Conference Agenda

Introduction

Tumour growth is a complex mechanosensitive process guided by feedback between cells and the extracellular matrix (ECM). However, the underlying biomechanisms by which external loading impacts tumour growth remain unknown. Here we develop an in-vitro culture system for heterogeneous tumour spheroids to identify key biomechanical factors that restrict spheroid growth. We further propose a novel framework consisting a novel hydromechanical cell growth model, a 3D deformable cell framework and a deep-neural network (DNN)-accelerated finite element (FE) solver to uncover the mechanisms underlying mechanosensitive growth.

Methods

Murine breast cancer (4T1) cells were cultured, isolated and propagated to obtain tumour spheroids of distinct phenotypes within gelatin hydrogels of varying stiffness to investigate stress-dependent responses. A mathematical model was developed to predict cell growth as driven by a competition between hydrostatic pressure arising from active cell stress and external loading, and osmotic pressure arising from biomolecule synthesis and ion fluxes [1]. Biomolecules are synthesized during the G1 growth phase, which drives a fluid influx and growth through entropic osmotic forces. This model was integrated with MPacts [2], a discrete element method platform for multicellular mechanics. Loading from cell and matrix contact interfaces governs the cell growth rate, and we consider that mitosis is subject to surpassing a critical volume checkpoint for which the underlying mechanisms are characterised. The deformable cell model is embedded in a 3D finite element model of a hyperelastic matrix. To efficiently simulate this matrix deformation, a deep neural network (DNN) framework was developed. Synthetic training data for a diverse range of loading scenarios was generated and subsequently provided to a fully connected DNN to obtain a converged solution.

Results and Discussion

Analysis of the in-vitro spheroids reveals that tumour spheroid size reduces with increasing gel stiffness. Importantly, there was a significant reduction in the number of cells per spheroid and lower number of proliferative cells as determined by Ki-67 immunofluorescence. 4T1 spheroids developed from predominantly amoeboid-like cells were observed to have 2-3 fold larger diameters than epithelial-like spheroids. Our computational models predict that cell growth increases with biomolecule synthesis and the subsequent increase in osmotic pressure, which deforms surrounding matrix. Tumour spheroid growth simulations suggest that cells at the tumour core experience higher pressure than cells at the periphery, as previously shown experimentally [3]. These cells are also predicted to exhibit higher levels of biomolecule crowding. Our models indicate that cell confinement and associated loading leads to an imbalance between hydrostatic and osmotic pressures, which drives fluid loss and ultimately a reduction in cell growth below the volume checkpoint and suppression of proliferation. Importantly, our simulations predict a reduction in spheroid size with increasing matrix stiffness in agreement with our experimental data, and correctly capture cell morphologies and spheroid compaction. The fully coupled multicellular model allows for a deep insight into the mechanics of tumour growth at the cellular level.

References

1. McEvoy, E. et al. (2020). Nat. Commun.

2. Ongenae, S. et al. (2024). biorXiv

3. Nia, H. et al. (2017). Nat Biomed Eng

Traditionally, cancer has been viewed as a disease originating from a single cell that accumulates genetic mutations, eventually leading to tumour formation. However, recent research emphasizes the crucial role of the tumour microenvironment, especially its mechanical properties, in influencing cancer progression. Understanding the tumour microenvironment is key to gaining deeper insights into tumour development and response to therapies.

To investigate these complex interactions, researchers rely on both in vitro and in vivo models. In vitro models provide controlled environments to study specific tumour behaviours, while in vivo models offer more realistic biological contexts. However, experimental methods are often limited by their inability to isolate specific factors and efficiently test new hypotheses.

Computational modelling provides a powerful complementary approach. These models can mimic experimental conditions, test novel ideas, and explore system characteristics that are otherwise difficult or impractical to examine experimentally. Nevertheless, for computational models to be effective, they must be carefully calibrated using experimental data and account for both computational and experimental uncertainties.

