**12/2/2017**

Performance limits and trade-offs in entropy-driven biochemical computers

or

In this paper the author defines ‘entropy driven computation’ as a chemical reaction network modelled as a continuous time Markov chain relaxing to its equilibrium distribution. They consider systems where the linear noise approximation is valid. They show that there is a trade-off between the accuracy of the computation and the entropy production. They also show that when you consider the fact that you have to measure the result of the computation there is a trade off between the entropy production and time, and accuracy and time.

Heterochiral DNA Strand-Displacement Circuits.

This work exploits the presence of chirality in nucleic acids, showing how to make circuits with different nucleic acids (D-DNA, L-DNA, D-RNA and PNA). The authors displayed the potential to work in parallel with the same inputs and controlled crosstalk and improved resilence to environmental RNA noise, expanding the functionalities of the strand displacement circuits.

Poster: Folding/Unfolding Thermodynamics of Three-Way and Four-Way Junctions

This poster continues previous work (see below) that discusses the thermodynamic parameters of Three-Way Junctions (TWJ) and Four-Way Junctions (FWJ) in a DNA complex. For TWJ the authors determine that the junctions unfold biphasically at low salt concentration (10 mM sodium phosphate buffer) and triphasically at high salt concentration (10 mM sodium phosphate buffer + 0.2 M NaCl) (ΔH= 118~119 kcal/mol; ΔG=12.6~17.5 kcal/mol respectively). The difference is produced because at high salt concentration, the unfolding of the two strands is sequential and not simultaneous. On the other hand, FWJ unfolds biphasically at low and high salt concentrations (ΔH= 135~149 kcal/mol; ΔG=17.5~24.9 kcal/mol respectively). The existence of only two steps during the unfolding suggest a high cooperativity. Single Value Decomposition analysis also suggest that FWJ have two possible folded conformations at low salt, but only one at high salt, that will likely correspond with the anti-parallel stacked X structure.

Full paper: Melting Behavior of a DNA Four-Way Junction Using Spectroscopic and Calorimetric Techniques

https://pubs.acs.org/doi/10.1021/jacs.7b06429

A short note on the Lyapunov function for
complex-balanced chemical reaction networks

This short note gives a crisp proof of the fact that free energy Helmholtz function is a true Lyapunov function for chemical reaction networks. This is the proof given by Horn and Jackson[1974], with the removal of the notion of “complex space”.

**24/1/2017**

Hierarchical control of enzymatic actuators using DNA-based switchable memories

https://www.nature.com/articles/s41467-017-01127-w?WT.feed_name=subjects_synthetic-biology

The authors demonstrate a mechanism for coupling nucleic acid/enzyme circuits in a pre-existing paradigm to the production of large DNA strands that can regulate protein function. They focus on the question of how coupling the downstream output to the system changes its behaviour, a phenomenon known as retroactivity.

Information Integration and Energy Expenditure in Gene Regulation

The paper studies the notion of information integration and energy consumption in the context of “sharpness of gene expression”. The define sharpness of a gene as the amount of gene expressed as a function of the concentration of the transcription factor. At thermodynamic equilibrium with n binding sites and higher order cooperatives, there is a “Hopfield barrier” to sharpness given by the Hill function of coefficient n. By expending energy, one can shift the system out of equilibrium and this Hopfield barrier can be breached.

Effective thermodynamics for a marginal observer

The Crooks fluctuation relation relates the ratio of the probability of a forward trajectory of a stochastic system to the probability of the backwards trajectory to the entropy production in the environment in that trajectory. Calculating the entropy production requires knowledge of transitions between all of the states of the system. This paper shows that if you can only observe a subset of the states a modified fluctuation relation still holds.

A self-assembled nanoscale robotic arm controlled by electric fields http://science.sciencemag.org/content/359/6373/296

This work features the description of DNA nanomachine consisting of an arm attached to a DNA origami platform capable of rotating, following the direction of an electric field. This design has proved to be able to displace cargoes in a directed manner while reducing the effect of thermal diffusion and augmenting the performance speed by 5 orders of magnitude when compared to similar designs based on chemical fuel consumption.

