Development
of a
Biological Physics Curriculum
at the
Physics Department of the University of
Illinois
at Urbana-Champaign
Report of Committee, December 4, 2000
Klaus Schulten (chair), Robert Clegg,
Enrico Gratton,
Taekjip Ha, Ioan Kosztin, Paul Selvin
Overview:
In the following we will first present our vision of a new curriculum in biological
physics. We combine in this section both the undergraduate
and graduate programs since they are inseparable and since many undergraduate students take graduate
courses. We will use HHMI funds, though, solely for the
development of the undergraduate courses, i.e., of 300 level courses.
In a second section we outline two of the new undergraduate courses and in a more extended third
section we describe the planned computational biology courses.
In the last section we outline the attempt to reach students on our campus and beyond as
well as describe a workshop for electronic media and molecular modeling, which constitutes
a core element of this proposal. Our Vision:
The beginnings of the 20th and
21st centuries show a remarkable similarity: the 20th century saw discoveries of the atomic level
structures of inorganic matter, the 21st century is currently experiencing the discovery of genomes
of organisms. Both discoveries are likely to make history as
having laid the foundations of new eras of research and industry.
From the former emerged material science and the electronics industry; the latter are expected
to spawn a new era of biomedicine and biotechnology. The physics
department of the University of Illinois at Urbana-Champaign (UIUC) played a great role in
the development of material science and electronics, having founded the renown materials
research laboratory on the UIUC campus with the inventor of the transistor, the late John Bardeen,
on its faculty; today the department is the US academic
leader in solid-state physics. The UIUC physics department
can play a similarly important role in the new century if it applies the same
farsighted vision that its leaders showed decades ago. In fact, at
this crucial moment the vision of the UIUC physics department can be important for the development
of the UIUC campus as a whole. On many US university campuses the birth of new laboratories
devoted to genomics and proteomics are being witnessed. Their research efforts are inventorying
genes and proteins of living organisms. Our campus is struggling
to position itself as an important national institution in these critical endeavors and one
wonders with a sense of great trepidation what role UIUC will play ten or twenty years from now.
Actually, one need not worry, provided we build on our strength.
The University of Illinois at Urbana-Champaign can place itself
ahead of others that are now leading the genomics and life science gold rush if it realizes its
strength and great traditions. Our strength lies in the integration
of physical science into emerging fields; just as this was done in material science and electronics
in the past, we can achieve this in the life sciences and biotechnology today.
Our intuition based on a strong physical background tells us
that although taking the inventory of an organism is a wonderful achievement,
the information accumulated - gene sequences and biopolymer structures - needs
to be woven into the same intellectual fabric that laid the foundation of 20th century
science and industry: a thorough understanding built on physical
principles and mathematics.
We at UIUC can prepare our students and ourselves for the great opportunities that will become
available when genes and protein structures have become largely known.
The realization is already becoming evident that having taken the inventory
leaves much unexplained and does not reveal how this enumerative knowledge can be turned
into new drugs and technical products. In addition, our ability to
acquire new physical data with such complex systems and to interpret intricately complex
interactive systems must improve dramatically, in order to keep pace with the enormous influx of
descriptive biological data. New paradigms of the organization and
functioning of large, complex, interactive living systems will be needed.
This will require a new generation of physically and mathematically
trained scientists with a sophisticated knowledge of the biological systems as
well as a solid physics background. Presently, such training and
education in the framework of a physics curriculum is offered almost nowhere in the United States,
and we have the opportunity to be pioneers in such an endeavor.
The genomes of about a hundred organisms have been sequenced and over 17,000 structures are available
in the protein data bank. Soon, most proteins from a single
organism will be structurally resolved. However, by now we know
that the knowledge of a relevant gene is not enough. We must know
what the gene product is and how it performs its function. Furthermore,
knowledge of a protein structure, with notable exceptions, most often reveals little about the
physical mechanisms underlying function. Indeed, drug development is
still mainly a fishing expedition. Rational design in pharmacology
and biotechnology will require an understanding beyond genes and structures - an
understanding of function, mechanisms, and system integration.
It is actually not difficult to imagine the postgenomics state of the life sciences.
We will, for the first time, have a truly global view of the state
of an organism. We will know at the various stages of its
life cycle the state of expression of all genes and the quantity of all proteins.
