ECS 289A: Theory of Molecular Computation
Winter 2021
Instructor
Dave Doty
doty@ucdavis.edu
Office: Zoom link
Office hours: Wed 10:0011:00am
Lectures
Tuesday and Thursday, 9:0010:20am, Zoom link
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 12 of
Probability and Computing: Randomization and Probabilistic Techniques in Algorithms and Data Analysis,
by Mitzenmacher and Upfal.
Campuswire
The Campuswire page
for the course can be used to ask questions about the course and
homework.
Please use Campuswire instead of email unless the question is of a personal nature.
Slides
slides (these are new this quarter, not as detailed as the notes, but I hope to be a bit easier to follow)
Videos
I recorded videos of the lectures in Winter 2021.
Notes
lecture notes (these are not
comprehensive since I often take material straight from a paper; they were used prior to Winter 2021, when I switched to slides, but they are more detailed in many proofs than the slides, while covering fewer total topics)
Homework
There is a Canvas page with the homework posted.
Project
Project ideas
Schedule
Algorithmic tile selfassembly

Tues, Jan 5, 2021
Introduction to course,
introduction to abstract Tile Assembly Model (aTAM)
aTAM video introduction
ISU TAS simulator

Thurs, Jan 7, 2021
tile complexity of assembling squares
O(log n) tile types for assembling an n x n square
Ω(log n / log log n) tile types necessary to assemble an n x n square
paper: The ProgramSize Complexity of SelfAssembled Squares,
O(log n / log log n) tile types sufficient to assemble an n x n square
paper: Running Time and Program Size for Selfassembled Squares

Tues, Jan 12, 2021
formal definition of the aTAM

Thurs, Jan 14, 2021
simulation of Turing machine with a tile assembly system
assembling scaledup version of any finite shape from optimal number of tile types
paper:
Complexity of SelfAssembled Shapes,
computable shape not strictly selfassembled by any TAS
paper:
Strict SelfAssembly of Discrete Sierpinski Triangles,
computable set not weakly selfassembled by any TAS
paper:
Computability and Complexity in SelfAssembly

Tues, Jan 19, 2021
concentration programming
paper: Randomized selfassembly for exact shapes
finite shape that requires more tile types to strictly selfassemble with a directed TAS than a nondirected TAS;
NP^{NP}completeness of computing minimum tile set strictly selfassembling a shape
paper: The Power of Nondeterminism in SelfAssembly

Thurs, Jan 21, 2021
kTAM for error analysis
paper: Simulations of Computing by SelfAssembly
proofreading for errorcorrection
paper: Proofreading Tile Sets: Error Correction for Algorithmic SelfAssembly
Some other topics we didn't cover on algorithmic selfassembly:
Chemical reaction networks

Tues, Jan 26, 2021
Introduction to chemical reaction networks (CRNs).
Examples of stable predicate and function computation.
paper (predicates):
Computation in Networks of Passively Mobile FiniteState Sensors
paper (functions):
Deterministic Function Computation with Chemical Reaction Networks

Thurs, Jan 28, 2021
Formal definition of stable predicate/function computation.
Characterizations of stable computation in terms of reachability, probability1, and fair executions
Feedforward CRNs.

Tues, Feb 2, 2021
Noncompetitive CRNs.
Formal definition discrete chemical kinetic model (Gillespie model).
paper:
Exact stochastic simulation of coupled chemical reactions

Thurs, Feb 4, 2021
Derivation of expected completion times for some simple CRNs.
time complexity analysis of computing functions/predicates with CRNs
Definition of semilinear sets and functions, claim that only they can be stably computed.

Tues, Feb 9, 2021
Every semilinear set/function can be stably computed by a CRN.
paper (predicates):
Computation in Networks of Passively Mobile FiniteState Sensors
paper (functions):
Deterministic Function Computation with Chemical Reaction Networks

Thurs, Feb 11, 2021
Only semilinear sets/functions can be stably computed by a CRN.
paper (predicates):
Stably Computable Predicates are Semilinear
paper (functions):
Deterministic Function Computation with Chemical Reaction Networks

Tues, Feb 16, 2021
Statement (without proofs) of what is known about predicates/functions stably computable in sublinear time
Brief overview of results under other modeling choices:
Register machines.
Turinguniversality: simulation of register machines by CRNs with a small probability of error;
statement of CRN time complexity lower bounds
paper:
Computation with Finite Stochastic Chemical Reaction Networks
paper:
Fast Computation by Population Protocols With a Leader
DNA strand displacement

Thurs, Feb 18, 2021
Guest lecture by Chris Thachuk.
Introduction to DNA strand displacement.
Visual DSD
(simulation tool)
papers:

Tues, Feb 23, 2021
Guest lecture by Chris Thachuk.
dualrail logic for Boolean circuits.
ABC for minimizing circuits.
Leaks and errorprevention in DNA strand displacement.
papers:
DNA sequence design

Thurs, Feb 25, 2021
DNA energy models
polynomialtime algorithm for minimum free energy
DNA sequence design for arbitrary constraints with stochastic local search
papers:
Thermodynamic binding networks

Tues, Mar 2, 2021
Thermodynamic binding networks
Boolean circuits
paper:
Thermodynamic binding networks

Thurs, Mar 4, 2021
Thermodynamic binding networks
Kinetic barriers
Exponential size bound on stable polymers
aTAM counter that is thermodynamically stable
papers:
Project presentations

Tues, Mar 9, 2021
Project presentations

Thurs, Mar 11, 2021
Project presentations