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Results for “systems biology”

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bioRxiv2026

Early detection of sudden transitions in Notch signalling

Identifying sudden transitions during phenotypic decision-making of complex biological systems can be crucial for our ability to control a cellular state. Yet, prior determination of these sudden transitions or tipping points remains challenging, as biological systems often exhibit only subtle early changes, which are often masked by inherent noise or rapid transition dynamics. Using Notch signaling as a model, we systematically analyze dynamical transitions in Notch-Delta (ND), Notch-Delta-Jagged (NDJ), and Fringe-mediated NDJ systems for both one and two-cell contexts. In the one-cell ND system, critical slowing down (CSD)-based early warning signals (EWSs) reliably capture transitions between sender (S) and receiver (R) states and remain robust to variation in forcing rate. We further find that flickering is a precursor to transitions in one-cell NDJ system. In contrast, flickering does not occur in the two-cell Notch model due to the presence of a supercritical bifurcation. Our analysis also offers insight into how NICD (Notch Intracellular Domain)-driven and Fringe-mediated asymmetries, along with the strength of external signals, control the emergence of flickering. Overall, this study identifies sudden transitions in Notch signaling under demographic noise and can be extended to other noisy biological systems, with potential applications in drug development and targeted therapeutic interventions.

systems biology↗

bioRxiv2022

KINOMO: A non-negative matrix factorization framework for recovering intra- and inter-tumoral heterogeneity from single-cell RNA-seq data

Single-cell RNA-sequencing (scRNA-seq) is a powerful technology to uncover cellular heterogeneity in tumor ecosystems. Due to differences in underlying gene load, direct comparison between patient samples is challenging, and this is further complicated by the sparsity of data matrices in scRNA-seq. Here, we present a factorization method called KINOMO (Kernel dIfferentiability correlation-based NOn-negative Matrix factorization algorithm using Kullback-Leibler divergence loss Optimization). This tool uses quadratic approximation approach for error correction and an iterative multiplicative approach, which improves the quality assessment of NMF-identified factorization, while mitigating biases introduced by inter-patient genomic variability. We benchmarked this new approach against nine different methods across 15 scRNA-seq experiments and find that KINOMO outperforms prior methods when evaluated with an adjusted Rand index (ARI), ranging 0.82-0.91 compared to 0.68-0.77. Thus, KINOMO provides an improved approach for determining coherent transcriptional programs (and meta-programs) from scRNA-seq data of cancer tissues, enabling comparison of patients with variable genomic backgrounds. ClassificationPhysical Sciences (Applied Mathematics; Biophysics and Computational Biology), Biological Sciences (Applied Biological Sciences; Biophysics and Computational Biology; Medical Sciences; Systems Biology.). Significance StatementIdentification of shared or distinct cell programs in single-cell RNA-seq data of patient cancer cells is challenging due to underlying variability of gene load which determines transcriptional output. We developed an analytical approach to define transcriptional variability more accurately across patients and therefore enable comparison of program expression despite inherent genetic heterogeneity. Thus, this method overcomes challenges not adequately addressed by other methods broadly used for the analysis of single-cell genomics data.

systems biology↗

bioRxiv2023

Creating Aesthetically Pleasing SBGN Visualisations for Presentation and Exploration

Visualisations are widely used to present, assess, and convey data and understanding in systems biology and other fields, and graphical representations of data and information should be precise, visually engaging, informative, and aesthetically pleasing. The Systems Biology Graphical Notation (SBGN) is a standard for visual representations of processes and networks in systems biology in the form of SBGN maps. It defines graphical elements and connection rules for knowledge representation in the form of maps. Whereas the form of the map elements is defined, those map elements have to be placed in a proper way in order to obtain useful and aesthetically pleasing visualisations. Here, we present layout considerations and guidelines for SBGN maps, as well as workflows for SBGN-ED as a tool for crafting visually pleasing SBGN visualisations for presentation and exploration.

systems biology↗

bioRxiv2025

Talk2Biomodels: AI agent-based open-source LLM initiative for kinetic biological models