Non-equilibrium effect in the allosteric regulation of the bacterial flagellar switch, and

The nonequilibrium mechanism for ultrasensitivity in a biological switch: Sensing by Maxwell's demons

The first paper provides the background for the second paper. Both discuss the switching of motors which drive bacterial flagella from clockwise to counterclockwise modes and vice versa. Due to the structure of the flagella, when the motors rotate counter clockwise, all the flagella wrap around each other and form a long tail, allowing straight line motion or runs. When they rotate clockwise they unwrap and the bacterium tumbles. The first paper discusses experimentally finding non-equilibrium effects in the switching mechanism due to motor torque. The second paper attempts to analyse this mathematically using familiar stochastic techniques.

**18/1/2017**

Local equilibrium in bird flocks

In this paper, a new method of dynamical inference is developed to compensate for slow sampling rates. This allows analysis of both local interactions and network rearrangement in the regime where network rearrangement times are slow with respect to local relaxation time; a fact which is demonstrated to be true for starling murmurations. Thus bird flocks can be considered to be in a state of local equilibrium, with the system quickly responding to slow changes in network.

Stochastic Thermodynamic Interpretation of Information Geometry

In this paper the author uses information geometric quantities to derive bounds in stochastic thermodynamics including a thermodynamic uncertainty relation.

Thermodynamically Consistent Coarse Graining of Biocatalysts beyond Michaelis--Menten

https://arxiv.org/abs/1709.06045

Many catalysts may couple to a range of cofactors and have a number of substrates/products. Is it possible to systematically coarse-grain the system, getting rid of individual transitions and instead simply have a small number of effective reactions (preferably one), each associated with an overall net current, in a way that preserves both the turnover of substrates/products AND the entropy generation?

**6/11/2017**

Computing properties of stable configurations of thermodynamic binding networks

This paper describes a method to calculate all the possible thermodynmaic tradeoffs (focused in enthalpy and entropy) in DNA chemical reaction networks allowing the prediction of all the possible pairings given at a domain level, which can result on the prediction and estimation of the rates of undesired leak reaction rates. Although very useful in principle, this work is only a first limited step since it only predicts and calculates at the abstracted domain level.

https://www.nature.com/articles/srep00656

The paper shows that a biologically plausible circuit, namely a cell-cycle switch, simulates the approximate majority algorithm. Deterministic (ODEs), stochastic (gillespie simulations) and probabilistic analyses are performed to compare the performance of the two circuits. Though the performance of the cycle-cycle switch is slightly sub-optimal compared to the circuit computing the approximate majority algorithm, the introduction of a feedback loop called the "greatwall kinase" corrects this effect, by improving both the speed and conversion to majority.

Synchrony and pattern formation of coupled genetic oscillators on a chip of artificial cells

In the paper, the authors produce a silicon microfluidics-chip with several compartments interconnected by a central channel. Each of these compartments are functionalized with several DNA sequences that encodes proteins for an oscillatory network and a reporter (GFP). The oscillatory behaviour is produced by flowing through the central channel an E.coli transcription-extract with a transcription activator and repressor that reach through diffusion to the functionalized compartments.

By altering the ratio of the different genes' promoters, the researchers are able to change the oscillation frequency of the cells. In addition, the connection of the compartments between them with the central channel produce a synchronization mediated only by diffusion. While the cells produce random oscillations without communication between them, when communicated they acquire the same frequency, determined by the slowest one. This synchronization strength is easily controlled by varying the geometry or breaking the symmetry of the flow.

This microfluidic approach is a useful bottom-up approach for genetic-oscillator interactions, which allows to precisely control the experimental parameters and observe a wide variety of oscillatory behaviours.

Mapping of uncertainty relations between continuous and discrete time

This paper shows a relationship between the thermodynamic uncertainty relation for discrete and continuous time Markov chains in the long time limit. The variance of a current is always greater in the continuous time case because of the uncertainty in the time of the transitions. They use this relationship to transform a bound called the Proesmans-Van den Broeck bound for discrete time process to one for continuous time processes and show that is tighter than the Barato-Gingrich bound.

