Two wrongs do not make a right: the assumption that an inhibitor acts as an inverse activator.

Models of biochemical networks are often large intractable sets of differential equations. To make sense of the complexity, relationships between genes/proteins are presented as connected graphs, the edges of which are drawn to indicate activation or inhibition relationships. These diagrams are useful for drawing qualitative conclusions in many cases by the identifying recurring of topological motifs, for example positive and negative feedback loops. These topological features are usually classified under the presumption that activation and inhibition are inverse relationships. For example, inhibition of an inhibitor is often classified the same as activation of an activator within a motif classification, effectively treating them as equivalent. Whilst in many contexts this may not lead to catastrophic errors, drawing conclusions about the behavior of motifs, pathways or networks from these broad classes of topological feature without adequate mathematical descriptions can lead to obverse outcomes. We investigate the extent to which a biochemical pathway/network will behave quantitatively dissimilar to pathway/ networks with similar typologies formed by swapping inhibitors as the inverse of activators. The purpose of the study is to determine under what circumstances rudimentary qualitative assessment of network structure can provide reliable conclusions as to the quantitative behaviour of the network. Whilst there are others, We focus on two main mathematical qualities which may cause a divergence in the behaviour of two pathways/networks which would otherwise be classified as similar; (i) a modelling feature we label 'bias' and (ii) the precise positioning of activators and inhibitors within simple pathways/motifs.

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.

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.

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.

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.

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.

Examining the efficacy of localised gemcitabine therapy for the treatment of pancreatic cancer using a hybrid agent-based model.

The prognosis for pancreatic ductal adenocarcinoma (PDAC) patients has not significantly improved in the past 3 decades, highlighting the need for more effective treatment approaches. Poor patient outcomes and lack of response to therapy can be attributed, in part, to a lack of uptake of perfusion of systemically administered chemotherapeutic drugs into the tumour. Wet-spun alginate fibres loaded with the chemotherapeutic agent gemcitabine have been developed as a potential tool for overcoming the barriers in delivery of systemically administrated drugs to the PDAC tumour microenvironment by delivering high concentrations of drug to the tumour directly over an extended period. While exciting, the practicality, safety, and effectiveness of these devices in a clinical setting requires further investigation. Furthermore, an in-depth assessment of the drug-release rate from these devices needs to be undertaken to determine whether an optimal release profile exists. Using a hybrid computational model (agent-based model and partial differential equation system), we developed a simulation of pancreatic tumour growth and response to treatment with gemcitabine loaded alginate fibres. The model was calibrated using in vitro and in vivo data and simulated using a finite volume method discretisation. We then used the model to compare different intratumoural implantation protocols and gemcitabine-release rates. In our model, the primary driver of pancreatic tumour growth was the rate of tumour cell division. We were able to demonstrate that intratumoural placement of gemcitabine loaded fibres was more effective than peritumoural placement. Additionally, we quantified the efficacy of different release profiles from the implanted fibres that have not yet been tested experimentally. Altogether, the model developed here is a tool that can be used to investigate other drug delivery devices to improve the arsenal of treatments available for PDAC and other difficult-to-treat cancers in the future.

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.

Evaluation of pathogen specific urinary peptides in tick-borne illnesses.

Mass spectrometry enhanced by nanotechnology can achieve previously unattainable sensitivity for characterizing urinary pathogen-derived peptides. We utilized mass spectrometry enhanced by affinity hydrogel particles (analytical sensitivity = 2.5 pg/mL) to study tick pathogen-specific proteins shed in the urine of patients with (1) erythema migrans rash and acute symptoms, (2) post treatment Lyme disease syndrome (PTLDS), and (3) clinical suspicion of tick-borne illnesses (TBI). Targeted pathogens were Borrelia, Babesia, Anaplasma, Rickettsia, Ehrlichia, Bartonella, Francisella, Powassan virus, tick-borne encephalitis virus, and Colorado tick fever virus. Specificity was defined by 100% amino acid sequence identity with tick-borne pathogen proteins, evolutionary taxonomic verification for related pathogens, and no identity with human or other organisms. Using a cut off of two pathogen peptides, 9/10 acute Lyme Borreliosis patients resulted positive, while we identified zero false positive in 250 controls. Two or more pathogen peptides were identified in 40% of samples from PTLDS and TBI patients (categories 2 and 3 above, n = 59/148). Collectively, 279 distinct unique tick-borne pathogen derived peptides were identified. The number of pathogen specific peptides was directly correlated with presence or absence of symptoms reported by patients (ordinal regression pseudo-R2 = 0.392, p = 0.010). Enhanced mass spectrometry is a new tool for studying tick-borne pathogen infections.