In this study, we present Talk2Biomodels (T2B), an open-source1, user-friendly, large language model-based agentic AI platform designed to democratize access to computational models of biological interactions and promote the FAIRification (Findability, Accessibility, Interoperability, and Reusability) of these models. T2B enables users to explore and analyse mathematical models of biological systems using natural language. It eschews the traditional graphical user interface (GUI) and minimally adaptable workflow in favour of a modern agentic framework to provide a dynamic and immersive experience to explore mathematical models of biological interactions through conversations in natural language. T2B supports models encoded in the open-source community format Systems Biology Markup Language (SBML) and is integrated with the BioModels database (https://www.ebi.ac.uk/biomodels/), enabling seamless exploration, simulation, and analysis of curated systems biology models. Use cases in precision medicine, epidemiology, and emergent systems properties of biological networks are presented to demonstrate how experts and non-experts in computational biology can benefit from T2B.

systems biology↗

bioRxiv2021

Biological complexity facilitates tuning of the neuronal parameter space

The electrical and computational properties of neurons in our brains are determined by a rich repertoire of membrane-spanning ion channels and elaborate dendritic trees. However, the precise reason for this inherent complexity remains unknown. Here, we generated large stochastic populations of biophysically realistic hippocampal granule cell models comparing those with all 15 ion channels to their reduced but functional counterparts containing only 5 ion channels. Strikingly, valid parameter combinations in the full models were more frequent and more stable in the face of perturbations to channel expression levels. Scaling up the numbers of ion channels artificially in the reduced models recovered these advantages confirming the key contribution of the actual number of ion channel types. We conclude that the diversity of ion channels gives a neuron greater flexibility and robustness to achieve target excitability. Significance statementOver the course of billions of years, evolution has led to a wide variety of biological systems. The emergence of the more complex among these seems surprising in the light of the high demands of searching for viable solutions in a correspondingly high-dimensional parameter space. In realistic neuron models with their inherently complex ion channel composition, we find a surprisingly large number of viable solutions when selecting parameters randomly. This effect is strongly reduced in models with fewer ion channel types but is recovered when inserting additional artificial ion channels. Because concepts from probability theory provide a plausible explanation for this improved distribution of valid model parameters, we propose that this may generalise to evolutionary selection in other complex biological systems. In briefStudying ion channel diversity in neuronal models we show how robust biological systems may evolve not despite but because of their complexity. HighlightsO_LI15 channel model of hippocampal granule cells (GCs) reduces to 5 ion channels without loss of spiking behaviour. C_LIO_LIBut knocking out ion channels can be compensated only in the full model. C_LIO_LIRandom sampling leads to ~ 6% solutions in full but only ~ 1% in reduced model. C_LIO_LILaw of large numbers generalises our observations to other complex biological systems. C_LI

neuroscience↗

bioRxiv2017

A Biomaterial Screening Approach to Reveal Microenvironmental Mechanisms of Drug Resistance

