The cell cycle switch computes approximate majority

Abstraction-based segmental simulation of reaction networks using adaptive memoization

BACKGROUND

 Stochastic models are commonly employed in the system and synthetic biology to study the effects of stochastic fluctuations emanating from reactions involving species with low copy-numbers. Many important models feature complex dynamics, involving a state-space explosion, stiffness, and multimodality, that complicate the quantitative analysis needed to understand their stochastic behavior. Direct numerical analysis of such models is typically not feasible and generating many simulation runs that adequately approximate the model's dynamics may take a prohibitively long time.

RESULTS

 We propose a new memoization technique that leverages a population-based abstraction and combines previously generated parts of simulations, called segments, to generate new simulations more efficiently while preserving the original system's dynamics and its diversity. Our algorithm adapts online to identify the most important abstract states and thus utilizes the available memory efficiently.

CONCLUSION

 We demonstrate that in combination with a novel fully automatic and adaptive hybrid simulation scheme, we can speed up the generation of trajectories significantly and correctly predict the transient behavior of complex stochastic systems.

There's Plenty of Room Right Here: Biological Systems as Evolved, Overloaded, Multi-Scale Machines

The applicability of computational models to the biological world is an active topic of debate. We argue that a useful path forward results from abandoning hard boundaries between categories and adopting an observer-dependent, pragmatic view. Such a view dissolves the contingent dichotomies driven by human cognitive biases (e.g., a tendency to oversimplify) and prior technological limitations in favor of a more continuous view, necessitated by the study of evolution, developmental biology, and intelligent machines. Form and function are tightly entwined in nature, and in some cases, in robotics as well. Thus, efforts to re-shape living systems for biomedical or bioengineering purposes require prediction and control of their function at multiple scales. This is challenging for many reasons, one of which is that living systems perform multiple functions in the same place at the same time. We refer to this as "polycomputing"-the ability of the same substrate to simultaneously compute different things, and make those computational results available to different observers. This ability is an important way in which living things are a kind of computer, but not the familiar, linear, deterministic kind; rather, living things are computers in the broad sense of their computational materials, as reported in the rapidly growing physical computing literature. We argue that an observer-centered framework for the computations performed by evolved and designed systems will improve the understanding of mesoscale events, as it has already done at quantum and relativistic scales. To develop our understanding of how life performs polycomputing, and how it can be convinced to alter one or more of those functions, we can first create technologies that polycompute and learn how to alter their functions. Here, we review examples of biological and technological polycomputing, and develop the idea that the overloading of different functions on the same hardware is an important design principle that helps to understand and build both evolved and designed systems. Learning to hack existing polycomputing substrates, as well as to evolve and design new ones, will have massive impacts on regenerative medicine, robotics, and computer engineering.

Operant conditioning of stochastic chemical reaction networks

Adapting one's behavior to environmental conditions and past experience is a key trait of living systems. In the biological world, there is evidence for adaptive behaviors such as learning even in naturally occurring, non-neural, single-celled organisms. In the bioengineered world, advances in synthetic cell engineering and biorobotics have created the possibility of implementing lifelike systems engineered from the bottom up. This will require the development of programmable control circuitry for such biomimetic systems that is capable of realizing such non-trivial and adaptive behavior, including modification of subsequent behavior in response to environmental feedback. To this end, we report the design of novel stochastic chemical reaction networks capable of probabilistic decision-making in response to stimuli. We show that a simple chemical reaction network motif can be tuned to produce arbitrary decision probabilities when choosing between two or more responses to a stimulus signal. We further show that simple feedback mechanisms from the environment can modify these probabilities over time, enabling the system to adapt its behavior dynamically in response to positive or negative reinforcement based on its decisions. This system thus acts as a form of operant conditioning of the chemical circuit, in the sense that feedback provided based on decisions taken by the circuit form the basis of the learning process. Our work thus demonstrates that simple chemical systems can be used to implement lifelike behavior in engineered biomimetic systems.

