Exact One-Pass Synthesis of Digital Microfluidic Biochips · Exact One-Pass Synthesis of Digital...

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


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



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?



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




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


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





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


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

?




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)



Verification Flow - In a nutshell

SynthesisActuationsequence

Input: Design constraints

3232

032

1632

832


Sample

Buffer Waste

1 Input sequencing graph is transformed to actuation sequencesby synthesis tool



SynthesisActuationsequence

Input: Design constraints

3232

032

1632

832


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



Interpreting symbolic instructions




t = 1

O W

S B

1 d(1, 1)d(1, 4)







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])







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)







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])







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)



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).



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



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.



Concluding remarks

A novel SAT based approach

Our formulation allows us to detect the optimal pathway

Experiments give good correlation with theory.



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.


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