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Mathematics in Biology??!!

Mathematics in Biology??!!. Mark Pernarowski Montana State University, Bozeman. What Kind of Biology?. Population of organisms - i.e., animals Spread of Disease - i.e., Flu, vaccines, How muscles work - even the heart Diabetes - insulin and glucose

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Mathematics in Biology??!!

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  1. Mathematics in Biology??!! Mark Pernarowski Montana State University, Bozeman

  2. What Kind of Biology? • Population of organisms - i.e., animals • Spread of Disease - i.e., Flu, vaccines, • How muscles work - even the heart • Diabetes - insulin and glucose • Patterns in natures - zebra stripes, leopard spots • Brain electrical behavior - sight, sound • Organism growth - embryos • Genetics …..and much more

  3. Population Problems • Predator-Prey • X=hare population • Y=lynx population

  4. Spread of Disease • Hong Kong Flu (1968-69 NYC). • Pre-vacinne flu related pneumonia

  5. SIR Model • Susceptibles S • Infected I • Recovered R

  6. How do leeches swim? • Physics of Fluids • F(x,t)=leech force • u=fluid velocity • p=pressure

  7. Patterns in Nature • Chemicals that react and diffuse in animal coats make visible patterns • c(x,t) concentration at time t location x.

  8. Embryo Development -genes • Young embryos form a body axis early on • Why? How? Chemicals cause cells to move.

  9. Models Reproduce Experiments • n=cell density • u=chemical

  10. Some Biology is “Stimulus/Response” • A stimulus I causes an output u • Sometimes get an output even if there is no stimulus (I=0)(i.e., people who talk to you even when you don’t talk to them)

  11. Lot’s of different kinds of math models:

  12. Visual System • The electrical firing rate of your visual system neurons changes with stimulus angle!

  13. Each neuron can be modeled. • Ions move across membrane • Voltage V changes in time

  14. Models of Visual System Orientation Patterns • Activity a(r,t) at time t, position r in your brain.

  15. On - neurons fire immediately • Off- neurons fire after light turned off • Math models explain both and more.

  16. Diabetes • An increase in glucose (sugar) causes pancreas cells to make insulin. Calcium plays a key role.

  17. Bursting Electrical Activity • Calcium makes cells voltage “burst” • Same kind of math models as neurons.

  18. World’s smallest engine! • Molecules which make “ATP” (your energy)

  19. A simpler math model of animal populations • is population at year n=1,2,3,…. • Less animals next year if population is too high. Why?

  20. Maybe population levels out http://www.math.montana.edu/frankw/ccp/modeling/discrete/logistic/appwindow.htm

  21. Maybe population alternates (period 2)

  22. Maybe population alternates (period 4)

  23. Maybe population chaotic

  24. Conclusion • There will be more math in biology and medicine in your lifetime. • Unlike other science the math models are being discovered right now!

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