Robust finite automata in stochastic chemical reaction networks

Finite-state automata (FSA) are simple computational devices that can nevertheless illustrate interesting behaviours. We propose that FSA can be employed as control circuits for engineered stochastic biological and biomolecular systems. We present an implementation of FSA using counts of chemical species in the range of hundreds to thousands, which is relevant for the counts of many key molecules such as mRNAs in prokaryotic cells. The challenge here is to ensure a robust representation of the current state in the face of stochastic noise. We achieve this by using a multistable approximate majority algorithm to stabilize and store the current state of the system. Arbitrary finite state machines can thus be compiled into robust stochastic chemical automata. We present two variants: one that consumes its input signals to initiate state transitions and one that does not. We characterize the state change dynamics of these systems and demonstrate their application to solve the four-bit binary square root problem. Our work lays the foundation for the use of chemical automata as control circuits in bioengineered systems and biorobotics.

The role of memory in non-genetic inheritance and its impact on cancer treatment resistance

Intra-tumour heterogeneity is a leading cause of treatment failure and disease progression in cancer. While genetic mutations have long been accepted as a primary mechanism of generating this heterogeneity, the role of phenotypic plasticity is becoming increasingly apparent as a driver of intra-tumour heterogeneity. Consequently, understanding the role of this plasticity in treatment resistance and failure is a key component of improving cancer therapy. We develop a mathematical model of stochastic phenotype switching that tracks the evolution of drug-sensitive and drug-tolerant subpopulations to clarify the role of phenotype switching on population growth rates and tumour persistence. By including cytotoxic therapy in the model, we show that, depending on the strategy of the drug-tolerant subpopulation, stochastic phenotype switching can lead to either transient or permanent drug resistance. We study the role of phenotypic heterogeneity in a drug-resistant, genetically homogeneous population of non-small cell lung cancer cells to derive a rational treatment schedule that drives population extinction and avoids competitive release of the drug-tolerant sub-population. This model-informed therapeutic schedule results in increased treatment efficacy when compared against periodic therapy, and, most importantly, sustained tumour decay without the development of resistance.

Communication cost of consensus for nodes with limited memory

Motivated by applications in wireless networks and the Internet of Things, we consider a model of n nodes trying to reach consensus with high probability on their majority bit. Each node i is assigned a bit at time 0 and is a finite automaton with m bits of memory (i.e., [Formula: see text] states) and a Poisson clock. When the clock of i rings, i can choose to communicate and is then matched to a uniformly chosen node j. The nodes j and i may update their states based on the state of the other node. Previous work has focused on minimizing the time to consensus and the probability of error, while our goal is minimizing the number of communications. We show that, when [Formula: see text], consensus can be reached with linear communication cost, but this is impossible if [Formula: see text] A key step is to distinguish when nodes can become aware of knowing the majority bit and stop communicating. We show that this is impossible if their memory is too low.

Consensus Dynamics

The term distributed system typically refers to a set of entities, called nodes, connected by point-topoint communication links. The set of nodes together with the set of links form a network, which is usually represented by a graph. The term ?system" is used to reflect the fact that nodes evolve over time, i.e., they change their internal states according to some local interaction-rule, which is applied in every time step (i.e. round).

Checking Qualitative Liveness Properties of Replicated Systems with Stochastic Scheduling

We present a sound and complete method for the verification of qualitative liveness properties of replicated systems under stochastic scheduling. These are systems consisting of a finite-state program, executed by an unknown number of indistinguishable agents, where the next agent to make a move is determined by the result of a random experiment. We show that if a property of such a system holds, then there is always a witness in the shape of a Presburger stage graph: a finite graph whose nodes are Presburger-definable sets of configurations. Due to the high complexity of the verification problem (non-elementary), we introduce an incomplete procedure for the construction of Presburger stage graphs, and implement it on top of an SMT solver. The procedure makes extensive use of the theory of well-quasi-orders, and of the structural theory of Petri nets and vector addition systems. We apply our results to a set of benchmarks, in particular to a large collection of population protocols, a model of distributed computation extensively studied by the distributed computing community.

