Computational Molecular Biology 2024, Vol.14, No.3, 125-133 http://bioscipublisher.com/index.php/cmb 127 3.2 Discrete element models Discrete element models, on the other hand, consider tissues and cells as collections of individual elements or particles. These models are particularly adept at capturing the behavior of individual cells and their interactions. For example, agent-based models, which fall under the category of discrete element models, simulate mechanical and physiological phenomena in cells and tissues by considering individual cell behaviors and interactions4. These models include lattice-based models (such as cellular automata and cellular Potts models) and off-lattice models (such as center-based and vertex models). Discrete models are valuable for understanding cell-cell interactions, cell division, and the emergence of complex spatial patterns from simple rules governing single-cell dynamics (Chaplain et al., 2018). 3.3 Hybrid models combining continuum and discrete approaches Hybrid models combine the strengths of both continuum and discrete approaches to provide a more comprehensive understanding of cellular mechanics. These models are particularly useful for simulating complex biological processes that involve both large-scale tissue deformations and individual cell behaviors. For instance, a mechanistic hybrid continuum-discrete model has been developed to simulate the dynamics of epithelial cell colonies, capturing both the collective cell dynamics and individual cell behaviors such as division and shape changes (Dallon, 2000). Another example is the use of hybrid models to study wound healing and cellular aggregation, where discrete and continuum variables are interpolated to solve the models using numerical techniques3. These hybrid approaches offer a versatile framework for studying a wide range of biomechanical phenomena in cellular mechanics. By integrating continuum and discrete models, researchers can achieve a more nuanced understanding of the mechanical behavior of cells and tissues, paving the way for advancements in areas such as tissue engineering, cancer research, and developmental biology (Aland et al., 2015). 4 Applications of Biophysical Models in Cellular Mechanics 4.1 Modeling cell deformation and migration 4.1.1 Deformation mechanics in different cell types Biophysical models have significantly advanced our understanding of cell deformation across various cell types. For instance, a mechanobiochemical model has been developed to simulate 3D cell deformation and movement, incorporating the actin filament network as a viscoelastic and contractile gel. This model uses a force balancing equation to account for displacements, pressure, and concentration forces driven by actin and myosin dynamics, which are modeled by reaction-diffusion equations on a moving cell domain. The numerical simulations from this model demonstrate complex cell deformations, including cell expansion, protrusion, and contraction1. Additionally, a high-resolution computational mechanics cell model has been used to study the regeneration of liver tissues, showing how cells respond to mechanical stress and migrate to close tissue lesions (Murphy and Madzvamuse, 2019). 4.1.2 Migration mechanisms under various stimuli Cell migration is influenced by a variety of mechanical and biochemical stimuli. A mechanobiochemical model has been developed to understand cell migration at the whole-cell scale, integrating cytoskeleton contraction mechanics with the signaling network of reaction-diffusion of biomolecules. This model can simulate cell polarization and shape-dependent localization of protrusion signals, recapitulating phenomena such as durotaxis (Boocock et al., 2020). Furthermore, a chemomechanical model has been used to study single cell migration during cell-to-cell interaction, considering the effects of chemoattractant concentration gradients, dynamic adhesion strength, and relative motion between cells. This model has been validated with experimental data, demonstrating that cell migration velocity can be influenced by dynamic adhesion forces (Sun et al., 2021). 4.1.3 Impact of biophysical models on understanding pathologies Biophysical models have also provided insights into pathological conditions. For example, the mechanobiology of cells interacting with their microenvironment has been studied to understand disease diagnosis and potential therapeutics. Mechanical measurements of cell deformability, migration on micro/nano-topographies, and traction in 3D matrices have highlighted the promise of these models in linking molecular and biophysical phenotypes
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