Modular probes for enriching and detecting complex nucleic acid sequences

The authors introduce a design for a DNA "probe" intended to detect the presence of complementary sequences in solution. This particular design is modular, allowing the authors to build longer probes than were previously possible, and includes small subsections in which the probe is not specific to a particular target sequence (at the joins between modules). This could be viewed as an advantage or a disadvantage, depending on context.

**30/10/2017**

Mixed analytical-stochastic simulation method for the recovery of a Brownian gradient source from probability fluxes to small windows

In this paper the authors show how a cell can detect the position of a source of Brownian particles using the particle flux into absorbing patches on its surface. They also demonstrate a simulation method that uses Green’s functions for efficient simulation of diffusion in some regions and explicit integration of Brownian motion via Euler’s method in others.

Robust Weak Chimeras in Oscillator Networks with Delayed Linear

and Quadratic Interactions

Chimera states are complex spatio-temporal patterns in which domains of synchronous and asynchronous dynamics coexist in coupled systems of oscillators. In this paper, the authors show the production of robust chimeras in networks of two populations of two oscillators. They obtain this with a weak coupling function with two sinusoidal terms: a linear and quadratic time-delayed interactions.

They test the approach numerically with the Brusselator model and experimentally with an electrochemical oscillatory reaction. The results show how complex collective dynamics in phase models translate into limit cycle oscillator networks in real biological processes.

Maximal aggregation of polynomial dynamical systems

The paper give an algorithm for the reduction of ordinary differential equations up to an equivalence relation over it’s variables. The algorithm preserves structure and variables of interest. Applications of this algorithm are presented in the context of regulatory networks, evolutionary game theory and molecular biology.

Post CMOS Computing Beyond Si: DNA Computing as Future Alternative. (http://ieeexplore.ieee.org/document/7829537/)

This paper is a brief review of the DNA computing field in which the different algorithmic operations that can be performed with DNA are described. The original approaches in the field (the Adelman-Lipton model and the stickers model) are also described in detail. This work also offers a very brief summary of the kind of problems that have been tackled, as well as their problems in implementing arithmetic operations. Worthy as a basis for introducing students to the field

Constructor Theory of Thermodynamics

Oxford-based researchers are endeavouring to re-frame fundamental ideas of physics in terms of whether it is theoretically possible to build devices (or "constructors") that can be guaranteed to achieve a certain "task". This paper seeks to do this for the laws of thermodynamics. In particular, much of the effort is spent trying to develop a rigorous and general definition of work and heat.

**16/10/2017**

Sufficient physical conditions for self-replication

https://arxiv.org/pdf/1709.09191.pdf

The authors introduce a simple model that can exhibit auto-catalytic cycles that eventually lead to exponential growth of finite-size clusters from a pool of monomers (for this it is crucial that the maximum cluster size is capped). They observe that this exponential growth is favoured when autocatalytic cycles involve reactions that are highly specific - ie., components involved in the cycle overwhelmingly undergo reactions in the cycle, rather than competing alternative reactions.

A tensegrity driven DNA nanopore.

This paper describes the design of a DNA nanopore the mimics the function of those at biological membrane. It consists in 6 B-DNA helixes forming the main structure of the pore, which is modified with hydrophobic domains that allow its insertion in lipid bilayers and block the pore lumen when closed. The opening mechanism of the pore involves a ssDNA sequence on the top of the pore that in presence of its complementary strand forms a stiff double helix that with its tension forces changes in the structure of the pore and consequently its opening.

Conservation Laws shape Dissipation

In this paper the authors describe a general formulation of stochastic thermodynamics with multiple reservoirs. They show how conserved quantities cause the forces from the reservoirs to be absorbed into the potentials of the states of the system in the local detailed balance equation. They also show how to separate the entropy production into a part that depends on how the potentials are changed over time, a part that depends on the difference between the potential of the initial and final state and a part that depends on the fundamental forces.

Iterated function systems for DNA replication

Here, Gaspard generalises his previous solutions for solving the mechanics of the creation of polymer copies by no longer allowing the simplification that all matches can be considered "correct" or "incorrect". Instead, for DNA, he considers the dynamics of all 16 possible base pair combinations. This extra heterogeneity leads to imbalances in concentration between nucleotides at different points in the chain. This, in turn, leads to regions of "anomalous drift" where the growth of the polymer is sub linear.

