Immunosuppressive Traits of the Hybrid Epithelial/Mesenchymal Phenotype

Recent preclinical and clinical data suggests enhanced metastatic fitness of hybrid epithelial/mesenchymal (E/M) phenotypes, but mechanistic details regarding their survival strategies during metastasis remain unclear. Here, we investigate immune-evasive strategies of hybrid E/M states. We construct and simulate the dynamics of a minimalistic regulatory network encompassing the known associations among regulators of EMT (epithelial-mesenchymal transition) and PD-L1, an established immune-suppressor. Our simulations for the network consisting of SLUG, ZEB1, miR-200, CDH1 and PD-L1, integrated with single-cell and bulk RNA-seq data analysis, elucidate that hybrid E/M cells can have high levels of PD-L1, similar to those seen in cells with a full EMT phenotype, thus obviating the need for cancer cells to undergo a full EMT to be immune-evasive. Specifically, in breast cancer, we show the co-existence of hybrid E/M phenotypes, enhanced resistance to anti-estrogen therapy and increased PD-L1 levels. Our results underscore how the emergent dynamics of interconnected regulatory networks can coordinate different axes of cellular fitness during metastasis.

Third party stabilization of unstable coordination in systems of coupled oscillators

The Haken-Kelso-Bunz (HKB) system of equations is a well-developed model for dyadic rhythmic coordination in biological systems. It captures ubiquitous empirical observations of bistability - the coexistence of in-phase and antiphase motion - in neural, behavioral, and social coordination. Recent work by Zhang and colleagues has generalized HKB to many oscillators to account for new empirical phenomena observed in multiagent interaction. Utilising this generalization, the present work examines how the coordination dynamics of a pair of oscillators can be augmented by virtue of their coupling to a third oscillator. We show that stable antiphase coordination emerges in pairs of oscillators even when their coupling parameters would have prohibited such coordination in their dyadic relation. We envision two lines of application for this theoretical work. In the social sciences, our model points toward the development of intervention strategies to support coordination behavior in heterogeneous groups (for instance in gerontology, when younger and older individuals interact). In neuroscience, our model will advance our understanding of how the direct functional connection of mesoscale or microscale neural ensembles might be switched by their changing coupling to other neural ensembles. Our findings illuminate a crucial property of complex systems: how the whole is different than the system's parts.

Context-Dependent Stability and Robustness of Genetic Toggle Switches with Leaky Promoters

Multistable switches are ubiquitous building blocks in both systems and synthetic biology. Given their central role, it is thus imperative to understand how their fundamental properties depend not only on the tunable biophysical properties of the switches themselves, but also on their genetic context. To this end, we reveal in this article how these factors shape the essential characteristics of toggle switches implemented using leaky promoters such as their stability and robustness to noise, both at single-cell and population levels. In particular, our results expose the roles that competition for scarce transcriptional and translational resources, promoter leakiness, and cell-to-cell heterogeneity collectively play. For instance, the interplay between protein expression from leaky promoters and the associated cost of relying on shared cellular resources can give rise to tristable dynamics even in the absence of positive feedback. Similarly, we demonstrate that while promoter leakiness always acts against multistability, resource competition can be leveraged to counteract this undesirable phenomenon. Underpinned by a mechanistic model, our results thus enable the context-aware rational design of multistable genetic switches that are directly translatable to experimental considerations, and can be further leveraged during the synthesis of large-scale genetic systems using computer-aided biodesign automation platforms.

Physical intelligence as a new paradigm

Intelligence of physical agents, such as human-made (e.g., robots, autonomous cars) and biological (e.g., animals, plants) ones, is not only enabled by their computational intelligence (CI) in their brain, but also by their physical intelligence (PI) encoded in their body. Therefore, it is essential to advance the PI of human-made agents as much as possible, in addition to their CI, to operate them in unstructured and complex real-world environments like the biological agents. This article gives a perspective on what PI paradigm is, when PI can be more significant and dominant in physical and biological agents at different length scales and how bioinspired and abstract PI methods can be created in agent bodies. PI paradigm aims to synergize and merge many research fields, such as mechanics, materials science, robotics, mechanical design, fluidics, active matter, biology, self-assembly and collective systems, to enable advanced PI capabilities in human-made agent bodies, comparable to the ones observed in biological organisms. Such capabilities would progress the future robots and other machines beyond what can be realized using the current frameworks.

