Monday 9 December 2019

Reading list from 2/12/2019:Cahos with no equilibrium, cellular supremacy, nanoclocks, and new ways to probe molecular systems

Dynamical behaviors of a chaotic system with no equilibria 
https://www.sciencedirect.com/journal/physics-letters-a/vol/376/issue/2

A relatively simple three-variable autonomous system of ordinary differential equations (ODEs) is presented, which, depending on the choice of the underlying parameters, displays zero, one or two stationary (equilibrium) points. Using Liapunov exponents, bifurcation diagrams and Poincare maps, the system is shown to display chaotic attractors, whose nature depends on the number of the underlying equilibria. In particular, the system displays a chaotic attractor even in the absence of equilibria.


Pathways to cellular supremacy in biocomputing
https://www.nature.com/articles/s41467-019-13232-z

In the present article, the authors try to settle a new perspective with regards synthetic biology by defining the notion of cellular supremacy as the  circumstance in which the implementation and execution of an algorithm would be tractable in a reasonable amount of time only in a cellular substrate rather than on a silicon microchip (akin to the notion of quantum supremacy). The authors acknowledge that analogies with the Boolean algebra logic underlying all digital computing have been used in biology since the time of Jacques Monod, but they argue that all cellular systems have a series of features (massive parallel exploration of all the space of solutions, use of stochasticity for synchronization and optimization of resources, analog signal treatment, concurrency of computational agents as well as the possibility of dealing with the increasing complexity of algorithms distributing them in cellular consortia) that put them far away from conventional computing paradigms and could lead the way to the aforementioned supremacy.


Bilingual Peptide Nucleic Acids: Encoding the Languages of Nucleic Acids and Proteins in a Single Self-Assembling Biopolymer
https://pubs.acs.org/doi/10.1021/jacs.9b09146

Peptide nucleic acids (PNA) are DNA/RNA mimic molecules comprising a sequence of nucleic acids joined by a peptide, rather than a de/oxyribose phosphate, backbone. PNA polymers acan exploit both the sequence-specific complementarity of the nucleotides as well as the complex chemistry of proteins. In this paper, PNA polymers were constructed with poly-peptide chain appendages, one half of which was hydrophobic and the other half hydrophilic. A fluorescent tag was attached to the hydrophobic end that increases in intensity in increasingly hydrophobic environments. The hydrophilic/phobic appendage drove the system of PNA molecules to self assemble into vesicles which, due to the accumulation of fluorophores in a hydrophobic region, had high fluorescence intensity at their centre. Upon addition of a disease-related RNA (the complement of the pre-designed PNA molecule's nucleotide sequence), binding between the PNA and the RNA destabilised the vesicles and disassembly was observed using TEM. This system brings together the highly directable chemistry of nucleotides and the structural versatility of proteins to create dynamical structures that can be triggered by their environment. The authors look to extend this system to generate many other tertiary structures using different polypeptide chains.


A rotary plasmonic nanoclock
https://www.nature.com/articles/s41467-019-13444-3
DNA-origami structures can be conjugated with metallic nanoparticles to localize them at defined positions to produce specific photoelectric effects. However, current structures are static or can only alternate between two states. This paper introduces a conjugated DNA structure that resembles a clock. The hands of this nanoclock are formed by a gold nanorod that can rotate 360 degrees with respect to an static gold nanorod. The different degrees of the rod rotation are determined by arbitrary binding points in the DNA structure and by the addition of specific strands in the solution.


