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.

Could Mathematics be the Key to Unlocking the Mysteries of Multiple Sclerosis?

Multiple sclerosis (MS) is an autoimmune, neurodegenerative disease that is driven by immune system-mediated demyelination of nerve axons. While diseases such as cancer, HIV, malaria and even COVID have realised notable benefits from the attention of the mathematical community, MS has received significantly less attention despite the increasing disease incidence rates, lack of curative treatment, and long-term impact on patient well-being. In this review, we highlight existing, MS-specific mathematical research and discuss the outstanding challenges and open problems that remain for mathematicians. We focus on how both non-spatial and spatial deterministic models have been used to successfully further our understanding of T cell responses and treatment in MS. We also review how agent-based models and other stochastic modelling techniques have begun to shed light on the highly stochastic and oscillatory nature of this disease. Reviewing the current mathematical work in MS, alongside the biology specific to MS immunology, it is clear that mathematical research dedicated to understanding immunotherapies in cancer or the immune responses to viral infections could be readily translatable to MS and might hold the key to unlocking some of its mysteries.

The effect of chemotaxis on T-cell regulatory dynamics.

Autoimmune diseases, such as Multiple Sclerosis, are often modelled through the dynamics of T-cell interactions. However, the spatial aspect of such diseases, and how dynamics may result in spatially heterogeneous outcomes, is often overlooked. We consider the effects of diffusion and chemotaxis on T-cell regulatory dynamics using a three-species model of effector and regulator T-cell populations, along with a chemical signalling agent. While diffusion alone cannot lead to instability and spatial patterning, the inclusion of chemotaxis can result in multiple forms of instability that produce highly complicated spatiotemporal behaviour. The parameter regimes in which different instabilities occur are determined through linear stability analysis and the full dynamics is explored through numerical simulation.

Mathematical modelling of the role of mucosal vaccine on the within-host dynamics of Chlamydia trachomatis.

A mathematical model of the within-host replicative dynamics of C. trachomatis infection and its interactions with the immune system, in the presence of a mucosal vaccine, is presented. Our aim is to estimate the requisite efficacy of an efficacious mucosal vaccine that could promote a stable disease-free state in vivo. Sensitivity analysis was used to quantify how variability in the model parameters influence the value of the disease threshold R0. This shows that the two most important factors to be considered for achieving a disease-free state state in vivo, based on their influence on R0, are the efficacy of the Chlamydia vaccine, and the rate at which the humoral immune response protects healthy epithelial cells from infection. Numerical simulations of the model show that a vaccine with a minimum efficacy of 86% may be required for the in vivo control of Chlamydia burden. Such effective but imperfect Chlamydia vaccine could confer long-term protective immunity to genital Chlamydia infections. Conditions under which lower vaccine efficacies may suffice are also explored.

Cholesterol Regulation in Age-Related Macular Degeneration: A Framework for Mathematical Modelling of Drusen Biogenesis.

In age-related macular degeneration (AMD), there is, in common with many other age-related diseases, the need to distinguish between changes in the ageing eye that lead to disease and those changes that are considered part of a healthy, ageing eye. Various studies investigating the multitude of mechanisms involved in the aetiology of AMD exist within the field of ophthalmology and related medical fields, yet many aspects of it remain poorly understood and only a limited number of therapies are available. A recent study relates drusen's topographically cellular characteristics to the neural retina's metabolic needs and associated cholesterol involvement within the retina. In particular, there is a need to fully understand the maintenance of cholesterol homeostasis in the retina to prevent normal ageing processes from being perturbed towards maculopathy. Here, we present an extensive review of the clinical and physiological features of the ageing retina, as well as mechanisms implicated in pathology, synthesised from a vast body of the published literature. We use this novel synthesis to construct a comprehensive process schematic, encompassing all key species and physiological processes such as nutrients, waste and lipoprotein management. We are therefore able to express these processes in a mathematical language via a comprehensive modelling framework, comprising a set of twenty-three equations spanning three distinct biological compartments. This very general modelling framework may now be adapted to more focused studies on individual mechanisms, processes or components underlying of the many facets of AMD. As an example of such a focused application, we conclude this article with a one-compartment, four-species model of the retinal pigment epithelium, which considers the parametric conditions under which either cholesterol homeostasis or unregulated accumulation of cholesterol may obtain in the ageing eye.

