ECS 289A: Theory of Molecular Computation
Winter 2018

Course announcement (PDF)

Instructor

Dave Doty
doty@ucdavis.edu
Office: 2069 Academic Surge
Office hours: Tues 2:10-3:00pm

Course objective

To study the fundamental abilities and limits to the engineering of automated (i.e., computational) molecular systems, in a mathematically rigorous way.

Prerequisites

ECS 120 or equivalent (familiarity with Chapters 1,3,4,7 of Introduction to the Theory of Computation by Sipser).

Prior experience with probability theory is useful; in particular, Chapters 1-2 of Probability in Computing: Randomized Algorithms and Probabilistic Analysis, by Mitzenmacher and Upfal.

Piazza

The Piazza page for the course can be used to ask questions about the course and homework. Use access code "ecs289a" to enroll. Please read this warning about Piazza as well.

Notes

lecture notes (note that these are not comprehensive since I often take material straight from a paper)

Homework

There is a Canvas page with the homework posted.

Project

Project ideas

Lectures

Tuesday and Thursday, 12:10-1:30pm, Olson 144

Algorithmic tile self-assembly

1. Tues, Jan 9, 2018
   Introduction to abstract Tile Assembly Model (aTAM)
   aTAM video introduction
   ISU TAS simulator
   pyTAS (newer version, easier to install, fewer features, likely to have more bugs)
2. Thurs, Jan 11, 2018
   tile complexity of assembling squares
   O(log n) tile types for assembling an n x n square
   paper: The Program-Size Complexity of Self-Assembled Squares
3. Tues, Jan 16, 2018
   formal definition of the aTAM
4. Thurs, Jan 18, 2018
   Brief introduction to Kolmogorov complexity
   Ω(log n / log log n) tile types necessary to assemble an n x n square
   O(log n / log log n) tile types sufficient to assemble an n x n square
   paper: Running Time and Program Size for Self-assembled Squares
5. Tues, Jan 23, 2018
   simulation of Turing machine with a tile assembly system
   assembling scaled-up version of any finite shape from optimal number of tile types
   paper: Complexity of Self-Assembled Shapes
6. Thurs, Jan 25, 2018
   
   • temperature 1 self assembly: powerful in 3D and probably limited in 2D
     slides (ODP), slides (PDF)
     paper (many systems limited in 2D): Limitations of Self-Assembly at Temperature 1
     paper (powerful in 3D): Temperature 1 Self-Assembly: Deterministic Assembly in 3D and Probabilistic Assembly in 2D
     paper (modest efficiency gains in 2D): Noncooperative algorithms in self-assembly
   • intrinsic universality
     slides (PPT)
     paper: The tile assembly model is intrinsically universal
   • alternative models of self-assembly
     slides (ODP), slides (PDF)
     • kinetic Tile Assembly Model and proofreading
       paper (defining kTAM): Simulations of Computing by Self-Assembly
       paper (proofreading): Proofreading Tile Sets: Error Correction for Algorithmic Self-Assembly
       paper:
     • concentration programming
       paper: Randomized self-assembly for exact shapes
   • Some other topics we didn't cover:
     
     • temperature programming
       paper: Reducing Tile Complexity for the Self-Assembly of Scaled Shapes Through Temperature Programming
     • hierarchical self-assembly
       paper (difference in power between aTAM and hierarchical model): Two Hands Are Better Than One
       paper (limitations on assembly speed): Parallelism and time in hierarchical self-assembly
     • staged self-assembly
       paper: Staged Self-Assembly: Nanomanufacture of Arbitrary Shapes with O(1) Glues
     • signal-passing tiles
       paper: Asynchronous Signal Passing for Tile Self-Assembly: Fuel Efficient Computation and Efficient Assembly of Shapes
     • different shapes of tiles
       paper (1x2 blocks): The Power of Duples (in Self-Assembly): It's Not So Hip To Be Square
       paper (other shapes made from squares): Universal Computation with Arbitrary Polyomino Tiles in Non-Cooperative Self-Assembly
       paper (regular polygons): Computing in continuous space with self-assembling polygonal tiles
     • finite shape that requires more tile types to strictly self-assemble with a directed TAS than a non-directed TAS
       paper: The Power of Nondeterminism in Self-Assembly
     • computable shape not strictly self-assembled by any TAS
       paper: Strict Self-Assembly of Discrete Sierpinski Triangles
     • computable set not weakly self-assembled by any TAS
       paper: Computability and Complexity in Self-Assembly

