DSP with Protein Molecules and DNA Strands · 2018-04-03 · Digital Signal Processing with Protein...
Transcript of DSP with Protein Molecules and DNA Strands · 2018-04-03 · Digital Signal Processing with Protein...
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