The blood peptidome: a higher dimension of information content for cancer biomarker discovery.

The low-molecular-weight range of the circulatory proteome is termed the 'peptidome', and could be a rich source of cancer-specific diagnostic information because it is a 'recording' of the cellular and extracellular enzymatic events that take place at the level of the cancer-tissue microenvironment. This new information archive seems to mainly exist in vivo, bound to high-abundance proteins such as albumin. Measuring panels of peptidome markers might be more sensitive and specific than conventional biomarker approaches. We discuss the advantages and disadvantages of various methods for studying the peptidome.

A Multivalent DNA Nanoparticle/Peptide Hybrid Molecular Modality for the Modulation of Protein-Protein Interactions in the Tumor Microenvironment.

Despite success in the treatment of some blood cancers and melanoma, positive response to immunotherapies remains disappointingly low in the treatment of solid tumors. The context of the molecular crosstalk within the tumor microenvironment can result in dysfunctional immune cell activation, leading to tumor tolerance and progression. Although modulating these protein-protein interactions (PPIs) is vital for appropriate immune cell activation and recognition, targeting nonenzymatic PPIs has proven to be fraught with challenges. To address this, we introduce a synthetic, multivalent molecular modality comprised of small interfering peptides precisely hybridized to a semi-rigid DNA scaffold. Herein, we describe a prototype of this modality that targets the IL-33/ST2 signaling axis, which is associated with tumor tolerance and immunotherapy treatment failure. Using peptides that mimic the specific high energy "hotspot" residues with which the IL-33/ST2 co-receptor, IL-1RAcP, interacts with the initial binary complex, we show this platform to effectively bind IL-33/ST2 with a K D of 110 nM. Additionally, this molecule effectively abrogates signal transduction in cell models at high nanomolar concentrations and is exquisitely selective for this complex over structurally similar PPIs within the same cytokine superfamily.

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.

Design Principles Underlying Robust Adaptation of Complex Biochemical Networks.

Biochemical networks are often characterized by tremendous complexity-both in terms of the sheer number of interacting molecules ("nodes") and in terms of the varied and incompletely understood interactions among these molecules ("interconnections" or "edges"). Strikingly, the vast and intricate networks of interacting proteins that exist within each living cell have the capacity to perform remarkably robustly, and reproducibly, despite significant variations in concentrations of the interacting components from one cell to the next and despite mutability over time of biochemical parameters. Here we consider the ubiquitously observed and fundamentally important signalling response known as robust perfect adaptation (RPA). We have recently shown that all RPA-capable networks, even the most complex ones, must satisfy an extremely rigid set of design principles, and are modular, being decomposable into just two types of network building-blocks-opposer modules and balancer modules. Here we present an overview of the design principles that characterize all RPA-capable network topologies through a detailed examination of a collection of simple examples. We also introduce a diagrammatic method for studying the potential of a network to exhibit RPA, which may be applied without a detailed knowledge of the complex mathematical principles governing RPA.

Universal structures for adaptation in biochemical reaction networks.

At the molecular level, the evolution of life is driven by the generation and diversification of adaptation mechanisms. A universal description of adaptation-capable chemical reaction network (CRN) structures has remained elusive until now, since currently-known criteria for adaptation apply only to a tiny subset of possible CRNs. Here we identify the definitive structural requirements that characterize all adaptation-capable collections of interacting molecules, however large or complex. We show that these network structures implement a form of integral control in which multiple independent integrals can collaborate to confer the capacity for adaptation on specific molecules. Using an algebraic algorithm informed by these findings, we demonstrate the existence of embedded integrals in a variety of biologically important CRNs that have eluded previous methods, and for which adaptation has been observed experimentally. This definitive picture of biological adaptation at the level of intermolecular interactions represents a blueprint for adaptation-capable signaling networks across all domains of life, and for the design of synthetic biosystems.

Mathematical measures of societal polarisation.

