High rates of fuel consumption are not required by insulating motifs to suppress retroactivity in biochemical circuits

Retroactivity arises when the coupling of a molecular network $\mathcal{U}$ to a downstream network $\mathcal{D}$ results in signal propagation back from $\mathcal{D}$ to $\mathcal{U}$. The phenomenon represents a breakdown in modularity of biochemical circuits and hampers the rational design of complex functional networks. Considering simple models of signal-transduction architectures, we demonstrate the strong dependence of retroactivity on the properties of the upstream system, and explore the cost and efficacy of fuel-consuming insulating motifs that can mitigate retroactive effects. We find that simple insulating motifs can suppress retroactivity at a low fuel cost by coupling only weakly to the upstream system $\mathcal{U}$. However, this design approach reduces the signalling network's robustness to perturbations from leak reactions, and potentially compromises its ability to respond to rapidly-varying signals.Comment: 26 pages, 19 figures, To appear in Engineering Biolog

The robustness of proofreading to crowding-induced pseudo-processivity in the MAPK pathway

Double phosphorylation of protein kinases is a common feature of signalling cascades. This motif may reduce cross-talk between signalling pathways, as the second phosphorylation site allows for proofreading, especially when phosphorylation is distributive rather than processive. Recent studies suggest that phosphorylation can be `pseudo-processive' in the crowded cellular environment, as rebinding after the first phosphorylation is enhanced by slow diffusion. Here, we use a simple model with unsaturated reactants to show that specificity for one substrate over another drops as rebinding increases and pseudo-processive behavior becomes possible. However, this loss of specificity with increased rebinding is typically also observed if two distinct enzyme species are required for phosphorylation, i.e. when the system is necessarily distributive. Thus the loss of specificity is due to an intrinsic reduction in selectivity with increased rebinding, which benefits inefficient reactions, rather than pseudo-processivity itself. We also show that proofreading can remain effective when the intended signalling pathway exhibits high levels of rebinding-induced pseudo-processivity, unlike other proposed advantages of the dual phosphorylation motif.Comment: To appear in Biohys.

The thermodynamics of computational copying in biochemical systems

Living cells use readout molecules to record the state of receptor proteins, similar to measurements or copies in typical computational devices. But is this analogy rigorous? Can cells be optimally efficient, and if not, why? We show that, as in computation, a canonical biochemical readout network generates correlations; extracting no work from these correlations sets a lower bound on dissipation. For general input, the biochemical network cannot reach this bound, even with arbitrarily slow reactions or weak thermodynamic driving. It faces an accuracy-dissipation trade-off that is qualitatively distinct from and worse than implied by the bound, and more complex steady-state copy processes cannot perform better. Nonetheless, the cost remains close to the thermodynamic bound unless accuracy is extremely high. Additionally, we show that biomolecular reactions could be used in thermodynamically optimal devices under exogenous manipulation of chemical fuels, suggesting an experimental system for testing computational thermodynamics.Comment: Accepted versio

Thermodynamics of deterministic finite automata operating locally and periodically

Real-world digital computers have operational constraints that cause nonzero entropy production (EP). In particular, almost all real-world computers are "periodic" in that they iteratively undergo the same physical process, and are "local" in that not all physical variables that are statistically coupled are also directly coupled physically. These constraints are so universal because the ability to decompose a complex computation into small, iterative logical updates is what makes digital computers so powerful. Here we first derive expressions for the nonzero EP caused by these two particular constraints in physical implementations of deterministic finite automata (DFA), a foundational system of computer science theory. We then relate this minimal EP to the computational characteristics of the DFA. Specifically, we show that DFA divide into two classes: those with an invertible local update map, which have zero local and periodic EP, and those with a non-invertible local update map, which have high minimal EP. We also demonstrate the thermodynamic advantages of implementing a DFA with a physical process that is agnostic about the inputs that it processes. \end{abstract

Force-induced rupture of a DNA duplex

The rupture of double-stranded DNA under stress is a key process in biophysics and nanotechnology. In this article we consider the shear-induced rupture of short DNA duplexes, a system that has been given new importance by recently designed force sensors and nanotechnological devices. We argue that rupture must be understood as an activated process, where the duplex state is metastable and the strands will separate in a finite time that depends on the duplex length and the force applied. Thus, the critical shearing force required to rupture a duplex within a given experiment depends strongly on the time scale of observation. We use simple models of DNA to demonstrate that this approach naturally captures the experimentally observed dependence of the critical force on duplex length for a given observation time. In particular, the critical force is zero for the shortest duplexes, before rising sharply and then plateauing in the long length limit. The prevailing approach, based on identifying when the presence of each additional base pair within the duplex is thermodynamically unfavorable rather than allowing for metastability, does not predict a time-scale-dependent critical force and does not naturally incorporate a critical force of zero for the shortest duplexes. Additionally, motivated by a recently proposed force sensor, we investigate application of stress to a duplex in a mixed mode that interpolates between shearing and unzipping. As with pure shearing, the critical force depends on the time scale of observation; at a fixed time scale and duplex length, the critical force exhibits a sigmoidal dependence on the fraction of the duplex that is subject to shearing.Comment: 10 pages, 6 figure

Modelling DNA Origami Self-Assembly at the Domain Level

We present a modelling framework, and basic model parameterization, for the study of DNA origami folding at the level of DNA domains. Our approach is explicitly kinetic and does not assume a specific folding pathway. The binding of each staple is associated with a free-energy change that depends on staple sequence, the possibility of coaxial stacking with neighbouring domains, and the entropic cost of constraining the scaffold by inserting staple crossovers. A rigorous thermodynamic model is difficult to implement as a result of the complex, multiply connected geometry of the scaffold: we present a solution to this problem for planar origami. Coaxial stacking and entropic terms, particularly when loop closure exponents are taken to be larger than those for ideal chains, introduce interactions between staples. These cooperative interactions lead to the prediction of sharp assembly transitions with notable hysteresis that are consistent with experimental observations. We show that the model reproduces the experimentally observed consequences of reducing staple concentration, accelerated cooling and absent staples. We also present a simpler methodology that gives consistent results and can be used to study a wider range of systems including non-planar origami