Modeling and Computational Tools for Contemporary Biology

By Jeff Krause, Ph.D. Shodor

2010 NCSI/iPlant CBBE Workshop

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

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

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

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

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.

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

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

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

The NCSI Library Will Go Here

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

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

Numerical IntegrationEuler Method: first-step 1

Calculate the slopeat the initial time

Euler Method: first-step 2

Use the slope at the initial time to estimate the value of the function after a time-step

Euler Method: first-step

This estimated value willserve as the initial time for the next interval

Euler Method: second-step 1

Calculate the slope atthe estimated value

Euler Method: second-step 2

Use the slope at the initial time to estimate the value of the function after the next time-step

Euler Method: second-step

Can Euler do better than this?

Euler Method at Higher Resolution: first-step

A smaller time-step resultsin an estimated value with less error than after a larger time-step

And we are able to adjust the slope closer to that of the actual function

Euler Method at Higher Resolution: second-step

Taking more time-steps results in a better estimate of the functions value ata particular time

Euler Method at Higher Resolution: comparison

Euler Method at Higher Resolution: third-step

Euler Method at Higher Resolution: fourth-step

Euler Method at Higher Resolution: comparison

Higher-Order Numerical Methods:Runge-Kutta 2

Start by finding simple Eulerestimate for populationat current time

Higher-Order Numerical Methods:Runge-Kutta 2

Estimate the slope after the time-step based on the simple Euler estimate

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

Higher-Order Numerical Methods:Runge-Kutta 2

Repeat the steps: Estimate the initial slope, estimate the final slope, averagethe slopes to estimatethe population

Higher-Order Numerical Methods:Runge-Kutta 2

Comparison of Simple Euler and Runge-Kutta 2

Higher resolution improves Runge-Kutta 2 estimates