The Algorithmic Origins of Life

Although it has been notoriously difficult to pin down precisely what it is that makes life so distinctive and remarkable, there is general agreement that its informational aspect is one key property, perhaps the key property. The unique informational narrative of living systems suggests that life may be characterized by context-dependent causal influences, and in particular, that top-down (or downward) causation -- where higher-levels influence and constrain the dynamics of lower-levels in organizational hierarchies -- may be a major contributor to the hierarchal structure of living systems. Here we propose that the origin of life may correspond to a physical transition associated with a shift in causal structure, where information gains direct, and context-dependent causal efficacy over the matter it is instantiated in. Such a transition may be akin to more traditional physical transitions (e.g. thermodynamic phase transitions), with the crucial distinction that determining which phase (non-life or life) a given system is in requires dynamical information and therefore can only be inferred by identifying causal architecture. We discuss some potential novel research directions based on this hypothesis, including potential measures of such a transition that may be amenable to laboratory study, and how the proposed mechanism corresponds to the onset of the unique mode of (algorithmic) information processing characteristic of living systems.Comment: 13 pages, 1 tabl

Programmability of Chemical Reaction Networks

Motivated by the intriguing complexity of biochemical circuitry within individual cells we study Stochastic Chemical Reaction Networks (SCRNs), a formal model that considers a set of chemical reactions acting on a finite number of molecules in a well-stirred solution according to standard chemical kinetics equations. SCRNs have been widely used for describing naturally occurring (bio)chemical systems, and with the advent of synthetic biology they become a promising language for the design of artificial biochemical circuits. Our interest here is the computational power of SCRNs and how they relate to more conventional models of computation. We survey known connections and give new connections between SCRNs and Boolean Logic Circuits, Vector Addition Systems, Petri Nets, Gate Implementability, Primitive Recursive Functions, Register Machines, Fractran, and Turing Machines. A theme to these investigations is the thin line between decidable and undecidable questions about SCRN behavior

An Ansatz for undecidable computation in RNA-world automata

In this Ansatz we consider theoretical constructions of RNA polymers into automata, a form of computational structure. The basis for transitions in our automata are plausible RNA-world enzymes that may perform ligation or cleavage. Limited to these operations, we construct RNA automata of increasing complexity; from the Finite Automaton (RNA-FA) to the Turing Machine equivalent 2-stack PDA (RNA-2PDA) and the universal RNA-UPDA. For each automaton we show how the enzymatic reactions match the logical operations of the RNA automaton, and describe how biological exploration of the corresponding evolutionary space is facilitated by the efficient arrangement of RNA polymers into a computational structure. A critical theme of the Ansatz is the self-reference in RNA automata configurations which exploits the program-data duality but results in undecidable computation. We describe how undecidable computation is exemplified in the self-referential Liar paradox that places a boundary on a logical system, and by construction, any RNA automata. We argue that an expansion of the evolutionary space for RNA-2PDA automata can be interpreted as a hierarchical resolution of the undecidable computation by a meta-system (akin to Turing's oracle), in a continual process analogous to Turing's ordinal logics and Post's extensible recursively generated logics. On this basis, we put forward the hypothesis that the resolution of undecidable configurations in RNA-world automata represents a mechanism for novelty generation in the evolutionary space, and propose avenues for future investigation of biological automata

Algorithmic Self-Assembly of DNA: Theoretical Motivations and 2D Assembly Experiments

Biology makes things far smaller and more complex than anything produced by human engineering. The biotechnology revolution has for the first time given us the tools necessary to consider engineering on the molecular level. Research in DNA computation, launched by Len Adleman, has opened the door for experimental study of programmable biochemical reactions. Here we focus on a single biochemical mechanism, the self-assembly of DNA structures, that is theoretically sufficient for Turing-universal computation. The theory combines Hao Wang?s purely mathematical Tiling Problem with the branched DNA constructions of Ned Seeman. In the context of mathematical logic, Wang showed how jigsaw-shaped tiles can be designed to simulate the operation of any Turing Machine. For a biochemical implementation, we will need molecular Wang tiles. DNA molecular structures and intermolecular interactions are particularly amenable to design and are sufficient for the creation of complex molecular objects. The structure of individual molecules can be designed by maximizing desired and minimizing undesired Watson-Crick complementarity. Intermolecular interactions are programmed by the design of sticky ends that determine which molecules associate, and how. The theory has been demonstrated experimentally using a system of synthetic DNA double-crossover molecules that self-assemble into two-dimensional crystals that have been visualized by atomic force microscopy. This experimental system provides an excellent platform for exploring the relationship between computation and molecular self-assembly, and thus represents a first step toward the ability to program molecular reactions and molecular structures

