BIS 132 – 4 units
Introduction to Dynamic Models in Modern Biology
Lecture: MWF 9:00-9:50, Bainer 1134
Laboratory: M 10:00-11:50, 2020 SLB
CRN: 45401
Fall 2007
Instructor: Dr. Carole L. Hom (“Carole”) clhom@ucdavis.edu
4314 Storer Hall, (530) 754-9733
Office hours:T 2:00-3:30;W 10:00-11:00; other times by appointment. I’m happy to arrange alternate times if these don’t work for you.
Course description. Dynamic modeling in the biological sciences, including matrix models, difference equations, differential equations, and complex dynamics. Examples include classic models in ecology, cell biology, physiology, and neuroscience. Emphasis on understanding models, their assumptions, and implications. Intended for students who seek to understand connections between quantitative tools and questions in modern biology.
Why take this course? Mathematics and scientific computation play an important role in virtually all areas of modern biology. When used in conjunction with laboratory and field work, these tools can provide insights into structure and function not easily attainable by empirical studies alone. Thus, students at all levels will need to be conversant with quantitative ideas and methods to understand a large corpus of state-of-the-art research in biology.
Prerequisites. One course in biology and a year of calculus.
Web site: at smartsite.ucdavis.edu
Text: Ellner and Guckenheimer, 2006, Dynamic Models in Biology, Princeton University Press.
Available in the bookstore for $45 and for a bit less from other vendors. It’s only a year old so used copies may be hard to come by. Other readings will be available on the course website.
Software: Mathcad 13.0, available to UC Davis students in the computer department of the UC
Davis Bookstore for less than $20.00. You need to go to the back of the computer section, flag someone down, and ask; they will get it from behind a locked chain link fence. The version on the shelf costs about ten times more. Note that the computer lab is equipped with Mathcad 14; the student version would have cost you $49 so we opted to stick with Mathcad 13.
Your lives will be happier if you download a patch to Mathcad (v. 13.1) from http://www.ptc.com/support/mathcad_downloads.htm
I also will try to put the patch on the course website. On the left sidebar, look under “resources” then in “mathcad info”. While there, download the .pdfs for future reference.
In addition, you need to update Windows (if you use “automatic updates”, you should be fine).
Mathcad only runs in Windows. If you are a Mac user who doesn’t use OS-X, you can use the campus computer labs to do homework.
Later in the quarter, we will download another (free!) program to analyze dynamical systems. Its preferred operating system is unix, but it runs on unix emulators (also free!).
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Lecture notes: I will prepare fill-in-the-blank lecture notes periodically and will warn you in advance, possibly in class and definitely via e-mail. It will be to your advantage to download these from the course website before class.
Final exam: Friday, December 14 at 10:30am-12:30pm.
Grading. Letter graded, based on weekly homework (35%), midterm exam (30%), and final paper (30%)/presentation during final exam slot (5%) OR final paper only (35%).
Midterm Exam. In class, closed book. The exam will test facility both in doing computations
(paper and pencil) and in interpreting modeling results.
Homework. Weekly homework will be assigned to give you practice in methods and to provide short-term feedback on understanding of central concepts. Homework will include paper-andpencil exercises assigned in class, computation assigned in the laboratory, and writing. It can be started in the lab session but also will require time outside formal class meetings. Homework will be due at the beginning of class on days indicated on the syllabus.
Some homework will be assigned as group problems. I am doing this for several reasons: (a) collaboration is an important skill and faculty should help you learn how to do it; (b) working in groups will help strengthen your knowledge; (c) for many problems, multiple heads are better than one. The group will turn in one paper, and everyone in the group will get the same grade. I expect that everyone in the group will participate and help the others to learn and understand
the material in the problem. I will assign groups and will shuffle them for each group assignment.
Lab. This course has a lab that meets M 10-11:50; we generally will work on computer exercises in the lab. If you have a class conflict, you can miss the lab but you will need to make it up on your own. I strongly recommend that you either bring a flash drive to class and save your work on the flash drive, or save it on smartsite.ucdavis.edu, or email it to yourself at the end of lab.
Term paper. A term paper of at least 7-8 pages in length is your chance to explore something involving math and biology that interests you.
what: You can work individually or as a group to:
(a) examine a (published) model that we didn’t cover in class, describe the biological setting and the model, and repeat and explain the analyses; or
(b) extend or modify a model to see what would happen if another biological feature were incorporated; or
(c) devise your own model.