Triggering mitosis

Entry into mitosis is triggered by the activation of cyclin-dependent kinase 1 (Cdk1). This simple reaction rapidly and irreversibly sets the cell up for division. Even though the core step in triggering mitosis is so simple, the regulation of this cellular switch is highly complex, involving a large number of interconnected signalling cascades. We do have a detailed knowledge of most of the components of this network, but only a poor understanding of how they work together to create a precise and robust system that ensures that mitosis is triggered at the right time and in an orderly fashion. In this review, we will give an overview of the literature that describes the Cdk1 activation network and then address questions relating to the systems biology of this switch. How is the timing of the trigger controlled? How is mitosis insulated from interphase? What determines the sequence of events, following the initial trigger of Cdk1 activation? Which elements ensure robustness in the timing and execution of the switch? How has this system been adapted to the high levels of replication stress in cancer cells?

Two Interlinked Bistable Switches Govern Mitotic Control in Mammalian Cells

Distinct protein phosphorylation levels in interphase and M phase require tight regulation of Cdk1 activity [1, 2]. A bistable switch, based on positive feedback in the Cdk1 activation loop, has been proposed to generate different thresholds for transitions between these cell-cycle states [3-5]. Recently, the activity of the major Cdk1-counteracting phosphatase, PP2A:B55, has also been found to be bistable due to Greatwall kinase-dependent regulation [6]. However, the interplay of the regulation of Cdk1 and PP2A:B55 in vivo remains unexplored. Here, we combine quantitative cell biology assays with mathematical modeling to explore the interplay of mitotic kinase activation and phosphatase inactivation in human cells. By measuring mitotic entry and exit thresholds using ATP-analog-sensitive Cdk1 mutants, we find evidence that the mitotic switch displays hysteresis and bistability, responding differentially to Cdk1 inhibition in the mitotic and interphase states. Cdk1 activation by Wee1/Cdc25 feedback loops and PP2A:B55 inactivation by Greatwall independently contributes to this hysteretic switch system. However, elimination of both Cdk1 and PP2A:B55 inactivation fully abrogates bistability, suggesting that hysteresis is an emergent property of mutual inhibition between the Cdk1 and PP2A:B55 feedback loops. Our model of the two interlinked feedback systems predicts an intermediate but hidden steady state between interphase and M phase. This could be verified experimentally by Cdk1 inhibition during mitotic entry, supporting the predictive value of our model. Furthermore, we demonstrate that dual inhibition of Wee1 and Gwl kinases causes loss of cell-cycle memory and synthetic lethality, which could be further exploited therapeutically.

Scaling up molecular pattern recognition with DNA-based winner-take-all neural networks

From bacteria following simple chemical gradients¹ to the brain distinguishing complex odour information², the ability to recognize molecular patterns is essential for biological organisms. This type of information-processing function has been implemented using DNA-based neural networks³, but has been limited to the recognition of a set of no more than four patterns, each composed of four distinct DNA molecules. Winner-take-all computation⁴ has been suggested^5,6 as a potential strategy for enhancing the capability of DNA-based neural networks. Compared to the linear-threshold circuits⁷ and Hopfield networks⁸ used previously³, winner-take-all circuits are computationally more powerful⁴, allow simpler molecular implementation and are not constrained by the number of patterns and their complexity, so both a large number of simple patterns and a small number of complex patterns can be recognized. Here we report a systematic implementation of winner-take-all neural networks based on DNA-strand-displacement^9,10 reactions. We use a previously developed seesaw DNA gate motif^3,11,12, extended to include a simple and robust component that facilitates the cooperative hybridization¹³ that is involved in the process of selecting a 'winner'. We show that with this extended seesaw motif DNA-based neural networks can classify patterns into up to nine categories. Each of these patterns consists of 20 distinct DNA molecules chosen from the set of 100 that represents the 100 bits in 10 × 10 patterns, with the 20 DNA molecules selected tracing one of the handwritten digits '1' to '9'. The network successfully classified test patterns with up to 30 of the 100 bits flipped relative to the digit patterns 'remembered' during training, suggesting that molecular circuits can robustly accomplish the sophisticated task of classifying highly complex and noisy information on the basis of similarity to a memory.

Single molecules can operate as primitive biological sensors, switches and oscillators

Background

Switch-like and oscillatory dynamical systems are widely observed in biology. We investigate the simplest biological switch that is composed of a single molecule that can be autocatalytically converted between two opposing activity forms. We test how this simple network can keep its switching behaviour under perturbations in the system.