In opinion dynamics, as in general usage, polarisation is subjective. To understand polarisation, we need to develop more precise methods to measure the agreement in society. This paper presents four mathematical measures of polarisation derived from graph and network representations of societies and information-theoretic divergences or distance metrics. Two of the methods, min-max flow and spectral radius, rely on graph theory and define polarisation in terms of the structural characteristics of networks. The other two methods represent opinions as probability density functions and use the Kullback-Leibler divergence and the Hellinger distance as polarisation measures. We present a series of opinion dynamics simulations from two common models to test the effectiveness of the methods. Results show that the four measures provide insight into the different aspects of polarisation and allow real-time monitoring of social networks for indicators of polarisation. The three measures, the spectral radius, Kullback-Leibler divergence and Hellinger distance, smoothly delineated between different amounts of polarisation, i.e. how many cluster there were in the simulation, while also measuring with more granularity how close simulations were to consensus. Min-max flow failed to accomplish such nuance.

Person-to-person opinion dynamics: An empirical study using an online game.

A model needs to make verifiable predictions to have any scientific value. In opinion dynamics, the study of how individuals exchange opinions with one another, there are many theoretical models which attempt to model opinion exchange, one of which is the Martins model, which differs from other models by using a parameter that is easier to control for in an experiment. In this paper, we have designed an experiment to verify the Martins model and contribute to the experimental design in opinion dynamic with our novel method.

A secretory form of Parkin-independent mitophagy contributes to the repertoire of extracellular vesicles released into the tumour interstitial fluid in vivo.

We characterized the in vivo interstitial fluid (IF) content of extracellular vesicles (EVs) using the GFP-4T1 syngeneic murine cancer model to study EVs in-transit to the draining lymph node. GFP labelling confirmed the IF EV tumour cell origin. Molecular analysis revealed an abundance of IF EV-associated proteins specifically involved in mitophagy and secretory autophagy. A set of proteins required for sequential steps of fission-induced mitophagy preferentially populated the CD81+/PD-L1+ IF EVs; PINK1, TOM20, and ARIH1 E3 ubiquitin ligase (required for Parkin-independent mitophagy), DRP1 and FIS1 (mitochondrial peripheral fission), VDAC-1 (ubiquitination state triggers mitophagy away from apoptosis), VPS35, SEC22b, and Rab33b (vacuolar sorting). Comparing in vivo IF EVs to in vitro EVs revealed 40% concordance, with an elevation of mitophagy proteins in the CD81+ EVs for both murine and human cell lines subjected to metabolic stress. The export of cellular mitochondria proteins to CD81+ EVs was confirmed by density gradient isolation from the bulk EV isolate followed by anti-CD81 immunoprecipitation, molecular sieve chromatography, and MitoTracker export into CD81+ EVs. We propose the 4T1 in vivo model as a versatile tool to functionally characterize IF EVs. IF EV export of fission mitophagy proteins has broad implications for mitochondrial function and cellular immunology.

Ultrasensitivity and bistability in covalent-modification cycles with positive autoregulation.

Switch-like behaviours in biochemical networks are of fundamental significance in biological signal processing, and exist as two distinct types: ultra-sensitivity and bistability. Here we propose two new models of a reversible covalent-modification cycle with positive autoregulation (PAR), a motif structure that is thought to be capable of both ultrasensitivity and bistability in different parameter regimes. These new models appeal to a modelling framework that we call complex-complete, which accounts fully for the molecular complexities of the underlying signalling mechanisms. Each of the two new models encodes a specific molecular mechanism for PAR. We demonstrate that the modelling simplifications for PAR models that have been used in previous work, which rely on Michaelian approximations, are unable to accurately recapitulate the qualitative signalling responses supported by our detailed models. Strikingly, we show that complex-complete PAR models are capable of new qualitative responses such as one-way switches and a 'prozone' effect, depending on the specific PAR-encoding mechanism, which are not supported by Michaelian simplifications. Our results highlight the critical importance of accurately representing the molecular details of biochemical signalling mechanisms, and strongly suggest that the Michaelian approximation is inadequate for predictive models of enzyme-mediated chemical reactions with added regulations such as PAR.

Phosphoprotein pathway mapping: Akt/mammalian target of rapamycin activation is negatively associated with childhood rhabdomyosarcoma survival.