TOC FigureDrug response screening, gene expression, and kinome signaling were combined across biomaterial platforms to combat adaptive resistance to sorafenib.\n\n\n\nO_FIG O_LINKSMALLFIG WIDTH=200 HEIGHT=158 SRC=\"FIGDIR/small/168039_ufig1.gif\" ALT=\"Figure 1\">\nView larger version (60K):\norg.highwire.dtl.DTLVardef@a7af0eorg.highwire.dtl.DTLVardef@d5f2bborg.highwire.dtl.DTLVardef@330bd6org.highwire.dtl.DTLVardef@14e1f1d_HPS_FORMAT_FIGEXP M_FIG C_FIG Insight BoxWe combined biomaterial platforms, drug screening, and systems biology to identify mechanisms of extracellular matrix-mediated adaptive resistance to RTK-targeted cancer therapies. Drug response was significantly varied across biomaterials with altered stiffness, dimensionality, and cell-cell contacts, and kinome reprogramming was responsible for these differences in drug sensitivity. Screening across many platforms and applying a systems biology analysis were necessary to identify MEK phosphorylation as the key factor associated with variation in drug response. This method uncovered the combination therapy of sorafenib with a MEK inhibitor, which decreased viability on and within biomaterials in vitro, but was not captured by screening on tissue culture plastic alone. This combination therapy also reduced tumor burden in vivo, and revealed a promising approach for combating adaptive drug resistance.\n\nAbstractTraditional drug screening methods lack features of the tumor microenvironment that contribute to resistance. Most studies examine cell response in a single biomaterial platform in depth, leaving a gap in understanding how extracellular signals such as stiffness, dimensionality, and cell-cell contacts act independently or are integrated within a cell to affect either drug sensitivity or resistance. This is critically important, as adaptive resistance is mediated, at least in part, by the extracellular matrix (ECM) of the tumor microenvironment. We developed an approach to screen drug responses in cells cultured on 2D and in 3D biomaterial environments to explore how key features of ECM mediate drug response. This approach uncovered that cells on 2D hydrogels and spheroids encapsulated in 3D hydrogels were less responsive to receptor tyrosine kinase (RTK)-targeting drugs sorafenib and lapatinib, but not cytotoxic drugs, compared to single cells in hydrogels and cells on plastic. We found that transcriptomic differences between these in vitro models and tumor xenografts did not reveal mechanisms of ECM-mediated resistance to sorafenib. However, a systems biology analysis of phospho-kinome data uncovered that variation in MEK phosphorylation was associated with RTK-targeted drug resistance. Using sorafenib as a model drug, we found that co-administration with a MEK inhibitor decreased ECM-mediated resistance in vitro and reduced in vivo tumor burden compared to sorafenib alone. In sum, we provide a novel strategy for identifying and overcoming ECM-mediated resistance mechanisms by performing drug screening, phospho-kinome analysis, and systems biology across multiple biomaterial environments.

bioengineering↗

bioRxiv2020

Calm on the surface, dynamic on the inside. Molecular homeostasis in response to regulatory and metabolic perturbation of Anabaena sp. 7120 nitrogen metabolism

Nitrogen is a key macro-nutrient required for the metabolism and growth of biological systems. Although multiple nitrogen sources can serve this purpose, they are all converted into ammonium/ammonia as a first step of assimilation. It is thus reasonable to expect that molecular parts involved in the transport of ammonium/ammonia across biological membranes (i.e. catalysed by AMT transporters) connect with the regulation of both nitrogen and central carbon metabolism. In order to test this hypothesis, we applied both (1) genetic (i.e. {Delta}amt mutation) and (2) environmental treatments to a target biological system, the cyanobacterium Anabaena sp. PCC 7120. Cyanobacteria have a key role in the global nitrogen cycle and thus represent a useful model system. The aim was to both (1) perturb sensing and low-affinity uptake of ammonium/ammonia and (2) induce multiple inner N states, followed by targeted quantification of key proteins, metabolites and enzyme activities, with experiments intentionally designed over a longer time-scale than the available studies in literature. We observed that the absence of AMT transporters triggered a substantial response at a whole-system level, affecting enzyme activities and the quantity of both proteins and metabolites, spanning both N and C metabolism. Moreover, the absence of AMT transporters left a molecular fingerprint indicating N-deficiency even under N replete conditions (i.e. greater GS activity, lower 2-OG content and faster nitrogenase activation upon N deprivation). Contrasting with all of the above dynamic adaptations was the striking near-complete lack of any externally measurable phenotype (i.e. growth, photosynthesis, pigments, metabolites). We thus conclude that this species evolved a highly robust and adaptable molecular network to maintain homeostasis, resulting in substantial internal but minimal external perturbations. The analytical data highlights several internal adaptations, including increased N assimilation (i.e. greater GS activity) and nitrogenase activity (i.e. faster activation upon N deprivation) together with altered amino acids metabolism, as indicated by changes in Gln, Glu and 2-OG, indicating an altered C/N balance. The analyses provides evidence for an active role of AMT transporters in the regulatory/signalling network of N metabolism in this biological system, and the existence of a novel fourth IF7A-independent regulatory mechanism controlling GS activity.