Results

We show that this molecule can work as a robust bistable system, even for alterations in the reactions that drive the switching between various conformations. We propose that this single molecule system could work as a primitive biological sensor and show by steady state analysis of a mathematical model of the system that it could switch between possible states for changes in environmental signals. Particularly, we show that a single molecule phosphorylation-dephosphorylation switch could work as a nucleotide or energy sensor. We also notice that a given set of reductions in the reaction network can lead to the emergence of oscillatory behaviour.

Conclusions

We propose that evolution could have converted this switch into a single molecule oscillator, which could have been used as a primitive timekeeper. We discuss how the structure of the simplest known circadian clock regulatory system, found in cyanobacteria, resembles the proposed single molecule oscillator. Besides, we speculate if such minimal systems could have existed in an RNA world.

Electronic supplementary material

The online version of this article (10.1186/s12918-018-0596-4) contains supplementary material, which is available to authorized users.

Computing with biological switches and clocks

The complex dynamics of biological systems is primarily driven by molecular interactions that underpin the regulatory networks of cells. These networks typically contain positive and negative feedback loops, which are responsible for switch-like and oscillatory dynamics, respectively. Many computing systems rely on switches and clocks as computational modules. While the combination of such modules in biological systems leads to a variety of dynamical behaviours, it is also driving development of new computing algorithms. Here we present a historical perspective on computation by biological systems, with a focus on switches and clocks, and discuss parallels between biology and computing. We also outline our vision for the future of biological computing.

Exploring the emergence of complexity using synthetic replicators

A significant number of synthetic systems capable of replicating themselves or entities that are complementary to themselves have appeared in the last 30 years. Building on an understanding of the operation of synthetic replicators in isolation, this field has progressed to examples where catalytic relationships between replicators within the same network and the extant reaction conditions play a role in driving phenomena at the level of the whole system. Systems chemistry has played a pivotal role in the attempts to understand the origin of biological complexity by exploiting the power of synthetic chemistry, in conjunction with the molecular recognition toolkit pioneered by the field of supramolecular chemistry, thereby permitting the bottom-up engineering of increasingly complex reaction networks from simple building blocks. This review describes the advances facilitated by the systems chemistry approach in relating the expression of complex and emergent behaviour in networks of replicators with the connectivity and catalytic relationships inherent within them. These systems, examined within well-stirred batch reactors, represent conceptual and practical frameworks that can then be translated to conditions that permit replicating systems to overcome the fundamental limits imposed on selection processes in networks operating under closed conditions. This shift away from traditional spatially homogeneous reactors towards dynamic and non-equilibrium conditions, such as those provided by reaction-diffusion reaction formats, constitutes a key change that mimics environments within cellular systems, which possess obvious compartmentalisation and inhomogeneity.

Chemical reaction network designs for asynchronous logic circuits

Chemical reaction networks (CRNs) are a versatile language for describing the dynamical behaviour of chemical kinetics, capable of modelling a variety of digital and analogue processes. While CRN designs for synchronous sequential logic circuits have been proposed and their implementation in DNA demonstrated, a physical realisation of these devices is difficult because of their reliance on a clock. Asynchronous sequential logic, on the other hand, does not require a clock, and instead relies on handshaking protocols to ensure the temporal ordering of different phases of the computation. This paper provides novel CRN designs for the construction of asynchronous logic, arithmetic and control flow elements based on a bi-molecular reaction motif with catalytic reactions and uniform reaction rates. We model and validate the designs for the deterministic and stochastic semantics using Microsoft's GEC tool and the probabilistic model checker PRISM, demonstrating their ability to emulate the function of asynchronous components under low molecular count.

Programming discrete distributions with chemical reaction networks

We explore the range of probabilistic behaviours that can be engineered with Chemical Reaction Networks (CRNs). We give methods to "program" CRNs so that their steady state is chosen from some desired target distribution that has finite support in [Formula: see text], with [Formula: see text]. Moreover, any distribution with countable infinite support can be approximated with arbitrarily small error under the [Formula: see text] norm. We also give optimized schemes for special distributions, including the uniform distribution. Finally, we formulate a calculus to compute on distributions that is complete for finite support distributions, and can be compiled to a restricted class of CRNs that at steady state realize those distributions.

