arXiv subjects

Thomas E. Ouldridge

Publications and source records attributed to Thomas E. Ouldridge.

At least 19 recordsLinked to original sources

arXiv2026

Recurrent neural chemical reaction networks trained to switch dynamical behaviours through learned bifurcations

Both natural and synthetic chemical systems not only exhibit a range of non-trivial dynamics, but also transition between qualitatively different dynamical behaviours as environmental parameters change. Such transitions are called bifurcations. Here, we show that recurrent neural chemical reaction networks (RNCRNs), a class of chemical reaction networks based on recurrent artificial neural networks that can be trained to reproduce a given dynamical behaviour, can also be trained to exhibit bifurcations. First, we show that RNCRNs can inherit some bifurcations defined by smooth ordinary differential equations (ODEs). Second, we demonstrate that the RNCRN can be trained to infer bifurcations that allow it to approximate different target behaviours within different regions of parameter space, without explicitly providing the bifurcation itself in the training. These behaviours can be specified using target ODEs that are discontinuous with respect to the parameters, or even simply by specifying certain desired dynamical features in certain regions of the parameter space. To achieve the latter, we introduce an ODE-free algorithm for training the RNCRN to display designer oscillations, such as a heart-shaped limit cycle or two coexisting limit cycles.

q-bio.MN↗

arXiv2025

Bit reset protocols that obey activity-constrained speed limits do not minimize work for a given speed

The goal of thermodynamic optimal control theory is to find protocols to change the state of a system from an initial to a desired final distribution, within a finite time, with the least possible expenditure of work. The optimal protocol is closely linked to the intrinsic dynamics of the system at hand. The fact that these dynamics can vary widely has made a general solution elusive. Recent years have seen great progress by recasting the question in terms of a quantity called total activity, i.e. the average number of jumps between states of the system, rather than the time that the operation is allowed to take. This perspective has allowed for general expressions for the minimal work as a function of the total activity, and the minimal total activity required for a given work. The expression for minimal total activity can be recast as an apparent minimal operation time or speed limit. However, it is unclear whether protocols optimized under a constrained activity actually require the lowest work input for a given operation time. In the context of bit reset, we show that directly minimizing work for a given operation time leads to protocols that require significantly less work to perform the operation than the activity-constrained protocol of the same duration. We show how the resulting protocols differ. One reason for the difference is the fact that the activity rate is not constant over the course of the protocol: it depends on both the transition rates and the distribution of the bit, both of which change during the copy operation. In the limit of long protocol duration, we find an expression for the difference between the resulting minimal work for both optimization schemes, for a general class of dynamics. The time-constrained approach always outperforms the activity-constrained approach for a given constrained duration, and the difference in work can be arbitrarily large.

cond-mat.stat-mech↗

arXiv2025

Design of DNA Strand Displacement Reactions

DNA strand displacement (SD) reactions are central to the operation of many synthetic nucleic acid systems, including molecular circuits, sensors, and machines. Over the years, a broad set of design frameworks has emerged to accommodate various functional goals, initial configurations, and environmental conditions. Nevertheless, key challenges persist, particularly in reliably predicting reaction kinetics. This review examines recent approaches to SD reaction design, with emphasis on the properties of single reactions, including kinetics, structural factors, and limitations in current modelling practices. We identify promising innovations while analysing the factors that continue to hinder predictive accuracy. We conclude by outlining future directions for achieving more robust and programmable behaviour in DNA-based systems.

q-bio.BM↗

arXiv2025

Thermodynamic limits on general far-from-equilibrium molecular templating networks

Cells produce RNA and proteins via molecular templating networks. We show that information transmission in such networks is bounded by functions of a simple thermodynamic property of the network, regardless of complexity. Surprisingly, putative systems operating at this bound do not have a high flux around the network. Instead, they have low entropy production, with each product in a ``pseudo-equilibrium'' determined by a single pathway. These pseudo-equilibrium limits constrain information transmission for the overall network, even if individual templates are arbitrarily specific.

