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Exact One-Pass Synthesis of Digital Microfluidic Biochips
Oliver Keszocze1 Robert Wille1
Tsung-Yi Ho2 Rolf Drechsler1
Presented by Sharbatanu Chatterjee for CS300A1Institute of Computer Science, University of Bremen, Bremen, Germany
E-mail: {keszocze,rwille,drechsle}@informatik.uni-bremen.de
2Dept. of CSIE, National Cheng Kung University, Tainan, Taiwan
21 October, 2014
Introduction Synthesis of Digital Microfluidic Biochip Scope of the Article and Contributions Verification Flow - In a nutshell Formalism Conclusions
Contents
1 Introduction
2 Synthesis of Digital Microfluidic Biochip
3 Scope of the Article and Contributions
4 Verification Flow - In a nutshell
5 Formalism
6 Conclusions
Exact One-Pass Synthesis of Digital Microfluidic Biochips 0
Introduction Synthesis of Digital Microfluidic Biochip Scope of the Article and Contributions Verification Flow - In a nutshell Formalism Conclusions
Digital Microfluidic Lab-on-a-chip
Idea: A complete biology lab on a single chip
Dispensing
Transporting
Mixing and Splitting
Detection . . .Digital microfluidic cartridge(Simultaneously performing 4 assays)
Benifits
Low cost
Less reagent consumption
High accuracy and throughput
Minimal human intervention
Applications
Point of care diagnosis
Automated drug discovery
DNA analysis
Toxicity monitoring
Exact One-Pass Synthesis of Digital Microfluidic Biochips 1
Introduction Synthesis of Digital Microfluidic Biochip Scope of the Article and Contributions Verification Flow - In a nutshell Formalism Conclusions
Automated synthesis of Digital Microfluidic Biochip
Increasing complexities of bio-chemical protocols demandautomated synthesis tools
Resourcebinding Schedule placement
Module Dropletrouting
Output: Actuation sequenceR3
R2
R2
R1
wastereservior output
reserviorReagents
Intermediatedroplets
OutputInput: Sequencing graph
R1 R2 R3
Synthesis flow of DMF Biochip
How can we synthesize it, in one step?
Exact One-Pass Synthesis of Digital Microfluidic Biochips 2
Introduction Synthesis of Digital Microfluidic Biochip Scope of the Article and Contributions Verification Flow - In a nutshell Formalism Conclusions
Automated synthesis of Digital Microfluidic Biochip
Increasing complexities of bio-chemical protocols demandautomated synthesis tools
Resourcebinding Schedule placement
Module Dropletrouting
Output: Actuation sequenceR3
R2
R2
R1
wastereservior output
reserviorReagents
Intermediatedroplets
OutputInput: Sequencing graph
R1 R2 R3
Synthesis flow of DMF Biochip
How can we synthesize it, in one step?
Exact One-Pass Synthesis of Digital Microfluidic Biochips 2
Introduction Synthesis of Digital Microfluidic Biochip Scope of the Article and Contributions Verification Flow - In a nutshell Formalism Conclusions
A motivating example
R1 R2 R3
(1 : 0 : 0) (0 : 1 : 0) (0 : 0 : 1)
(1 : 1 : 0) (0 : 1 : 1)
(1 : 2 : 1)