Polariton multistability in a nonlinear optomechanical cavity

We theoretically study the polariton multistability in a solid state based optomechanical resonator embedded with a quantum well and aχ⁽²⁾second order nonlinear medium. The excitonic transition inside the quantum well is strongly coupled to the optical cavity mode. The polariton formed due to the mixing of cavity photons and exciton states are coupled to the mechanical mode which gives rise to the bistable behavior. A transition from bistability to tristability occurs in the presence of a strongχ⁽²⁾nonlinearity. Switching between bistability and tristability can also be controlled using exciton-cavity and optomechanical coupling making the system highly tunable. Tristability appears at low input power making it a suitable candidate for polaritonic devices which requires low input power.

Designing an irreversible metabolic switch for scalable induction of microbial chemical production

Bacteria can be harnessed to synthesise high-value chemicals. A promising strategy for increasing productivity uses inducible control systems to switch metabolism from growth to chemical synthesis once a large population of cell factories are generated. However, use of expensive chemical inducers limits scalability of this approach for biotechnological applications. Switching using cheap nutrients is an appealing alternative, but their tightly regulated uptake and consumption again limits scalability. Here, using mathematical models of fatty acid uptake in E. coli as an exemplary case study, we unravel how the cell's native regulation and program of induction can be engineered to minimise inducer usage. We show that integrating positive feedback loops into the circuitry creates an irreversible metabolic switch, which, requiring only temporary induction, drastically reduces inducer usage. Our proposed switch should be widely applicable, irrespective of the product of interest, and brings closer the realization of scalable and sustainable microbial chemical production.

Dynamical landscape and multistability of a climate model

We apply two independent data analysis methodologies to locate stable climate states in an intermediate complexity climate model and analyse their interplay. First, drawing from the theory of quasi-potentials, and viewing the state space as an energy landscape with valleys and mountain ridges, we infer the relative likelihood of the identified multistable climate states and investigate the most likely transition trajectories as well as the expected transition times between them. Second, harnessing techniques from data science, and specifically manifold learning, we characterize the data landscape of the simulation output to find climate states and basin boundaries within a fully agnostic and unsupervised framework. Both approaches show remarkable agreement, and reveal, apart from the well known warm and snowball earth states, a third intermediate stable state in one of the two versions of PLASIM, the climate model used in this study. The combination of our approaches allows to identify how the negative feedback of ocean heat transport and entropy production via the hydrological cycle drastically change the topography of the dynamical landscape of Earth’s climate.

Operating principles of circular toggle polygons

Decoding the dynamics of cellular decision-making and cell differentiation is a central question in cell and developmental biology. A common network motif involved in many cell-fate decisions is a mutually inhibitory feedback loop between two self-activating 'master regulators' A and B, also called as toggle switch. Typically, it can allow for three stable states-(high A, low B), (low A, high B) and (medium A, medium B). A toggle triad-three mutually repressing regulators A, B and C, i.e. three toggle switches arranged circularly (between A and B, between B and C, and between A and C)-can allow for six stable states: three 'single positive' and three 'double positive' ones. However, the operating principles of larger toggle polygons, i.e. toggle switches arranged circularly to form a polygon, remain unclear. Here, we simulate using both discrete and continuous methods the dynamics of different sized toggle polygons. We observed a pattern in their steady state frequency depending on whether the polygon was an even or odd numbered one. The even-numbered toggle polygons result in two dominant states with consecutive components of the network expressing alternating high and low levels. The odd-numbered toggle polygons, on the other hand, enable more number of states, usually twice the number of components with the states that follow 'circular permutation' patterns in their composition. Incorporating self-activations preserved these trends while increasing the frequency of multistability in the corresponding network. Our results offer insights into design principles of circular arrangement of regulatory units involved in cell-fate decision making, and can offer design strategies for synthesizing genetic circuits.