In past years, (a) has tended to be MUCH harder than (b) or (c). Repeating an analysis often is more difficult than it sounds. I can help you keep (c) doable.
who: I expect you to write this up as a scientific paper in terms that one of your classmates could understand. If written as a collaborative project, then all collaborators should have input on all sections of the paper.
when: I will include comments on your work submitted at the interim deadlines. The more information you include, the more feedback you’ll get.
7 Nov: tentative paper topic (2pts)
16 Nov: annotated bibliography – this is a list of 5 sources for your paper, with a few sentences that describe each source (3pts)
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21 Nov: submit a 2-3 page literature review on your topic and describe what you plan to do in your model. This will become the basis for the introduction and model description in your final paper. Your literature review could be a discussion of the paper that contains the model that you intend to revise and description of the relevance of your work to biology. Eventually, you will need to incorporate additional information and
references into this review, but for now, three references will suffice, cited as described below. (5pts).
28 Nov: submit a progress report that contains at least a preliminary analysis of your model. If you run into difficulty, I need to know about it no later than this date. (5pts).
7 Dec: (optional) Hand in a final version of your paper. I will comment on it and indicate corrections. You may revise and resubmit at the final exam, or you may keep the grade earned on this paper. (85 pts)
13 Dec: final presentations (optional with advance notice) and written paper due. (85 pts)
how: The paper should be written in standard scientific format (abstract, introduction/literature review, model description, results/analysis, conclusions and discussion, acknowledgements, literature cited). Please type prose. You can handwrite equations neatly.
If you are apt to do a lot of this sort of stuff in the future, I encourage you to learn a typesetting program called LaTeX. Your handouts (other than this one) and text are prepared with this (www.miktex.org has a nice freeware version). It has a steep learning curve but is the standard for producing equations. Please, no cover page or report cover – just put the title of your paper, the course number, and your name at the top.
length: Your paper should be as long as it needs to be. Generally, students use 2-3 pages for the introduction, another 2 pages to describe the model (that includes defining variables, listing assumptions, explaining what the equations represent, and so on), a page to describe analytical methods, another 1-3 pages of results (graphs are good – but be sure to include a narrative interpretation), a page or two that puts the results into biological context, and references. That’s 7-8 pages at a minimum. If you find yourself using big fonts and margins to stretch your paper to this length, your introduction, analysis, and discussion may be fairly superficial and your grade will reflect it.
plagiarism and how to avoid it: please don’t plagiarize. On the simplest level, that means not purchasing a paper on the internet and claiming that you wrote it. More subtly, it means that anything in your paper must be (a) the product of your thoughts; (b) attributed to the person
(s) who wrote it; or (c) a fact so well known that it does not require attribution. Specifically,

 cite sources rephrase what your source wrote in your own words
 use quotation marks for text that you did not write.
Generally, scientific writing does not use direct quotes, thus everything should be rephrased.
The exception to this is a pithy (and generally well-known) statement that would lose meaning if rephrased.
Examples: Nowak et al., 1998, Integrative Biology 1:3-15, is an original sources:
Prion proteins have been linked to several rare and fatal brain diseases, including
Creutzfeldt-Jakob disease, kuru (specific reference cited here), scrapie (specific reference cited here), and bovine spongiform encephalopathy…Apparently, prion proteins, which are present in healthy brains, are somehow converted to a pathological configuration for each of the diseases listed above.
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plagiophrased: DO NOT do something like the following. It’s virtually identical to the above.
Prion proteins have been linked to several rare and fatal brain diseases, including kuru
(specific reference cited here), scrapie (specific reference cited here), Creutzfeldt-Jakob disease, and bovine spongiform encephalopathy. The prion proteins, which are present in healthy brains, are somehow converted to a pathological configuration for each of these diseases (Nowak et al. 1998).
rephrased version: if I were writing on prion proteins and disease and citing Nowak et al.
(1988), I would do something like the following.
A class of diseases that includes kuru, Creutzfeldt-Jakob disease, and ‘mad cow’ disease are thought to be caused by prions, which are self-reproducing protein structures. Prion proteins exist in a healthy state in all mammalian brains and transform via an unknown mechanism to become pathogenic prions (Nowak et al., 1998).
a quote: “To those who do now know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty of nature…If you want to learn nature, to appreciate nature, it is necessary to understand the language that she speaks in.” – Richard
Feynman, The Character of Physical Law
a well-known fact: the dominant eigenvalue of a population projection model gives the long-term rate of growth or decline of a population. (because this is general knowledge, no citation is needed)
Acceptable sources: I expect that most sources in your paper will be from the primary literature. You may cite at most one textbook and one source from the “grey literature”
(technical reports, web pages) in your paper. A published, peer reviewed paper that you got from an electronic journal on library.ucdavis.edu is a primary source; www.iknowitall.com is a web page. FYI, wikipedia is grey literature. I expect at least 6 sources.
