Optimal Control of Immune Checkpoint Inhibitor Therapy in a Heart-Tumour Model.

Autoimmune myocarditis, or cardiac muscle inflammation, is a rare but frequently fatal side-effect of immune checkpoint inhibitors (ICIs), a class of cancer therapies. Despite the dangers that side-effects such as these pose to patients, they are rarely, if ever, included explicitly when mechanistic mathematical modelling of cancer therapy is used for optimization of treatment. In this paper, we develop a two-compartment mathematical model which incorporates the impact of ICIs on both the heart and the tumour.

Modeling cell differentiation in neuroblastoma: Insights into development, malignancy, and treatment relapse.

Neuroblastoma is a paediatric extracranial solid cancer that arises from the developing sympathetic nervous system and is characterised by an abnormal distribution of cell types in tumours compared to healthy infant tissues. In this paper, we propose a new mathematical model of cell differentiation during sympathoadrenal development. By performing Bayesian inference of the model parameters using clinical data from patient samples, we show that the model successfully accounts for the observed differences in cell type heterogeneity among healthy adrenal tissues and four common types of neuroblastomas.

Modelling the Impact of Phenotypic Heterogeneity on Cell Migration: A Continuum Framework Derived from Individual-Based Principles.

Collective cell migration plays a crucial role in numerous biological processes, including tumour growth, wound healing, and the immune response. Often, the migrating population consists of cells with various different phenotypes. This study derives a general mathematical framework for modelling cell migration in the local environment, which is coarse-grained from an underlying individual-based model that captures the dynamics of cell migration that are influenced by the phenotype of the cell, such as random movement, proliferation, phenotypic transitions, and interactions with the local environment.

Modularity of the segmentation clock and morphogenesis.

Vertebrates have evolved great diversity in the number of segments dividing the trunk body, however, the developmental origin of the evolvability of this trait is poorly understood. The number of segments is thought to be determined in embryogenesis as a product of morphogenesis of the pre-somitic mesoderm (PSM) and the periodicity of a molecular oscillator active within the PSM known as the segmentation clock. Here, we explore whether the clock and PSM morphogenesis exhibit developmental modularity, as independent evolution of these two processes may explain the high evolvability of segment number.

Approximate Solutions of a General Stochastic Velocity-Jump Model Subject to Discrete-Time Noisy Observations.

Advances in experimental techniques allow the collection of high-resolution spatio-temporal data that track individual motile entities over time. These tracking data motivate the use of mathematical models to characterise the motion observed. In this paper, we aim to describe the solutions of velocity-jump models for single-agent motion in one spatial dimension, characterised by successive Markovian transitions within a finite network of n states, each with a specified velocity and a fixed rate of switching to every other state.

Random walk models in the life sciences: including births, deaths and local interactions.

Random walks and related spatial stochastic models have been used in a range of application areas, including animal and plant ecology, infectious disease epidemiology, developmental biology, wound healing and oncology. Classical random walk models assume that all individuals in a population behave independently, ignoring local physical and biological interactions. This assumption simplifies the mathematical description of the population considerably, enabling continuum-limit descriptions to be derived and used in model analysis and fitting.

Smoothing in linear multicompartment biological processes subject to stochastic input.

Many physical and biological systems rely on the progression of material through multiple independent stages. In viral replication, for example, virions enter a cell to undergo a complex process comprising several disparate stages before the eventual accumulation and release of replicated virions. While such systems may have some control over the internal dynamics that make up this progression, a challenge for many is to regulate behavior under what are often highly variable external environments acting as system inputs.

Phenotypic switching mechanisms determine the structure of cell migration into extracellular matrix under the 'go-or-grow' hypothesis.

A fundamental feature of collective cell migration is phenotypic heterogeneity which, for example, influences tumour progression and relapse. While current mathematical models often consider discrete phenotypic structuring of the cell population, in-line with the 'go-or-grow' hypothesis (Hatzikirou et al., 2012; Stepien et al.

Optimal control of collective electrotaxis in epithelial monolayers.

Epithelial monolayers are some of the best-studied models for collective cell migration due to their abundance in multicellular systems and their tractability. Experimentally, the collective migration of epithelial monolayers can be robustly steered using electric fields, via a process termed electrotaxis. Theoretically, however, the question of how to design an electric field to achieve a desired spatiotemporal movement pattern is underexplored.