In this work, we develop a comprehensive workflow that enables the integration between experimental data and computational tumour models. The process begins with the formulation of a flexible multiphase poroelastic model capable of simulating tumour growth, where the extracellular matrix is represented as a solid scaffold and the tumour and healthy cells, along with interstitial fluid, occupy the pore space. Once the computational model is established, we perform a global sensitivity analysis on a reduced-order version to identify the most influential parameters driving tumour behaviour. This step not only helps to simplify the model but also guides the design of future experiments by highlighting key variables. Building on this, we apply Bayesian inference techniques to explore and estimate the values of these parameters, accounting for uncertainty and variability inherent to biological systems. By treating parameters as probability distributions rather than fixed values, the model achieves a more realistic and robust representation of tumour dynamics. The proposed workflow is successfully applied to a case study of tumour spheroid growth, demonstrating its potential to bridge experimental observations with predictive computational modelling in a systematic and efficient way.

The vertebrate limb has long served as a paradigm to understand morphogenesis. Numerical models have played a key role in understanding how cells self-organize based on positional cues and local interactions to specify their fate, thereby driving skeletal patterning. Classical approaches typically rely on reaction-diffusion systems and positional information frameworks, and recent work has begun to explore their integration [1]. While these approaches have yielded valuable insights into localized patterning, they often fail to explain how multiple structures emerge sequentially and coherently within a growing domain.

In this work, we introduce a computational framework that integrates growth dynamics with self-organization and positional cues to predict the full skeletal pattern of a vertebrate limb for the first time. The new Growth-Processing-Propagation (GPP) framework [2] is formulated as a system of reaction-diffusion equations on a time-evolving domain. The model is governed by two non-dimensional parameters, α_R and β_D, which represent the ratio of growth rate to reaction and diffusion, respectively. These parameters determine the influence of bio-signal processing (reaction) and communication (diffusion) in relation to the growth rate on skeletal pattern formation. Unlike traditional models that rely on static or idealized domains, GPP captures the dynamic interplay between limb growth and patterning mechanisms in both space and time.

We apply the GPP framework to axolotl limb development, a classical system for studying morphogenesis due to its accessibility and regenerative capabilities. To constrain the model, we use time-lapse imaging to extract real limb geometries in developing axolotls. Additionally, we incorporate fluorescence images of molecular markers to define positional inputs and to validate the predicted skeletal patterns, focusing on the sequential emergence of the stylopod (upper arm), zeugopod (forearm), and autopod (digits).

The model reproduces the order and spatial distribution of skeletal elements without explicitly specifying when or where each segment should emerge. The number of digits and spacing emerge from a Turing-like instability modulated by domain growth, while transitions between limb segments arise naturally from growth-driven changes in effective patterning timescales. This suggests that variation in growth rate across space and time can shape skeletal complexity by influencing the dynamics of pattern formation.

To our knowledge, this is the first computational model to predict complete skeletal limb patterning, constrained by experimental measurements of domain shape, growth, and molecular marker distribution. The GPP framework offers a generalizable and interpretable modeling approach for simulating pattern formation on growing domains. It bridges classical morphogen-based theories with mechanical expansion, and provides a compact set of parameters to explore biological design space. We anticipate this approach will be broadly applicable to problems in morphogenesis, developmental and regenerative biology, where understanding the coupling between growth and patterning is essential.

[1] Raspopovic et al. (2014), Science 345(6196):566-70, doi: 10.1126/science.1252960.

[2] Ben Tahar et al. (2025), bioRxiv preprint, doi:10.1101/2025.03.20.644440.

Biological systems leverage gradients to direct structural organization and assembly with remarkable precision. In contrast, achieving precise structural control in synthetic materials remains challenging. Here, we report a gradient-mediated self-assembly mechanism where insect cuticle peptides (ICPs) spontaneously form nanocapsules through a single-step solvent exchange process. The concentration gradient formed by water-acetone diffusion directs peptide localization and self-organization, enabling precise structural control without templating. Molecular dynamics simulations reveal how solvent interactions modulate peptide binding and assembly. This work provides insight into mechanics-guided self-assembly, offering strategies for biomimetic nanomaterials, drug delivery, and responsive biointerfaces.