A multiplexed, electrochemical interface for gene-circuit-based sensors
https://www.nature.com/articles/s41557-019-0366-y
This paper describes the first electrochemical interface that allows expanded multiplexed reporting for cell-free gene-circuit-based sensors. The authors were able to activate gene circuits using DNA nanostructured microelectrodes as electrochemical detectors. This approach uses toehold switch-based RNA sensors, which, in the presence of corresponding trigger RNA, express one of ten restriction-enzyme-based reporters to catalyse the release of specific reporter DNA. This single-stranded DNA can interact with its complementary ssDNA that is conjugated to the electronic surface. A redox reporter molecule attached to the reporter DNA is close enough to an electrode surface to produce generate an electrochemical signal. Thus, each toehold switch is engineered to produce a unique restriction-enzyme-based reporter that is coupled to a distinct reporter DNA and capture DNA pair for multiplexed signalling. The authors demonstrated with this work the power of the electrochemical interface by detecting the activation of specific toehold switch-based RNA sensors allowing to distinct and multiplexed signals to operate without crosstalk.


Thermodynamics guided strand-displacement-based DNA probe for determination of the average methylation levels of multiple CpG sites
https://pubs.acs.org/doi/10.1021/acs.analchem.9b03198
The authors measured the average degree of methylation using a mismatch-driven shift in the output of strand-displacement reactions. The substrate DNA was amplified with bisulfite PCR which changes non-methylated T base into A base which creates mismatches that participate in the strand displacement process.

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.

Friday 21 June 2019


The Problem With Copying
Jenny Poulton

The system successfully demonstrated in the recent PNAS paper “Litters of self-replicating origami cross tiles” is impressive, but it doesn’t address two key challenges with building fully-functional autonomous Darwinian replicators.

Copying is a process ubiquitous in nature, and indeed the accurate transmission of information from the molecular sequence of one  polymer to another is the core process at the heart of the central dogma of molecular biology. Our best understanding of origin-of-life scenarios is that of simple chain molecules  that are able to produce new copies of themselves that carry the same sequence of constituent units: minimal self-replicators. If these molecules  increase in population exponentially, it allows for Darwinian competition and evolution. Synthesising a successful copying process is a non-trivial task problem which many groups, including that of Braun, Schulman and Otto, have come up with interesting solutions to.


The core issue with creating a copying process can be illustrated as follows. In order for an object to be reasonably defined as a copy of a template, it needs to 1) have a sequence that matches, or correlates with, thetemplate and 2) exist separately from the template. In nature, correlations between copy and template are encouraged by bond specificity, with “matching” bonds being much stronger than unmatched bonds. If we consider a simple system, as in figure 1, this allows the settling on the template at stages 1 and 2. However, these same bonds which encourage accuracy in stages 1 and 2, discourage separation in stage 4. It is very difficult to create a system which successfully manages both of these processes.

Professor Seeman’s new paper follows on from the group’s previous work: “Exponential growth and selection in self-replicating materials from DNA origami rafts”. In the earlier paper, the group design rafts of DNA origami, which are highly programmable, meaning that sticky ends can be designed to encourage matching at stages 1 and 2. DNA origami can also be designed to have bonds which are activated via UV light, and in this system, these are used to create the backbone bonds of the dimers; so that at stage 3, the backbone bonds are created irreversibly. Once this process has been designed, stages 1 and 2 can be achieved through cooling, and stage 4 by heating. The heating at stage 4 does not run the risk of blowing apart the dimers, because of the strong UV activated backbone bonds. This somewhat bypasses the major challenge of replication. This system manages a growth factor of 1.7, with each dimer becoming on average 1.7 dimers at the end of a cycle.



The new paper improves on this system by allowing multiple layers of dimers to be formed in one cycle by increasing the number of sticky ends per monomer to two, figure 2 illustrates this difference. With this setup, the system achieves a growth factor of 4-8.