physics.bio-ph↗

arXiv2025

Recurrent neural chemical reaction networks that approximate arbitrary dynamics

Many important phenomena in biochemistry and biology exploit dynamical features such as multi-stability, oscillations, and chaos. Construction of novel chemical systems with such rich dynamics is a challenging problem central to the fields of synthetic biology and molecular nanotechnology. In this paper, we address this problem by putting forward a molecular version of a recurrent artificial neural network, which we call recurrent neural chemical reaction network (RNCRN). The RNCRN uses a modular architecture - a network of chemical neurons - to approximate arbitrary dynamics. We first prove that with sufficiently many chemical neurons and suitably fast reactions, the RNCRN can be systematically trained to achieve any dynamics. RNCRNs with relatively small number of chemical neurons and a moderate range of reaction rates are then trained to display a variety of biologically-important dynamical features. We also demonstrate that such RNCRNs are experimentally implementable with DNA-strand-displacement technologies.

q-bio.MN↗

arXiv2025

Exploiting bias in optimal finite-time copying protocols

We study a finite-time cyclic copy protocol that creates persisting correlations between a memory and a data bit. The average work to copy the two states of the data bit consists of the mutual information created between the memory and data bit after copying, a cost due to the difference between the initial and final states of the memory bit, and a finite-time cost. At low copy speeds, the optimal initial distribution of the memory bit matches the bias in the expected outcome, set by the bias in the data bit and the copying accuracies. However, if both states of the data are copied with the same accuracy, then in the high-speed regime copying the unlikely data bit state becomes prohibitively costly with a biased memory; the optimal initial distribution is then pushed towards 50:50. Copying with unequal accuracies, at fixed copy-generated mutual information, yields an opposite yet more effective strategy. Here, the initial memory distribution becomes increasingly biased as the copy speed increases, drastically lowering the work and raising the maximum speed. This strategy is so effective that it induces a symmetry breaking transition for an unbiased data bit.

cond-mat.stat-mech↗

arXiv2025

The Interplay of Heterogeneity and Product Detachment in Templated Polymer Copying

Templated copolymerization, in which information stored in the sequence of a heteropolymer template is copied into another polymer product, is the mechanism behind all known methods of genetic information transfer. A key aspect of templated copolymerization is the eventual detachment of the product from the template. A second key feature of natural biochemical systems is that the template-binding free energies of both correctly-matched and incorrect monomers are heterogeneous. Previous work has considered the thermodynamic consequences of detachment, and the consequences of heterogeniety for polymerisation speed and accuracy, but the interplay of both separation and heterogeniety remains unexplored. In this work, we investigate a minimal model of templated copying that simultaneously incorporates both detachment from behind the leading edge of the growing copy and heterogeneous interactions. We first extend existing coarse-graining methods for models of polymerisation to allow for heterogeneous interactions. We then show that heterogeneous copying systems with explicit detachment do not exhibit the subdiffusive behaviour observed in the absence of detachment when near equilibrium. Next, we show that heterogeneity in correct monomer interactions tends to result in slower, less accurate copying, while heterogeneity in incorrect monomer interactions tends to result in faster, more accurate copying, due to an increased roughness in the free energy landscape of either correct or incorrect monomer pairs. Finally, we show that heterogeneity can improve on known thermodynamic efficiencies of homogeneous copying, but these increased thermodynamic efficiencies do not always translate to increased efficiencies of information transfer.

physics.bio-ph↗

arXiv2024

Is stochastic thermodynamics the key to understanding the energy costs of computation?

The relationship between the thermodynamic and computational characteristics of dynamical physical systems has been a major theoretical interest since at least the 19th century, and has been of increasing practical importance as the energetic cost of digital devices has exploded over the last half century. One of the most important thermodynamic features of real-world computers is that they operate very far from thermal equilibrium, in finite time, with many quickly (co-)evolving degrees of freedom. Such computers also must almost always obey multiple physical constraints on how they work. For example, all modern digital computers are periodic processes, governed by a global clock. Another example is that many computers are modular, hierarchical systems, with strong restrictions on the connectivity of their subsystems. This properties hold both for naturally occurring computers, like brains or Eukaryotic cells, as well as digital systems. These features of real-world computers are absent in 20th century analyses of the thermodynamics of computational processes, which focused on quasi-statically slow processes. However, the field of stochastic thermodynamics has been developed in the last few decades - and it provides the formal tools for analyzing systems that have exactly these features of real-world computers. We argue here that these tools, together with other tools currently being developed in stochastic thermodynamics, may help us understand at a far deeper level just how the fundamental physical properties of dynamic systems are related to the computation that they perform.

cond-mat.stat-mech↗

arXiv2023

Autonomous Learning of Generative Models with Chemical Reaction Network Ensembles