Interlinked bistable mechanisms generate robust mitotic transitions

The transitions between phases of the cell cycle have evolved to be robust and switch-like, which ensures temporal separation of DNA replication, sister chromatid separation, and cell division. Mathematical models describing the biochemical interaction networks of cell cycle regulators attribute these properties to underlying bistable switches, which inherently generate robust, switch-like, and irreversible transitions between states. We have recently presented new mathematical models for two control systems that regulate crucial transitions in the cell cycle: mitotic entry and exit, 1 and the mitotic checkpoint. 2 Each of the two control systems is characterized by two interlinked bistable switches. In the case of mitotic checkpoint control, these switches are mutually activating, whereas in the case of the mitotic entry/exit network, the switches are mutually inhibiting. In this Perspective we describe the qualitative features of these regulatory motifs and show that having two interlinked bistable mechanisms further enhances robustness and irreversibility. We speculate that these network motifs also underlie other cell cycle transitions and cellular transitions between distinct biochemical states.

Modelling the spread of innovation in wild birds

We apply three plausible algorithms in agent-based computer simulations to recent experiments on social learning in wild birds. Although some of the phenomena are simulated by all three learning algorithms, several manifestations of social conformity bias are simulated by only the approximate majority (AM) algorithm, which has roots in chemistry, molecular biology and theoretical computer science. The simulations generate testable predictions and provide several explanatory insights into the diffusion of innovation through a population. The AM algorithm's success raises the possibility of its usefulness in studying group dynamics more generally, in several different scientific domains. Our differential-equation model matches simulation results and provides mathematical insights into the dynamics of these algorithms.

Stochasticity in the Genotype-Phenotype Map: Implications for the Robustness and Persistence of Bet-Hedging

Nongenetic variation in phenotypes, or bet-hedging, has been observed as a driver of drug resistance in both bacterial infections and cancers. Here, we study how bet-hedging emerges in genotype-phenotype (GP) mapping through a simple interaction model: a molecular switch. We use simple chemical reaction networks to implement stochastic switches that map gene products to phenotypes, and investigate the impact of structurally distinct mappings on the evolution of phenotypic heterogeneity. Bet-hedging naturally emerges within this model, and is robust to evolutionary loss through mutations to both the expression of individual genes, and to the network itself. This robustness explains an apparent paradox of bet-hedging-why does it persist in environments where natural selection necessarily acts to remove it? The structure of the underlying molecular mechanism, itself subject to selection, can slow the evolutionary loss of bet-hedging to ensure a survival mechanism against environmental catastrophes even when they are rare. Critically, these properties, taken together, have profound implications for the use of treatment-holidays to combat bet-hedging-driven resistant disease, as the efficacy of breaks from treatment will ultimately be determined by the structure of the GP mapping.

Modular verification of chemical reaction network encodings via serializability analysis

Chemical reaction networks are a powerful means of specifying the intended behaviour of synthetic biochemical systems. A high-level formal specification, expressed as a chemical reaction network, may be compiled into a lower-level encoding, which can be directly implemented in wet chemistry and may itself be expressed as a chemical reaction network. Here we present conditions under which a lower-level encoding correctly emulates the sequential dynamics of a high-level chemical reaction network. We require that encodings are transactional, such that their execution is divided by a "commit reaction" that irreversibly separates the reactant-consuming phase of the encoding from the product-generating phase. We also impose restrictions on the sharing of species between reaction encodings, based on a notion of "extra tolerance", which defines species that may be shared between encodings without enabling unwanted reactions. Our notion of correctness is serializability of interleaved reaction encodings, and if all reaction encodings satisfy our correctness properties then we can infer that the global dynamics of the system are correct. This allows us to infer correctness of any system constructed using verified encodings. As an example, we show how this approach may be used to verify two- and four-domain DNA strand displacement encodings of chemical reaction networks, and we generalize our result to the limit where the populations of helper species are unlimited.