systems biology↗

bioRxiv2019

Scale free topology as an effective feedback system

Biological networks are often heterogeneous in their connectivity pattern, with degree distributions featuring a heavy tail of highly connected hubs. The implications of this heterogeneity on dynamical properties are a topic of much interest. Here we introduce a novel approach to analyze such networks the lumped hub approximation. Based on the observation that in finite networks a small number of hubs have a disproportionate effect on the entire system, we construct an approximation by lumping these nodes into a single effective hub, and replacing the rest by a homogeneous bulk. We use this approximation to study dynamics of networks with scale-free degree distributions, focusing on their probability of convergence to fixed points. We find that the approximation preserves convergence statistics over a wide range of settings. Our mapping provides a parametrization of scale free topology which is predictive at the ensemble level and also retains properties of individual realizations. Specifically for outgoing scale-free distributions, the role of the effective hub on the network can be elucidated by feedback analysis. We show that outgoing hubs have an organizing role that can drive the network to convergence, in analogy to suppression of chaos by an external drive. In contrast, incoming hubs have no such property, resulting in a marked difference between the behavior of networks with outgoing vs. incoming scale free degree distribution. Combining feedback analysis with mean field theory predicts a transition between convergent and divergent dynamics which is corroborated by numerical simulations. Our results show how interpreting topology as a feedback circuit can provide novel insights on dynamics. Furthermore, we highlight the effect of a handful of outlying hubs, rather than of the connectivity distribution law as a whole, on network dynamics.

biophysics↗

bioRxiv2018

Unifying mutualism diversity for interpretation and prediction

Coarse-grained rules are widely used in chemistry, physics and engineering. In biology, however, such rules are less common and under-appreciated. This gap can be attributed to the difficulty in establishing general rules to encompass the immense diversity and complexity of biological systems. Even when a rule is established, it is often challenging to map it to mechanistic details and to quantify these details. We here address these challenges on a study of mutualism, an essential type of ecological interaction in nature. Using an appropriate level of abstraction, we deduced a general rule that predicts the outcomes of mutualistic systems, including coexistence and productivity. We further developed a standardized calibration procedure to apply the rule to mutualistic systems without the need to fully elucidate or characterize their mechanistic underpinnings. Our approach consistently provides explanatory and predictive power with various simulated and experimental mutualistic systems. Our strategy can pave the way for establishing and implementing other simple rules for biological systems.

systems biology↗

bioRxiv2018

An enriched network motif family regulates multistep cell fate transitions with restricted reversibility

Multistep cell fate transitions with stepwise changes of transcriptional profiles are common to many developmental, regenerative and pathological processes. The multiple intermediate cell lineage states can serve as differentiation checkpoints or branching points for channeling cells to more than one lineages. However, mechanisms underlying these transitions remain elusive. Here, we explored gene regulatory circuits that can generate multiple intermediate cellular states with stepwise modulations of transcription factors. With unbiased searching in the network topology space, we found a motif family containing a large set of networks can give rise to four attractors with the stepwise regulations of transcription factors, which limit the reversibility of three consecutive steps of the lineage transition. We found that there is an enrichment of these motifs in a transcriptional network controlling the early T cell development, and a mathematical model based on this network recapitulates multistep transitions in the early T cell lineage commitment. By calculating the energy landscape and minimum action paths for the T cell model, we quantified the stochastic dynamics of the critical factors in response to the differentiation signal with fluctuations. These results are in good agreement with experimental observations and they suggest the stable characteristics of the intermediate states in the T cell differentiation. These dynamical features may help to direct the cells to correct lineages during development. Our findings provide general design principles for multistep cell linage transitions and new insights into the early T cell development. The network motifs containing a large family of topologies can be useful for analyzing diverse biological systems with multistep transitions.\n\nAuthor summaryThe functions of cells are dynamically controlled in many biological processes including development, regeneration and disease progression. Cell fate transition, or the switch of cellular functions, often involves multiple steps. The intermediate stages of the transition provide the biological systems with the opportunities to regulate the transitions in a precise manner. These transitions are controlled by key regulatory genes of which the expression shows stepwise patterns, but how the interactions of these genes can determine the multistep processes were unclear. Here, we present a comprehensive analysis on the design principles of gene circuits that govern multistep cell fate transition. We found a large network family with common structural features that can generate systems with the ability to control three consecutive steps of the transition. We found that this type of networks is enriched in a gene circuit controlling the development of T lymphocyte, a crucial type of immune cells. We performed mathematical modeling using this gene circuit and we recapitulated the stepwise and irreversible loss of stem cell properties of the developing T lymphocytes. Our findings can be useful to analyze a wide range of gene regulatory networks controlling multistep cell fate transitions.