Output
waste
12 12
6
tmix
Reagents
Mixing operation
Input sequencing graph
R1 R3 R2
(1 : 0 : 0) (0 : 0 : 1) (0 : 1 : 0)
(1 : 0 : 1) (0 : 1 : 1)
(1 : 1 : 2)
Output
ts = 5te = 17
ts = 10te = 16
ts = 16te = 22
Synthesized sequencing graph
Exact One-Pass Synthesis of Digital Microfluidic Biochips 3
Introduction Synthesis of Digital Microfluidic Biochip Scope of the Article and Contributions Verification Flow - In a nutshell Formalism Conclusions
A motivating example
R1 R2 R3
(1 : 0 : 0) (0 : 1 : 0) (0 : 0 : 1)
(1 : 1 : 0) (0 : 1 : 1)
(1 : 2 : 1)
Output
waste
12 12
6
tmix
Reagents
Mixing operation
Input sequencing graph
R1 R3 R2
(1 : 0 : 0) (0 : 0 : 1) (0 : 1 : 0)
(1 : 0 : 1) (0 : 1 : 1)
(1 : 1 : 2)
Output
ts = 5te = 17
ts = 10te = 16
ts = 16te = 22
Synthesized sequencing graph
Exact One-Pass Synthesis of Digital Microfluidic Biochips 3
Introduction Synthesis of Digital Microfluidic Biochip Scope of the Article and Contributions Verification Flow - In a nutshell Formalism Conclusions
A motivating example
R1 R2 R3
(1 : 0 : 0) (0 : 1 : 0) (0 : 0 : 1)
(1 : 1 : 0) (0 : 1 : 1)
(1 : 2 : 1)
Output
waste
12 12
6
tmix
Reagents
Mixing operation
Input sequencing graph
R1 R3 R2
(1 : 0 : 0) (0 : 0 : 1) (0 : 1 : 0)
(1 : 0 : 1) (0 : 1 : 1)
(1 : 1 : 2)
Output
ts = 5te = 17
ts = 10te = 16
ts = 16te = 22
tmix = 6
Synthesized sequencing graph
Exact One-Pass Synthesis of Digital Microfluidic Biochips 3
Introduction Synthesis of Digital Microfluidic Biochip Scope of the Article and Contributions Verification Flow - In a nutshell Formalism Conclusions
A motivating example
R1 R2 R3
(1 : 0 : 0) (0 : 1 : 0) (0 : 0 : 1)
(1 : 1 : 0) (0 : 1 : 1)
(1 : 2 : 1)
Output
waste
12 12
6
tmix
Reagents
Mixing operation
Input sequencing graph
R1 R3 R2
(1 : 0 : 0) (0 : 0 : 1) (0 : 1 : 0)
(1 : 0 : 1) (0 : 1 : 1)
(1 : 1 : 2)
Output
ts = 5te = 17
ts = 10te = 16
ts = 16te = 22
tmix = 6
?
Synthesized sequencing graph
Exact One-Pass Synthesis of Digital Microfluidic Biochips 3
Introduction Synthesis of Digital Microfluidic Biochip Scope of the Article and Contributions Verification Flow - In a nutshell Formalism Conclusions
Scope of the article
An exact one pass synthesis method for manufacturingbio-chemical protocol realizations on a target DMF architecture
Contributions
Performing a one-pass synthesis and, at the same time,guaranteeing minimality (a computationally hard problem)
Integrating several distributed approaches
A verification tool that implements the proposed verificationscheme (SimBioSys)
Exact One-Pass Synthesis of Digital Microfluidic Biochips 4
Introduction Synthesis of Digital Microfluidic Biochip Scope of the Article and Contributions Verification Flow - In a nutshell Formalism Conclusions
Verification Flow - In a nutshell
SynthesisActuationsequence
Input: Design constraints
3232
032
1632
832
Input sequencing graph
Sample
Buffer Waste
1 Input sequencing graph is transformed to actuation sequencesby synthesis tool