Noise Reduction in Complex Biological Switches

Cells operate in noisy molecular environments via complex regulatory networks. It is possible to understand how molecular counts are related to noise in specific networks, but it is not generally clear how noise relates to network complexity, because different levels of complexity also imply different overall number of molecules. For a fixed function, does increased network complexity reduce noise, beyond the mere increase of overall molecular counts? If so, complexity could provide an advantage counteracting the costs involved in maintaining larger networks. For that purpose, we investigate how noise affects multistable systems, where a small amount of noise could lead to very different outcomes; thus we turn to biochemical switches. Our method for comparing networks of different structure and complexity is to place them in conditions where they produce exactly the same deterministic function. We are then in a good position to compare their noise characteristics relatively to their identical deterministic traces. We show that more complex networks are better at coping with both intrinsic and extrinsic noise. Intrinsic noise tends to decrease with complexity, and extrinsic noise tends to have less impact. Our findings suggest a new role for increased complexity in biological networks, at parity of function.

Plasmid-derived DNA Strand Displacement Gates for Implementing Chemical Reaction Networks

DNA nanotechnology requires large amounts of highly pure DNA as an engineering material. Plasmid DNA could meet this need since it is replicated with high fidelity, is readily amplified through bacterial culture and can be stored indefinitely in the form of bacterial glycerol stocks. However, the double-stranded nature of plasmid DNA has so far hindered its efficient use for construction of DNA nanostructures or devices that typically contain single-stranded or branched domains. In recent work, it was found that nicked double stranded DNA (ndsDNA) strand displacement gates could be sourced from plasmid DNA. The following is a protocol that details how these ndsDNA gates can be efficiently encoded in plasmids and can be derived from the plasmids through a small number of enzymatic processing steps. Also given is a protocol for testing ndsDNA gates using fluorescence kinetics measurements. NdsDNA gates can be used to implement arbitrary chemical reaction networks (CRNs) and thus provide a pathway towards the use of the CRN formalism as a prescriptive molecular programming language. To demonstrate this technology, a multi-step reaction cascade with catalytic kinetics is constructed. Further it is shown that plasmid-derived components perform better than identical components assembled from synthetic DNA.

Neurospora crassa as a model organism to explore the interconnected network of the cell cycle and the circadian clock

Budding and fission yeast pioneered uncovering molecular mechanisms of eukaryotic cell division cycles. However, they do not possess canonical circadian clock machinery that regulates physiological processes with a period of about 24h. On the other hand, Neurospora crassa played a critical role in elucidating molecular mechanisms of circadian rhythms, but have not been utilized frequently for cell cycle studies. Recent findings demonstrate that there exists a conserved coupling between the cell cycle and the circadian clock from N.crassa to Mus musculus, which poses Neurospora as an ideal model organism to investigate molecular mechanisms and emerging behavior of the coupled network of the cell cycle and circadian rhythms. In this review, we briefly describe generic eukaryotic cell cycle regulation focusing on G1/S and G2/M transitions, and highlight that these transitions may be targeted for the circadian clock to influence timing of cell division cycles.

Morphisms of reaction networks that couple structure to function

BACKGROUND

The mechanisms underlying complex biological systems are routinely represented as networks. Network kinetics is widely studied, and so is the connection between network structure and behavior. However, similarity of mechanism is better revealed by relationships between network structures.

RESULTS

We define morphisms (mappings) between reaction networks that establish structural connections between them. Some morphisms imply kinetic similarity, and yet their properties can be checked statically on the structure of the networks. In particular we can determine statically that a complex network will emulate a simpler network: it will reproduce its kinetics for all corresponding choices of reaction rates and initial conditions. We use this property to relate the kinetics of many common biological networks of different sizes, also relating them to a fundamental population algorithm.

CONCLUSIONS

Structural similarity between reaction networks can be revealed by network morphisms, elucidating mechanistic and functional aspects of complex networks in terms of simpler networks.

The linear interplay of intrinsic and extrinsic noises ensures a high accuracy of cell fate selection in budding yeast

To gain insights into the mechanisms of cell fate decision in a noisy environment, the effects of intrinsic and extrinsic noises on cell fate are explored at the single cell level. Specifically, we theoretically define the impulse of Cln1/2 as an indication of cell fates. The strong dependence between the impulse of Cln1/2 and cell fates is exhibited. Based on the simulation results, we illustrate that increasing intrinsic fluctuations causes the parallel shift of the separation ratio of Whi5P but that increasing extrinsic fluctuations leads to the mixture of different cell fates. Our quantitative study also suggests that the strengths of intrinsic and extrinsic noises around an approximate linear model can ensure a high accuracy of cell fate selection. Furthermore, this study demonstrates that the selection of cell fates is an entropy-decreasing process. In addition, we reveal that cell fates are significantly correlated with the range of entropy decreases.

