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Chemical reaction networks (CRNs) model systems where molecules interact according to a finite set of reactions such as A + B → C, representing that if a molecule of A and B collide, they disappear and a molecule of C is produced. CRNs can compute Boolean-valued predicates ϕ:ℕ^d → {0,1} and integer-valued functions f:ℕ^d → ℕ; for instance X₁ + X₂ → Y computes the function min(x₁,x₂), since starting with x_i copies of X_i, eventually min(x₁,x₂) copies of Y are produced. We study the computational power of execution bounded CRNs, in which only a finite number of reactions can occur from the initial configuration (e.g., ruling out reversible reactions such as A ⇌ B). The power and composability of such CRNs depend crucially on some other modeling choices that do not affect the computational power of CRNs with unbounded executions, namely whether an initial leader is present, and whether (for predicates) all species are required to "vote" for the Boolean output. If the CRN starts with an initial leader, and can allow only the leader to vote, then all semilinear predicates and functions can be stably computed in O(n log n) parallel time by execution bounded CRNs. However, if no initial leader is allowed, all species vote, and the CRN is "non-collapsing" (does not shrink from initially large to final O(1) size configurations), then execution bounded CRNs are severely limited, able to compute only eventually constant predicates. A key tool is a characterization of execution bounded CRNs as precisely those with a nonnegative linear potential function that is strictly decreased by every reaction [Czerner et al., 2024]. 

We present an abstract model of self-assembly of systems composed of "crisscross slats", which have been experimentally implemented as a single-stranded piece of DNA [Minev et al., 2021] or as a complete DNA origami structure [Wintersinger et al., 2022]. We then introduce a more physically realistic *kinetic* model and show how important constants in the model were derived and tuned, and compare simulation-based results to experimental results [Minev et al., 2021; Wintersinger et al., 2022]. Using these models, we show how we can apply optimizations to designs of slat systems in order to lower the numbers of unique slat types required to build target structures. In general, we apply two types of techniques to achieve greatly reduced numbers of slat types. Similar to the experimental work implementing DNA origami-based slats, in our designs the slats oriented in horizontal and vertical directions are each restricted to their own plane and sets of them overlap each other in square regions which we refer to as macrotiles. Our first technique extends their previous work of reusing slat types within macrotiles and requires analyses of binding domain patterns to determine the potential for errors consisting of incorrect slat types attaching at undesired translations and reflections. The second technique leverages the power of algorithmic self-assembly to efficiently reuse entire macrotiles which self-assemble in patterns following designed algorithms that dictate the dimensions and patterns of growth. Using these designs, we demonstrate that in kinetic simulations the systems with reduced numbers of slat types self-assemble more quickly than those with greater numbers. This provides evidence that such optimizations will also result in greater assembly speeds in experimental systems. Furthermore, the reduced numbers of slat types required have the potential to vastly reduce the cost and number of lab steps for crisscross assembly experiments.