Exact One-Pass Synthesis of Digital Microfluidic Biochips 5
Introduction Synthesis of Digital Microfluidic Biochip Scope of the Article and Contributions Verification Flow - In a nutshell Formalism Conclusions
SynthesisActuationsequence
Input: Design constraints
3232
032
1632
832
Input sequencing graph
Sample
Buffer Waste
dim 5 4accuracy 5R(1, 1, S)R(1, 4, B)O(5, 1)W (5, 4)
1 d(1, 1)d(1, 4)2 m([1, 1] → [2, 1])m([1, 4] → [2, 4])3 m([2, 1] → [3, 1])m([2, 4] → [3, 4])4 mix([3,1]↔[3,4],12,14)d(1, 1)d(1, 4)17 m([3, 4] → [4, 4])18 m([4, 4] → [5, 4])m([1, 4] → [2, 4])19 m([2, 4] → [3, 4])waste(5, 4)20 mix([3, 1] ↔ [3, 4], 12, 14)33 m([3, 1] → [4, 1])m([3, 4] → [4, 4])34 m([4, 1] → [5, 1])m([4, 4] → [5, 4])35 output(5, 1)waste(5, 4)36 end
Symbolic representation ofsynthesized output
1 Input sequencing graph is transformed to actuation sequencesby synthesis tool
2 Actuation sequences are represented in symbolic form
Exact One-Pass Synthesis of Digital Microfluidic Biochips 5
Introduction Synthesis of Digital Microfluidic Biochip Scope of the Article and Contributions Verification Flow - In a nutshell Formalism Conclusions
Interpreting symbolic instructions
dim 5 4accuracy 5R(1, 1, S)R(1, 4, B)O(5, 1)W (5, 4)
1 d(1, 1)d(1, 4)2 m([1, 1] → [2, 1])m([1, 4] → [2, 4])3 m([2, 1] → [3, 1])m([2, 4] → [3, 4])4 mix([3,1]↔[3,4],12,14)d(1, 1)d(1, 4)17 m([3, 4] → [4, 4])18 m([4, 4] → [5, 4])m([1, 4] → [2, 4])19 m([2, 4] → [3, 4])waste(5, 4)20 mix([3, 1] ↔ [3, 4], 12, 14)33 m([3, 1] → [4, 1])m([3, 4] → [4, 4])34 m([4, 1] → [5, 1])m([4, 4] → [5, 4])35 output(5, 1)waste(5, 4)36 end
Symbolic representation ofsynthesized output
t = 1
O W
S B
1 d(1, 1)d(1, 4)
Exact One-Pass Synthesis of Digital Microfluidic Biochips 6
Introduction Synthesis of Digital Microfluidic Biochip Scope of the Article and Contributions Verification Flow - In a nutshell Formalism Conclusions
Interpreting symbolic instructions
dim 5 4accuracy 5R(1, 1, S)R(1, 4, B)O(5, 1)W (5, 4)
1 d(1, 1)d(1, 4)2 m([1, 1] → [2, 1])m([1, 4] → [2, 4])3 m([2, 1] → [3, 1])m([2, 4] → [3, 4])4 mix([3,1]↔[3,4],12,14)d(1, 1)d(1, 4)17 m([3, 4] → [4, 4])18 m([4, 4] → [5, 4])m([1, 4] → [2, 4])19 m([2, 4] → [3, 4])waste(5, 4)20 mix([3, 1] ↔ [3, 4], 12, 14)33 m([3, 1] → [4, 1])m([3, 4] → [4, 4])34 m([4, 1] → [5, 1])m([4, 4] → [5, 4])35 output(5, 1)waste(5, 4)36 end
Symbolic representation ofsynthesized output
t = 1
O W
S B
1 d(1, 1)d(1, 4)
t = [1, 3]
S B
O W
2 m([1, 1] → [2, 1])m([1, 4] → [2, 4])3 m([2, 1] → [3, 1])m([2, 4] → [3, 4])
Exact One-Pass Synthesis of Digital Microfluidic Biochips 6
Introduction Synthesis of Digital Microfluidic Biochip Scope of the Article and Contributions Verification Flow - In a nutshell Formalism Conclusions
Interpreting symbolic instructions
dim 5 4accuracy 5R(1, 1, S)R(1, 4, B)O(5, 1)W (5, 4)
