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Course Name: Modeling in Biology Course
Author(s): Alex Mogilner and Satarupa Dey
Institutions University of California, Davis, CA
Keywords: ODE, Matlab, cells, predator-prey
UG Course Level: Beginner
Tool(s): Virtual Cell
Other tool(s): MATLAB
Module Created: 2008/9/22
Course Abstract These modules are class lectures and labs from a single semester course. Each lecture is followed by a lab in which students create models of biological topics discussed in lecture. The lectures often begin with a slide based on previous week's models. All course models are available in the public folders of Education in the VCell. To access a model from this course, launch VCELL (Release or Beta), click on File > Open > BioModel... or MathModel... > Education. Another way to access models is to right-click on the related VCML file and "Save Target As" somewhere on your computer as a ".vcml" file then "Open" or double-click on the file to open. The file should open in VCell if VCell software is installed. If problems occur, take a look at VirtualCellPage.
Contact email: mogilner@math.ucdavis.edu , satarupadey@yahoo.com

CategoryCourse -- RaquellHOlmes - 14 Apr 2009


Wordle: KN

Week 1

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Abstract This module is an Introduction to VCell. The Virtual cell (or VCell) is a software developed by NRCAM. This software platform has been designed to model cell biological processes. Examples of various biological phenomenas and corresponding mathematical models will be introduced. We will simulate models during lecture and do more exercises during lab.
Physiology MyLec1.pdf : The first class is an introduction to the course, where first-time VCell users get familiarized with the software and try to solve the reactor model.
Model description This lab illustrates the Reactor Model using VCell. User must have local client to run VCell application, in order to view this model. If model doesn't open, see the VirtualCellPage for more info.
Model files reactor.vcml: Reactor Model
Model exercises Lab1.ppt

Week 2

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Abstract Mass action is dependent on the amount of each reactant in a reaction mixture and temperature. The Michaelis-Menten BioModel describes the kinetics of the enzyme and substrate, through a mathematical equation, and visualization through a graph.
Physiology MyLec2.pdf
Model description This lab illustrates the Law of mass action and Michaelis-Menten. User must have local client to run VCell application, in order to view this model. If model doesn't open, see the VirtualCellPage for more info.
Model files massactive_new.vcml: Mass Active (bio model) Virtual Cell Client must be installed for files to open with click. Models are shared in Virtual Cell Public Folder Education.
  michaelismenten_new.vcml: Michaelis Menten (BioModel)
Model exercises Lab2.ppt

Week 3

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Abstract In this lecture, there are two topics: the Flagellar length control and the Lotka-Volterra Predator-Prey model. The lab models experiments of flagellar length control in which flagella is amputated. Rates of population growth in the Predator-Prey model of rabbit and sheep are illustrated in a BioModel.
Physiology MyLec3.pdf : Flagellar length control at the distal end is dynamic and undergoes continuous turnover even after the flagellum has fully formed. Intraflagellar transport is driven by molecular motors. The Predator-Prey model predicts populations of animals over time.
Model description This lab consists of exercises in flagella length control in Chlamydomonus, Lotka-Volterra, and Predator-Prey. User must have local client to run VCell application, in order to view this model. If model doesn't open, see the VirtualCellPage for more info.
Model files flagella.vcml: flagella length control
  _2flagella.vcml : 2flagella (math model)
  Lotka_Volterra_new.vcml : L-V (math)
  rabbit_sheep.vcml:: rabbit - sheep population exercise (math)
Model exercises Lab3.ppt

Week 4

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Abstract The lecture continues from previous lectures with slides on Flagella. Susceptible-Infect-Recovered (SIR) is a simple model of infection in populations. This model can be used to study rates of infection or death or influx of people on population. The lecture links the models to a few historical epidemics. Neuronal models are briefly introduced. The lab links VC models to lecture examples.
Physiology MyLec4.pdf : Exercises on creating BioModels for the SIR and neuronal models are introduced.
Model description This lab consist of the SIR model of flu epidemics and Fitzhugh-Nagumo math model. User must have local client to run VCell application, in order to view this model. If model doesn't open, see the VirtualCellPage for more info.
Model files SIR_NEW_MODEL.vcml: SIR (math model)
  FHN_model.vcml: Fitzhugh-Nagumo Model (math model)
  sir_exercise1.vcml: SIR 1 exercise (math)
  sir_exercise2.vcml: SIR 2 exercise (math)
Model exercises Lab4.ppt