Soft Adaptive Mechanical Metamaterials

Soft materials are inherently flexible and make suitable candidates for soft robots intended for specific tasks that would otherwise not be achievable (e.g., smart grips capable of picking up objects without prior knowledge of their stiffness). Moreover, soft robots exploit the mechanics of their fundamental building blocks and aim to provide targeted functionality without the use of electronics or wiring. Despite recent progress, locomotion in soft robotics applications has remained a relatively young field with open challenges yet to overcome. Justly, harnessing structural instabilities and utilizing bistable actuators have gained importance as a solution. This report focuses on substrate-free reconfigurable structures composed of multistable unit cells with a nonconvex strain energy potential, which can exhibit structural transitions and produce strongly nonlinear transition waves. The energy released during the transition, if sufficient, balances the dissipation and kinetic energy of the system and forms a wave front that travels through the structure to effect its permanent or reversible reconfiguration. We exploit a triangular unit cell’s design space and provide general guidelines for unit cell selection. Using a continuum description, we predict and map the resulting structure’s behavior for various geometric and material properties. The structural motion created by these strongly nonlinear metamaterials has potential applications in propulsion in soft robotics, morphing surfaces, reconfigurable devices, mechanical logic, and controlled energy absorption.

Stability and Robustness of Unbalanced Genetic Toggle Switches in the Presence of Scarce Resources

While the vision of synthetic biology is to create complex genetic systems in a rational fashion, system-level behaviors are often perplexing due to the context-dependent dynamics of modules. One major source of context-dependence emerges due to the limited availability of shared resources, coupling the behavior of disconnected components. Motivated by the ubiquitous role of toggle switches in genetic circuits ranging from controlling cell fate differentiation to optimizing cellular performance, here we reveal how their fundamental dynamic properties are affected by competition for scarce resources. Combining a mechanistic model with nullcline-based stability analysis and potential landscape-based robustness analysis, we uncover not only the detrimental impacts of resource competition, but also how the unbalancedness of the switch further exacerbates them. While in general both of these factors undermine the performance of the switch (by pushing the dynamics toward monostability and increased sensitivity to noise), we also demonstrate that some of the unwanted effects can be alleviated by strategically optimized resource competition. Our results provide explicit guidelines for the context-aware rational design of toggle switches to mitigate our reliance on lengthy and expensive trial-and-error processes, and can be seamlessly integrated into the computer-aided synthesis of complex genetic systems.

Topological signatures in regulatory network enable phenotypic heterogeneity in small cell lung cancer

Phenotypic (non-genetic) heterogeneity has significant implications for the development and evolution of organs, organisms, and populations. Recent observations in multiple cancers have unraveled the role of phenotypic heterogeneity in driving metastasis and therapy recalcitrance. However, the origins of such phenotypic heterogeneity are poorly understood in most cancers. Here, we investigate a regulatory network underlying phenotypic heterogeneity in small cell lung cancer, a devastating disease with no molecular targeted therapy. Discrete and continuous dynamical simulations of this network reveal its multistable behavior that can explain co-existence of four experimentally observed phenotypes. Analysis of the network topology uncovers that multistability emerges from two teams of players that mutually inhibit each other, but members of a team activate one another, forming a 'toggle switch' between the two teams. Deciphering these topological signatures in cancer-related regulatory networks can unravel their 'latent' design principles and offer a rational approach to characterize phenotypic heterogeneity in a tumor.

Coupled Feedback Loops Involving PAGE4, EMT and Notch Signaling Can Give Rise to Non-genetic Heterogeneity in Prostate Cancer Cells

Non-genetic heterogeneity is emerging as a crucial factor underlying therapy resistance in multiple cancers. However, the design principles of regulatory networks underlying non-genetic heterogeneity in cancer remain poorly understood. Here, we investigate the coupled dynamics of feedback loops involving (a) oscillations in androgen receptor (AR) signaling mediated through an intrinsically disordered protein PAGE4, (b) multistability in epithelial-mesenchymal transition (EMT), and c) Notch-Delta-Jagged signaling mediated cell-cell communication, each of which can generate non-genetic heterogeneity through multistability and/or oscillations. Our results show how different coupling strengths between AR and EMT signaling can lead to monostability, bistability, or oscillations in the levels of AR, as well as propagation of oscillations to EMT dynamics. These results reveal the emergent dynamics of coupled oscillatory and multi-stable systems and unravel mechanisms by which non-genetic heterogeneity in AR levels can be generated, which can act as a barrier to most existing therapies for prostate cancer patients.

