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Modeling and Computational Tools for Contemporary Biology

Modeling and Computational Tools for Contemporary Biology. By Jeff Krause, Ph.D. Shodor 2010 NCSI/ iPlant CBBE Workshop. What is Computational Biology?. The scientific method enhanced: Observe -> Explain -> Predict -> Test But, with the explanation in the form of a computational model

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Modeling and Computational Tools for Contemporary Biology

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  1. Modeling and Computational Tools for Contemporary Biology By Jeff Krause, Ph.D. Shodor 2010 NCSI/iPlant CBBE Workshop

  2. What is Computational Biology? • The scientific method enhanced: • Observe -> Explain -> Predict -> Test • But, with the explanation in the form of a computational model • Using computers to find meaning in data • Performing calculations • Filtering out less interesting cases • Presenting data in ways that are easy to interpret

  3. People are Really Smart … Computers are Really Dumb … • They can solve hard problems • But they often get distracted and make mistakes • But they do what they’re told, • They do it quickly • They don’t get distracted • And they don’t make many mistakes

  4. Why do we needcomputational modeling in the classroom? Dynamic models are used to represent and understand how change happens based on cause and effect In teaching: • Models can be used to help students go from a list of facts to a functional understanding In science: • Models can be used to evaluate whether our understanding of a natural phenomenon is sufficient to account for it’s behavior

  5. Computational Science Pedagogy • Seeing a dynamic simulation - help students to form a functional representation • Adjust a simulation – learn about the system by studing it with virtual experiments • Modify a model – practice abstracting to an algortihmic explanation (mechanistic explanation) • Create a model – put the pieces together

  6. Things move, interact and transform in living (and non-living) systems “Things” tend to redistribute themselves to fill a space. When two “things” come together, one, or both, of them is changed. Each moment, some of the “things” will become something else.

  7. Biological macromolecules are the building blocks of life • Lipids, DNA and protein don’t occur naturally in high abundance. • Cell’s expend energy to produce them in a regulated way in order to maintain their compartmental order, and control over the chemical and physical processes of life. • DNA - information storage • Lipids - membrane structure • Proteins - molecular workhorses

  8. Some ground rules for chemical kinetics Consider each basic step individually – most can be reduced to a first, or second-order process • First order • Rate depends on the amount of a single species • Example - some of the enzyme-substrate complex will form product and release enzyme • Simple exponential kinetics for irreversible reaction

  9. More ground rules for chemical kinetics Steps that involve more than two species should be treated as multiple steps involving two species, where one of the species is a complex of multiple species • Second order • Rate depends on the amount of two species • Example - substrate and enzyme combine to form a complex (or, a second substrate combines with the complex to form a two-substrate complex) • Kinetics

  10. The NCSI Library Will Go Here

  11. Exponential Growth Integrated rate equation Pt=P0e-kt allows us to calculate Pt exactly* at any time (t) *were still likely to use a calculator or computer, so some estimation will be involved

  12. Sometimes there is no integrated rate equation What can we do if we don’t have an integrated rate equation to calculate our population exactly? • Numerical integration

  13. Numerical IntegrationEuler Method: first-step 1 Calculate the slope at the initial time

  14. Euler Method: first-step 2 Use the slope at the initial time to estimate the value of the function after a time-step

  15. Euler Method: first-step This estimated value will serve as the initial time for the next interval

  16. Euler Method: second-step 1 Calculate the slope at the estimated value

  17. Euler Method: second-step 2 Use the slope at the initial time to estimate the value of the function after the next time-step

  18. Euler Method: second-step Can Euler do better than this?

  19. Euler Method at Higher Resolution: first-step A smaller time-step results in an estimated value with less error than after a larger time-step

  20. Euler Method at Higher Resolution: second-step And we are able to adjust the slope closer to that of the actual function

  21. Euler Method at Higher Resolution: comparison Taking more time-steps results in a better estimate of the functions value at a particular time

  22. Euler Method at Higher Resolution: third-step

  23. Euler Method at Higher Resolution: fourth-step

  24. Euler Method at Higher Resolution: comparison

  25. Higher-Order Numerical Methods:Runge-Kutta 2 Start by finding simple Euler estimate for population at current time

  26. Higher-Order Numerical Methods:Runge-Kutta 2 Estimate the slope after the time-step based on the simple Euler estimate

  27. Higher-Order Numerical Methods:Runge-Kutta 2 Average the slopes at either end of the interval and use the average slope to estimate the population after the time-step

  28. Higher-Order Numerical Methods:Runge-Kutta 2 Repeat the steps: Estimate the initial slope, estimate the final slope, average the slopes to estimate the population

  29. Higher-Order Numerical Methods:Runge-Kutta 2

  30. Comparison of Simple Euler and Runge-Kutta 2

  31. Higher resolution improves Runge-Kutta 2 estimates

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