Modeling the Chemical Reactions Involved in Biological

Digital Inverters

Rick Corley

Mentor: Geo Homsy

• High level goal: Program biological cells

• Implement digital gates using gene/protein interactions in cells

• Potential applications:

– “smart” drugs/medicine– agriculture– embedded systems

Cellular Computing

Contributions

• Described a detailed model of a biological inverter– the most basic logic circuit

• Simulated and analyzed the model

• Result:– evidence that system may work in Biology

An Inverter

• A Logic Gate

• Takes one input, true or false

• Outputs the opposite

True False False True

A Biological Inverter

• Proteins are the inputs and outputs– a high concentration represents true– a low concentration represents false

• The input represses the creation of the output

Biological Inversion

Promoter Operator

DNA

RNA Polymerase

RepressorProtein

Promoter Operator

DNA

RNA Polymerase

False -> True True -> False

The Simulation Model

• Select chemical reactions for circuit

• Model reactions with differential equations

• Use real-life kinetic constants (-phage virus)

XY

YXk

k

2

1

])[(])[(][

])[(])[(][

21

12

YkXkdt

Yd

XkYkdt

Xd

input

output

The Transfer Curve

• Describes “steady-state” behavior

• Gives the output for a certain input

• Has a point where the output equals the input

Our Transfer Curve

• Upper bound = 4258• Flip Point =24.6

Dynamic Behavior

• Simulation shows:– lack of input protein X results in high concentrations of output protein Y– X suppresses the creation of Y– The recovery time is very long

Y

X2

X

time

Conclusion

• design and analysis of a more detailed model• better understanding of the characteristics of a

realistic biological inverter• actual system may be realized in biological cells