Universal structures for adaptation in biochemical reaction networks

Hypergraph animals

Here we introduce simple structures for the analysis of complex hypergraphs, hypergraph animals. These structures are designed to describe the local node neighborhoods of nodes in hypergraphs. We establish their relationships to lattice animals and network motifs, and we develop their combinatorial properties for sparse and uncorrelated hypergraphs. We make use of the tight link of hypergraph animals to partition numbers, which opens up a vast mathematical framework for the analysis of hypergraph animals. We then study their abundances in random hypergraphs. Two transferable insights result from this analysis: (i) it establishes the importance of high-cardinality edges in ensembles of random hypergraphs that are inspired by the classical Erdös-Renyí random graphs; and (ii) there is a close connection between degree and hyperedge cardinality in random hypergraphs that shapes animal abundances and spectra profoundly. Both findings imply that hypergraph animals can have the potential to affect information flow and processing in complex systems. Our analysis also suggests that we need to spend more effort on investigating and developing suitable conditional ensembles of random hypergraphs that can capture real-world structures and their complex dependency structures.

A distributed integral control mechanism for regulation of cholesterol concentration in the human retina

Tight homeostatic control of cholesterol concentration within the complex tissue microenvironment of the retina is the hallmark of a healthy eye. By contrast, dysregulation of biochemical mechanisms governing retinal cholesterol homeostasis likely contributes to the aetiology and progression of age-related macular degeneration (AMD). While the signalling mechanisms maintaining cellular cholesterol homeostasis are well-studied, a systems-level description of molecular interactions regulating cholesterol balance within the human retina remains elusive. Here, we provide a comprehensive overview of all currently-known molecular-level interactions involved in cholesterol regulation across the major compartments of the human retina, encompassing the retinal pigment epithelium (RPE), photoreceptor cell layer, Müller cell layer and Bruch's membrane. We develop a comprehensive chemical reaction network (CRN) of these interactions, involving 71 molecular species, partitioned into 10 independent subnetworks. These subnetworks collectively ensure robust homeostasis of 14 forms of cholesterol across distinct retinal cellular compartments. We provide mathematical evidence that three independent antithetic integral feedback controllers tightly regulate ER cholesterol in retinal cells, with additional independent mechanisms extending this regulation to other forms of cholesterol throughout the retina. Our novel mathematical model of retinal cholesterol regulation provides a framework for understanding the mechanisms of cholesterol dysregulation in diseased eyes and for exploring potential therapeutic strategies.

Identifying and explaining resilience in ecological networks

Resilient ecological systems are more likely to persist and function in the Anthropocene. Current methods for estimating an ecosystem's resilience rely on accurately parameterized ecosystem models, which is a significant empirical challenge. In this paper, we adapt tools from biochemical kinetics to identify ecological networks that exhibit 'structural resilience', a strong form of resilience that is solely a property of the network structure and is independent of model parameters. We undertake an exhaustive search for structural resilience across all three-species ecological networks, under a generalized Lotka-Volterra modelling framework. Out of 20,000 possible network structures, approximately 2% display structural resilience. The properties of these networks provide important insights into the mechanisms that could promote resilience in ecosystems, provide new theoretical avenues for qualitative modelling approaches and provide a foundation for identifying robust forms of ecological resilience in large, realistic ecological networks.

Exploring Emergent Properties in Enzymatic Reaction Networks: Design and Control of Dynamic Functional Systems

The intricate and complex features of enzymatic reaction networks (ERNs) play a key role in the emergence and sustenance of life. Constructing such networks in vitro enables stepwise build up in complexity and introduces the opportunity to control enzymatic activity using physicochemical stimuli. Rational design and modulation of network motifs enable the engineering of artificial systems with emergent functionalities. Such functional systems are useful for a variety of reasons such as creating new-to-nature dynamic materials, producing value-added chemicals, constructing metabolic modules for synthetic cells, and even enabling molecular computation. In this review, we offer insights into the chemical characteristics of ERNs while also delving into their potential applications and associated challenges.

DNA Reaction System That Acquires Classical Conditioning

Biochemical reaction networks can exhibit plastic adaptation to alter their functions in response to environmental changes. This capability is derived from the structure and dynamics of the reaction networks and the functionality of the biomolecule. This plastic adaptation in biochemical reaction systems is essentially related to memory and learning capabilities, which have been studied in DNA computing applications for the past decade. However, designing DNA reaction systems with memory and learning capabilities using the dynamic properties of biochemical reactions remains challenging. In this study, we propose a basic DNA reaction system design that acquires classical conditioning, a phenomenon underlying memory and learning, as a typical learning task. Our design is based on a simple mechanism of five DNA strand displacement reactions and two degradative reactions. The proposed DNA circuit can acquire or lose a new function under specific conditions, depending on the input history formed by repetitive stimuli, by exploiting the dynamic properties of biochemical reactions induced by different input timings.

Robust homeostasis of cellular cholesterol is a consequence of endogenous antithetic integral control

Although cholesterol is essential for cellular viability and proliferation, it is highly toxic in excess. The concentration of cellular cholesterol must therefore be maintained within tight tolerances, and is thought to be subject to a stringent form of homeostasis known as Robust Perfect Adaptation (RPA). While much is known about the cellular signalling interactions involved in cholesterol regulation, the specific chemical reaction network structures that might be responsible for the robust homeostatic regulation of cellular cholesterol have been entirely unclear until now. In particular, the molecular mechanisms responsible for sensing excess whole-cell cholesterol levels have not been identified previously, and no mathematical models to date have been able to capture an integral control implementation that could impose RPA on cellular cholesterol. Here we provide a detailed mathematical description of cholesterol regulation pathways in terms of biochemical reactions, based on an extensive review of experimental and clinical literature. We are able to decompose the associated chemical reaction network structures into several independent subnetworks, one of which is responsible for conferring RPA on several intracellular forms of cholesterol. Remarkably, our analysis reveals that RPA in the cholesterol concentration in the endoplasmic reticulum (ER) is almost certainly due to a well-characterised control strategy known as antithetic integral control which, in this case, involves the high-affinity binding of a multi-molecular transcription factor complex with cholesterol molecules that are excluded from the ER membrane. Our model provides a detailed framework for exploring the necessary biochemical conditions for robust homeostatic control of essential and tightly regulated cellular molecules such as cholesterol.

Sensitivity analysis of biochemical systems using bond graphs

The sensitivity of systems biology models to parameter variation can give insights into which parameters are most important for physiological function, and also direct efforts to estimate parameters. However, in general, kinetic models of biochemical systems do not remain thermodynamically consistent after perturbing parameters. To address this issue, we analyse the sensitivity of biological reaction networks in the context of a bond graph representation. We find that the parameter sensitivities can themselves be represented as bond graph components, mirroring potential mechanisms for controlling biochemistry. In particular, a sensitivity system is derived which re-expresses parameter variation as additional system inputs. The sensitivity system is then linearized with respect to these new inputs to derive a linear system which can be used to give local sensitivity to parameters in terms of linear system properties such as gain and time constant. This linear system can also be used to find so-called sloppy parameters in biological models. We verify our approach using a model of the Pentose Phosphate Pathway, confirming the reactions and metabolites most essential to maintaining the function of the pathway.