1 d(1, 1)d(1, 4)2 m([1, 1] → [2, 1])m([1, 4] → [2, 4])3 m([2, 1] → [3, 1])m([2, 4] → [3, 4])4 mix([3,1]↔[3,4],12,14)d(1, 1)d(1, 4)17 m([3, 4] → [4, 4])18 m([4, 4] → [5, 4])m([1, 4] → [2, 4])19 m([2, 4] → [3, 4])waste(5, 4)20 mix([3, 1] ↔ [3, 4], 12, 14)33 m([3, 1] → [4, 1])m([3, 4] → [4, 4])34 m([4, 1] → [5, 1])m([4, 4] → [5, 4])35 output(5, 1)waste(5, 4)36 end
Symbolic representation ofsynthesized output
t = [1, 3]
S B
O W
2 m([1, 1] → [2, 1])m([1, 4] → [2, 4])3 m([2, 1] → [3, 1])m([2, 4] → [3, 4])
Mixer
t = [4, 16]
S B
O W
4 mix([3,1]↔[3,4],12,14)d(1, 1)d(1, 4)
Exact One-Pass Synthesis of Digital Microfluidic Biochips 6
Introduction Synthesis of Digital Microfluidic Biochip Scope of the Article and Contributions Verification Flow - In a nutshell Formalism Conclusions
Interpreting symbolic instructions
dim 5 4accuracy 5R(1, 1, S)R(1, 4, B)O(5, 1)W (5, 4)
1 d(1, 1)d(1, 4)2 m([1, 1] → [2, 1])m([1, 4] → [2, 4])3 m([2, 1] → [3, 1])m([2, 4] → [3, 4])4 mix([3,1]↔[3,4],12,14)d(1, 1)d(1, 4)17 m([3, 4] → [4, 4])18 m([4, 4] → [5, 4])m([1, 4] → [2, 4])19 m([2, 4] → [3, 4])waste(5, 4)20 mix([3, 1] ↔ [3, 4], 12, 14)33 m([3, 1] → [4, 1])m([3, 4] → [4, 4])34 m([4, 1] → [5, 1])m([4, 4] → [5, 4])35 output(5, 1)waste(5, 4)36 end
Symbolic representation ofsynthesized output
Mixer
t = [4, 16]
S B
O W
4 mix([3,1]↔[3,4],12,14)d(1, 1)d(1, 4)
t = [17, 18]
B
W
17 m([3, 4] → [4, 4])
S
O
18 m([4, 4] → [5, 4])m([1, 4] → [2, 4])
Exact One-Pass Synthesis of Digital Microfluidic Biochips 6
Introduction Synthesis of Digital Microfluidic Biochip Scope of the Article and Contributions Verification Flow - In a nutshell Formalism Conclusions
Interpreting symbolic instructions
dim 5 4accuracy 5R(1, 1, S)R(1, 4, B)O(5, 1)W (5, 4)
1 d(1, 1)d(1, 4)2 m([1, 1] → [2, 1])m([1, 4] → [2, 4])3 m([2, 1] → [3, 1])m([2, 4] → [3, 4])4 mix([3,1]↔[3,4],12,14)d(1, 1)d(1, 4)17 m([3, 4] → [4, 4])18 m([4, 4] → [5, 4])m([1, 4] → [2, 4])19 m([2, 4] → [3, 4])waste(5, 4)20 mix([3, 1] ↔ [3, 4], 12, 14)33 m([3, 1] → [4, 1])m([3, 4] → [4, 4])34 m([4, 1] → [5, 1])m([4, 4] → [5, 4])35 output(5, 1)waste(5, 4)36 end
Symbolic representation ofsynthesized output
t = [17, 18]
B
W
17 m([3, 4] → [4, 4])
S
O
18 m([4, 4] → [5, 4])m([1, 4] → [2, 4])
t = 19S B
O
19 m([2, 4] → [3, 4])waste(5, 4)
Exact One-Pass Synthesis of Digital Microfluidic Biochips 6
Introduction Synthesis of Digital Microfluidic Biochip Scope of the Article and Contributions Verification Flow - In a nutshell Formalism Conclusions
Notations
xt2,2 xt2,4
Wastereservoir
Outputreservoir
Reagentreservoir
D1 D2
1 2 3 4 5 6
5
6
4
3
2
1 Dt6×6(2, 6)
Reservoir
M t6×6([5, 2], [5, 5],m1×4)
St6×6(3, 3)
Boolean function Constraint
Btr×c Symbolic description of biochip of size r × c at time instant t.
Str×c (i, j) Defined on state variables at time t, that represents the static FC of a droplet
at (i, j) in a biochip of size r × c.
Dtr×c (i, j) Represents FCs that must be satisfied before dispensing droplet at (i, j).