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.

Lipoarabinomannan antigenic epitope differences in tuberculosis disease subtypes.

An accurate urine test for diverse populations with active tuberculosis could be transformative for preventing TB deaths. Urinary liporabinomannan (LAM) testing has been previously restricted to HIV co-infected TB patients. In this study we evaluate urinary LAM in HIV negative, pediatric and adult, pulmonary and extrapulmonary tuberculosis patients. We measured 430 microbiologically confirmed pretreatment tuberculosis patients and controls from Peru, Guinea Bissau, Venezuela, Uganda and the United States using three monoclonal antibodies, MoAb1, CS35, and A194, which recognize distinct LAM epitopes, a one-sided immunoassay, and blinded cohorts. We evaluated sources of assay variability and comorbidities (HIV and diabetes). All antibodies successfully discriminated TB positive from TB negative patients. ROAUC from the average of three antibodies' responses was 0.90; 95% CI 0.87-0.93, 90% sensitivity, 73.5% specificity (80 pg/mL). MoAb1, recognizing the 5-methylthio-D-xylofuranose(MTX)-mannose(Man) cap epitope, performed the best, was less influenced by glycosuria and identified culture positive pediatric (N = 19) and extrapulmonary (N = 24) patients with high accuracy (ROAUC 0.87, 95% CI 0.77-0.98, 0.90 sensitivity 0.80 specificity at 80 pg/mL; ROAUC = 0.96, 95% CI 0.92-0.99, 96% sensitivity, 80% specificity at 82 pg/mL, respectively). The MoAb1 antibody, recognizing the MTX-Man cap epitope, is a novel analyte for active TB detection in pediatric and extrapulmonary disease.

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.

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.

Affinity enrichment for mass spectrometry: improving the yield of low abundance biomarkers.

INTRODUCTION: Mass spectrometry (MS) is the premier tool for discovering novel disease-associated protein biomarkers. Unfortunately, when applied to complex body fluid samples, MS has poor sensitivity for the detection of low abundance biomarkers (≪10 ng/mL), derived directly from the diseased tissue cells or pathogens. Areas covered: Herein we discuss the strengths and drawbacks of technologies used to concentrate low abundance analytes in body fluids, with the aim to improve the effective sensitivity for MS discovery. Solvent removal by dry-down or dialysis, and immune-depletion of high abundance serum or plasma proteins, is shown to have disadvantages compared to positive selection of the candidate biomarkers by affinity enrichment. A theoretical analysis of affinity enrichment reveals that the yield for low abundance biomarkers is a direct function of the binding affinity (Association/Dissociation rates) used for biomarker capture. In addition, a high affinity capture pre processing step can effectively dissociate the candidate biomarker from partitioning with high abundance proteins such as albumin. Expert commentary: Properly designed high affinity capture materials can enrich the yield of low abundance (0.1-10 picograms/mL) candidate biomarkers for MS detection. Affinity capture and concentration, as an upfront step in sample preparation for MS, combined with MS advances in software and hardware that improve the resolution of the chromatographic separation can yield a transformative new class of low abundance biomarkers predicting disease risk or disease latency.

Urine lipoarabinomannan glycan in HIV-negative patients with pulmonary tuberculosis correlates with disease severity.

An accurate urine test for pulmonary tuberculosis (TB), affecting 9.6 million patients worldwide, is critically needed for surveillance and treatment management. Past attempts failed to reliably detect the mycobacterial glycan antigen lipoarabinomannan (LAM), a marker of active TB, in HIV-negative, pulmonary TB-infected patients' urine (85% of 9.6 million patients). We apply a copper complex dye within a hydrogel nanocage that captures LAM with very high affinity, displacing interfering urine proteins. The technology was applied to study pretreatment urine from 48 Peruvian patients, all negative for HIV, with microbiologically confirmed active pulmonary TB. LAM was quantitatively measured in the urine with a sensitivity of >95% and a specificity of >80% (n = 101) in a concentration range of 14 to 2000 picograms per milliliter, as compared to non-TB, healthy and diseased, age-matched controls (evaluated by receiver operating characteristic analysis; area under the curve, 0.95; 95% confidence interval, 0.9005 to 0.9957). Urinary LAM was elevated in patients with a higher mycobacterial burden (n = 42), a higher proportion of weight loss (n = 37), or cough (n = 50). The technology can be configured in a variety of formats to detect a panel of previously undetectable very-low-abundance TB urinary analytes. Eight of nine patients who were smear-negative and culture-positive for TB tested positive for urinary LAM. This technology has broad implications for pulmonary TB screening, transmission control, and treatment management for HIV-negative patients.