Week 5

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Abstract The lecture details molecular movement in cell diffusion and active transport. Slides present the mathematical description of diffusion and the effect of boundary conditions. The lab use VCell to explain similar effects of BC on diffusion and concentration accross the cell over time.
Physiology MyLec5.pdf : Lecture begins with a description of lab models. There are two ways that the molecules move: through passive transport or active transport. The principle means of passive transport is diffusion. Random walks and diffusion are discussed.
Model description This lab explores the various diffusion problems and exercises. User must have local client to run VCell application, in order to view this model. If model doesn't open, see the VirtualCellPage for more info.
Model files simple_diffusion.vcml: simple diffusion (bio)
  diff_0value_BC.vcml: diffusion where boundary value is zero at all boundaries (bio)
  diff_box.vcml: diffusion -- this is for flux and value mixed boundary conditions (bio)
  diff_rentangle.vcml: diff rentangle (bio)
  diff_sq_rectangle.vcml: diff sq rectangle (bio)
Model exercises Lab5.ppt

Week 6

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Abstract Using chemical gradients can help the cell measure distance. One can study the bicoid protein in fruit fly and the simple exponential graph. In different organisms, eggs are of varying sizes, but each egg identifies the middle. Models of Lotka-Volterra, Turing Instability, Fitzhugh-Nagumo system of ion voltage spreading along the axon, and the electrical pulse are explored in this lecture and lab.
Physiology MyLec6.pdf This lecture starts with a slide on chemical gradients. The Lotka-Volterra and Predator-Prey are the same model from previous class, but now introduced with diffusion. There is an activator-substrate exercise, Fitzhugh-Nagumo exercise, Fisher equation, and epidemics with moving people exercises. Each model problems introduced during lecture are followed by an exercise.
Model description This lab includes the reaction-diffusion, Lotka-Volterra, and Fitzhugh-Nagumo exercises. User must have local client to run VCell application, in order to view this model. If model doesn't open, see the VirtualCellPage for more info.
Model files diff_ellipse.vcml: diffusion ellipse (bio)
  diff_dumble.vcml: diffusion of dumble (bio)
  diffusion_die.vcml: diffusion die (bio)
  ellipse_1source_diff_reaction.vcml: ellipse 1 source diff reaction (bio)
  ellipse_2source_Diff_reac.vcml: ellipse 2 source diff reaction (bio)
  DIFF_LOTKA_VOLTERRA_New.vcml: Diff L-V new (math)
  DIFF_LOTKA_VOLTERRA_newshape.vcml: Diff L-V new shape (math)
  DIFF_F_N_MODEL.vcml: Diff Fitzhugh-Nagumo model (math)
Model exercises Lab6.ppt

Week 7

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Abstract The lecture and lab introduces patterns, waves, in 2D space. The combination of reactions (activator and Inhibitors) distributed over space creates spatial temporial patterns. The reactions differ based on the type of model, eg. chemical patterns, population growths on disease spread. Turing's "The Chemical Basis of Morphogenesis" is a classic example of spatial modelling. The activator-substrate model. When activator spreads more slowly than the inhibitor, periodically spaced peaks of activator evolve (predict when stripes and spots would appear). Fitzhugh-Nagumo system with voltage (ions) spreading along the axon. Excitable system; refractory period. Traveling electrical pulse. Animals or bacteria grow until the local environment cannot handle the population and then spread by diffusion. The result is the invasion and colonization. Mathematically, you see the traveling wave. In Fisher's equation, P is the “frequency of the mutant gene” and m is “intensity of selection in favour of the mutant gene”. Black plague. Double source in E. Coli and B subtilis. Spruce Budworm outbreak.
Physiology MyLec7.pdf Can you increase the parameters and get periodic firing of a neuron? Learn how models look in 2D from different parameters through exercises.
Model description This lab is on the SIR, Fitzhugh-Nagumo, G-M, and Fisher math models. Keywords: Turing machine, algorithm, computer, Bletchley park, Enigma, AI - Turing test; RD eqs - morphogenesis. User must have local client to run VCell application, in order to view this model. If model doesn't open, see the VirtualCellPage for more info.
Model files diff_sir_in_box.vcml: diff SIR in box (math)
  Diff_SIR_2nests.vcml: diff SIR 2 nests (math)
  DIFF_F_N_MODEL.vcml: Diff F-N model (math)
  DIFF_G_M_Model.vcml: Diff G-M model (math)
  DIFF_Fisher_equation.vcml: Diff Fisher equation
Model exercises Lab7.ppt