Exponential growth and selection in self-replicating materials from DNA origami rafts

The authors have successfully created a system in which DNA origami rafts form dimers that co-operatively catalyse their own formation in a specific manner, leading to exponential growth of specific dimer pairs. This process involves a complex external protocol involving cycling of temperatures and periodic UV exposure.

Thermodynamically Consistent Coarse Graining of Biocatalysts

The paper provides a mechanism to understand properties of the reaction network at the coarse grained level. In particular, physical quantities like flux, reaction stoichiometry and force relations are provided at the coarse-grained level of the reaction network. The entire mechanism is ensured to be thermodynamically consistent. Examples are illustrated using a single catalyst that reacts with two substrates to form a product, and a representative model of active membrane protein transport.

**25/09/2017**

A cargo-shorting DNA robot.

The most recent work from the Winfree and Qian groups describes the construction of a modular DNA walker capable of carrying DNA cargoes. Through a random walk process the aforementioned cargoes are selectively transported to a specific zone of a DNA origami.

Associative Pattern Recognition Through Macro-molecular Self-Assembly

Multifarious assembly mixtures: Systems allowing retrieval of diverse stored structures

The authors ask how many separate self-assembly targets can be programmed into the interactions between a mixture of monomers, assuming that monomers must be re-used (in different patterns) in each fully-assembled structure. They explore the conditions under which a single well-formed assembly can be triggered by seeding a small part of it, and then relate this process to the idea of retrieving memories.

**11/09/2017**

This paper considers chemical reaction networks forced out of equilibrium by a generalised chemical driving force (which is justified by appealing to implicit degrees of freedom). They watch the system evolve with time and observe a bi-modal distribution of outcomes in which, while most of the possible networks are in equilibrium or lowly dissipative, a small fraction of the configurations evolves to become much more highly dissipative and finely tuned to the work source of the environment than the rest. These finely-tuned setups occur much more often than would be expected by chance.

This paper analysis a system which involves polymer creation through processes of random ligation and auto-catalysis. It finds that, in a regime dominated by auto-catalysis, repetitive, highly patterned structures are by far the most common. It suggests two possible explanations, one short term and far from equilibrium, and one in the steady state. Both explanations hinge on the idea that longer polymers can absorb more different kinds of material when creating themselves through auto-catalysis, and for a given amount of input material, and regular polymers can form longer chains than irregular ones when creating themselves by random ligation.

Marzen and Crutchfield present a theoretical treatment of conditionally Markovian systems Y driven by hidden-Markovian environments X. They are able to derive expressions for certain information-theoretic and thermodynamic quantities related to the combined process. They use these expressions to study information and dissipation in the sensing of ligands that bind cooperatively to a sensor.

The paper gives a sufficient condition for a chemical reaction network to have an extinction event. More explicitly, they introduce the notion of a dominated expanded reaction network and provide a set of conditions on this network that do not need to be satisfied for an extinction event to occur. Solving such a system of equalities/inequalities makes the question of finding an extinction event in the reaction network amenable to algorithmic approaches.

**07/08/2017**

Markov chain models of stochastic processes without detailed balance implicitly contain external degrees of freedom that drive the system. This paper shows how to embed the Markov chain in a larger Markov chain that explicitly includes these degrees of freedom. This larger Markov chain allows detailed balance (it satisfies Kolmogorov’s criterion) but is out of equilibrium and the embedding is only accurate for short times compared to the relaxation time of the driving degrees of freedom.

In this paper, the authors demonstrate the ability to correlate the number of photons in an optical cavity with the state of a qbit, based on the fact that the interactions between the cavity change the energy gap of the qbit/resonant frequency of the cavity. This correlation allows for an excess of stimulated emission over absorption when the qbit is exposed to light at the natural frequency f the isolated qbit.

**24/07/2017**

A first major step towards a systematic predictor for DNA hybridisation rates. Based on a wealth of data, the authors use a combination of metrics that can be easily calculated from the sequences to predict hybridisation rates. The approach is largely phenomenological, and currently only applies to one strand length, but its a big step forward non the less.