Harnessing the Multistability of Kresling Origami for Reconfigurable Articulation in Soft Robotic Arms

This study examines a biology-inspired approach of using reconfigurable articulation to reduce the control requirement for soft robotic arms. We construct a robotic arm by assembling Kresling origami modules that exhibit predictable bistability. By switching between their two stable states, these origami modules can behave either like a flexible joint with low bending stiffness or like a stiff link with high stiffness, without requiring any continuous power supply. In this way, the robotic arm can exhibit pseudo-linkage kinematics with lower control requirements and improved motion accuracy. A unique advantage of using origami as the robotic arm skeleton is that its bending stiffness ratio between stable states is directly related to the underlying Kresling design. Therefore, we conduct extensive parametric analyses and experimental validations to identify the optimized Kresling pattern for articulation. The results indicate that a higher angle ratio, a smaller resting length at contracted stable state, and a large number of polygon sides can offer more significant and robust bending stiffness tuning. Based on this insight, we construct a proof-of-concept, tendon-driven robotic arm consisting of three modules and show that it can exhibit the desired reconfigurable articulation behavior. Moreover, the deformations of this manipulator are consistent with kinematic model predictions, which validate the possibility of using simple controllers for such compliant robotic systems.

Enhancing Chaos Complexity of a Plasma Model through Power Input with Desirable Random Features

The present work introduces an analysis framework to comprehend the dynamics of a 3D plasma model, which has been proposed to describe the pellet injection in tokamaks. The analysis of the system reveals the existence of a complex transition from transient chaos to steady periodic behavior. Additionally, without adding any kind of forcing term or controllers, we demonstrate that the system can be changed to become a multi-stable model by injecting more power input. In this regard, we observe that increasing the power input can fluctuate the numerical solution of the system from coexisting symmetric chaotic attractors to the coexistence of infinitely many quasi-periodic attractors. Besides that, complexity analyses based on Sample entropy are conducted, and they show that boosting power input spreads the trajectory to occupy a larger range in the phase space, thus enhancing the time series to be more complex and random. Therefore, our analysis could be important to further understand the dynamics of such models, and it can demonstrate the possibility of applying this system for generating pseudorandom sequences.

Multistability and Reversibility of Aerobic Granular Sludge Microbial Communities Upon Changes From Simple to Complex Synthetic Wastewater and Back

Aerobic granular sludge (AGS) is a promising alternative wastewater treatment to the conventional activated sludge system allowing space and energy saving. Basic understanding of AGS has mainly been obtained using simple wastewater containing acetate and propionate as carbon source. Yet, the aspect and performances of AGS grown in such model systems are different from those obtained in reactor treating real wastewater. The impact of fermentable and hydrolyzable compounds on already formed AGS was assessed separately by changing the composition of the influent from simple wastewater containing volatile fatty acids to complex monomeric wastewater containing amino acids and glucose, and then to complex polymeric wastewater containing also starch and peptone. The reversibility of the observed changes was assessed by changing the composition of the wastewater from complex monomeric back to simple. The introduction of fermentable compounds in the influent left the settling properties and nutrient removal performance unchanged, but had a significant impact on the bacterial community. The proportion of Gammaproteobacteria diminished to the benefit of Actinobacteria and the Saccharibateria phylum. On the other hand, the introduction of polymeric compounds altered the settling properties and denitrification efficiency, but induced smaller changes in the bacterial community. The changes induced by the wastewater transition were only partly reversed. Seven distinct stables states of the bacterial community were detected during the 921 days of experiment, four of them observed with the complex monomeric wastewater. The transitions between these states were not only caused by wastewater changes but also by operation failures and other incidences. However, the nutrient removal performance and settling properties of the AGS were globally maintained due to the functional redundancy of its bacterial community.

Enhanced models for the nonlinear bending of planar rods: localization phenomena and multistability

We deduce a one-dimensional model of elastic planar rods starting from the Föppl-von Kármán model of thin shells. Such model is enhanced by additional kinematical descriptors that keep explicit track of the compatibility condition requested in the two-dimensional parent continuum, that in the standard rods models are identically satisfied after the dimensional reduction. An inextensible model is also proposed, starting from the nonlinear Koiter model of inextensible shells. These enhanced models describe the nonlinear planar bending of rods and allow to account for some phenomena of preeminent importance even in one-dimensional bodies, such as formation of singularities and localization (d-cones), otherwise inaccessible by the classical one-dimensional models. Moreover, the effects of the compatibility translate into the possibility to obtain multiple stable equilibrium configurations.