Phosphorelays provide tunable signal processing capabilities for the cell

Achieving a complete understanding of cellular signal transduction requires deciphering the relation between structural and biochemical features of a signaling system and the shape of the signal-response relationship it embeds. Using explicit analytical expressions and numerical simulations, we present here this relation for four-layered phosphorelays, which are signaling systems that are ubiquitous in prokaryotes and also found in lower eukaryotes and plants. We derive an analytical expression that relates the shape of the signal-response relationship in a relay to the kinetic rates of forward, reverse phosphorylation and hydrolysis reactions. This reveals a set of mathematical conditions which, when satisfied, dictate the shape of the signal-response relationship. We find that a specific topology also observed in nature can satisfy these conditions in such a way to allow plasticity among hyperbolic and sigmoidal signal-response relationships. Particularly, the shape of the signal-response relationship of this relay topology can be tuned by altering kinetic rates and total protein levels at different parts of the relay. These findings provide an important step towards predicting response dynamics of phosphorelays, and the nature of subsequent physiological responses that they mediate, solely from topological features and few composite measurements; measuring the ratio of reverse and forward phosphorylation rate constants could be sufficient to determine the shape of the signal-response relationship the relay exhibits. Furthermore, they highlight the potential ways in which selective pressures on signal processing could have played a role in the evolution of the observed structural and biochemical characteristic in phosphorelays.

Two-component phosphorelays constitute the key signaling pathways in all prokaryotes, lower eukaryotes, and plants, where they underline diverse physiological responses such as virulence, cell-cycle progression and sporulation. Despite such prevalence, our understanding of the dynamics and function of these systems remains incomplete. In particular, it is not clear why all phosphorelays studied to date embed a four-layer architecture and how their dynamics could relate to phenotypic variability in the resulting responses. Here, we use analytical approaches and numerical simulations to analyze all possible phosphorelay topologies of length four and embedding reverse phosphorylation. We find that only two topologies can embed both hyperbolic and sigmoidal signal-response relationships, and that one of these can underlie high noise (i.e. phenotypic variability) in population responses. All of the remaining topologies are either non-functional or can embed only a hyperbolic signal-response relationship. Using analytical solutions of relay dynamics, we find that reverse phosphorylation from the third layer, a topological featured commonly observed in nature, is a necessary condition for sigmoidal signal-response relationship.

Programmable chemical controllers made from DNA

Biological organisms use complex molecular networks to navigate their environment and regulate their internal state. The development of synthetic systems with similar capabilities could lead to applications such as smart therapeutics or fabrication methods based on self-organization. To achieve this, molecular control circuits need to be engineered to perform integrated sensing, computation and actuation. Here we report a DNA-based technology for implementing the computational core of such controllers. We use the formalism of chemical reaction networks as a 'programming language' and our DNA architecture can, in principle, implement any behaviour that can be mathematically expressed as such. Unlike logic circuits, our formulation naturally allows complex signal processing of intrinsically analogue biological and chemical inputs. Controller components can be derived from biologically synthesized (plasmid) DNA, which reduces errors associated with chemically synthesized DNA. We implement several building-block reaction types and then combine them into a network that realizes, at the molecular level, an algorithm used in distributed control systems for achieving consensus between multiple agents.