We will have detailed insight into the structures of active
biopolymers, as well as tools that image the morphology of organisms from the atomic level
to the cellular level and beyond. This information will create a
renaissance of physical life science and will set the stage for the physicist.
Progress in this new field will be focused on a detailed
understanding of the material substrate of living systems, and physicists will make
major contributions to this new field as they now do in material science.
Biological physics is already a strong discipline, but
progress in our physical descriptions has been largely limited by the lack of available information.
For example, much of biophysics dealt for decades with a single
protein, myoglobin, simply because it was the first protein to be structurally resolved.
In the near future, a biological physicist can study any
biomolecular system. We will be able to base our choice on
functional relevance rather than on what is available. For example,
we will be able to investigate all proteins of the photosynthetic
and respiratory apparatus that convert light and food energy into the synthesis of ATP,
and we will not only be able to study the proteins one by one,
but how they assemble and function together.
One can safely predict that biological physics will play the same role in the sciences
and engineering as condensed matter physics did in the last century.
The UIUC physics department is already well positioned for its part in the renaissance of the
life sciences provided we orient ourselves appropriately and timely.
It has pioneered the field of biological physics in the US over three decades long, before
any other US physics department. We have recently consolidated
and extended our faculty, now numbering five primary members (Clegg, Gratton, Ha, Schulten, Selvin)
and several affiliated members. However, in keeping with the
tradition and mission of an academic institution, the hiring of faculty must be complemented by
a strong teaching program. The department seeks to accomplish
this through a system of undergraduate and graduate level courses that is described below.
This system replaces the single currently existing biological
physics course through a set of three undergraduate and three graduate courses, with possibilities
to be expanded and modified in the future (as is required for such a fast moving field).
This set of courses will establish biological physics as a core
discipline in the UIUC physics department, which is commensurate to the other main areas in
the department, such as astrophysics, condensed matter physics, elementary particle physics,
and nuclear physics. These proposed courses will also address
the needs of these latter fields, as well as those of other departments.
This is especially apparent for the planned spectroscopy and
non-equilibrium statistical mechanics courses. The courses promise
to be very valuable to all physics graduate students, irrespective of their chosen fields,
familiarizing them with concepts and methods of the life science industries that
may serve them well in future employment situations.
The entire biological physics faculty at UIUC has contributed to the outline of the new curriculum.
The suggestions are based on deliberations that included other
members of the department as well as numerous faculty from related fields such as chemistry and
the life sciences. A curriculum emerged from these discussions
that promises to strengthen our department. In addition,
it complements teaching in other campus units and thereby strengthens UIUC as a whole.
The consultation with faculty from other units revealed that
the physics department must play the leading role in establishing the physical life
sciences on our campus, both because of the centrality of the physics discipline and because of
the coherence and size of its participating faculty. The rapid
evolution of modern life sciences brought about many new methodologies, new imaging technologies,
as well as new types of spectroscopy, and biological computing, for which an urgent need for a
curriculum has emerged. It is clear that these are best taught
in physics, especially at this early stage of methodologies. The
hiring of new faculty in biological physics has placed the physics department ahead of other
units in terms of size and strength, in particular since the department has also key members
from other departments that are affiliated with physics, such as chemistry (Gruebele and Makri).
Our faculty members collaborate and communicate closely with these
and other chemistry faculty (Luthey-Schulten, Leckband, Martinez), and we also have well-established
affiliations with the life science departments and collaborations with their faculty,
for example with Crofts, Jakobsson, Wraight, and Whitmarsh.
The six planned biological courses actually emerged from deliberations that closely followed the
mold of existing physics courses, in particular in the condensed matter field and in the
undergraduate service courses curriculum. Below we provide brief
explanations for the biological physics courses that draw parallels to existing physics courses.
The explanations are followed by a summary of the entire curriculum
and by comments regarding the feasibility of realizing the necessary faculty resources.
The suggested curriculum addresses both the needs of undergraduate
as well as graduate level instruction, and includes general introductory courses focusing
on the broad concepts of the field as well as core courses that prepare students for research and
development work in biological physics. The courses in spectroscopy
and non-equilibrium statistical mechanics would satisfy the strongly voiced needs of other
fields, e.g., condensed matter physics or chemistry. These courses
could be shared with those fields and faculty, broadening the faculty participation and very
likely providing better courses than each field could individually achieve.