Design and Testing of Bistable Lattices with Tensegrity Architecture and Nanoscale Features Fabricated by Multiphoton Lithography

A bistable response is an innate feature of tensegrity metamaterials, which is a conundrum to attain in other metamaterials, since it ushers unconventional static and dynamical mechanical behaviors. This paper investigates the design, modeling, fabrication and testing of bistable lattices with tensegrity architecture and nanoscale features. First, a method to design bistable lattices tessellating tensegrity units is formulated. The additive manufacturing of these structures is performed through multiphoton lithography, which enables the fabrication of microscale structures with nanoscale features and extremely high resolution. Different modular lattices, comprised of struts with 250 nm minimum radius, are tested under loading-unloading uniaxial compression nanoindentation tests. The compression tests confirmed the activation of the designed bistable twisting mechanism in the examined lattices, combined with a moderate viscoelastic response. The force-displacement plots of the 3D assemblies of bistable tensegrity prisms reveal a softening behavior during the loading from the primary stable configuration and a subsequent snapping event that drives the structure into a secondary stable configuration. The twisting mechanism that characterizes such a transition is preserved after unloading and during repeated loading-unloading cycles. The results of the present study elucidate that fabrication of multistable tensegrity lattices is highly feasible via multiphoton lithography and promulgates the fabrication of multi-cell tensegrity metamaterials with unprecedented static and dynamic responses.

Planar Mechanical Metamaterials with Embedded Permanent Magnets

The design space of mechanical metamaterials can be drastically enriched by the employment of non-mechanical interactions between unit cells. Here, the mechanical behavior of planar metamaterials consisting of rotating squares is controlled through the periodic embedment of modified elementary cells with attractive and repulsive configurations of the magnets. The proposed design of mechanical metamaterials produced by three-dimensional printing enables the efficient and quick reprogramming of their mechanical properties through the insertion of the magnets into various locations within the metamaterial. Experimental and numerical studies reveal that under equibiaxial compression various mechanical characteristics, such as buckling strain and post-buckling stiffness, can be finely tuned through the rational placement of the magnets. Moreover, this strategy is shown to be efficient in introducing bistability into the metamaterial with an initially single equilibrium state.

Underactuated fluidic control of a continuous multistable membrane

This work addresses the challenge of underactuated pattern generation in continuous multistable structures. The examined configuration is a slender membrane which can concurrently sustain two different equilibria states, separated by transition regions, and is actuated by a viscous fluid. We first demonstrate the formation and motion of a single transition region and then sequencing of several such moving transition regions to achieve arbitrary patterns by controlling the inlet pressure of the actuating fluid. Finally, we show that nonuniform membrane properties, along with transient dynamics of the fluid, can be leveraged to directly snap through any segment of the membrane.

The Basal Level of Gene Expression Associated with Chromatin Loosening Shapes Waddington Landscapes and Controls Cell Differentiation

The baseline level of transcription, which is variable and difficult to quantify, seriously complicates the normalization of comparative transcriptomic data, but its biological importance remains unappreciated. We show that this currently neglected ingredient is essential for controlling gene network multistability and therefore cellular differentiation. Basal expression is correlated to the degree of chromatin loosening measured by DNA accessibility and systematically leads to cellular dedifferentiation as assessed by transcriptomic signatures, irrespective of the molecular and cellular tools used. Modeling gene network motifs formally involved in developmental bifurcations reveals that the epigenetic landscapes of Waddington are restructured by the level of nonspecific expression, such that the attractors of progenitor and differentiated cells can be mutually exclusive. This mechanism is universal and holds beyond the particular nature of the genes involved, provided the multistable circuits are correctly described with autonomous basal expression. These results explain the relationships long established between gene expression noise, chromatin decondensation and cellular dedifferentiation, and highlight how heterochromatin maintenance is essential for preventing pathological cellular reprogramming, age-related diseases, and cancer.

Harnessing transition waves to realize deployable structures

Transition waves that sequentially switch bistable elements from one stable configuration to another have received significant interest in recent years not only because of their rich physics but also, for their potential applications, including unidirectional propagation, energy harvesting, and mechanical computation. Here, we exploit the propagation of transition waves in a bistable one-dimensional (1D) linkage as a robust mechanism to realize structures that can be quickly deployed. We first use a combination of experiments and analyses to show that, if the bistable joints are properly designed, transition waves can propagate throughout the entire structure and transform the initial straight configuration into a curved one. We then demonstrate that such bistable linkages can be used as building blocks to realize deployable three-dimensional (3D) structures of arbitrary shape.