Mtr×c ((r1, c1), (r2, c2), mtype) Represents static FC for an active mixer of type mtype at time t.
Table DescriptionTmixer Maintains active mixers. Each entry is in the form of
((r1, c1), (r2, c2), ts , te , mtype), where (r1, c1), (r2, c2) are the positionsof two droplets to be mixed with a mtype mixer and ts , te are start and endtimes of the mixing operation.
Treservoir Stores the description of on-chip reservoir. Each entry is of the form (i, j, rtype),where (i, j) is the dispense location and rtype is the reservoir type (reagent,output, waste).
Exact One-Pass Synthesis of Digital Microfluidic Biochips 7
Introduction Synthesis of Digital Microfluidic Biochip Scope of the Article and Contributions Verification Flow - In a nutshell Formalism Conclusions
Initial Configuration
xt1,1 xt1,2 xt1,3 xt1,4 xt1,5 xt1,6
xt5,1 xt5,2 xt5,3 xt5,4 xt5,5 xt5,6
xt2,1 xt2,2 xt2,3 xt2,4 xt2,5 xt2,6
xt3,1 xt3,2 xt3,3 xt3,4 xt3,5 x
t3,6
xt4,1 xt4,2 xt4,3 xt4,4 xt4,5 xt4,6
xt6,1 xt6,2 xt6,3 xt6,4 xt6,5 xt6,6
R1 R2
O2 W2
O1 W1
x ti ,j =
{1 if a droplet is present on (i , j) cell at t0 otherwise
At t = 0 biochip has no droplets. Hence, Btr×c = ∧(∀i ,j)¬x0
i ,j
Transition
Btr×c
fluidic instructions−−−−−−−−−−−→ Bt+1r×c
Exact One-Pass Synthesis of Digital Microfluidic Biochips 8
Introduction Synthesis of Digital Microfluidic Biochip Scope of the Article and Contributions Verification Flow - In a nutshell Formalism Conclusions
Method
We propose to run through the created clauses using anefficient SAT solver (metaSMT)The experiments shown for several time steps showsatisfactory results, as shown below.
Exact One-Pass Synthesis of Digital Microfluidic Biochips 9
Introduction Synthesis of Digital Microfluidic Biochip Scope of the Article and Contributions Verification Flow - In a nutshell Formalism Conclusions
Concluding remarks
A novel SAT based approach
Our formulation allows us to detect the optimal pathway
Experiments give good correlation with theory.
Exact One-Pass Synthesis of Digital Microfluidic Biochips 10
Introduction Synthesis of Digital Microfluidic Biochip Scope of the Article and Contributions Verification Flow - In a nutshell Formalism Conclusions
References I
D. Grissom, K. O’Neal, B. Preciado, H. Patel, R. Doherty, N. Liao, and P. Brisk, “Adigital microfluidic biochip synthesis framework,” in VLSI-SoC, 2012, pp. 177–182.
J. McDaniel, A. Baez, B. Crites, A. Tammewar, and P. Brisk, “Design and verificationtools for continuous fluid flow-based microfluidic devices,” in ASP-DAC, 2013, pp.219–224.
V. D’Silva, D. Kroening, and G. Weissenbacher, “A survey of automated techniquesfor formal software verification,” IEEE Trans. on CAD of Integrated Circuits andSystems, vol. 27, no. 7, pp. 1165–1178, 2008.
Y. S. Mahajan, Z. Fu, and S. Malik, “Zchaff2004: An efficient sat solver,” in SAT(Selected Papers), 2004, pp. 360–375.
K. Chakrabarty and F. Su, Digital Microfluidic Biochips - Synthesis, Testing, andReconfiguration Techniques. CRC Press, 2007.
C. Baier and J.-P. Katoen, Principles of Model Checking. MIT Press, 2008.
E. M. Clarke, O. Grumberg, and D. Peled, Model Checking. MIT Press, 2001.
J. Berthier, Micro-Drops and Digital Microfluidics. William Andrew, 2008.
S. Meltzer, PCR in Bioanalysis. Humana Press, 1998.
Exact One-Pass Synthesis of Digital Microfluidic Biochips 11