Monday 25 November 2019

Reading list from 18/11/2019: fluctuation relations and some novel nucleic acid nanotech

Independent control of the thermodynamic and kinetic properties of aptamer switches
https://www.nature.com/articles/s41467-019-13137-x
Aptamers are nucleic acids strands that, by adapting a particular conformation, are able to selectively bind a sepecific molecule. The present paper proposes to modfiy the kinetics and equilbrium response of aptamers by enclosing them within a hairpin. The hairpin stem consists of a sequence of variable length, complementary to the aptamer, and linked to it by a inert poly-T linker. The length of the stem and linker provide two independent ways to tune the kinetics, response and background produced by the aptamers.

Programming molecular topologies from single-stranded nucleic acids
https://www.nature.com/articles/s41467-019-09953-w.pdf
The objective of this work is to demonstrate that the CRISPR system can be used for RNA-based gene regulation thanks to toehold-mediated strand displacement reactions. This system depends on a guide RNA that can bind to a CRISPR-associated protein. Then, the authors designed an artificial guide RNA in which binding of the protein is suppressed by occluding the handle domain of the gRNA. Only when a complementary RNA trigger molecule is expressed, the occluding domain is unfolded via toehold-mediated strand displacement. This facilitates the Cas protein binding and processing of the gRNA. With this work, it is demonstrated that strand displacement reactions can be implemented in living cells for many applications such as molecular computing, sensing, and control of bacterial gene expression.

Programmable DNA nanoindicator-based platform for Large-Scale Square Root Logic Biocomputing
https://onlinelibrary.wiley.com/doi/epdf/10.1002/smll.201903489
In the present paper, a new architecture for DNA computing in which using two types of DNA species are used: 5 3-stranded complexes that generate the different fluorescense output signals and 14 input species that are able to interact with each other, thus producing 30 different binary signals given by the same number of combinations of inputs. With this architechture, the authors are able to produce a classifier in which they code an algorithm that is able to calculate the square root of a 10-bit number being (larger than the 4 bit number that was demonstrated with the seesaw-gate-based architectures). The design requires very few species, although the new implementation relies in a higher level abstraction for the implementation with the limitations that this entails.

Thermodynamic uncertainty relations constrain non-equilibrium fluctuations
https://www.nature.com/articles/s41567-019-0702-6
A perspective on the origins and uses of a class of non-equilibrium fluctuation relations called "thermodynamic uncertainty relations". The tools of equilibrium thermodynamics enable us to calculate the properties of large equilibrium systems, circumventing any equations of motion, or other dynamical equations. These tools break down as systems are brought out of equilibrium. In non-equilibrium systems, fluctuations in observables of the system can be large (due to small system size, or external driving, perhaps). New (last 20-15 yrs) tools, called 'fluctuation theorems', can be used to calculate constraints that bound the size of these fluctuations by exploiting various symmetry arguments that hold in steady states that are out of equilibrium. The symmetries are features of the coupling between the non-equilibrium system and a large equilibrium thermodynamic reservoir (of heat, particles, charge etc.). Here, a fluctuation in the non-equilibrium system must be coupled to a near-equilibrium complementing fluctuation in the equilibrium bath, the properties of which can be calculated.

Thermodynamic uncertainty relations are the result of asking how currents (of charge, mass, chemical species, entropy) fluctuate in non-equilibrium steady states. The symmetries that underlie the exchange between the non-equilibrium system and the reservoir can be used to show that ratio of the variance of the integrated current to its mean value squared in a given time period is bounded from below by 1/(The entropy produced in the reservoir) in that time period. The authors go on to provide some examples and applications, they discuss the long-time limit of these results, and emphasise that there is much more work to be done to generalise and extend these relations. They note that constructing some hierarchy of fluctuation theorems/ relations may be beneficial in guiding the field toward unified principles.

Kinetic Proofreading and the Limits of Thermodynamic Uncertainty
https://arxiv.org/abs/1911.04673
The authors apply a thermodynamic uncertainty relation, of the type discussed above, to models of kinetic proofreading during copying via templated polymerisation. They explore system behaviour, but never really tackle the issue that thermodynamic uncertainty relations bound the predictability of the number of steps in a given time, not the accuracy with which copies are made.

Antithetic integral feedback control of monostable and oscillatory biomolecular circuits
https://www.biorxiv.org/content/10.1101/838748v1
The paper applies a mathematical method, called dominance analysis, in order to analyse the deterministic dynamics of the antithetic integral feedback controller (AIC - a molecular circuit designed to control the level of another molecular species). Dominance analysis is applied on a linear and a non-linear input network, both controlled with AIC. For fixed regions of the state-space, it has been numerically verified that AIC can give rise to stable equilibria and stable limit cycles, depending on the choice of the underlying rate coefficients.

