Dual role of the nucleus in cell migration on planar substrates

Optimization-based synthesis with directed cell migration

Collective behavior of biological agents from cells to herds of organisms is a fundamental feature in systems biology and in the emergence of new phenomena in the biological environment. Collective cell migration (CCM) under a physical or chemical cue is an example of this fundamental phenomenon where the individual migration of a cell is driven by the collective behavior of the neighboring cells and vice versa. The goal of this research is to discover the mathematical rules of collective cell migration with dynamic mode decomposition (DMD) with the use of experimental data and to test the predictive nature of the models with independent experimental data sets subject to Dirichlet, Neumann, and mixed boundary conditions. Both single and multi-cellular systems are investigated in this process. Additionally, the goal of this research is to create an optimal trajectory for microscopic robots in the presence of an obstacle course made of both static and dynamic obstacles. Such an optimization is made possible by synthesizing the discovered dynamics for cell migration with a numerical approach to dynamic optimization known as collocation by augmenting the discovered dynamics to the constraint equations. The optimal trajectory results presented in silico have potential design applications for the path planning of microrobots for therapeutic purposes such as cancer cell drug delivery, microsurgery, microsensing for early disease detection, and cleaning of toxic substances.

The role of the nucleus for cell mechanics: an elastic phase field approach

The nucleus of eukaryotic cells typically makes up around 30% of the cell volume and has significantly different mechanics, which can make it effectively up to ten times stiffer than the surrounding cytoplasm. Therefore it is an important element for cell mechanics, but a quantitative understanding of its mechanical role during whole cell dynamics is largely missing. Here we demonstrate that elastic phase fields can be used to describe dynamical cell processes in adhesive or confining environments in which the nucleus acts as a stiff inclusion in an elastic cytoplasm. We first introduce and verify our computational method and then study several prevalent cell-mechanical measurement methods. For cells on adhesive patterns, we find that nuclear stress is shielded by the adhesive pattern. For cell compression between two parallel plates, we obtain force-compression curves that allow us to extract an effective modulus for the cell-nucleus composite. For micropipette aspiration, the effect of the nucleus on the effective modulus is found to be much weaker, highlighting the complicated interplay between extracellular geometry and cell mechanics that is captured by our approach. We also show that our phase field approach can be used to investigate the effects of Kelvin-Voigt-type viscoelasticity and cortical tension.

Cross-Scale Topography Achieved by MOPL with Positive Photoresist to Regulate the Cell Behavior

Cross-scale micro-nano structures play an important role in semiconductors, MEMS, chemistry, and cell biology. Positive photoresist is widely used in lithography due to the advantages of high resolution and environmental friendliness. However, cross-scale micro-nano structures of positive photoresist are difficult to flexibly pattern, and the feature resolution is limited by the optical diffraction. Here, cross-scale patterned micro-nano structures are achieved using the positive photoresist based on the femtosecond laser maskless optical projection lithography (MOPL) technique. The dependence between exposure dose and groove width is comprehensively analyzed, and a feature size of 112 nm is obtained at 110 µW. Furthermore, large-area topography considering cell size is efficiently fabricated by the MOPL technique, which enables the regulation of cell behavior. The proposed protocol of achieving cross-scale structures with the exact size by MOPL of positive photoresist would provide new avenues for potential applications in nanoelectronics and tissue engineering.

The Influence of Nucleus Mechanics in Modelling Adhesion-independent Cell Migration in Structured and Confined Environments

Recent biological experiments (Lämmermann et al. in Nature 453(7191):51-55, 2008; Reversat et al. in Nature 7813:582-585, 2020; Balzer et al. in ASEB J Off Publ Fed Am Soc Exp Biol 26(10):4045-4056, 2012) have shown that certain types of cells are able to move in structured and confined environments even without the activation of focal adhesion. Focusing on this particular phenomenon and based on previous works (Jankowiak et al. in Math Models Methods Appl Sci 30(03):513-537, 2020), we derive a novel two-dimensional mechanical model, which relies on the following physical ingredients: the asymmetrical renewal of the actin cortex supporting the membrane, resulting in a backward flow of material; the mechanical description of the nuclear membrane and the inner nuclear material; the microtubule network guiding nucleus location; the contact interactions between the cell and the external environment. The resulting fourth order system of partial differential equations is then solved numerically to conduct a study of the qualitative effects of the model parameters, mainly those governing the mechanical properties of the nucleus and the geometry of the confining structure. Coherently with biological observations, we find that cells characterized by a stiff nucleus are unable to migrate in channels that can be crossed by cells with a softer nucleus. Regarding the geometry, cell velocity and ability to migrate are influenced by the width of the channel and the wavelength of the external structure. Even though still preliminary, these results may be potentially useful in determining the physical limit of cell migration in confined environments and in designing scaffolds for tissue engineering.