Chemical reaction networks

7. Tues, Jan 30, 2018
   Introduction to chemical reaction networks (CRNs). Examples of stable function computation.
   paper (functions): Deterministic Function Computation with Chemical Reaction Networks
8. Thurs, Feb 1, 2018
   Formal definition of stable function computation.
   Examples of stable predicate computation.
   Formal definition of stable predicate computation.
   paper (predicates): Computation in Networks of Passively Mobile Finite-State Sensors
9. Tues, Feb 6, 2018
   Definition of semilinear sets and functions, claim that only they can be stably computed.
   Formal definition discrete chemical kinetic model (Gillespie model).
   Derivation of expected completion times for some simple CRNs.
   paper: Exact stochastic simulation of coupled chemical reactions
10. Thurs, Feb 8, 2018
    time complexity analysis of computing functions/predicates with CRNs
    Register machines.
    Simulation of register machines by CRNs with a large probability of error.
11. Tues, Feb 13, 2018
    Turing-universality: simulation of register machines by CRNs with a small probability of error.
    paper: Computation with Finite Stochastic Chemical Reaction Networks
    paper: Fast Computation by Population Protocols With a Leader
12. Thurs, Feb 15, 2018
    Every semilinear set can be stably decided by a CRN.
    paper: Computation in Networks of Passively Mobile Finite-State Sensors
13. Tues, Feb 20, 2018
    Only semilinear sets can be stably decided by a CRN.
    paper: Stably Computable Predicates are Semilinear

DNA strand displacement

14. Thurs, Feb 22, 2018
    Introduction to DNA strand displacement.
    Visual DSD (simulation tool)
    papers:
    • paper introducing DNA strand displacement as a tool for DNA nanotechnology: A DNA-fuelled molecular machine made of DNA
    • paper introducing the first "CRN-to-DNA compiler": DNA as a universal substrate for chemical kinetics
    • an alternate (very elegant) CRN-to-DNA compiler: Two-Domain DNA Strand Displacement
    • implementation of a multi-stack machine using all reversible (hence zero-energy dissipation) strand displacement reactions: Efficient Turing-Universal Computation with DNA Polymers
    • large Boolean circuit (computing square root of a 4-bit number) using nothing but DNA strand displacement: Scaling Up Digital Circuit Computation with DNA Strand Displacement Cascades
    • DNA strand displacement implementation (through the "two-domain" compiler above) of approximate majority algorithm from the distributed computing literature: Programmable chemical controllers made from DNA
    • first oscillating CRN to use only DNA strand displacement: Programming chemical kinetics: engineering dynamic reaction networks with DNA strand displacement

Thermodynamic binding networks

15. Tues, Feb 27, 2018
    Thermodynamic binding networks
    Boolean circuits
    paper: Thermodynamic binding networks
    slides
16. Thurs, Mar 1, 2018
    Thermodynamic binding networks
    Exponential size bound on stable polymers
    aTAM counter that is thermodynamically stable

Experimental self-assembly

17. Tues, Mar 6, 2018
    Introduction to DNA origami.
    Design of geometric molecular bonds
    papers:
    Programmable molecular recognition based on the geometry of DNA nanostructures
    Dynamic DNA devices and assemblies formed by shape-complementary, non-base pairing 3D components
    Design of geometric molecular bonds
18. Thurs, Mar 8, 2018
    Algorithmic self-assembly with single-stranded tiles.

Project presentations

19. Tues, Mar 13, 2018
    Project presentations
20. Thurs, Mar 15, 2018
    Project presentations