This achievement is very impressive, but let’s consider which interesting questions about copying that this system answers. This system is profoundly non autonomous, with successive cycles of heating, UV activation and cooling rendering human intervention inevitable. One of the most interesting scenarios of self-replication is the origin of life. By bypassing the issue of creating a system which needs to both have accuracy enhancing copy template interactions, and separation of copy and template, this system ignores the question of  the conditions under which spontaneous self-replication could develop without intervention. Speculation on plausible scenarios can be instructive;  heating/cooling or wetting/drying cycles seem plausible, but Seeman’s cycle seems too complex and contrived to occur naturally.  As an example of someone who uses a plausible cycle, the work of Dieter Braun considers a temperature gradient across a capillary, encouraging thermal cycling. Because there is no external creation of an unbreakable backbone bond, the bond strengths and relative temperatures in the gradient need to be extremely finely tuned. The accumulation of polymers in this system is a genuine breakthrough in our understanding of a plausible origin of life scenario, as it gives us important information on the nature of the chemical building blocks of self replicator. We then come to the next, arguably more complex question: how can we create a system driven purely by chemistry, without any changes in the environment needed at all? Our cells do this by means of enzymes, but are there other ways, and how could they have evolved from the semi-autonomous setting with the cyclic background conditions?

Returning to the Seeman’s paper, to what extent can the system developed be truly considered copying? The mechanism is that there are AA and BB dimers which catalyse the formation of each other. An AA dimer can only create a BB dimer and vice versa. It is difficult to see how the system is generalizable to one in which one arbitrary information is propagated.  In this system, while it is possible for this system to fail to create a dimer during a cycle, the propagation of information is reduced whether an object is created or not. In this system there can be no error propagation because in the event that the object is not created, it cannot then duplicate. The fact that the system is creating dimers only means that you can exactly design the origami rafts so that they are both “end pieces”, with no probability that the system could produce polymers of alternative lengths. If the system was successfully producing trimers, like the work of Otto, then there would be a pool of “centre pieces”. Successfully designing a system which accurately incorporated the correct number of “centre pieces” relative to the template would be a much more sophisticated and generalisable information transfer, with the information being transferred being the length of the polymer.



So what questions does this system answer? The major claim of this paper is that the incorporation of the ability to increase the number of offsprings per cycle would make systems of this nature more evolutionarily competitive. While this is true, another vital component of a system’s competitiveness is its ability to self-replicate autonomously in a naturally occurring environment. It should be noted that the more offsprings per cycle, the more difficult the tradeoff between accuracy and separation would become. While the UV activated bond is clever, it allows the authors to sidestep this issue, and therefore ignore many subtleties about the issues with copying.


Monday 4 March 2019

Ribosomes and traffic jams

Blog post by Jordan Juritz

What do rush-hour traffic jams have to do with protein production? As we are all quite familiar with,  congestion arises and the overall flow rate of cars decreases when many vehicles travel on a relatively small number of routes. In “Networks of ribosome flow models for modelling and analyzing intracellular traffic”, Nanikashvili et al. present a model that describes this same phenomenon during protein translation.

The ribosome is the molecular machine responsible for piecing together amino acids to form proteins. mRNA, a long polymer molecule, serves as the working blueprint for the protein. The order in which the amino acids are added is encoded in the sequence of nucleotides on the mRNA. Much like a car on a road, the ribosome binds around the mRNA, and proceeds to synthesise the protein as it steps along the mRNA molecule, reading its instructions from the mRNA as it goes.

A typical yeast cell contains about 60,000 mRNA molecules and about 240,000 ribosomes at any given moment. Space is tight, and the competition for mRNA among ribosomes is very high. As a result, it is expected that there will be multiple ribosomes translating a single mRNA at any one time.
The authors of this paper have employed a network of “ribosome flow models with inputs and outputs (RFMIO)” to describe the precession of the ribosomes through this highly congested system. 

A single RFMIO describes the dynamics of the probability density of ribosomes along a region of mRNA that encodes for a single protein. A single RFMIO describes the progression of a ribosome along a single section of protein-encoding mRNA. Within each RFMIO, the progression of the ribosome is bundled into an arbitrary number of steps. These steps can be fast or slow depending on the depending on the shape of the mRNA (is it straight or bundled up?) or the availability of the required resources, such as tRNAs. Therefore, the authors assign a unique rate to the transition between one step and the next, but only ever permit ribosomes to flow in the forward direction, just as cars can only drive one way down one side of the motorway. Cars travel much more slowly if there are many more cars bunched up ahead of them. Accordingly, in RFMIO models the flow of ribosomes to the next step is high (low) if the next state is free (full).