(Course
numbers provided are provisional; each course is to be taught once per academic
year; detailed descriptions of the courses are provided at the end of this
document) Physics 350: Introduction to Biological Physics. This course is the biological physics
equivalent of Physics 389, Introduction to Solid-State Physics. [to be
taught by all biological physics faculty] Physics 351: Spectroscopic Methods. This course resurrects a popular course on the subject "Optical Methods
for the Investigation of Biological Materials" that was taught in the life sciences and ceased
to exist after the retirement of Gregorio Weber, whose research area is now continued in physics.
A demand for this course has been voiced strongly by a broad group of faculty far beyond biological
physics. The course should contain a laboratory section. [to be taught by all faculty in
experimental biological physics as well as by some faculty in experimental condensed matter
physics] Physics 352: Computational Biophysics. This course is the biological physics equivalent to Physics 398
"Atomic-Scale Simulation Methods" that has been taught regularly and with great success during
the past years. There is only minor overlap between the new course and Physics 398;
computational methods included in the new course are more central to biological physics than to
condensed matter. Many campus units have expressed a strong demand for this course since computing
is expected to become a core methodology in the life sciences and biotechnology, i.e., the new
course is likely to become a popular service course. The course should be taught jointly with the
Chemical Biology program of the UIUC chemistry department, the UIUC Center for Biophysics and
Computational Biology of the UIUC school of Cell and Molecular Biology. The course will contain a
laboratory section. Three related computational biology courses will be taught on the UIUC campus
with different emphasis, e.g., regarding physical modeling and bioinformatics, but in close
collaboration and with exchange of faculty. [to be taught in physics by faculty in theoretical
biological physics with participation from Computational Chemical Biology and Molecular and Cell
Biology] Physics 450: Biomolecular Physics. This is an existing "cafeteria" course, i.e., one of
five courses from which physics graduate students have to select one. It remains
relevant but will be revised; this is the biological physics equivalent to Physics
489 (Introduction to Solid State Physics). [to be taught by all biological
physics faculty] Physics 451: Biosystems Physics. This course is the biological physics equivalent of Physics 490
(Advanced Solid State Physics), except that the latter builds on Physics 489, whereas Physics
451 does not build on Physics 450. Since the course can be taken independently from Physics
450 it should provide to physics graduate students an alternative "cafeteria'' course choice.
This course is taught in Spring 2002 as Physics 498TBP. [to be taught by all biological physics
faculty]
Physics 463: Non-Equilibrium Statistical Mechanics. This course is the biological physics equivalent to Physics 483.
This course prepares graduate students for research in theoretical biophysics, covering
stochastic classical and quantum mechanics as well as non-equilibrium statistical mechanics
in a biophysics context as well as using examples from other fields. Detailed lecture notes
are available on Schulten's web site; he is presently completing a textbook on the subject
to be published by Cambridge U. Press.
Physics 498: Advanced Spectroscopy with Biophysical Applications. This course will be initially taught as a special topics course;
we expect demand sufficient to warrant a regular course later on. It would be
taught jointly with faculty in condensed matter physics and chemistry.
Faculty that can teach one or more of the suggested Physics 350, 352, 450, 451 courses are Clegg,
Dahmen, Gratton, Ha, Robinson, Schulten, Selvin, as well as potential new faculty to be hired in
theoretical biophysics. Physics 351 (spectroscopy) and Physics
463 (non-equilibrium stat.mech.) can be taught by various other members of the physics department.
Physics 352 can be taught jointly with chemistry faculty.
This co-teaching has the advantage that it will bring in students
from other departments and break down departmental walls, a concept which is encouraged on our campus.
The suggested curriculum will be attractive to new generations
of undergraduate and graduate students, who are very likely to seek a biological physics
specialization and expect systematic instruction, lest they choose other schools.
The close integration of biological physics with research and teaching
in other campus units will likely attract many students from outside the department to the
suggested courses. The new curriculum strengthens the department in
the general area of molecular physics, a discipline that promises to rise to the same prominent
level as solid-state physics has done in shaping the electronics industry.
The new curriculum places significant demands on the department,
in particular during the initial stage when five new courses (Physics 350, 351, 352, 451, 452) need
to be developed along with a special topics course in advanced spectroscopy.
