ECS 289A: Theory of Molecular Computation
Winter 2021
Instructor
Dave Doty
doty@ucdavis.edu
Office: Zoom link
Office hours: Wed 10:00-11:00am
Lectures
Tuesday and Thursday, 9:00-10:20am, 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 1-2 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 self-assembly
-
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 Program-Size Complexity of Self-Assembled Squares,
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
-
Tues, Jan 12, 2021
formal definition of the aTAM
-
Thurs, Jan 14, 2021
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,
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
-
Tues, Jan 19, 2021
concentration programming
paper: Randomized self-assembly for exact shapes
finite shape that requires more tile types to strictly self-assemble with a directed TAS than a non-directed TAS;
NPNP-completeness of computing minimum tile set strictly self-assembling a shape
paper: The Power of Nondeterminism in Self-Assembly
-
Thurs, Jan 21, 2021
kTAM for error analysis
paper: Simulations of Computing by Self-Assembly
proofreading for error-correction
paper: Proofreading Tile Sets: Error Correction for Algorithmic Self-Assembly
Some other topics we didn't cover on algorithmic self-assembly:
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 Finite-State 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, probability-1, and fair executions
Feedforward CRNs.
-
Tues, Feb 2, 2021
Non-competitive 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 Finite-State 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.
Turing-universality: 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.
dual-rail logic for Boolean circuits.
ABC for minimizing circuits.
Leaks and error-prevention in DNA strand displacement.
papers:
DNA sequence design
-
Thurs, Feb 25, 2021
DNA energy models
polynomial-time 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