In this paper, the authors discuss fluctuations in the ‘information flow’, which is part of the time derivative of the mutual information between two interacting stochastic systems. They show that when considering just one of the two coupled systems, the information flow must be added to the entropy production for a fluctuation theorem to hold. They apply this to a system of two interacting Brownian particles.

The paper makes a connection between stochastic and deterministic chemical reaction networks. In particular, it shows that for complex balanced networks, the Lyapunov function of the deterministic reaction network arises as a scaling limit of the non-equilibrium potential corresponding to the stationary distribution of it’s stochastic network. In addition, it extends this result to some birth-death processes which are not complex balanced, however does not prove results in a greater generality.

This paper sets up a simple system that trains a neural network the form of a rule for generating outputs. It takes an input drawn randomly from a set potential, and acts on it with a teacher rule and a student rule, giving two different outcomes. The two outputs are compared and the student rule is updated to give an output closer to the output given by the teacher rule. This paper states that the increase in mutual information between the teacher and student rules must be less than the free energy dissipated for the process of the student learning from the teacher.

This paper features the description of the development of an aptamer-based platform for the Influenza virus diagnosis. The aptamers obtained through artificial evolution in this work are characterized by their capability of binding to many influenza virus subtypes, making it more robust to variations on the virus due to mutations and recombination.

Leak reactions are one of the main problems affecting reliability and performance of programmable DNA reaction networks. In this paper a solution to this problem is proposed through the combined use of 3-way and 4-way branch migration reaction motifs. 4-way branch migration offers a higher free-energy barrier to the metastable initial conditions of the reaction network lowering the leak reaction rates by two orders of magnitude, while 3-way branch migration allows partial compensation of the speed trade-offs in the network.

Effective dissipation: Breaking time-reversal symmetry in driven microscopic energy transmission

An analysis of when a simple device for driving a particle up a step is most dissipative.

Catalysis in reaction networks

Proof that in weakly reversible reaction networks that don't involve catalysis, it is impossible for the concentration of any subset of species to tend asymptotically to zero.

Stochastic Analysis of Retroactivity in Transcriptional Networks through Singular Perturbation

An analysis of the restroactive effect on transcription factor abundance due to its interaction (and subsequent sequestration) with a downstream transcription site.

Information theory, predictability, and the emergence of complex life

Construction and analysis of a simple model in which the cost of being complex can be compensated by an increased ability to predict the environment.

A DNA kinetics competition strategy of hybridization chain reaction for molecular information processing circuit construction

A molecular circuit that responds not just to the presence of multiple signals, but distinguishes between signals in different orders.

**03/07/2017**
The authors find a bound on the distribution of the infimum of entropy production in a trajectory of a stochastic process. This can be used to find a bound on the average maximum backwards detour of a molecular motor. They calculate other quantities such as the probability of a trajectory reaching a positive entropy production before reaching the same magnitude negative entropy production and the ratio of the probability distribution of the time to reach those two states.

The RNA world hypothesis suggests that early life used RNA as both an information carrier and as chemically active catalysts. In particular, an RNA-based RNAp could in principle allow for RNA-based copying of RNA. Whilst some RNA-based polymerases do exist in nature, they are not effective at polymerising long, arbitrary sequences. Here, the authors obtain an RNA-based RNAp that can do just that by several rounds of selective evolution. Note that the functioning of the RNAp is restricted to growing a copy sequence on a single-stranded template; persistent copies can only be produced by thermal cycling.

**12/06/2017**

This paper argues that the problem of finding the first passage time of a stochastic process is equivalent to a sequential Bayesian inference problem. It then uses approximations to efficiently calculate the first passage time distribution.

This works shows the design of a strand displacement gate that can be regenerated through the consumption of fuel molecules of DNA. The concept is extended to the implementation of two boolean gates using on this motif. It should be noted that enthalpic and entropic components of the reactions have different weights in each direction, and that the regeneration reactions must have different kinetic orders in order to allow proper activation.

