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

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

Enzymes are central to both metabolism and information processing in cells. In both cases, an enzyme’s ability to accelerate a reaction without being consumed in the reaction is crucial. Nevertheless, enzymes are transiently sequestered when they bind to their substrates; this sequestration limits activity and potentially compromises information processing and signal transduction. In this article, we analyse the mechanism of enzyme–substrate catalysis from the perspective of minimizing the load on the enzymes through sequestration, while 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 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

New Langevin and Gradient Thermostats for Rigid Body Dynamics

We introduce two new thermostats, one of Langevin type and one of gradient (Brownian) type, for rigid body dynamics. We formulate rotation using the quaternion representation of angular coordinates; both thermostats preserve the unit length of quaternions. The Langevin thermostat also ensures that the conjugate angular momenta stay within the tangent space of the quaternion coordinates, as required by the Hamiltonian dynamics of rigid bodies. We have constructed three geometric numerical integrators for the Langevin thermostat and one for the gradient thermostat. The numerical integrators reflect key properties of the thermostats themselves. Namely, they all preserve the unit length of quaternions, automatically, without the need of a projection onto the unit sphere. The Langevin integrators also ensure that the angular momenta remain within the tangent space of the quaternion coordinates. The Langevin integrators are quasi-symplectic and of weak order two. The numerical method for the gradient thermostat is of weak order one. Its construction exploits ideas of Lie-group type integrators for differential equations on manifolds. We numerically compare the discretization errors of the Langevin integrators, as well as the efficiency of the gradient integrator compared to the Langevin ones when used in the simulation of rigid TIP4P water model with smoothly truncated electrostatic interactions. We observe that the gradient integrator is computationally less efficient than the Langevin integrators. We also compare the relative accuracy of the Langevin integrators in evaluating various static quantities and give recommendations as to the choice of an appropriate integrator.Comment: 16 pages, 4 figure

Identifying Physical Causes of Apparent Enhanced Cyclization of Short DNA Molecules with a Coarse-Grained Model

DNA cyclization is a powerful technique to gain insight into the nature of DNA bending. While the wormlike chain model provides a good description of small to moderate bending fluctuations, it is expected to break down for large bending. Recent cyclization experiments on strongly bent shorter molecules indeed suggest enhanced flexibility over and above that expected from the wormlike chain. Here, we use a coarse-grained model of DNA to investigate the subtle thermodynamics of DNA cyclization for molecules ranging from 30 to 210 base pairs. As the molecules get shorter, we find increasing deviations between our computed equilibrium j-factor and the classic wormlike chain predictions of Shimada and Yamakawa for a torsionally aligned looped molecule. These deviations are due to sharp kinking, first at nicks, and only subsequently in the body of the duplex. At the shortest lengths, substantial fraying at the ends of duplex domains is the dominant method of relaxation. We also estimate the dynamic j-factor measured in recent FRET experiments. We find that the dynamic j-factor is systematically larger than its equilibrium counterpart - with the deviation larger for shorter molecules - because not all the stress present in the fully cyclized state is present in the transition state. These observations are important for the interpretation of recent cyclization experiments, suggesting that measured anomalously high j-factors may not necessarily indicate non-WLC behavior in the body of duplexes

Design of hidden thermodynamic driving for non-equilibrium systems via mismatch elimination during DNA strand displacement

Recent years have seen great advances in the development of synthetic self-assembling molecular systems. Designing out-of-equilibrium architectures, however, requires a more subtle control over the thermodynamics and kinetics of reactions. We propose a mechanism for enhancing the thermodynamic drive of DNA strand-displacement reactions whilst barely perturbing forward reaction rates: the introduction of mismatches within the initial duplex. Through a combination of experiment and simulation, we demonstrate that displacement rates are strongly sensitive to mismatch location and can be tuned by rational design. By placing mismatches away from duplex ends, the thermodynamic drive for a strand-displacement reaction can be varied without significantly affecting the forward reaction rate. This hidden thermodynamic driving motif is ideal for the engineering of non-equilibrium systems that rely on catalytic control and must be robust to leak reactions

Multi-scale coarse-graining for the study of assembly pathways in DNA-brick self-assembly