Mechanics of citing sources: scientific writing generally uses one of two styles. Either all sources are numbered and cited by number when used in the text, or the source is referenced when cited using the last name of the first author and the publication year. Our text uses the second method, and I recommend it because it’s easier to use than the numerical method. In both cases, all references are listed at the end of the paper. See our text for examples of how to cite references.
final paper grading rubric: 4 points each for the following 5 components – introduction/literature review, model description, analysis/results, conclusions/discussion, grammar/clarity/writing mechanics (scaled to 85 points). I will pass out a detailed rubric later.
I expect you to schedule appointments with me if you get stuck. Do not wait until 13 December to do this. Remember, your paper should be written so that a classmate could understand it.
Even if you are writing an individual paper, it might be useful to team up with a classmate and read each other’s papers for clarity (be sure to thank them in the acknowledgements)
presentation: For the presentation, you can use Mathcad, Power Point, overheads, etc.
Other general grading info.
Scores for written work will be based on quality of exposition and demonstration of biological
insights gained from modeling, as well as on mathematics. Written exposition will be an integral part of every homework assignment; these should total 10-20 pages of expository English prose over the span of the quarter. Explaining mathematical models and how their results lend insight
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into biological situations will provide many opportunities for demonstrating organization, logical coherence, and technical aspects of writing. Every assignment will include two scores: one for mathematics and integration of biology, and one for writing. Students will receive comments on their work and will be expected to demonstrate improvement over the quarter.
Writing will be assigned a score of 1-4 as follows (adapted from the grading standards for the
GRE analytical writing exam):
4 work is thoughtful, clear, and well-written. Ideas are logically connected and wellorganized, documented appropriately, expressed precisely, and demonstrates facility with standard written English
3 work is competent but contains flaws in organization, clarity, documentation, or logic.
Work generally follows the norms for standard written English
2 work demonstrates some competence but also contains serious flaws with regard to clarity, focus, organization, language, sentence structure, or basics of English grammar
1 work demonstrates fundamental deficiencies in writing
0 no writing demonstrated
This course can be counted toward the writing experience component of the GE requirement.
Grading scale. Grades will be assigned based on your performance on homework and examinations. Cutoffs will be no higher than the following scale: A: over 89%; B: 78-88%; C:
60-77%, D: 50-60%, F less than 50% (that is, you might have an 88% average and get an ‘A’, but if you have an 89% you can be confident that you won’t get a ‘B’.)
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Tentative course outline. What follows is subject to change depending on needs of the class.
We will adjust the pacing, as necessary. So, if something seems too fast, or too slow, or just plain unclear, please let me know.
Monday Wednesday Friday
28 Sep Introduction
1 Oct Ch 1, bathtub models
3 Oct Ch 1, bathtub models 5 Oct Ch 2, introduction to matrices lab 1 Mathcad intro
8 Oct lab 2
15 Oct lab 3
Ch 2, matrix computations matrices
10 Oct Ch 2, more matrix computations
Ch 2, applications of matrix models
17 Oct Ch 3, applications of matrix models programming, matrices
Ch 3, Markov chains 24 Oct Ch 3, Markov chains
12 Oct Ch 2, eigenvalues etc.
19 Oct Ch 3, membrane channels
22 Oct lab 4
29 Oct lab 5
more programming
Ch 5 ODE overview
Ch 6 epidemiology
Markov chains
31 Oct
Nov
Ch 5, change of variables
26 Oct Ch 3, membrane channel models
2 Nov Ch 6, epidemiology
5 Nov lab 6
12 Nov
Exam, Ch 1-3
ODEs
Holiday
7 Nov Ch 5, numerical methods term paper topic due
14
Nov
9 Nov Ch 5, phase plane
Ch 5, more phase plane 16 Nov Ch 5, linearization annotated bib
due
21
Nov
Ch 6 models of epidemics
lit review due
23 Nov holiday 19 Nov Ch 5, linearization cont’d lab 7 stability
26 Nov lab
Ch 4, cellular-level phenomena time for projects
28
Nov
Ch 4, cellular-level phenomena: toggle progress report due
30 Nov
Dec
Ch 5, membrane potentials
3 Dec lab
Ch 5, bifurcations time for projects
5 Dec Ch 5 bifurcations
Final exam/project presentations: 14 December, 10:30am-noon
7 Dec Ch 9, building models early paper deadline
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