Week 8

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Abstract Today a different software, called MATLAB, is introduced. Chaos occurs when the initial condition changes just a little; dynamics changes a lot and unpredictably. Bifurcation plot illustrates qualitative changes in a continuous system or discrete system. A different plot visualizes dynamics generated by the fish population model. First, there are no oscillations. Second, tiny increase in harvest drives fish to extinction. The Wenckebach phenomenon is a sequence of cardiac cycles in a heart beat model. The electric potential value determines whether the heart recovers or not. Try to simulate a heart beating.
Physiology MyLec8.pdf : Explore MATLAB software with short math exercises, such as what happens when growth parameter changes. A small change in parameters can cause qualitative change in behavior.
Model description To start Matlab, click Start > All programs > Class Software > MATLAB. The lab illustrates the logistic growth model, Ricker model of fish population, and the Wenckebach phenomenon of heart models.
Model files MATLAB
Model exercises Lab8.ppt

Week 9

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Abstract This lecture introduces lateral vision, vision, optical illusion and pattern detection problems. A timeline of great discoveries related with vision is given and exercises consist of mathematical solutions.
Physiology MyLec9.pdf : Several vision and illusion problems are explained.
Model description This lab consists of modeling vision: light sensitivity and pattern detection.
Model files MATLAB
Model exercises (lab9)

Week 10

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Abstract This lecture re-examines molecular movement as a stochastic process. Let us consider a one-dimentional random walk of N particles. There is equal probability for a particle to take a fixed step size to the left or right. Each particle spreads in both negative and positive direction. To quantify the spreading, we can randomly move thousands of particles, plot particle trajectories, and simulate diffusion using "randn" command. The stochastic model for a simple chemical reaction is studied with the Monte Carlo method.
Physiology MyLec10.pdf : The Monte Carlo method is often used for randomized systems such as fluid, or particles, and it is used to simulate physical and mathematical systems. Understanding stochastic systems is important in this lecture.
Model description This lab includes the Monte Carlo method and stochastic model.
Model files MATLAB
Model exercises (lab10)