In the long run, 2.5 regular biological physics courses will be
taught every fall and 3.0 courses every spring; this implies that, in the worst case,
three biological physics faculty will not be available for the teaching of other physics
courses, in the best case (other faculty teaching Physics 351, 452) 1.5 in the fall and 2.0 in
the spring will not be available.
While the suggested curriculum places a significant burden on the department, it has to be realized
that an intellectually complete program in biological physics requires a minimum number of courses.
Hence, if the number of faculty in biological physics is relatively
small, it requires a higher percentage of faculty devoted to the field, compared to a larger field
such as condensed matter physics. The physics department has
already committed to strengthening its faculty engaged in biological physics research and in
doing so has proven worthy of its leadership role in US physics; many other US universities try
to follow the same course today. The department will now take the
second bold and farsighted step and build a strong curriculum in biological physics that
matches the high quality of its other physics teaching..
New Undergraduate
Courses Physics 350, 351:
As outlined above, the new biological physics curriculum introduces Physics 350 and Physics 351
as new courses that are summarized here.
Physics 350 (Prepared by Paul
Selvin) Title: Introduction to Biological
Physics
Physics 351 (Prepared by
Enrico Gratton) Title: Spectroscopic Methods
Teaching Computational
Biophysics (Physics 352) jointly with other UIUC departments:
The third undergraduate course in biological physics will be taught in the physics department
in close cooperation with the Chemical Biology program in our chemistry department and
the Center for Biophysics and Computational Biology in our School of Cell and Molecular Biology.
The three mentioned units will each teach a separate course,
but faculty from the different units will contribute to all courses.
Through joint affiliations, e.g., Klaus Schulten is affiliated
with all three units, such course sharing is already practiced today.
Physics 352 (Prepared by
Klaus Schulten) Title: Computational Biophysics
Chemistry 391
(prepared by Zaida Luthey-Schulten)
Title: Computational
Chemical Biology
Molecular and Cell Biology 350
(prepared by Eric Jakobsson)
Title: Biomolecular Modeling and
Simulation
Molecular and Cell
Biology 351 (prepared by Eric Jakobsson)
Title: Bioinformatics
Outreach:
Much of the envisioned course material will be supplied to students through the web.
Schulten's Theoretical Biophysics Group, funded by NIH as a National Research Resource,
has developed the software BioCoRE that permits faculty members to set up web portals for
the courses with numerous services for communication with students and for students to form
project groups. The revolutionary software, described on Schulten's
web site, has already been employed successfully for teaching classes and workshops.
It provides access to all course material and most software
through standard web browsers. BioCoRE will permit students
to share lecture material, homework sets, tests, graphics sessions, modeling tasks,
sequence analysis, and discussions from off-campus locations.
Through BioCoRE, courses can be offered readily at any US or foreign university.
Schulten has demonstrated this through a course in molecular
modeling at EMBL in Heidelberg, Germany, as well as at Carnegie Mellon U. and U. of Pittsburgh.
Almost all courses will rely heavily on molecular graphics and sequence analysis.
Schulten's VMD software (over 16,000 registered users, described on
the Schulten web site) will furnish the necessary tools. VMD runs
on PCs, Macs (OS X), Linux and most Unix workstations. VMD supports
lecturers in scripting graphics sessions through a web browser, permitting push-button operation
during a lecture. Lecturers can also readily produce graphics
and movies for Power Point presentations. The ongoing development of
VMD will soon permit running VMD sessions within Power Point windows.
The material can be shared with students through BioCoRE, allowing students in depth
viewing of the lecture material and automated downloading of related protein structures
through the web.
Most courses will also invoke molecular modeling. For this purpose BioCoRE will be employed
to simplify greatly through web forms the submission and analysis of molecular modeling
runs based on the Schulten group NAMD program. NAMD is a widely
used (most recent version downloaded by over a thousand users) modeling package that excels
in large-scale simulations, e.g., of integral membrane channels in the native environment.
NAMD is currently being enhanced to simplify its use by
novices, e.g., permitting automated generation of simulation runs for chemically modified
as well as solvated proteins and DNA. The Schulten group has
developed and tested the training and use of NAMD by students.
Workshop for electronic
media and molecular modeling:
The development of the undergraduate curricula in biological
physics and computational biology
require great investments of personal effort in the development of course material in four
particular respects: (i) the complexity of biomolecular systems benefits greatly from
representations using advanced electronic media such as molecular graphics images and movies;
(ii) developing student exercises in molecular modeling requires robust
software and excellent user interfaces, lest the students get involved more in
technology than science; (iii) the material should be provided preferably in electronic
form on web sites and as electronic text books both for the convenience of the students
and to reap the benefit of reaching a much wider audience; (iv) it is desirable to develop the
courses quickly, i.e., within the next few years.
