arXiv subjects

Chris Thachuk

Publications and source records attributed to Chris Thachuk.

7 recordsLinked to original sources

arXiv2019

Computing properties of stable configurations of thermodynamic binding networks

The promise of chemical computation lies in controlling systems incompatible with traditional electronic micro-controllers, with applications in synthetic biology and nano-scale manufacturing. Computation is typically embedded in kinetics---the specific time evolution of a chemical system. However, if the desired output is not thermodynamically stable, basic physical chemistry dictates that thermodynamic forces will drive the system toward error throughout the computation. The thermodynamic binding network (TBN) model was introduced to formally study how the thermodynamic equilibrium can be made consistent with the desired computation, and it idealizes tradeoffs between configurational entropy and binding. Here we prove the computational hardness of natural questions about TBNs and develop a practical algorithm for verifying the correctness of constructions by translating the problem into propositional logic and solving the resulting formula. The TBN model together with automated verification tools will help inform strategies for error reduction in molecular computing, including the extensively studied models of strand displacement cascades and algorithmic tile assembly.

cs.ET↗

arXiv2018

Absolute and arbitrary orientation of single molecule shapes

DNA origami is a modular platform for the combination of molecular and colloidal components to create optical, electronic, and biological devices. Integration of such nanoscale devices with microfabricated connectors and circuits is challenging: large numbers of freely diffusing devices must be fixed at desired locations with desired alignment. We present a DNA origami molecule whose energy landscape on lithographic binding sites has a unique maximum. This property enables device alignment within 3.2$^{\circ}$ on SiO$_2$. Orientation is absolute (all degrees of freedom are specified) and arbitrary (every molecule's orientation is independently specified). The use of orientation to optimize device performance is shown by aligning fluorescent emission dipoles within microfabricated optical cavities. Large-scale integration is demonstrated via an array of 3,456 DNA origami with 12 distinct orientations, which indicates the polarization of excitation light.

physics.app-ph↗

arXiv2017

Thermodynamic Binding Networks

Strand displacement and tile assembly systems are designed to follow prescribed kinetic rules (i.e., exhibit a specific time-evolution). However, the expected behavior in the limit of infinite time--known as thermodynamic equilibrium--is often incompatible with the desired computation. Basic physical chemistry implicates this inconsistency as a source of unavoidable error. Can the thermodynamic equilibrium be made consistent with the desired computational pathway? In order to formally study this question, we introduce a new model of molecular computing in which computation is driven by the thermodynamic driving forces of enthalpy and entropy. To ensure greatest generality we do not assume that there are any constraints imposed by geometry and treat monomers as unstructured collections of binding sites. In this model we design Boolean AND/OR formulas, as well as a self-assembling binary counter, where the thermodynamically favored states are exactly the desired final output configurations. Though inspired by DNA nanotechnology, the model is sufficiently general to apply to a wide variety of chemical systems.

cs.ET↗

arXiv2017

Verifying Chemical Reaction Network Implementations: A Pathway Decomposition Approach

Here we focus on the challenge of verifying the correctness of molecular implementations of abstract chemical reaction networks, where operation in a well-mixed "soup" of molecules is stochastic, asynchronous, concurrent, and often involves multiple intermediate steps in the implementation, parallel pathways, and side reactions. This problem relates to the verification of Petri nets, but existing approaches are not sufficient for providing a single guarantee covering an infinite set of possible initial states (molecule counts) and an infinite state space potentially explored by the system given any initial state. We address these issues by formulating a new theory of pathway decomposition that provides an elegant formal basis for comparing chemical reaction network implementations, and we present an algorithm that computes this basis. Our theory naturally handles certain situations that commonly arise in molecular implementations, such as what we call "delayed choice," that are not easily accommodated by other approaches. We further show how pathway decomposition can be combined with weak bisimulation to handle a wider class that includes most currently known enzyme-free DNA implementation techniques. We anticipate that our notion of logical equivalence between chemical reaction network implementations will be valuable for other molecular implementations such as biochemical enzyme systems, and perhaps even more broadly in concurrency theory.

cs.CE↗

arXiv2014

Fast algorithmic self-assembly of simple shapes using random agitation

We study the power of uncontrolled random molecular movement in the nubot model of self-assembly. The nubot model is an asynchronous nondeterministic cellular automaton augmented with rigid-body movement rules (push/pull, deterministically and programmatically applied to specific monomers) and random agitations (nondeterministically applied to every monomer and direction with equal probability all of the time). Previous work on the nubot model showed how to build simple shapes such as lines and squares quickly---in expected time that is merely logarithmic of their size. These results crucially make use of the programmable rigid-body movement rule: the ability for a single monomer to control the movement of a large objects quickly, and only at a time and place of the programmers' choosing. However, in engineered molecular systems, molecular motion is largely uncontrolled and fundamentally random. This raises the question of whether similar results can be achieved in a more restrictive, and perhaps easier to justify, model where uncontrolled random movements, or agitations, are happening throughout the self-assembly process and are the only form of rigid-body movement. We show that this is indeed the case: we give a polylogarithmic expected time construction for squares using agitation, and a sublinear expected time construction to build a line. Such results are impossible in an agitation-free (and movement-free) setting and thus show the benefits of exploiting uncontrolled random movement.

cs.DS↗

arXiv2012

The complexity of string partitioning

Given a string $w$ over a finite alphabet $Σ$ and an integer $K$, can $w$ be partitioned into strings of length at most $K$, such that there are no \emph{collisions}? We refer to this question as the \emph{string partition} problem and show it is \NP-complete for various definitions of collision and for a number of interesting restrictions including $|Σ|=2$. This establishes the hardness of an important problem in contemporary synthetic biology, namely, oligo design for gene synthesis.

cs.CC↗

arXiv2011

Succincter Text Indexing with Wildcards

We study the problem of indexing text with wildcard positions, motivated by the challenge of aligning sequencing data to large genomes that contain millions of single nucleotide polymorphisms (SNPs)---positions known to differ between individuals. SNPs modeled as wildcards can lead to more informed and biologically relevant alignments. We improve the space complexity of previous approaches by giving a succinct index requiring $(2 + o(1))n \log σ+ O(n) + O(d \log n) + O(k \log k)$ bits for a text of length $n$ over an alphabet of size $σ$ containing $d$ groups of $k$ wildcards. A key to the space reduction is a result we give showing how any compressed suffix array can be supplemented with auxiliary data structures occupying $O(n) + O(d \log \frac{n}{d})$ bits to also support efficient dictionary matching queries. The query algorithm for our wildcard index is faster than previous approaches using reasonable working space. More importantly our new algorithm greatly reduces the query working space to $O(d m + m \log n)$ bits. We note that compared to previous results this reduces the working space by two orders of magnitude when aligning short read data to the Human genome.

cs.DS↗