systems biology↗

bioRxiv2020

A geometric and structural approach to the analysis and design of biological circuit dynamics: a theory tailored for synthetic biology

Much of the progress in developing our ability to successfully design genetic circuits with predictable dynamics has followed the strategy of molding biological systems to fit into conceptual frameworks used in other disciplines, most notably the engineering sciences. Because biological systems have fundamental differences from systems in these other disciplines, this approach is challenging and the insights obtained from such analyses are often not framed in a biologically-intuitive way. Here, we present a new theoretical framework for analyzing the dynamics of genetic circuits that is tailored towards the unique properties associated with biological systems and experiments. Our framework approximates a complex circuit as a set of simpler circuits, which the system can transition between by saturating its various internal components. These approximations are connected to the intrinsic structure of the system, so this representation allows the analysis of dynamics which emerge solely from the systems structure. Using our framework, we analyze the presence of structural bistability in a leaky autoactivation motif and the presence of structural oscillations in the Repressilator.

synthetic biology↗

bioRxiv2024

MICROCOSM FABRICATION PLATFORM FOR LIVE MICROSCOPY OF PLANT-SOIL SYSTEMS

Biological processes in soil pores are critical to crop nutrition and productivity, but live observations of these processes at that scale have been difficult to accomplish. To address this challenge, we have developed new techniques for the fabrication of microcosms dedicated to live imaging of the rhizosphere which incorporate the ability to control water content in transparent soil. Chambers were assembled using poly(dimethyl siloxane) (PDMS) parts fabricated by injection moulding and subsequently joined to glass slides. The control of liquid fluxes in the microcosm was achieved by syringes passing through the PDMS parts or through custom made PDMS sponges. We then tested various low refractive index materials for the fabrication of transparent soils and carried out live microscopy using Fluorescence Light Sheet microscopy. The proposed fabrication techniques are modular and enabled the construction of a wide range of experimental systems, including split chamber systems for the control of water content in soil, heterogeneous distribution of water content, monitoring of dye tracers, and live observation of plant roots. Using the techniques, we show how plant roots increase water infiltration through increased permeability of dry soil layers. This study therefore establishes that material property control and microfabrication in model rhizosphere systems can greatly enhance our understanding of plant-soil interactions.

bioengineering↗

bioRxiv2018

Inverse sensitivity analysis of mathematical models avoiding the curse of dimensionality