Mapping of protein signaling networks within tumors can identify new targets for therapy and provide a means to stratify patients for individualized therapy. Despite advances in combination chemotherapy, the overall survival for childhood rhabdomyosarcoma remains approximately 60%. A critical goal is to identify functionally important protein signaling defects associated with treatment failure for the 40% nonresponder cohort. Here, we show, by phosphoproteomic network analysis of microdissected tumor cells, that interlinked components of the Akt/mammalian target of rapamycin (mTOR) pathway exhibited increased levels of phosphorylation for tumors of patients with short-term survival. Specimens (n = 59) were obtained from the Children's Oncology Group Intergroup Rhabdomyosarcoma Study (IRS) IV, D9502 and D9803, with 12-year follow-up. High phosphorylation levels were associated with poor overall and poor disease-free survival: Akt Ser(473) (overall survival P < 0.001, recurrence-free survival P < 0.0009), 4EBP1 Thr(37/46) (overall survival P < 0.0110, recurrence-free survival P < 0.0106), eIF4G Ser(1108) (overall survival P < 0.0017, recurrence-free survival P < 0.0072), and p70S6 Thr(389) (overall survival P < 0.0085, recurrence-free survival P < 0.0296). Moreover, the findings support an altered interrelationship between the insulin receptor substrate (IRS-1) and Akt/mTOR pathway proteins (P < 0.0027) for tumors from patients with poor survival. The functional significance of this pathway was tested using CCI-779 in a mouse xenograft model. CCI-779 suppressed phosphorylation of mTOR downstream proteins and greatly reduced the growth of two different rhabdomyosarcoma (RD embryonal P = 0.00008; Rh30 alveolar P = 0.0002) cell lines compared with controls. These results suggest that phosphoprotein mapping of the Akt/mTOR pathway should be studied further as a means to select patients to receive mTOR/IRS pathway inhibitors before administration of chemotherapy.

The topological requirements for robust perfect adaptation in networks of any size.

Robustness, and the ability to function and thrive amid changing and unfavorable environments, is a fundamental requirement for living systems. Until now it has been an open question how large and complex biological networks can exhibit robust behaviors, such as perfect adaptation to a variable stimulus, since complexity is generally associated with fragility. Here we report that all networks that exhibit robust perfect adaptation (RPA) to a persistent change in stimulus are decomposable into well-defined modules, of which there exist two distinct classes. These two modular classes represent a topological basis for all RPA-capable networks, and generate the full set of topological realizations of the internal model principle for RPA in complex, self-organizing, evolvable bionetworks. This unexpected result supports the notion that evolutionary processes are empowered by simple and scalable modular design principles that promote robust performance no matter how large or complex the underlying networks become.

A control theoretic paradigm for cell signaling networks: a simple complexity for a sensitive robustness.

The fields of molecular biology and cell biology are being flooded with complex genomic and proteomic datasets of large dimensions. We now recognize that each molecule in the cell and tissue can no longer be viewed as an isolated entity. Instead, each molecule must be considered as one member of an interacting network. Consequently, there is an urgent need for mathematical models to understand the behavior of cell signaling networks in health and in disease.

The amplified peptidome: the new treasure chest of candidate biomarkers.

Mass spectrometric analysis of the low-molecular weight (LMW) range of the serum/plasma proteome is revealing the existence of large numbers of previously unknown peptides and protein fragments predicted to be derived from low-abundance proteins. This raises the question of why such low abundance molecules would be retained at detectable levels in the circulation, instead of being rapidly cleared and excreted. Theoretical models of biomarker production and association with serum carrier proteins have been developed to elucidate the mechanisms governing biomarker half-life in the bloodstream. These models predict that the vast majority of LMW biomarkers exist in association with circulating high molecular mass carrier proteins. Moreover, the total serum/plasma concentration of the biomarker is largely determined by the clearance rate of the carrier protein, not the free-phase biomarker clearance itself. These predictions have been verified experimentally using molecular mass fractionation of human serum before mass spectrometry sequence analysis. These principles have profound implications for biomarker discovery and measurement.

Proteins, drug targets and the mechanisms they control: the simple truth about complex networks.

Realizing the promise of molecularly targeted inhibitors for cancer therapy will require a new level of knowledge about how a drug target is wired into the control circuitry of a complex cellular network. Here we review general homeostatic principles of cellular networks that enable the cell to be resilient in the face of molecular perturbations, while at the same time being sensitive to subtle input signals. Insights into such mechanisms may facilitate the development of combination therapies that take advantage of the cellular control circuitry, with the aim of achieving higher efficacy at a lower drug dosage and with a reduced probability of drug-resistance development.