Sunday 10 November 2019

Reading list from 4/11/2019 - loads in molecular circuits, quantum systems as Markov processes, and much more

The Effect of Loads in Molecular Communications
https://ieeexplore.ieee.org/abstract/document/8721451
In the present paper from the Del Vecchio lab, the authors expose retroactivity as the main cause that accounts for the breakdown of modularity in biomolecular circuits, defining two different types of retroactivity in biomolecular systems (the one due of the sequestration of a protein of a circuit by a downstream protein/module and the one corresponding to the burden to the common pool of resources that a new component poses to the system, being this type one that appears even if the modules of a network are not connected). The paper details a number of useful tools to account mathematically for these phenomena (including a set of rules to translate burden retroactivity into internal interaction equivalent edges of a network and a biochemical equivalent to Thevenin theorem that allows us to study whole circuits as a single black box with an output). It also highights design strategies to limit the effect of retroactivity (use of insulator motifs in local interactions and implementation of negative feedback loops for attenuating the burden-based retroactivity).


Incompatibility of the Schrödinger equation with Langevin and Fokker-Planck equations 
https://link.springer.com/article/10.1007/BF02059525
Quantum mechanics posits that the wave function of a one-particle system evolves with time according to the Schrödinger equation, and furthermore has a square modulus that serves as a probability density function for the position of the particle. It is natural to wonder if this stochastic characterization of the particle's position can be framed as a univariate continuous Markov process, sometimes also called a classical diffusion process, whose temporal evolution is governed by the classically transparent equations of Langevin and Fokker-Planck. It is shown here that this cannot generally be done in a consistent way, despite recent suggestions to the contrary.


A universal biomolecular integral feedback controller for robust perfect adaptation

The authors demonstrate the application of their antithetic integral controller (AIC) to fix the levels of certain proteins in E coli, and provide theoretical results showing that the AIC is, in some sense, a minimal molecular integral feedback controller. 

The experimental results are undeniably impressive, but perhaps gloss over a number of subtleties. In particular, the underlying reactions show some important differences with respect to the ideal reaction equations of the AIC, and not all aspects of this are clearly addressed. In addition, the perturbation is necessarily of a particular kind in order for the control to work.


Weight-agnostic neural networks
The authors explore the idea of creating artificial neural network structures with topologies suitable for a problem without explicit weight training. The networks are evolved from a set of minimal networks by adding random connections, nodes, and activation functions, and selecting the best performing networks for further evolution. The performance is measured by sampling a shared weight from a uniform distribution for all network connections and averaged over multiple samples.

The networks are tested on continuous control tasks as well as multi-label classification. In control tasks, the architectures outperform a fixed topology for random, random shared, and tuned shared weights and achieve comparable performance with fine-tuned weights. For classification, random shared weights result in equal performance to linear regression.

None of the results are close to any state-of-the-art performance but the general idea is interesting and might be useful in designing computational networks in settings where the ability to tune weights is limited.


Magnetic quadrupole assemblies with arbitrary shapes and magnetizations
Unlike magnetic dipole particles that can only assembled into 2D chain structures, magnetic quadrupole particles have potential to be assembled into arbitrary 2D patterns. By placing two magnetic particles in 3D-printed square case, a magnetic quadrupole was assembled with small residual dipole moment that allows final 2D patterns to align with external magnetic field with specific angle.


DNA-Mediated Proximity-Based Assembly Circuit for Actuation of Biochemical Reactions
DNA strand displacement allows he design of complex networks capable of producing exotic dynamics. However, the toolbox for output transducer is still quite limited. In the present paper, Won Oh et al. demonstrate the experimental viability of a new transducer method: Enzyme/Cofactor co-localization. The method consists of  and invader and target strands functionalised with an enzyme and an enzymatic cofactor, respectively. During the system initial state, the cofactor is hidden inside a hairpin to avoid the interaction between enzyme and cofactor,  cancelling the enzymatic activity.

In the described system the enzyme is bound to a DNA sequence complementary to the target enzyme containing the cofactor. After the DNA system is triggered by a defined input, the enzyme-functionalised strand is able to form a duplex with the cofactor strand, co-localizing both molecules. The catalytic activity after the co-localization increases up to 110-fold from the initial activity for the tested enzyme (Glucose-6-phosphate deshydrogenase) producing a discernible signal.

This new transduction method will allow to further increase the capabilities of DNA logic circuits to regulate in a direct way molecular processes, outside and inside living systems.