1Biological systems have evolved a degree of robustness with respect to perturbations in their environment and this capability is essential for their survival. In applications ranging from therapeutics to conservation, it is important to understand not only the sensitivity of biological systems to changes in their environments, but which features of these systems are necessary to achieve a given outcome. Mathematical models are increasingly employed to understand these mechanisms. Sensitivity analyses of such mathematical models provide insight into the responsiveness of the system when experimental manipulation is difficult. One common approach is to seek the probability distribution of the outputs of the system corresponding to a known distribution of inputs. By contrast, inverse sensitivity analysis determines the probability distribution of model inputs which produces a known distribution of outputs. The computational complexity of the methods used to conduct inverse sensitivity analyses for deterministic systems has limited their application to models with relatively few parameters. Here we describe a novel Markov Chain Monte Carlo method we call \"Contour Monte Carlo\", which can be used to invert systems with a large number of parameters. We demonstrate the utility of this method by inverting a range of frequently-used deterministic models of biological systems, including the logistic growth equation, the Michaelis-Menten equation, and an SIR model of disease transmission with nine input parameters. We argue that the simplicity of our approach means it is amenable to a large class of problems of practical significance and, more generally, provides a probabilistic framework for understanding the inversion of deterministic models.\n\n2 Author summaryMathematical models of complex systems are constructed to provide insight into their underlying functioning. Statistical inversion can probe the often unobserved processes underlying biological systems, by proceeding from a given distribution of a models outputs (the aggregate \"effects\") to a distribution over input parameters (the constituent \"causes\"). The process of inversion is well-defined for systems involving randomness and can be described by Bayesian inference. The inversion of a deterministic system, however, cannot be performed by the standard Bayesian approach. We develop a conceptual framework that describes the inversion of deterministic systems with fewer outputs than input parameters. Like Bayesian inference, our approach uses probability distributions to describe the uncertainty over inputs and outputs, and requires a prior input distribution to ensure a unique \"posterior\" probability distribution over inputs. We describe a computational Monte Carlo method that allows efficient sampling from the posterior distribution even as the dimension of the input parameter space grows. This is a two-step process where we first estimate a \"contour volume density\" associated with each output value which is then used to define a sampling algorithm that yields the requisite input distribution asymptotically. Our approach is simple, broadly applicable and could be widely adopted.

systems biology↗

bioRxiv2025

Analytical approach of synchronous and asynchronous update schemes applied to solving biological Boolean networks

Characterizing the minimum, necessary and sufficient components to generate the dynamics of a biological system has always been a priority to understand its functioning. In this sense, the canonical form of biological systems modeled by Boolean networks accurately defines the components in charge of controlling the dynamics of such systems. However, the calculation of the canonical form might be complicated in mathematical terms. In addition, computing the canonical form does not consider the dynamical properties found when using the synchronous and asynchronous update schemes to solve Boolean networks. Here, we analyze both update schemes and their connection with the canonical form of Boolean networks. We found that the synchronous scheme can be expressed by the Chapman-Kolmogorov equation, being a particular case of Markov chains. We also discovered that the canonical form of any Boolean network can be easily obtained by solving this matrix equation. Finally, we found that the update order of the asynchronous scheme generates a set of functions that, when composed together, produce characteristic properties of this scheme, such as the conservation of fixed-point attractors or the variability in the basins of attraction. We concluded that the canonical form of Boolean networks can only be obtained for systems that use the synchronous update scheme, which opens up new possibilities for study.

systems biology↗

bioRxiv2025

Trajectory-matching ABC-MCMC for simulating heterogeneous dynamics in mechanistic models

The inherent heterogeneity of complex biological systems makes it difficult to experimentally and clinically explore individual outcomes. Mechanistic mathematical models are essential tools for studying such heterogeneity. Thus, there is increasing interest in integrating newer mechanistic model-based techniques, like virtual patient cohorts and virtual clinical trials, within experimental and regulatory pipelines to probe relationships that may be difficult or impossible to ascertain through traditional wet-lab or clinical experimentation alone. Approximate Bayesian Computation (ABC) is an attractive method for generating virtual patient cohorts and running virtual clinical trials. However, ABC-based approaches can become computationally demanding when stringent acceptance criteria are imposed. In response, we developed a model-based technique called trajectory-matching random-walk feasibility sampling (TM-RWFS) that captures the variability of complex biological systems by constraining model trajectories between the upper and lower bounds of available data to generate heterogeneity. By testing the method's performance on existing mechanistic models, we show that TM-RWS generates parameter sets whose simulated trajectories reproduce the observed variability in biological systems of varying complexity while maintaining computational efficiency. Thus, TM-RWFS is a fast, new approach for generating heterogeneity in mechanistic mathematical models with implications for model-based experimental design, virtual patient cohorts, and virtual clinical trials.