Complexity, parallel computation and statistical physics

The intuition that a long history is required for the emergence of complexity in natural systems is formalized using the notion of depth. The depth of a system is defined in terms of the number of parallel computational steps needed to simulate it. Depth provides an objective, irreducible measure of history applicable to systems of the kind studied in statistical physics. It is argued that physical complexity cannot occur in the absence of substantial depth and that depth is a useful proxy for physical complexity. The ideas are illustrated for a variety of systems in statistical physics.Comment: 21 pages, 7 figure

Simulating 3-Symbol Turing Machines with SIMD||DNA

SIMD||DNA [Wang et al., 2019] is a model of DNA strand displacement allowing parallel in-memory computation on DNA storage. We show how to simulate an arbitrary 3-symbol space-bounded Turing machine with a SIMD||DNA program, giving a more direct and efficient route to general-purpose information manipulation on DNA storage than the Rule 110 simulation of Wang, Chalk, and Soloveichik [Wang et al., 2019]. We also develop software (https://github.com/UC-Davis-molecular-computing/simd-dna) that can simulate SIMD||DNA programs and produce SVG figures

Contrasting Geometric Variations of Mathematical Models of Self-assembling Systems

Self-assembly is the process by which complex systems are formed and behave due to the interactions of relatively simple units. In this thesis, we explore multiple augmentations of well known models of self-assembly to gain a better understanding of the roles that geometry and space play in their dynamics. We begin in the abstract Tile Assembly Model (aTAM) with some examples and a brief survey of previous results to provide a foundation. We then introduce the Geometric Thermodynamic Binding Network model, a model that focuses on the thermodynamic stability of its systems while utilizing geometrically rigid components (dissimilar to other thermodynamic models). We show that this model is computationally universal, an ability conjectured to be impossible in similar models with non-rigid components. We continue by introducing the Flexible Tile Assembly Model, a generalization of the 2D aTAM that allows bonds between tiles to flex and assemblies to therefore reconfigure. We show how systems in this model can deterministically assemble shapes that adhere to a number of certain restrictions. Finally, we introduce the Spatial abstract Tile Assembly Model, a variation of the 3D aTAM that restricts tiles from attaching without a diffusion path. We show that this model is intrinsically universal, a property of computational models to simulate themselves which has been shown for the 3D aTAM and other similar models. We conclude this thesis with a summary of the presented results, a brief impact analysis, and potential directions for future research within this area

Verifying polymer reaction networks using bisimulation

The Chemical Reaction Network model has been proposed as a programming language for molecular programming. Methods to implement arbitrary CRNs using DNA strand displacement circuits have been investigated, as have methods to prove the correctness of those or other implementations. However, the stochastic Chemical Reaction Network model is provably not deterministically Turing-universal, that is, it is impossible to create a stochastic CRN where a given output molecule is produced if and only if an arbitrary Turing machine accepts. A DNA stack machine that can simulate arbitrary Turing machines with minimal slowdown deterministically has been proposed, but it uses unbounded polymers that cannot be modeled as a Chemical Reaction Network. We propose an extended version of a Chemical Reaction Network that models unbounded linear polymers made from a finite number of monomers. This Polymer Reaction Network model covers the DNA stack machine, as well as copy-tolerant Turing machines and some examples from biochemistry. We adapt the bisimulation method of verifying DNA implementations of Chemical Reaction Networks to our model, and use it to prove the correctness of the DNA stack machine implementation. We define a subclass of single-locus Polymer Reaction Networks and show that any member of that class can be bisimulated by a network using only four primitives, suggesting a method of DNA implementation. Finally, we prove that deciding whether an implementation is a bisimulation is Π⁰₂-complete, and thus undecidable in the general case, although it is tractable in many special cases of interest. We hope that the ability to model and verify implementations of Polymer Reaction Networks will aid in the rational design of molecular systems