All four aspects imply a strenuous demand on lecturers that cannot be met with ordinary resources.
However, it is entirely feasible to hire personnel for support,
which makes the stated goals feasible.
We suggest in this respect to proceed in a manner that has been well tested on a smaller scale
by the Schulten group and by the department of chemistry at UIUC.
The core position to be filled would be a software consultant with a Ph. D.
degree such as has been employed by the chemistry department, the employees been recruited
from the Schulten group. In addition three teaching assistants
would be recruited from graduate students in computational biology for typically one year time
periods. Lastly, an artist would be hired on demand to provide
drawings that have been proven to be often better means of presentations than overly
detailed computer drawings. The personnel would remain located
together in order to share expertise, workloads, and equipment.
During the past Schulten as well as faculty in chemistry has benefited much from the
described personnel in the development of computational laboratories, e.g., for chemical biology,
and for course development. However, personnel were available only sporadically.
We expect that a workshop for electronic media and molecular
modeling would permit faculty in biological physics, chemical biology, and the school of molecular
and cell biology to enhance the quality of their courses, speed up development,
and provide great student training sessions and tutorials, as well as integrate web
sites and electronic textbooks into their teaching. The workshop
will benefit from the services of the NIH Resource directed by Schulten that has highly
trained professionals on its staff and can assist the teaching personnel.
Summary: This course is an introduction to biological physics
covering many scales: from the microscopic behavior of individual biomolecules, to cellular responses,
to systems (e.g. vision) to whole populations (e.g. food webs).
It is primarily a survey course although a few topics (such as the role of diffusion) will be
covered in more detail so students can get a sense of both the breadth and possible depth of field.
Prerequisites: This course is intended for undergraduate students who have completed the
111-114 series and have a familiarity with differential equations.
A biology course is not a prerequisite but is desirable.
Role of course in physics curriculum: This course will be part of a new biological physics
emphasis for physics majors. It is anticipated that the emphasis will include the standard physics
core requirements (including statistical mechanics, Physics 361), a year of introductory chemistry
(plus organic chemistry, recommended, but not required), an introductory biology and also
biochemistry course, Physics 350, plus one other, more advanced biophysics course such as
Physics 351, Physics 450, Biophysics 301 or Biophysics 320
Outline: A. Experimental techniques with applications include an introduction to
interaction of electromagnetic waves with biological matter and applications in spectroscopy
(absorption, fluorescence, Raman, NMR, EPR) and medical imaging (CAT, PET, MRI).
Also included are modern molecular techniques such as AFM (atomic force microscopy)
and optical traps, each with a particular biological application. B.
Structure and dynamics of biomolecules, including equilibrium, kinetics and fluctuations
(including diffusion). Basics of equilibrium configurations and fluctuations from equilibrium.
Diffusion and Brownian motion, with applications including
synaptic transmission in nerves. Some molecular dynamics simulations and computer models
will be used to aide in understanding and to introduce the idea of modeling.
C. Molecular Biophysics, including ion transport and ion channels,
molecular motors (RNA polymerase, F1-Fo ATPase, Kinesin and myosin) and photosynthesis.
This section will end by examining whole systems such as
vision beginning with the first elementary steps of photon absorption, to cellular changes,
to brain recognition. Photosynthesis and chemotaxis can also
be similarly analyzed. Computer simulations will also be used here. D.
Theoretical Modeling of systems: including food webs, population dynamics.
Summary: This course introduces the basic spectroscopic methods for the study of
optical properties of biological materials and for imaging of biological samples.
Emphasis is on modern techniques and instrumentation.
Prerequisite: The course is intended for advanced undergraduates and beginning graduates
students in physics, chemistry, engineering, and life sciences. Basic knowledge of experimental
physics, optics and mathematics is required.
Role of course in physics curriculum: The course will provide students with a working knowledge of
modern optical instrumentation. The course should be taken by all physics students (both undergraduate
and graduate) who intend to specialize in experimental Biological Physics.
The course is likely to draw students from life science and bioengineering.