Predicting Radiotherapy Patient Outcomes with Real-Time Clinical Data Using Mathematical Modelling.

Longitudinal tumour volume data from head-and-neck cancer patients show that tumours of comparable pre-treatment size and stage may respond very differently to the same radiotherapy fractionation protocol. Mathematical models are often proposed to predict treatment outcome in this context, and have the potential to guide clinical decision-making and inform personalised fractionation protocols. Hindering effective use of models in this context is the sparsity of clinical measurements juxtaposed with the model complexity required to produce the full range of possible patient responses.

Efficient multifidelity likelihood-free Bayesian inference with adaptive computational resource allocation.

Likelihood-free Bayesian inference algorithms are popular methods for inferring the parameters of complex stochastic models with intractable likelihoods. These algorithms characteristically rely heavily on repeated model simulations. However, whenever the computational cost of simulation is even moderately expensive, the significant burden incurred by likelihood-free algorithms leaves them infeasible for many practical applications.

A mathematical framework for the emergence of winners and losers in cell competition.

Cell competition is a process in multicellular organisms where cells interact with their neighbours to determine a "winner" or "loser" status. The loser cells are eliminated through programmed cell death, leaving only the winner cells to populate the tissue. Cell competition is context-dependent; the same cell type can win or lose depending on the cell type it is competing against.

Quantifying tissue growth, shape and collision via continuum models and Bayesian inference.

Although tissues are usually studied in isolation, this situation rarely occurs in biology, as cells, tissues and organs coexist and interact across scales to determine both shape and function. Here, we take a quantitative approach combining data from recent experiments, mathematical modelling and Bayesian parameter inference, to describe the self-assembly of multiple epithelial sheets by growth and collision. We use two simple and well-studied continuum models, where cells move either randomly or following population pressure gradients.

Dynamic fibronectin assembly and remodeling by leader neural crest cells prevents jamming in collective cell migration.

Collective cell migration plays an essential role in vertebrate development, yet the extent to which dynamically changing microenvironments influence this phenomenon remains unclear. Observations of the distribution of the extracellular matrix (ECM) component fibronectin during the migration of loosely connected neural crest cells (NCCs) lead us to hypothesize that NCC remodeling of an initially punctate ECM creates a scaffold for trailing cells, enabling them to form robust and coherent stream patterns. We evaluate this idea in a theoretical setting by developing an individual-based computational model that incorporates reciprocal interactions between NCCs and their ECM.

Colec12 and Trail signaling confine cranial neural crest cell trajectories and promote collective cell migration.

Background: Collective and discrete neural crest cell (NCC) migratory streams are crucial to vertebrate head patterning. However, the factors that confine NCC trajectories and promote collective cell migration remain unclear.

Results: Computational simulations predicted that confinement is required only along the initial one-third of the cranial NCC migratory pathway.

A model-informed approach to assess the risk of immune checkpoint inhibitor-induced autoimmune myocarditis.

Immune checkpoint inhibitors (ICIs), as a novel immunotherapy, are designed to modulate the immune system to attack malignancies. Despite their promising benefits, immune-related adverse events (IRAEs) may occur, and incidences are bound to increase with surging demand of this class of drugs in treating cancer. Myocarditis, although rare compared to other IRAEs, has a significantly higher fatal frequency.

Reliable and efficient parameter estimation using approximate continuum limit descriptions of stochastic models.

Stochastic individual-based mathematical models are attractive for modelling biological phenomena because they naturally capture the stochasticity and variability that is often evident in biological data. Such models also allow us to track the motion of individuals within the population of interest. Unfortunately, capturing this microscopic detail means that simulation and parameter inference can become computationally expensive.

Efficient Bayesian inference for mechanistic modelling with high-throughput data.

Bayesian methods are routinely used to combine experimental data with detailed mathematical models to obtain insights into physical phenomena. However, the computational cost of Bayesian computation with detailed models has been a notorious problem. Moreover, while high-throughput data presents opportunities to calibrate sophisticated models, comparing large amounts of data with model simulations quickly becomes computationally prohibitive.