Digital Signal Processing

with Protein Molecules

and DNA Strands

Keshab K. Parhi

Electrical and Computer Engineering

University of Minnesota, Minneapolis

Nov. 10, 2010

Talk at EECS Dept., Berkeley

Sasha

Kharam

Acknowledgements

Hua Jiang Prof. Marc

Riedel

• Chemical Computations

• Chemical Signal Processing

• Biochemical/Biomolecular Signal Processing:

RGB Clock

• Biochemical/Biomolecular FIR Filter

• Biochemical/Biomolecular IIR Filter

• Biochemical/Biomolecular Counter

• Applications/Future Work

Outline

Signal processing everywhere

Applications of Signal Processing

• Echo cancellation

• Crosstalk cancellation

• Equalization

• Data transmission

• Audio/Video/Image processing

• Time-domain/Frequency-domain

processing

Applications of Signal Processing

Fast Fourier transform

Echo cancellation

• Finite Impulse Response (FIR) Filter

• Infinite Impulse Response (IIR) Filter

For n = 0 to ∞ {y(n) = 0.5x(n) + 0.5x(n-1)

}

For n = 0 to ∞{y(n) = u(n)/8 + u(n-1)/8 + u(n-2)/8

u(n) = x(n) + u(n-1)/8 + u(n-2)/8

}

Non-Terminating/DSP

Computations

Non-Terminating/DSP

Computations

Chemical Reactions

• Modeled by mass action kinetics

• Reaction speed determined by rate

constant and concentration of reactants

22 COOC k

]O][[C][CO]O[][C

222 k

dt

d

dt

d

dt

d

Chemical Reactions:

Assumptions

• Chemical A generated from a large and

replenishable source

• Chemical A transferred to some chemical

type no longer part of the system

A

A

Previous Works: Analog Multiplier

• An analog implementation of multiplier

(Hayat et al, HFSP Journal, Oct 08)

• Dependent on chemical equilibrium

• Reaction rates (k1, k2) affect precision

CBk

ABA 1

]][[][2

1 BAk

kC

2kC

0][]][[][C

21 CkBAkdt

d

Previous Works: Biochemical Signal

Processing“The band-pass behavior is of most interest to us because it is

this behavior that allows the usage of the same medium (e.g.

calcium) for selective signal transmission to different systems.

That is, if two pathways act as band-pass filters at different

frequencies with respect to the same signaling molecule, then

the molecule may be used to signal to each of the two

pathways at those respective frequencies, independently.”

“A class of bimolecular reaction mechanisms can behave as a

band-pass filter, but the behavior is very sensitive to the

kinetic parameters.”

(Samoilov, Arkin, Ross, J. Phys. Chem. A, Oct 02)

… …

DSP with Reactions

Reactions

Input molecular type Output molecular type

10, 2, 12, 8, 4, 8, 10, 2, … 5, 6, 7, 10, 6, 6, 9, 6, …

How do we find

such reactions?

Chemical

Reactions

time time

But how do we

implement DSP

functions with

reactions?

Moving Average Filter: Chemical

Constant Multiplier

Computational Modules

12 XX

][8

1][ XY

212 XX

YX 22

Constant Multiplier

Computational Modules

21

1

2

2

XX

XX

][2

][ Xn

Ym

m

n

2

nYX

XX

m

mm

1

12

2

2

Computational Modules

Adder

Fanout

Computational Modules

BAX

][][][ BAX

Delay Element

Molecular quantities are preserved over

“computational cycles”. Contents in different

delay elements are transferred synchronously.

RGB Scheme

We use a three compartment

configuration for delay elements:

we categorize the types into three

groups: red, green and blue.

Every delay element Di is

assigned Ri, Gi, and Bi

R

r

Absence Indicators

But how do we know that a

group of molecules is absent?

RGB Scheme

R, G, and B converge!

RGB Scheme

Oscillating!

Moving Average FilterSignal transfer

Computation

Absence indicator

Moving Average Filter

New cycle!

General DSP System

Biquad Filter

Biquad Filter Absence indicator

Signal transfer

Computation

• Output obtained by solving system kinetics equations

Simulation Results: Moving Average

Simulation Results: Moving Average

Simulation Results: Biquad Filter

• Output obtained by solving system kinetics equations

Simulation Results: Biquad Filter

Binary Counter

Z Y X

0 0 0

0 0 1

0 1 0

0 1 1

1 0 0

1 0 1

1 1 0

1 1 1

XXa injx

xinjy aYXXa

XXa injx

ZaaXYXa yxinjz

XXa injx

xinjy aYXXa

XXa injx

zyxinj aaaXZYX

:injX signal of incremental

:,, zyx aaa absence indicator

3-bit Counter

• Counts from 0 to 7, and then resets to 0

• Requires 4 reactions

• N-bit counter requires N+1 reactions

DNA Strand Displacement

X1 X2 X3+

D. Soloveichik et al: “DNA as a Universal Substrate for

Chemical Kinetics.” PNAS, Mar 2010

DNA Strand Displacement

X1 X3X2+

D. Soloveichik et al: “DNA as a Universal Substrate for

Chemical Kinetics.” PNAS, Mar 2010

Moving Average Filter: DNA

Level Reactions

Relationship to CMOS Digital Design

CMOS Chemical

Synchronization Clock RGB cycle

Redundant signal Dual rail Absence indicator

Fanout operation Free Not free

Addition Not free Free

Bottleneck Computations Molecule transfers

Fast operations Clock setup/hold/margin Computations

Impact of DSP Transformations

• Retiming (Reduce Number of Delay elements)

• Unfolding (Increase rate of computation)

• Folding (Protein folding, fewer proteins): Demonstrate

FFT Computation by chemical reactions, use counter for

control circuitrt

Limitations

• Not prototyped yet

• Concept not proven until prototyped!

• Precision of filters

• DNA strands too slow

Applications: Drug Delivery

• Decision can be used to deliver a drug or not or to trigger

other actions

Applications: Pathway Activation

• Different pathways are activated with signals of different

frequencies

Applications: Protein Cross-Talk

Equalization/Cancellation ?

PCS

PCS

R

R

R

R R

R

R

R

T

T

T

T

T

T

TH

yb

rid

Hyb

rid

Hyb

rid

Hyb

rid

Hyb

rid

Hyb

rid

Hyb

rid

Hyb

rid

Far EchoNear Echo

T

FEXT

NEXT

ANEXT & Others

Cable Attenuation and ISI

Intel® Xeon® Processor, 2010

1.9 billion transistors

3 GHz

Intel® 4004 Processor, 1971

2300 transistors

740 kHz

DSP with chemical reactions

???

• Key Contributions

• Implementation of a delay element in chemical

reactions

• RGB clock for biochemical systems

• Signal processing at biochemical and

biomolecular level

• Implement filters and transforms with

biochemical signal processing

• Applications in drug delivery, gene therapy, and

cancer treatment

Conclusions