systems biology↗

bioRxiv2020

Sex dependent gene activity in the human body

Many pathophysiological mechanisms in human health and disease are dependent on sex. Systems biology approaches are successfully used to decipher human disease etiology, yet the effect of sex on gene network biology is mostly unknown. To address this, we used RNA-sequencing data of over 700 individuals spanning 24 tissues from the Genotype-Tissue Expression project to generate a whole-body gene activity map and quantified the sex differences per tissue. We found that of the 13,787 genes analyzed in 24 tissues, 20.1% of the gene activity is influenced by sex. For example, skeletal muscle was predominantly enriched with genes more active in males, whereas thyroid primarily contained genes more active in females. This was accompanied by consistent sex differences in pathway activity, including hypoxia, epithelial-to-mesenchymal transition, and inflammation over the human body. Furthermore, multi-organ analyses revealed consistent sex-dependent gene activity over numerous tissues which was accompanied by enrichment of transcription factor binding motifs in the promoters of these genes. Finally, we show that many sex-biased genes are known druggable targets. This emphasizes sex as a biological variable and the need to incorporate sex in systems biology studies.

systems biology↗

bioRxiv2019

Programmable patterns in a DNA-based reaction-diffusion system

Biology offers compelling proof that macroscopic "living materials" can emerge from reactions between diffusing biomolecules. Here, we show that molecular self-organization could be a similarly powerful approach for engineering functional synthetic materials. We introduce a programmable DNA-hydrogel that produces tunable patterns at the centimeter length scale. We generate these patterns by implementing chemical reaction networks through synthetic DNA complexes, embedding the complexes in hydrogel, and triggering with locally applied input DNA strands. We first demonstrate ring pattern formation around a circular input cavity and show that the ring width and intensity can be predictably tuned. Then, we create patterns of increasing complexity, including concentric rings and non-isotropic patterns. Finally, we show "destructive" and "constructive" interference patterns, by combining several ring-forming modules in the gel and triggering them from multiple sources. We further show that computer simulations based on the reaction-diffusion model can predict and inform the programming of target patterns.

synthetic biology↗

bioRxiv2021

Controlled bio-inspired self-organised criticality

The control of extensive complex biological systems is considered to depend on feedback mechanisms. Reduced systems modelling has been effective to describe these mechanisms, but this approach does not sufficiently encompass the required complexity that is needed to understand how localised control in a biological system can provide global stable states. Self-Organised Criticality (SOC) is a characteristic property of locally interacting physical systems which readily emerges from changes to its dynamic state due to small nonlinear perturbations. Small changes in the local states, or in local interactions, can greatly affect the total system state of critical systems. It has long been conjectured that SOC is cardinal to biological systems that show similar critical dynamics and also may exhibit near power-law relations. Rate Control of Chaos (RCC) provides a suitable robust mechanism to generate SOC systems which operates at the edge of chaos. The bio-inspired RCC method requires only local instantaneous knowledge of some of the variables of the system, and is capable of adapting to local perturbations. Importantly, connected RCC controlled oscillators can maintain global multi-stable states, and domains with power-law relations may emerge. The network of oscillators deterministically stabilises into different orbits for different perturbations and the relation between the perturbation and amplitude can show exponential and power-law correlations. This is representative of a basic mechanism of protein production and control, that underlies complex processes such as homeostasis. Providing feedback from the global state, the total system dynamic behaviour can be boosted or reduced. Controlled SOC can provide much greater understanding of biological control mechanisms, that are based on distributed local producers, remote consumers of biological resources, with globally defined control. Author summaryUsing a nonlinear control method inspired by enzymatic control, which is capable of stabilising chaotic systems into periodic orbits or steady-states, it is shown that a controlled system can be created that is scale-free and in a critical state. This means that the system can easily move from one stable orbit to another using only a small local perturbation. Such a system is known as self-organised criticality, and is shown in this system to be deterministic. Using a known perturbation, it will result in a scale-free response of the system that can be in a power law relation. It has been conjectured that biosystems are in a self-organised critical state, and these models show that this is a suitable approach to allow local systems to control a global state, such as homeostatic control. The underlying principle is based on rate control of chaos, and can be used to understand how biosystems can use localised control to ensure stability at different dynamic scales without supervising mechanisms.

biophysics↗