Dynamics of SIN asymmetry establishment

Timing of cell division is coordinated by the Septation Initiation Network (SIN) in fission yeast. SIN activation is initiated at the two spindle pole bodies (SPB) of the cell in metaphase, but only one of these SPBs contains an active SIN in anaphase, while SIN is inactivated in the other by the Cdc16-Byr4 GAP complex. Most of the factors that are needed for such asymmetry establishment have been already characterized, but we lack the molecular details that drive such quick asymmetric distribution of molecules at the two SPBs. Here we investigate the problem by computational modeling and, after establishing a minimal system with two antagonists that can drive reliable asymmetry establishment, we incorporate the current knowledge on the basic SIN regulators into an extended model with molecular details of the key regulators. The model can capture several peculiar earlier experimental findings and also predicts the behavior of double and triple SIN mutants. We experimentally tested one prediction, that phosphorylation of the scaffold protein Cdc11 by a SIN kinase and the core cell cycle regulatory Cyclin dependent kinase (Cdk) can compensate for mutations in the SIN inhibitor Cdc16 with different efficiencies. One aspect of the prediction failed, highlighting a potential hole in our current knowledge. Further experimental tests revealed that SIN induced Cdc11 phosphorylation might have two separate effects. We conclude that SIN asymmetry is established by the antagonistic interactions between SIN and its inhibitor Cdc16-Byr4, partially through the regulation of Cdc11 phosphorylation states.

Algorithmic modeling quantifies the complementary contribution of metabolic inhibitions to gemcitabine efficacy

Gemcitabine (2,2-difluorodeoxycytidine, dFdC) is a prodrug widely used for treating various carcinomas. Gemcitabine exerts its clinical effect by depleting the deoxyribonucleotide pools, and incorporating its triphosphate metabolite (dFdC-TP) into DNA, thereby inhibiting DNA synthesis. This process blocks the cell cycle in the early S phase, eventually resulting in apoptosis. The incorporation of gemcitabine into DNA takes place in competition with the natural nucleoside dCTP. The mechanisms of indirect competition between these cascades for common resources are given with the race for DNA incorporation; in clinical studies dedicated to singling out mechanisms of resistance, ribonucleotide reductase (RR) and deoxycytidine kinase (dCK) and human equilibrative nucleoside transporter1 (hENT1) have been associated to efficacy of gemcitabine with respect to their roles in the synthesis cascades of dFdC-TP and dCTP. However, the direct competition, which manifests itself in terms of inhibitions between these cascades, remains to be quantified. We propose an algorithmic model of gemcitabine mechanism of action, verified with respect to independent experimental data. We performed in silico experiments in different virtual conditions, otherwise difficult in vivo, to evaluate the contribution of the inhibitory mechanisms to gemcitabine efficacy. In agreement with the experimental data, our model indicates that the inhibitions due to the association of dCTP with dCK and the association of gemcitabine diphosphate metabolite (dFdC-DP) with RR play a key role in adjusting the efficacy. While the former tunes the catalysis of the rate-limiting first phosphorylation of dFdC, the latter is responsible for depletion of dCTP pools, thereby contributing to gemcitabine efficacy with a dependency on nucleoside transport efficiency. Our simulations predict the existence of a continuum of non-efficacy to high-efficacy regimes, where the levels of dFdC-TP and dCTP are coupled in a complementary manner, which can explain the resistance to this drug in some patients.

Deterministic Function Computation with Chemical Reaction Networks

Chemical reaction networks (CRNs) formally model chemistry in a well-mixed solution. CRNs are widely used to describe information processing occurring in natural cellular regulatory networks, and with upcoming advances in synthetic biology, CRNs are a promising language for the design of artificial molecular control circuitry. Nonetheless, despite the widespread use of CRNs in the natural sciences, the range of computational behaviors exhibited by CRNs is not well understood. CRNs have been shown to be efficiently Turing-universal (i.e., able to simulate arbitrary algorithms) when allowing for a small probability of error. CRNs that are guaranteed to converge on a correct answer, on the other hand, have been shown to decide only the semilinear predicates (a multi-dimensional generalization of "eventually periodic" sets). We introduce the notion of function, rather than predicate, computation by representing the output of a function f : ℕ k → ℕ l by a count of some molecular species, i.e., if the CRN starts with x1, …, xk molecules of some "input" species X1, …, Xk , the CRN is guaranteed to converge to having f(x1, …, xk ) molecules of the "output" species Y1, …, Yl . We show that a function f : ℕ k → ℕ l is deterministically computed by a CRN if and only if its graph {(x, y) ∈ ℕ k × ℕ l ∣ f(x) = y} is a semilinear set. Finally, we show that each semilinear function f (a function whose graph is a semilinear set) can be computed by a CRN on input x in expected time O(polylog ∥x∥1).