Inspired by recent successes using single-stranded DNA tiles to produce complex structures, we develop a two-step coarse-graining approach that uses detailed thermodynamic calculations with oxDNA, a nucleotide-based model of DNA, to parametrize a coarser kinetic model that can reach the time and length scales needed to study the assembly mechanisms of these structures. We test the model by performing a detailed study of the assembly pathways for a two-dimensional target structure made up of 334 unique strands each of which are 42 nucleotides long. Without adjustable parameters, the model reproduces a critical temperature for the formation of the assembly that is close to the temperature at which assembly first occurs in experiments. Furthermore, the model allows us to investigate in detail the nucleation barriers and the distribution of critical nucleus shapes for the assembly of a single target structure. The assembly intermediates are compact and highly connected (although not maximally so), and classical nucleation theory provides a good fit to the height and shape of the nucleation barrier at temperatures close to where assembly first occurs

Students go through the gears at the iGEM competition for engineering biology

The annual International Genetically Engineered Machine (iGEM) competition, represents an exciting opportunity for students to experience first-hand the potential of synthetic biology approaches to solve real-world problems. In this article, an iGEM team based at Imperial College London share some of the highlights from their participation in the 2018 iGEM event, including sharing their work at the annual Jamboree in Boston, Massachusetts

DNA cruciform arms nucleate through a correlated but non-synchronous cooperative mechanism

Inverted repeat (IR) sequences in DNA can form non-canonical cruciform structures to relieve torsional stress. We use Monte Carlo simulations of a recently developed coarse-grained model of DNA to demonstrate that the nucleation of a cruciform can proceed through a cooperative mechanism. Firstly, a twist-induced denaturation bubble must diffuse so that its midpoint is near the centre of symmetry of the IR sequence. Secondly, bubble fluctuations must be large enough to allow one of the arms to form a small number of hairpin bonds. Once the first arm is partially formed, the second arm can rapidly grow to a similar size. Because bubbles can twist back on themselves, they need considerably fewer bases to resolve torsional stress than the final cruciform state does. The initially stabilised cruciform therefore continues to grow, which typically proceeds synchronously, reminiscent of the S-type mechanism of cruciform formation. By using umbrella sampling techniques we calculate, for different temperatures and superhelical densities, the free energy as a function of the number of bonds in each cruciform along the correlated but non-synchronous nucleation pathways we observed in direct simulations.Comment: 12 pages main paper + 11 pages supplementary dat

Geometric integrator for Langevin systems with quaternion-based rotational degrees of freedom and hydrodynamic interactions

We introduce new Langevin-type equations describing the rotational and translational motion of rigid bodies interacting through conservative and non-conservative forces, and hydrodynamic coupling. In the absence of non-conservative forces the Langevin-type equations sample from the canonical ensemble. The rotational degrees of freedom are described using quaternions, the lengths of which are exactly preserved by the stochastic dynamics. For the proposed Langevin-type equations, we construct a weak 2nd order geometric integrator which preserves the main geometric features of the continuous dynamics. The integrator uses Verlet-type splitting for the deterministic part of Langevin equations appropriately combined with an exactly integrated Ornstein-Uhlenbeck process. Numerical experiments are presented to illustrate both the new Langevin model and the numerical method for it, as well as to demonstrate how inertia and the coupling of rotational and translational motion can introduce qualitatively distinct behaviours

Second law, entropy production, and reversibility in thermodynamics of information

We present a pedagogical review of the fundamental concepts in thermodynamics of information, by focusing on the second law of thermodynamics and the entropy production. Especially, we discuss the relationship among thermodynamic reversibility, logical reversibility, and heat emission in the context of the Landauer principle and clarify that these three concepts are fundamentally distinct to each other. We also discuss thermodynamics of measurement and feedback control by Maxwell's demon. We clarify that the demon and the second law are indeed consistent in the measurement and the feedback processes individually, by including the mutual information to the entropy production.Comment: 43 pages, 10 figures. As a chapter of: G. Snider et al. (eds.), "Energy Limits in Computation: A Review of Landauer's Principle, Theory and Experiments