Guided transition waves in multistable mechanical metamaterials

Transition fronts, moving through solids and fluids in the form of propagating domain or phase boundaries, have recently been mimicked at the structural level in bistable architectures. What has been limited to simple one-dimensional (1D) examples is here cast into a blueprint for higher dimensions, demonstrated through 2D experiments and described by a continuum mechanical model that draws inspiration from phase transition theory in crystalline solids. Unlike materials, the presented structural analogs admit precise control of the transition wave's direction, shape, and velocity through spatially tailoring the underlying periodic network architecture (locally varying the shape or stiffness of the fundamental building blocks, and exploiting interactions of transition fronts with lattice defects such as point defects and free surfaces). The outcome is a predictable and programmable strongly nonlinear metamaterial motion with potential for, for example, propulsion in soft robotics, morphing surfaces, reconfigurable devices, mechanical logic, and controlled energy absorption.

Intraindividual Consistency Between Auditory and Visual Multistability

We compared perceptual multistability across modalities, using a visual plaid pattern (composed of two transparently overlaid drifting gratings) and auditory streaming (elicited by a repeating “ABA_” tone sequence). Both stimuli can be perceived as integrated (one plaid pattern, one stream comprising “A” and “B” tones) or segregated (two individual gratings, two tone streams). In the segregated case, either stream or grating can be perceived in the foreground. We queried auditory and visual perception with these three response options. We found that perceptual dominance of the integrated states was correlated across modalities: Participants who were more likely to perceive the plaid were also more likely to perceive the integrated auditory stream. When presenting both stimuli simultaneously and querying the auditory percept, eye-movement data showed that perceiving auditory and visual integration is related on a moment-by-moment basis. This suggests that in part common mechanisms underlie multistability in visual and auditory perception.

Multistable properties of human subthalamic nucleus neurons in Parkinson's disease

Behaviors are realized through concerted activity in neural circuits. This activity results from a combination of neural connectivity and the properties of the involved neurons. By studying the activity of neurons in the human subthalamic nucleus during surgery for Parkinson’s disease, we report that these neurons have multiple stable states, and that brief electrical stimuli can lead to transitions between states. We thus suggest that these neurons function as finite state machines. The different states could influence the function of key motor circuits of the basal ganglia, and thus knowledge of these states in disease or in response to treatment could help to define new treatment strategies for people with movement disorders.

To understand the function and dysfunction of neural circuits, it is necessary to understand the properties of the neurons participating in the behavior, the connectivity between these neurons, and the neuromodulatory status of the circuits at the time they are producing the behavior. Such knowledge of human neural circuits is difficult, at best, to obtain. Here, we study firing properties of human subthalamic neurons, using microelectrode recordings and microstimulation during awake surgery for Parkinson’s disease. We demonstrate that low-amplitude, brief trains of microstimulation can lead to persistent changes in neuronal firing behavior including switching between firing rates, entering silent periods, or firing several bursts then entering a silent period. We suggest that these multistable states reflect properties of finite state machines and could have implications for the function of circuits involving the subthalamic nucleus. Furthermore, understanding these states could lead to therapeutic strategies aimed at regulating the transitions between states.

Exploring the intrinsic behaviour of multisite phosphorylation systems as part of signalling pathways

Multisite phosphorylation is a basic way of chemically encoding substrate function and a recurring feature of cell signalling pathways. A number of studies have explored information processing characteristics of multisite phosphorylation, through studies of the intrinsic kinetics. Many of these studies focus on the module in isolation. In this paper, we build a bridge to connect the behaviour of multisite modification in isolation to that as part of pathways. We study the effect of activation of the enzymes (which are basic ways in which the module may be regulated), as well the effects of the modified substrates being involved in further modifications or exiting reaction compartments. We find that these effects can induce multiple kinds of transitions, including to behaviour not seen intrinsically in the multisite modification module. We then build on these insights to investigate how these multisite modification systems can be tuned by enzyme activation to realize a range of information processing outcomes for the design of synthetic phosphorylation circuits. Connecting the complexity of multisite modification kinetics, with the pathways in which they are embedded, serves as a basis for teasing out many aspects of their interaction, providing insights of relevance in systems biology, synthetic biology/chemistry and chemical information processing.