Reshma P. Shetty†‡ and Thomas F. Knight, Jr.‡
†Biological Engineering Division, ‡Computer Science and Artificial Intelligence Laboratory, MIT
Model formulation
α sensitivity analysis
i
8
K1=αi*100 and K2=αi/10000
7
Noise margin (%)
6
3
0
2
10
3
4
10
5
10
10
αi (proteins/cell)
K1 sensitivity analysis
K2 sensitivity analysis
8
8
α =49561 and K =α /10000
i
Figure 3: The swing, noise margin and trip point are
quantitative measures of the quality of the transfer
characteristic. Ideal devices maximize the noise margin
and have a trip point close to half the device swing.
Transfer curve of C0051, R0051 (λ)
Geometric mean fluorescence (AU)
Geometric mean fluorescence (AU)
20
15
10
5
0
0
10
1
2
10
10
3
10
250
200
150
100
50
0
0
10
1
[IPTG] uM
Geometric mean fluorescence (AU)
1400
1200
1000
800
600
400
200
1
3
10
2
10
i
7
6
6
5
4
3
4
3
2
1
1
1
2
10
3
10
4
5
10
K (proteins/cell)
10
6
10
0
0
10
7
10
1
10
1
K1K2
So =
K1K2 + [pi]2
Figure 6: Key parameters that affect device behavior are
the steady-state maximum protein level αi, promoter
copy number [do]T and dissociation constants K1 and
K2.
i
5
2
10
1
2
10
3
10
K (proteins/cell)
4
10
5
10
6
10
2
Figure 8: Noise margin as a function of parameter value
for αi, K1 and K2.
Device performance is sensitive to K1
and K2 but not αi.
Alternative design
Transfer curve of C0053, R0053 (P22)
1600
10
10
[IPTG] uM
Transfer curve of C0052, R0052 (434)
0
0
10
2
10
α =49561 and K =α *100
i
7
0
0
10
T
2
]
[p
]
2[d
o
i
T
−1
2
[pi] =Siαi = [pi] + 2K1 [pi] +
K1K2 + [pi]2
kspiksmi T
αi ≡
[di]
kdpikdmi
Existing devices fail
25
Model equations
2
Noise margin (%)
Figure 5: Model includes synthesis, degradation and
binding reactions.
3
10
150
Target parameter values
100
Inverter transfer curve
1
S vs S
50
o
i
S vs S
0.9
i
o
0.8
0
0
10
[IPTG] uM
Figure 1: An inverter is a simple digital logic device.
The work presented here focuses on characterizing and
modeling a transcriptional inverter.
4
1
Geometric mean fluorescence (AU)
Implement in vivo combinational digital logic using
transcription-based devices.
5
2
Transfer curve of C0050, R0050 (HK022)
Goal
Sensitivity analysis
Noise margin (%)
The goal of Synthetic Biology is to engineer systems from biological parts.
One class of systems are those whose
purpose is to process information. My
work seeks to build transcription-based
devices for use in combinational digital
logic. Preliminary characterization experiments show that existing devices
fall short of desired device behavior.
I propose to develop a novel implementation of transcription-based logic
by designing synthetic transcription
factors from well-characterized DNA
binding and dimerization domains. Initial modeling work serves to inform design of these devices.
Device performance
1
2
10
10
So (blue) or Si (green)
Abstract
3
10
[IPTG] uM
Figure 4: Experimentally-determined transfer characteristics for 4 transcriptional inverter prototypes.
0.7
N =0.05
0.6
SM =0.2
0.5
0.4
0.3
Figure 9: A possible alternate device design includes additional nonfunctional protein binding sites on the DNA.
0.2
0.1
0
0
0.2
0.4
0.6
Si (blue) or So (green)
0.8
1
Inverter transfer curve
So vs Si
Figure 7: These parameter values lead to acceptable
device behavior.
K1 ≈ αi ∗ 100 ≈ 10 mM (dimerization)
K2 ≈ αi/10000 ≈ 10 nM (DNA binding)
(assuming αi ≈ 50, 000 proteins/cell)
0.8
0.7
N =0.1
=0.05
0.6
S =0.4
=0.2
Modeling informs design of synthetic
transcription factors for digital logic.
Simplifying assumptions
Figure 2: A transfer characteristic is a plot of device
output as a function of device input. It describes static
device performance.
1. Use reaction rate equations
2. Neglect cell growth and DNA replication
3. Ignore details of synthesis and degradation reactions
4. All or none repression
5. Binding reactions at equilibrium
6. Steady-state
• Steady-state maximum input protein
concentration αi is the input protein
swing.
• Value of dissociation constants relative to αi determines noise margin.
• Inverter skew may be a problem.
References
[1] G. K. Ackers, A. D. Johnson, and M. A. Shea. Quantitative model for gene regulation by λ phage repressor.
Proc Natl Acad Sci USA, 79(4):1129–33, 1982.
[2] M. A. Gibson and E. Mjolsness. Computational Modeling of Genetic and Biochemical Networks, chapter 1,
pages 3–48. The MIT Press, Cambridge, Massachusetts, 2001.
[3] C. F. Hill. Noise margin and noise immunity in logic circuits. Microelectronics, 1:16–22, April 1968.
[4] R. Weiss, T. F. Knight Jr, and G. Sussman. Cellular Computing, chapter 4, pages 43–73. Series in Systems
Biology. Oxford University Press, 2004.
M
0.5
0.4
0.3
0.2
0.1
0
0
Device behavior
Si vs So
0.9
So (blue) or Si (green)
To engineer good devices, we need device performance metrics and measurement methods.
One inverter has good performance
characteristics; however, the other devices fail to function properly.
1
0.2
0.4
0.6
Si (blue) or So (green)
0.8
1
[da]T = 0.1αi and K6 = K2/10
Figure 10: This alternate design can lead to enhanced
device performance.
Alternate device designs may lead to
improved transfer characteristics.
Acknowledgements
I would like to thank Tom Knight, Drew Endy, Austin Che, Scot
Wolfe, Keith Joung, Bruce Tidor, Bob Sauer, Bambang Adiwijaya,
the Knight lab and the MIT Synthetic Biology Working Group for
valuable discussions and support.
Funding for this work has been generously provided by the NSF
Graduate Research Fellowship, the Whitaker Foundation Graduate
Research Fellowship and the Andy and Erna Viterbi Graduate Fellowship in Computational Biology.