DNA as a universal substrate for chemical kinetics

Molecular programming aims to systematically engineer molecular and chemical systems of autonomous function and ever-increasing complexity. A key goal is to develop embedded control circuitry within a chemical system to direct molecular events. Here we show that systems of DNA molecules can be constructed that closely approximate the dynamic behavior of arbitrary systems of coupled chemical reactions. By using strand displacement reactions as a primitive, we construct reaction cascades with effectively unimolecular and bimolecular kinetics. Our construction allows individual reactions to be coupled in arbitrary ways such that reactants can participate in multiple reactions simultaneously, reproducing the desired dynamical properties. Thus arbitrary systems of chemical equations can be compiled into real chemical systems. We illustrate our method on the Lotka–Volterra oscillator, a limit-cycle oscillator, a chaotic system, and systems implementing feedback digital logic and algorithmic behavior

Proofreading tile sets: Error correction for algorithmic self-assembly

For robust molecular implementation of tile-based algorithmic self-assembly, methods for reducing errors must be developed. Previous studies suggested that by control of physical conditions, such as temperature and the concentration of tiles, errors (ε) can be reduced to an arbitrarily low rate - but at the cost of reduced speed (r) for the self-assembly process. For tile sets directly implementing blocked cellular automata, it was shown that r ≈ βε^2 was optimal. Here, we show that an improved construction, which we refer to as proofreading tile sets, can in principle exploit the cooperativity of tile assembly reactions to dramatically improve the scaling behavior to r ≈ βε and better. This suggests that existing DNA-based molecular tile approaches may be improved to produce macroscopic algorithmic crystals with few errors. Generalizations and limitations of the proofreading tile set construction are discussed

Thermodynamic simulation of deoxyoligonucleotide hybridization, polymerization, and ligation

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1997.Includes bibliographical references (leaves 54-55).by Alexander J. Hartemink.M.S

Simulations of Computing by Self-Assembly

Winfree (1996) proposed a Turing-universal model of DNA self-assembly. In this abstract model, DNA double-crossover molecules self-assemble to form an algorithmically-patterned two-dimensional lattice. Here, we develop a more realistic model based on the thermodynamics and kinetics of oligonucleotide hydridization. Using a computer simulation, we investigate what physical factors influence the error rates, i.e., when the more realistic model deviates from the ideal of the abstract model. We find, in agreement with rules of thumb for crystal growth, that the lowest error rates occur at the melting temperature when crystal growth is slowest, and that error rates can be made arbitrarily low by decreasing concentration and increasing binding strengths

Dissecting the sharp response of a canonical developmental enhancer reveals multiple sources of cooperativity.

Developmental enhancers integrate graded concentrations of transcription factors (TFs) to create sharp gene expression boundaries. Here we examine the hunchback P2 (HbP2) enhancer which drives a sharp expression pattern in the Drosophila blastoderm embryo in response to the transcriptional activator Bicoid (Bcd). We systematically interrogate cis and trans factors that influence the shape and position of expression driven by HbP2, and find that the prevailing model, based on pairwise cooperative binding of Bcd to HbP2 is not adequate. We demonstrate that other proteins, such as pioneer factors, Mediator and histone modifiers influence the shape and position of the HbP2 expression pattern. Comparing our results to theory reveals how higher-order cooperativity and energy expenditure impact boundary location and sharpness. Our results emphasize that the bacterial view of transcription regulation, where pairwise interactions between regulatory proteins dominate, must be reexamined in animals, where multiple molecular mechanisms collaborate to shape the gene regulatory function

Tropical geometries and dynamics of biochemical networks. Application to hybrid cell cycle models

We use the Litvinov-Maslov correspondence principle to reduce and hybridize networks of biochemical reactions. We apply this method to a cell cycle oscillator model. The reduced and hybridized model can be used as a hybrid model for the cell cycle. We also propose a practical recipe for detecting quasi-equilibrium QE reactions and quasi-steady state QSS species in biochemical models with rational rate functions and use this recipe for model reduction. Interestingly, the QE/QSS invariant manifold of the smooth model and the reduced dynamics along this manifold can be put into correspondence to the tropical variety of the hybridization and to sliding modes along this variety, respectivelyComment: conference SASB 2011, to be published in Electronic Notes in Theoretical Computer Scienc

Synthesis of crystals with a programmable kinetic barrier to nucleation

A central goal of chemistry is to fabricate supramolecular structures of defined function and composition. In biology, control of supramolecular synthesis is often achieved through precise control over nucleation and growth processes: A seed molecule initiates growth of a structure, but this growth is kinetically inhibited in the seed's absence. Here we show how such control can be systematically designed into self-assembling structures made of DNA tiles. These structures, "zig-zag ribbons," are designed to have a fixed width but can grow arbitrarily long. Under slightly supersaturated conditions, theory predicts that elongation is always favorable but that nucleation rates decrease exponentially with increasing width. We confirm experimentally that although ribbons of different widths have similar thermodynamics, nucleation rates decrease for wider ribbons. It is therefore possible to program the nucleation rate by choosing a ribbon width. The presence of a seed molecule, a stabilized version of the presumed critical nucleus, removes the kinetic barrier to nucleation of a ribbon. Thus, we demonstrate the ability to grow supramolecular structures from rationally designed seeds, while suppressing spurious nucleation. Control over DNA tile nucleation allows for proper initiation of algorithmic crystal growth, which could lead to the high-yield synthesis of micrometer-scale structures with complex programmed features. More generally, this work shows how a self-assembly subroutine can be initiated

Reduction of dynamical biochemical reaction networks in computational biology

Biochemical networks are used in computational biology, to model the static and dynamical details of systems involved in cell signaling, metabolism, and regulation of gene expression. Parametric and structural uncertainty, as well as combinatorial explosion are strong obstacles against analyzing the dynamics of large models of this type. Multi-scaleness is another property of these networks, that can be used to get past some of these obstacles. Networks with many well separated time scales, can be reduced to simpler networks, in a way that depends only on the orders of magnitude and not on the exact values of the kinetic parameters. The main idea used for such robust simplifications of networks is the concept of dominance among model elements, allowing hierarchical organization of these elements according to their effects on the network dynamics. This concept finds a natural formulation in tropical geometry. We revisit, in the light of these new ideas, the main approaches to model reduction of reaction networks, such as quasi-steady state and quasi-equilibrium approximations, and provide practical recipes for model reduction of linear and nonlinear networks. We also discuss the application of model reduction to backward pruning machine learning techniques

Timing molecular motion and production with a synthetic transcriptional clock

The realization of artificial biochemical reaction networks with unique functionality is one of the main challenges for the development of synthetic biology. Due to the reduced number of components, biochemical circuits constructed in vitro promise to be more amenable to systematic design and quantitative assessment than circuits embedded within living organisms. To make good on that promise, effective methods for composing subsystems into larger systems are needed. Here we used an artificial biochemical oscillator based on in vitro transcription and RNA degradation reactions to drive a variety of “load” processes such as the operation of a DNA-based nanomechanical device (“DNA tweezers”) or the production of a functional RNA molecule (an aptamer for malachite green). We implemented several mechanisms for coupling the load processes to the oscillator circuit and compared them based on how much the load affected the frequency and amplitude of the core oscillator, and how much of the load was effectively driven. Based on heuristic insights and computational modeling, an “insulator circuit” was developed, which strongly reduced the detrimental influence of the load on the oscillator circuit. Understanding how to design effective insulation between biochemical subsystems will be critical for the synthesis of larger and more complex systems