Can a micron sized sack of interacting molecules autonomously learn an internal model of a complex and fluctuating environment? We draw insights from control theory, machine learning theory, chemical reaction network theory, and statistical physics to develop a general architecture whereby a broad class of chemical systems can autonomously learn complex distributions. Our construction takes the form of a chemical implementation of machine learning's optimization workhorse: gradient descent on the relative entropy cost function. We show how this method can be applied to optimize any detailed balanced chemical reaction network and that the construction is capable of using hidden units to learn complex distributions. This result is then recast as a form of integral feedback control. Finally, due to our use of an explicit physical model of learning, we are able to derive thermodynamic costs and trade-offs associated to this process.

q-bio.MN↗

arXiv2023

Thermodynamics of deterministic finite automata operating locally and periodically

Real-world computers have operational constraints that cause nonzero entropy production (EP). In particular, almost all real-world computers are ``periodic'', iteratively undergoing the same physical process; and ``local", in that subsystems evolve whilst physically decoupled from the rest of the computer. These constraints are so universal because decomposing a complex computation into small, iterative calculations is what makes computers so powerful. We first derive the nonzero EP caused by the locality and periodicity constraints for deterministic finite automata (DFA), a foundational system of computer science theory. We then relate this minimal EP to the computational characteristics of the DFA. We thus divide the languages recognised by DFA into two classes: those that can be recognised with zero EP, and those that necessarily have non-zero EP. We also demonstrate the thermodynamic advantages of implementing a DFA with a physical process that is agnostic about the inputs that it processes.

cond-mat.stat-mech↗

arXiv2023

Pipelined information flow in molecular mechanical circuits leads to increased error and irreversibility

Pipelining is a design technique for logical circuits that allows for higher throughput than circuits in which multiple computations are fed through the system one after the other. It allows for much faster computation than architectures in which inputs must pass through every layer of the circuit before the next computation can begin (phased chaining). We explore the hypothesis that these advantages may be offset by a higher error rate, logical irreversibility and greater thermodynamic costs by simulating pipelined molecular mechanical circuits using an explicit physical model. We observe the emergent logical irreversibility, and see that the simultaneous action of multiple components indeed leads to a higher error rate than in phase-chained circuits. The thermodynamic costs of operating the gates are much larger than in equivalent phase-chained circuits, and these costs do not appear to tend to zero in the limit of slow gate operation. Redesigning the gates to eliminate errors and artificially enforcing logical reversibility reduces the thermodynamic costs and recovers thermodynamically reversible behaviour in the limit of slow gate operation. The breakdown of logical reversibility and accuracy are both associated with a breakdown of the digital behaviour of the device, likely contributing to thermodynamic costs that are large relative to the scale of the information being processed.

physics.comp-ph↗

arXiv2023

A Universal Method for Analysing Copolymer Growth

Polymers consisting of more than one type of monomer, known as copolymers, are vital to both living and synthetic systems. Copolymerisation has been studied theoretically in a number of contexts, often by considering a Markov process in which monomers are added or removed from the growing tip of a long copolymer. To date, the analysis of the most general models of this class has necessitated simulation. We present a general method for analysing such processes without resorting to simulation. Our method can be applied to models with an arbitrary network of sub-steps prior to addition or removal of a monomer, including non-equilibrium kinetic proofreading cycles. Moreover, the approach allows for a dependency of addition and removal reactions on the neighbouring site in the copolymer, and thermodynamically self-consistent models in which all steps are assumed to be microscopically reversible. Using our approach, thermodynamic quantities such as chemical work; kinetic quantities such as time taken to grow; and statistical quantities such as the distribution of monomer types in the growing copolymer can be derived either analytically or numerically directly from the model definition.

physics.chem-ph↗

arXiv2022

Simulation of reversible molecular mechanical logic gates and circuits

Landauer's principle places a fundamental lower limit on the work required to perform a logically irreversible operation. Logically reversible gates provide a way to avoid these work costs, and also simplify the task of making the computation as a whole thermodynamically reversible. The inherent reversibility of mechanical logic gates would make them good candidates for the design of practical logically reversible computing systems if not for the relatively large size and mass of such systems. In this paper, we outline the design and simulation of reversible molecular mechanical logic gates that come close to the limits of thermodynamic reversibility even under the effects of thermal noise, and outline associated circuit components from which arbitrary combinatorial reversible circuits can be constructed and simulated. We demonstrate that isolated components can be operated in a thermodynamically reversible manner, and explore the complexities of combining components to implement more complex computations. Finally, we demonstrate a method to construct arbitrarily large reversible combinatorial circuits using multiple external controls and signal boosters with a working half-adder circuit.