Two papers that aim to mimic some of the most remarkable biomolecular machines - powered rotary motors. In the first paper, the construct a freely-rotating axle from DNA, but do not power its motion. In the second case, the authors are able to set the rotational angle of one piece of DNA with repect ot the other. However, the system does not possess a truly free axle and consistent motion in a specific direction is not possible.

**26/05/2017**

The authors discuss the minimum rate at which energy must be supplied to maintain a non-equilibrium steady state in a discreet state Markov chain. It is the rate at which the system relaxes back towards equilibrium in the absence of the control.

This paper features the development of a recombinased-based framework for gene circuits design for synthethic biology. It must be remarked that this framework allows incredibly robust designs with little need for optimization, reduction of transcriptional layers as well as real time reprogrammability using CRISPR-Cas9 systems.

Recent work has suggested that heat engines operating between two temperature reservoirs can approach the limiting Carnot efficiency at finite power. This work argues that doing so is associated with a growing variance in the output power from one point in time to another.

An analysis of the time taken to reach a certain threshold concentration in some biological systems. This time is less variable if the threshold is compared to an integral of concentrations over time, rather than instantaneous concentrations.

**11/05/2017**

Encoding a classification problem into DNA molecules.

A review of the possibilities of using computing architectures built from components that are not themselves Turing complete.

The authors present an approach for calculating the relative values of factorial moments for stochastic Chemical Reaction Networks in the steady state. Factorial moments are quantities related to means and variances of chemical populations.

By applying the recently-derived thermodynamic uncertainty relation, the authors find a bound on the efficiency of molecular motors that depends purely on observible quantities like the average velocity and diffusion constant.

**27/04/2017**

A new mechanism for controlling of DNA strand displacement with regulator strands.

**23/03/2017**

Calculating the information passed by a signalling system. This work, by considering simple gaussian fluctuations, is able to analyse the information between entire trajectories, rather than just the instantaneous information.

Certain types of probability distribution can be marginalised through an algorithm known as message passing. This paper discusses how to implement chemical reactions that achieve such a goal.

A proposal to implement an unconventional computing architecture in which the inherent stochasticity of molecular processes is employed to simultaneously explore many possible solutions to a problem.

First in a series of papers that explore the connection between the entropy generation around a cycle of molecular states and the uncertainty in the number of cycles completed in a given time.

**16/02/2017**

Effective dissipation: Breaking time-reversal symmetry in driven microscopic energy transmission

An analysis of when a simple device for driving a particle up a step is most dissipative.

Catalysis in reaction networks

Proof that in weakly reversible reaction networks that don't involve catalysis, it is impossible for the concentration of any subset of species to tend asymptotically to zero.

# Towards a DNA Nanoprocessor: Reusable Tile-Integrated DNA Circuits

An implementation of DNA-based logic gates that can be incorporated into a small DNA tile.

An analysis of information exchange between multiple interacting systems.

An analysis of an experiment in which measurement and feedback allows photons from two competing beams to charge a capacitor (no charging occurs when photons are not measured). This paper discusses the case in which fluctuations of photon numbers in both beams are correlated, allowing more work extraction.

**02/02/2017**

Localised DNA strand displacement reactions for implementing logic in which a single signal can be branched into a multiple finite number of outputs.

A technique for analyzing the growth of polymers with multiple different constituent monomers, in which monomer addition/removal rates depend upon the neighbouring monomers.

Implementing a simple neuron using molecular reactions.

Implementing a learning algorithm using chemical reactions.

and

Icosahedral cages assembled from genetically modified proteins, with components produced and assembling in living E coli cells.

**19/01/2017**

Stochastic Analysis of Retroactivity in Transcriptional Networks through Singular Perturbation

An analysis of the restroactive effect on transcription factor abundance due to its interaction (and subsequent sequestration) with a downstream transcription site.

Information theory, predictability, and the emergence of complex life

Construction and analysis of a simple model in which the cost of being complex can be compensated by an increased ability to predict the environment.

A DNA kinetics competition strategy of hybridization chain reaction for molecular information processing circuit construction

A molecular circuit that responds not just to the presence of multiple signals, but distinguishes between signals in different orders.

An analysis of the costs of generating periodic behaviour in simple stochastic systems.

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