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

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What is Computational Biology? 1.The scientific method enhanced: – Observe -> Explain -> Predict -> Test – But, with the explanation in the form of a computational model 2.Using computers to find meaning in data – Performing calculations – Filtering out less interesting cases – Presenting data in ways that are easy to interpret

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

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Why do we need computational 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

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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

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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.

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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

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Some ground rules for chemical kinetics 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 Consider each basic step individually – most can be reduced to a first, or second-order process

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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

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The NCSI Library Will Go Here

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Exponential Growth Integrated rate equation P t =P 0 e -kt allows us to calculate P t exactly* at any time (t) *were still likely to use a calculator or computer, so some estimation will be involved

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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

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Numerical Integration Euler Method: first-step 1 Calculate the slope at the initial time

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

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

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

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

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

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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

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

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

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Euler Method at Higher Resolution: third-step

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Euler Method at Higher Resolution: fourth-step

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Euler Method at Higher Resolution: comparison

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

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

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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

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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

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Higher-Order Numerical Methods: Runge-Kutta 2

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Comparison of Simple Euler and Runge-Kutta 2

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Higher resolution improves Runge-Kutta 2 estimates

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