Outline: Introduction to optical properties of biological materials; Absorption (UV/VIS)
Theory; Absorption (UV/VIS) Instrumentation; Absorption (IR) Theory; Absorption (IR)
Instrumentation; Linear and circular dichroism; Dynamic light scattering;
Scattering in turbid media: Theory; Optical properties of tissues; Scattering in tissues:
Instrumentation; Synchrotron radiation, EXAFS; Synchrotron radiation:
Instrumentation; Fluorescence principles: Excitation-emission; Fluorescence steady-state:
Instrumentation; Fluorescence anisotropy; Fluorescence time-domain; Fluorescence frequency-domain; M
ultiphoton excitation; Pump-probe methods: Stimulated emission; Microscopy full-field: Theory;
Microscopy full-field: Instrumentation; Microscopy laser-scanning: Theory; Microscopy laser-scanning:
Instrumentation; Fluctuation spectroscopy: Theory; Fluorescence Correlation Spectroscopy (FCS):
diffusion and populations; FCS: chemical kinetics; FCS: Instrumentation; Single molecule spectroscopy;
Spatio-temporal correlations.Lab sessions: UV-VIS absorption;
Tissue spectroscopy; Steady-state fluorescence; Microscopy; Fluctuation spectroscopy.
Comments: The course is organized in 30 lectures (biweekly) and 5 laboratory sessions, each
one to be completed within three weeks. Material for this course has been prepared already by the
Experimental Biophysics Group, which has taught several lab sessions for courses in chemistry and
life sciences.
Summary: This course introduces concepts and applications of biomolecular modeling
methods and bioinformatics. Emphasis will be on visualization,
computer simulation, analysis of simulation results, quantum chemistry methods, protein sequences,
genomics linking an atomic perspective with function and genome.
The course will be based on case studies, integrating physical modeling,
sequence analysis, and genomics: Transport in aquaporins; Photosynthesis; ATPase;
Muscle elasticity; DNA mechanics; Vision.
Prerequisite: The course is intended for undergraduate and beginning graduate students
in the physical and chemical sciences interested in learning how to apply the concepts and methods of
their field of specialization in the biological sciences. The course
is also suitable for students from life sciences interested in extending and deepening their
knowledge in the mathematical and physical foundations of molecular modeling and bioinformatics.
Basic knowledge of molecular and cell biology, as well as of
mathematics, physics and chemistry is required.
Role of course in physics curriculum: The course will provide students with a working
knowledge of biomolecular modeling and bioinformatics. The course
should be taken by all physics students (both undergraduate and graduate) who intend to specialize
in Biological Physics. The course is likely to draw students
from life science and bioengineering. The course will be taught
jointly with the chemistry department.
Outline: Molecular Graphics; Protein data bases; Amino acid sequence analysis;
Empirical force fields of biopolymers; Molecular Dynamics; O(N) algorithms for long-range
interactions; Thermodynamic properties; NVT, NpT ensemble simulations; Correlation and response
functions; Gene banks and gene sequence analysis; Homology and comparative modeling; Evolutionary
and phylogenetic analysis; Monte Carlo simulations; Free energy calculations; Steered Molecular
Dynamics; Quantum chemical calculation of force fields; Ab-initio Molecular Dynamics
(Car-Parinello method);
Comments: The course will include regular lab sections; teaching in a lecture room will
alternate with teaching in a computer laboratory. Material for this course has been prepared by
the Theoretical Biophysics Group, which has taught several modeling courses,
and by the Chemical Biology program that has previously taught a related course w
ith emphasis on bioinformatics.
This course was first given in the Spring 2000 and will be given next in the Fall 2002
Syllabus: Introduction to building blocks of macromolecules and structure of the genome;
Energy landscape of proteins; Algorithms for molecular dynamics simulations; Lattice simulations
of protein folding; Conformational sampling and histogram techniques; Sequence alignment algorithms;
GCG workshop; Approaches to protein structure prediction; Bioinformatics; Structural genomics;
Properties and Simulations of DNA; Computational Projects in Chemical Biology.
Molecular modeling, computational quantum chemistry, electrostatics, molecular dynamics, stochastic
dynamics, and computational statistical mechanics of biomolecules.
Introduction to biological databases, dynamic programming, sequence search and analysis,
gene annotation, alignment, comparative structure analysis, structure prediction, phylogeny,
metabolic reconstruction.