A single protein is produced once a ribosome has reached the end of an encoding region of mRNA, therefore, the outflow of ribosomes in an RFMIO model is interpreted as the protein production rate. Once a ribosome has reached the end of a single gene on an mRNA, it can stay attached to the mRNA to continue to translate another gene, or it can detach and diffuse back into solution.

The authors proved that after a long time has elapsed the probability distribution of ribosomes within a single RFMIO settles to a steady value. In this steady state, ribosomes produce proteins at a fixed, average rate. However, we know that living systems contain not just one, but many genes. Therefore, the authors considered networks of RFMIOs that enable ribosomes to be shared or recycled by many different genes. The authors proved that for arbitrary interconnection strengths the probability density of ribosomes still converges to a steady state across many different RFMIOs. As a result, many different proteins can be produced at steady rates, the ratios of which are determined by the strength and structure of the network. Crucially, outputs such as the total production rate or ribosome recycling rate are often convex functions of the interconnection parameters. The property of convexity implies that there exists an optimal protein production value that can be found easily (using efficient algorithms) even when the network of RFMIOs becomes very large. It’s like finding the highest point in a country with only one hill.

How do traffic jams arise in these systems? The figure below shows a simple network of two RFMIO connected in series. Both RFMIOs are arbitrarily made up of 3 internal substeps. In the first RFMIO, the rate at which ribosomes flow from internal step 2 to internal step 3 has been chosen to be very slow. As indicated in the corresponding graph, the probability densities after this bottle-neck are much lower than they were before, indicating a ribosome traffic jam has occurred in RFMIO 1! RFMIO 2 takes its input of ribosomes directly from RFMIO 1, therefore the slow transition in the first system has a long-range effect on the probability distribution and production rate of the second system. The implication of this is that, in the case that two genes are present on the same transcript mRNA, a bottle-neck in the ribosome flow on the first gene would reduce the production rate of the second protein. 

Figure 1: A series of RMIOs. A bottleneck in the first RFMIO causes a low turnover of proteins in the second RFMIO.

This model can be used to do more than just simulate biological traffic jams. Consider the network of parallel RFMIOs shown in Figure 2. These two RFMIOs represent two genes that compete for a common pool of ribosomes, with a proportion “v” going into RFMIO 1 and proportion “1-v” going into RFMIO 2. “v” represents the binding strength of ribosomes with the starting point of the gene represented by RFMIO 1. This model can be solved to find the binding strengths that optimise the combined protein production rate, “y”. This class of models can be used to aid the design of synthetic biological circuits to tune the production rates of the system.


Figure 2: Two RFMIOs in parallel. The pair of systems compete for a share of the total ribosome pool. The protein production rate is maximised for the most efficient resource allocation.

An understanding of the properties of flowing traffic helps engineers to design more efficient transport systems, and the same is true for engineering projects within the cell. Bioengineers employ modelling techniques, such as these networks of RFMIOs, to aid in the design of smarter, more efficient nano-machines and biological systems. Bioengineering can give rise to novel medicines and technologies, and it helps us to understand just a little bit more about how nature solved these tricky problems in the first place.


Figure 3: A complex genetic regulatory pathway, introducing metabolites and enzyme concentrations. This system can be described by RFMIOs.

References:
    Nanikashvili, I., Zarai, Y., Ovseevich, A., Tuller, T., & Margaliot, M. (2019). Networks of ribosome flow models for modeling and analyzing intracellular traffic. Scientific Reports, 9(1), 1703. https://doi.org/10.1038/s41598-018-37864-1