physics.comp-ph↗

arXiv2021

Free-energy landscapes of DNA and its assemblies: Perspectives from coarse-grained modelling

This chapter will provide an overview of how characterizing free-energy landscapes can provide insights into the biophysical properties of DNA, as well as into the behaviour of the DNA assemblies used in the field of DNA nanotechnology. The landscapes for these complex systems are accessible through the use of accurate coarse-grained descriptions of DNA. Particular foci will be the landscapes associated with DNA self-assembly and mechanical deformation, where the latter can arise from either externally imposed forces or internal stresses.

cond-mat.soft↗

arXiv2021

Integral feedback in synthetic biology: Negative-equilibrium catastrophe

A central goal of synthetic biology is the design of molecular controllers that can manipulate the dynamics of intracellular networks in a stable and accurate manner. To address the fact that detailed knowledge about intracellular networks is unavailable, integral-feedback controllers (IFCs) have been put forward for controlling molecular abundances. These controllers can maintain accuracy in spite of the uncertainties in the controlled networks. However, this desirable feature is achieved only if stability is also maintained. In this paper, we show that molecular IFCs can suffer from a hazardous instability called negative-equilibrium catastrophe (NEC), whereby all nonnegative equilibria vanish under the action of the controllers, and some of the molecular abundances blow up. We show that unimolecular IFCs do not exist due to a NEC. We then derive a family of bimolecular IFCs that are safeguarded against NECs when uncertain unimolecular networks, with any number of molecular species, are controlled. However, when IFCs are applied on uncertain bimolecular (and hence most intracellular) networks, we show that preventing NECs generally becomes an intractable problem as the number of interacting molecular species increases.

q-bio.MN↗

arXiv2021

A primer on the oxDNA model of DNA: When to use it, how to simulate it and how to interpret the results

The oxDNA model of DNA has been applied widely to systems in biology, biophysics and nanotechnology. It is currently available via two independent open source packages. Here we present a set of clearly-documented exemplar simulations that simultaneously provide both an introduction to simulating the model, and a review of the model's fundamental properties. We outline how simulation results can be interpreted in terms of -- and feed into our understanding of -- less detailed models that operate at larger length scales, and provide guidance on whether simulating a system with oxDNA is worthwhile.

q-bio.BM↗

arXiv2021

What would it take to build a thermodynamically reversible Universal Turing machine? Computational and thermodynamic constraints in a molecular design

We outline the construction of a molecular system that could, in principle, implement a thermodynamically reversible Universal Turing Machine (UTM). By proposing a concrete-albeit idealised-design and operational protocol, we reveal fundamental challenges that arise when attempting to implement arbitrary computations reversibly. Firstly, the requirements of thermodynamic reversibility inevitably lead to an intricate design. Secondly, thermodynamically reversible UTMs, unlike simpler devices, must also be logically reversible. Finally, implementing multiple distinct computations in parallel is necessary to take the cost of external control per computation to zero, but this approach is complicated the distinct halting times of different computations.

cond-mat.stat-mech↗

arXiv2020

Optimizing enzymatic catalysts for rapid turnover of substrates with low enzyme sequestration

We analyse the mechanism of enzyme-substrate catalysis from the perspective of minimizing the load on the enzymes through sequestration, whilst maintaining at least a minimum reaction flux. In particular, we ask: which binding free energies of the enzyme-substrate and enzyme-product reaction intermediates minimize the fraction of enzymes sequestered in complexes, while sustaining at a certain minimal flux? Under reasonable biophysical assumptions, we find that the optimal design will saturate the bound on the minimal flux, and reflects a basic trade-off in catalytic operation. If both binding free energies are too high, there is low sequestration, but the effective progress of the reaction is hampered. If both binding free energies are too low, there is high sequestration, and the reaction flux may also be suppressed in extreme cases. The optimal binding free energies are therefore neither too high nor too low, but in fact moderate. Moreover, the optimal difference in substrate and product binding free energies, which contributes to the thermodynamic driving force of the reaction, is in general strongly constrained by the intrinsic free-energy difference between products and reactants. Both the strategies of using a negative binding free-energy difference to drive the catalyst-bound reaction forward, and of using a positive binding free-energy difference to enhance detachment of the product, are limited in their efficacy.

q-bio.MN↗