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.

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.

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.

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.

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.

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.

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.

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).

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.

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.

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.

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 , which accounts fully for the molecular complexities of the underlying signalling mechanisms.

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.

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.

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.

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.

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.

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.

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.

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.

Analysis of albumin-associated peptides and proteins from ovarian cancer patients.

Background: Albumin binds low-molecular-weight molecules, including proteins and peptides, which then acquire its longer half-life, thereby protecting the bound species from kidney clearance. We developed an experimental method to isolate albumin in its native state and to then identify [mass spectrometry (MS) sequencing] the corresponding bound low-molecular-weight molecules. We used this method to analyze pooled sera from a human disease study set (high-risk persons without cancer, n = 40; stage I ovarian cancer, n = 30; stage III ovarian cancer, n = 40) to demonstrate the feasibility of this approach as a discovery method.