Partial differential equation (PDE) models are often used to study biological phenomena involving movement-birth-death processes, including ecological population dynamics and the invasion of populations cells. Count data, by definition, is non-negative, count data relating bounded above some carrying capacity that arises through competition for space or nutrients. Parameter estimation, parameter identifiability, making model predictions usually involves working with a measurement error...

Tumour spheroid experiments are routinely used to study cancer progression and treatment. Various inconsistent experimental designs used, leading challenges in interpretation reproducibility. Using multiple designs, live-dead cell staining, real-time cycle imaging, we measure necrotic proliferation-inhibited regions over 1000 4D tumour spheroids (3D space plus status). By intentionally varying the initial size temporal sampling frequencies across lines, collect an abundance of measurements...

tumour spheroids have been used to study avascular growth and drug design for over 50 years. Tumour exhibit heterogeneity within the growing population that is thought be related spatial temporal differences in nutrient availability. The recent development of real-time fluorescent cell cycle imaging allows us identify position status individual cells spheroid, giving rise notion a four-dimensional (4D) spheroid. We develop first stochastic individual-based model (IBM) 4D spheroid show IBM...

Abstract We propose a simple mathematical model to describe the mechanical relaxation of cells within curved epithelial tissue layer represented by an arbitrary curve in two-dimensional space. This generalises previous one-dimensional models flat epithelia investigate influence curvature for relaxation. represent mechanics cell body either straight springs, or springs that follow curve’s shape. To understand collective dynamics cells, we devise appropriate continuum limit which number and...

Tumours are subject to external environmental variability. However, in vitro tumour spheroid experiments, used understand cancer progression and develop therapies, have been routinely performed for the past fifty years constant environments. Furthermore, spheroids typically grown ambient atmospheric oxygen (normoxia), whereas most vivo tumours exist hypoxic Therefore, there clear discrepancies between conditions. We explore these by combining tools from experimental biology, mathematical...

Abstract Nano-engineered particles are a promising tool for medical diagnostics, biomedical imaging, and targeted drug delivery. Fundamental to the assessment of particle performance in vitro particle-cell interaction experiments. These experiments can be summarised with key parameters that facilitate objective comparisons across various cell pairs, such as association rate. Previous studies often focus on point estimates neglect heterogeneity routine measurements. In this study, we develop...

Mechanical heterogeneity in biological tissues, particular stiffness, can be used to distinguish between healthy and diseased states. However, it is often difficult explore relationships cellular-level properties tissue-level outcomes when experiments are performed at a single scale only. To overcome this difficulty, we develop multi-scale mathematical model which provides clear framework these connections across scales. Starting with an individual-based mechanical of cell movement,...

Tumour spheroids are common in vitro experimental models of avascular tumour growth. Compared with traditional two-dimensional culture, more closely mimic the microenvironment where spatial differences nutrient availability strongly influence We show that initiated using significantly different numbers cells grow to similar limiting sizes, suggesting tumours have a structure; agreement untested predictions classical mathematical spheroids. develop novel and statistical framework study...

Throughout the life sciences, biological populations undergo multiple phases of growth, often referred to as

Abstract Regulation of cytoskeletal structure and dynamics is essential for multiple aspects cellular behavior, yet there much to learn about the molecular machinery underlying coordination between cytoskeleton its effector systems. One group proteins that regulate microtubule behavior interaction with other components, such as actin-regulatory transport machinery, plus-end tracking (MT+TIPs). In particular, evidence suggests MT+TIP, CLASP, may play a pivotal role in microtubules structures...

Abstract Integrated continuous simulation‐optimization models can be effective predictors of a process‐based responses for cost‐benefit optimization best management practices (BMPs) selection and placement. However, practical application model is computationally prohibitive large‐scale systems. This study proposes an enhanced Nonlinearity Interval Mapping Scheme (NIMS) to solve watershed problems several orders magnitude faster than other commonly used algorithms. An efficient interval...

Abstract The detachment of cells from the boundary an epithelial tissue and subsequent invasion these into surrounding tissues is important for cancer development wound healing, strongly associated with epithelial–mesenchymal transition (EMT). Chemical signals, such as TGF- β , produced by can be uptaken induce EMT. In this work, we present a novel cell-based discrete mathematical model mechanical cellular relaxation, cell proliferation, driven chemically-dependent EMT in tissue. A continuum...

Abstract Tumour spheroids are common in vitro experimental models of avascular tumour growth. Compared with traditional two-dimensional culture, more closely mimic the microenvironment where spatial differences nutrient availability strongly influence We show that initiated using significantly different numbers cells grow to similar limiting sizes, suggesting tumours have a structure; agreement untested predictions classical mathematical spheroids. develop novel and statistical framework...

In this study, we couple intracellular signalling and cell-based mechanical properties to develop a novel free boundary mechanobiological model of epithelial tissue dynamics. Mechanobiological coupling is introduced at the cell level in discrete modelling framework, new reaction–diffusion equations are derived describe tissue-level outcomes. The evolves as result underlying biological mechanisms included model. To demonstrate accuracy continuum model, compare numerical solutions models for...

EB1 is a highly conserved microtubule (MT) plus end tracking protein (+TIP) involved in regulating MT dynamics, but the mechanisms of its effects on polymerization remain undefined. Resolving this question requires understanding how interacts with MTs. Previous electron microscopy S. pombe homolog Mal3p suggested that binds specifically to seam, implying family members promote by stabilizing seam. However, more recent indicates everywhere except Neither set experiments investigated behavior...

Throughout the life sciences we routinely seek to interpret measurements and observations using parameterised mechanistic mathematical models. A fundamental often overlooked choice in this approach involves relating solution of a model with noisy incomplete measurement data. This is achieved by assuming that data are deterministic model, errors additive normally distributed. While assumption Gaussian noise extremely common simple implement interpret, it unjustified can lead poor parameter...

The epithelial-mesenchymal (E/M) hybrid state has emerged as an important mediator of the elements cancer progression facilitated by epithelial mesenchymal plasticity (EMP). We review here evidence for presence and prognostic potential E/M in carcinoma, modelling predictions validations studies to demonstrate stabilised intermediates along spectrum EMP, computational approaches characterising quantifying EMP phenotypes, with particular attention emerging realm single-cell through RNA...

Abstract Partial differential equation (PDE) models are often used to study biological phenomena involving movement-birth-death processes, including ecological population dynamics and the invasion of populations cells. Count data, by definition, is non-negative, count data relating bounded above some carrying capacity that arises through competition for space or nutrients. Parameter estimation, parameter identifiability, making model predictions usually involves working with a measurement...

Abstract Throughout the life sciences, biological populations undergo multiple phases of growth, often referred to as biphasic growth for commonly-encountered situation involving two phases. Biphasic population occurs over a massive range spatial and temporal scales, ranging from microscopic tumours several days, decades-long re-growth corals in coral reefs that can extend hundreds kilometres. Different mathematical models statistical methods are used diagnose, understand, predict growth....