Modeling and Computational Tools for Contemporary Biology
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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 equationPt=P0e-kt allows us to calculate Pt exactly*at any time (t)
*were still likely to use a calculator orcomputer, so someestimation 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 IntegrationEuler Method: first-step 1
Calculate the slopeat 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 willserve as the initial time for the next interval
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Euler Method: second-step 1
Calculate the slope atthe 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 resultsin 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 ata 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 Eulerestimate for populationat 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 eitherend of the interval and usethe 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, averagethe slopes to estimatethe 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