--Main.KhanhNguyen - 29 Jun 2009

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Topic attachments
I Attachment Action Size Date Who Comment
elsevcml DIFF_F_N_MODEL.vcml manage 4.8 K 2009-05-28 - 06:44 KhanhNguyen Diff F-N model (math)
elsevcml DIFF_Fisher_equation.vcml manage 4.5 K 2009-05-28 - 06:46 KhanhNguyen Diff Fisher equation
elsevcml DIFF_G_M_Model.vcml manage 4.1 K 2009-05-28 - 06:45 KhanhNguyen Diff G-M model (math)
elsevcml DIFF_LOTKA_VOLTERRA_New.vcml manage 6.5 K 2009-05-28 - 06:19 KhanhNguyen Diff L-V new (math)
elsevcml DIFF_LOTKA_VOLTERRA_newshape.vcml manage 5.5 K 2009-05-28 - 06:20 KhanhNguyen Diff L-V new shape (math)
elsevcml Diff_SIR_2nests.vcml manage 5.3 K 2009-05-28 - 06:44 KhanhNguyen diff SIR 2 nests (math)
elsevcml FHN_model.vcml manage 6.8 K 2009-05-28 - 07:15 KhanhNguyen FHN model (math)
pptppt Lab1.ppt manage 3781.0 K 2009-04-28 - 16:39 RaquellHOlmes First lab for Modeling In Biology Course
pptppt Lab2.ppt manage 1204.5 K 2009-04-14 - 13:55 RaquellHOlmes Lab instructions for lab 2
pptppt Lab3.ppt manage 2056.0 K 2009-05-02 - 20:17 KhanhNguyen creating mathematical models for lecture 3
pptppt Lab4.ppt manage 1824.5 K 2009-05-02 - 20:22 KhanhNguyen creating mathematical models for lab 4
pptppt Lab5.ppt manage 3106.0 K 2009-05-02 - 20:30 KhanhNguyen simulation of diffusion
pptppt Lab6.ppt manage 6164.0 K 2009-05-02 - 20:59 KhanhNguyen Lotka-Voltera simulation
pptppt Lab7.ppt manage 5179.0 K 2009-05-02 - 21:21 KhanhNguyen SIR model simulation
pptppt Lab8.ppt manage 1568.0 K 2009-05-02 - 21:33 KhanhNguyen Matlab for lab 8
elsevcml Lotka_Volterra_new.vcml manage 8.5 K 2009-05-28 - 00:24 KhanhNguyen Lotka-Volterra model exercise
pdfpdf MyLec1.pdf manage 1835.7 K 2009-04-14 - 12:10 RaquellHOlmes First lecture introducing and reviewing math in biology
pdfpdf MyLec10.pdf manage 616.2 K 2009-05-02 - 19:59 KhanhNguyen Lec 10 - Random Numbers
pdfpdf MyLec2.pdf manage 574.8 K 2009-04-14 - 13:54 RaquellHOlmes Lecture 2 in Modeling in Biology Course
pdfpdf MyLec3.pdf manage 719.6 K 2009-05-02 - 18:02 KhanhNguyen Lecture 3 - Flagella and Animal Survival/Prey Equations
pdfpdf MyLec4.pdf manage 1254.2 K 2009-05-02 - 18:16 KhanhNguyen Lecture 4 - The SIR Epidemic and Fitzhugh-Nagumo models
pdfpdf MyLec5.pdf manage 425.8 K 2009-05-02 - 18:37 KhanhNguyen Lec 5 - Diffusion and Active Transport
pdfpdf MyLec6.pdf manage 1555.6 K 2009-05-02 - 19:25 KhanhNguyen Lec 6 - Chemical Gradients
pdfpdf MyLec7.pdf manage 1758.7 K 2009-05-02 - 19:37 KhanhNguyen Lec 7 - Model Exercises and Epidemic Outbreaks
pdfpdf MyLec8.pdf manage 207.2 K 2009-05-02 - 19:43 KhanhNguyen Lec 7 - Population Growth and Heart Beat exercise
pdfpdf MyLec9.pdf manage 793.6 K 2009-05-02 - 19:49 KhanhNguyen Lec 9 - Visual Perceptions
elsevcml SIR_NEW_MODEL.vcml manage 5.4 K 2009-05-28 - 05:50 KhanhNguyen SIR (math model)
elsevcml diff_0value_BC.vcml manage 6.4 K 2009-05-28 - 06:02 KhanhNguyen diffusion where boundary value is zero at all boundaries (bio model)
elsevcml diff_box.vcml manage 5.6 K 2009-05-28 - 06:04 KhanhNguyen diffusion -- this is for flux and value mixed boundary conditions (bio model)
elsevcml diff_dumble.vcml manage 10.2 K 2009-05-28 - 06:13 KhanhNguyen diffusion of dumble (bio)
elsevcml diff_ellipse.vcml manage 9.1 K 2009-05-28 - 06:12 KhanhNguyen diffusion ellipse (bio)
elsevcml diff_rentangle.vcml manage 7.5 K 2009-05-28 - 06:05 KhanhNguyen diff rentangle (bio model)
elsevcml diff_sir_in_box.vcml manage 5.1 K 2009-05-28 - 06:43 KhanhNguyen diff SIR in box (math model)
elsevcml diff_sq_rectangle.vcml manage 9.2 K 2009-05-28 - 06:06 KhanhNguyen diff sq rectangle (biomolde)
elsevcml diffusion_die.vcml manage 7.4 K 2009-05-28 - 06:14 KhanhNguyen diffusion die (bio)
elsevcml ellipse_1source_diff_reaction.vcml manage 10.2 K 2009-05-28 - 06:16 KhanhNguyen ellipse 1 source diff reaction (bio)
elsevcml ellipse_2source_Diff_reac.vcml manage 10.1 K 2009-05-28 - 06:17 KhanhNguyen ellipse 2 source diff reaction (bio)
elsevcml flagella.vcml manage 6.7 K 2009-06-10 - 21:50 KhanhNguyen flagella length control
elsevcml massactive_new.vcml manage 11.3 K 2009-05-18 - 00:39 KhanhNguyen Mass Active Model (new)
elsevcml michaelismenten_new.vcml manage 14.5 K 2009-05-18 - 00:37 KhanhNguyen Michaelis Menten model (new)
elsevcml rabbit_sheep.vcml manage 4.9 K 2009-05-28 - 00:25 KhanhNguyen rabbit and sheep population model exercise
elsevcml reactor.vcml manage 13.2 K 2009-05-18 - 00:42 KhanhNguyen Reactor Model
elsevcml simple_diffusion.vcml manage 5.6 K 2009-05-28 - 06:01 KhanhNguyen simple diffusion (bio model)
elsevcml sir_exercise1.vcml manage 5.7 K 2009-05-28 - 05:51 KhanhNguyen SIR 1 exercise
elsevcml sir_exercise2.vcml manage 4.1 K 2009-05-28 - 05:52 KhanhNguyen SIR 2 exercise
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Topic revision: r36 - 2009-11-21 - 18:33:21 - KhanhNguyen
 
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