as a major component of biology curricula. Although there will be a number of additional consequences, it would be well worth considering the restructuring of the undergraduate major so that pre-meds follow a separate track and their presence does not determine the future of an academic discipline.

It is incumbent upon those who practice cross-disciplinary science and mathematics/CS to become both role models and mentors for others. It is particularly important for representatives of under-represented groups to make an effort to encourage others.

Several members of the group have suggested that a new type of biology course should be developed. It would cover the elements of modern biology, but highlighting the contributions of other disciplines. The hope is that someone will be inspired to write a founding text, one that will change the _eld.

Graduate Education

Continue to create opportunities for cross-disciplinary work. NIH programs in molecular biophysics and the NSF research training groups are examples of attempts to encourage this type of interaction.

One-on-one mentor/student relationships are not suf_cient to maintain cross-disciplinary development. Direct support for cross-disciplinary efforts would help to break down the interdepartmental barriers that frequently exist. Seminar groups or other frequent interactions should be encouraged.

New graduate students (and postdocs) might acquire an elementary grounding in a new _eld through summer institutes or some other "crash course." The courses would be taught by highly interactive, expert, senior level researchers. For example, a course in basic molecular biological concepts could include molecular biology, biochemistry, and molecular biophysics. Emphasis would be on the vocabulary and point of view, that is, how the science is done and what are its assumptions. For a course on computation in genetics, this material might include basic computer science concepts, e.g., _les, databases, algorithms and their use, graphics and statistics. The bene_ts of such a course could also be made available to more senior investigators.

6. Women And Other Under-Represented Groups

In high school, women represent a reasonable proportion, approximately 30-40%, of those students who are interested in the physical sciences and mathematics. Partitioning begins in college and is nearly _nished by graduate school. Some disciplines within the biological sciences do have equivalent or even over-balanced representation by women. Increasing the level of course work in mathematics and computer science may be threatening to some of these women. In order to prevent this, speci_c actions may well be necessary. Similarly, for some students from other under-represented groups, it may be necessary to have additional courses available at the undergraduate level to improve the level of computational competence of entering students.

Table of Contents

Appendix 4