A cell membrane model that reproduces cortical flow-driven cell migration and collective movement

Many fundamental biological processes are dependent on cellular migration. Although the mechanical mechanisms of single-cell migration are relatively well understood, those underlying migration of multiple cells adhered to each other in a cluster, referred to as cluster migration, are poorly understood. A key reason for this knowledge gap is that many forces-including contraction forces from actomyosin networks, hydrostatic pressure from the cytosol, frictional forces from the substrate, and forces from adjacent cells-contribute to cell cluster movement, making it challenging to model, and ultimately elucidate, the final result of these forces. This paper describes a two-dimensional cell membrane model that represents cells on a substrate with polygons and expresses various mechanical forces on the cell surface, keeping these forces balanced at all times by neglecting cell inertia. The model is discrete but equivalent to a continuous model if appropriate replacement rules for cell surface segments are chosen. When cells are given a polarity, expressed by a direction-dependent surface tension reflecting the location dependence of contraction and adhesion on a cell boundary, the cell surface begins to flow from front to rear as a result of force balance. This flow produces unidirectional cell movement, not only for a single cell but also for multiple cells in a cluster, with migration speeds that coincide with analytical results from a continuous model. Further, if the direction of cell polarity is tilted with respect to the cluster center, surface flow induces cell cluster rotation. The reason why this model moves while keeping force balance on cell surface (i.e., under no net forces from outside) is because of the implicit inflow and outflow of cell surface components through the inside of the cell. An analytical formula connecting cell migration speed and turnover rate of cell surface components is presented.

Biophysical models of early mammalian embryogenesis

Embryo development is a critical and fascinating stage in the life cycle of many organisms. Despite decades of research, the earliest stages of mammalian embryogenesis are still poorly understood, caused by a scarcity of high-resolution spatial and temporal data, the use of only a few model organisms, and a paucity of truly multidisciplinary approaches that combine biological research with biophysical modeling and computational simulation. Here, we explain the theoretical frameworks and biophysical processes that are best suited to modeling the early mammalian embryo, review a comprehensive list of previous models, and discuss the most promising avenues for future work.

Unravelling cell migration: defining movement from the cell surface

Cell motility is essential for life and development. Unfortunately, cell migration is also linked to several pathological processes, such as cancer metastasis. Cells' ability to migrate relies on many actors. Cells change their migratory strategy based on their phenotype and the properties of the surrounding microenvironment. Cell migration is, therefore, an extremely complex phenomenon. Researchers have investigated cell motility for more than a century. Recent discoveries have uncovered some of the mysteries associated with the mechanisms involved in cell migration, such as intracellular signaling and cell mechanics. These findings involve different players, including transmembrane receptors, adhesive complexes, cytoskeletal components , the nucleus, and the extracellular matrix. This review aims to give a global overview of our current understanding of cell migration.

Mechanical and Physical Regulation of Fibroblast-Myofibroblast Transition: From Cellular Mechanoresponse to Tissue Pathology

Fibroblasts are cells present throughout the human body that are primarily responsible for the production and maintenance of the extracellular matrix (ECM) within the tissues. They have the capability to modify the mechanical properties of the ECM within the tissue and transition into myofibroblasts, a cell type that is associated with the development of fibrotic tissue through an acute increase of cell density and protein deposition. This transition from fibroblast to myofibroblast-a well-known cellular hallmark of the pathological state of tissues-and the environmental stimuli that can induce this transition have received a lot of attention, for example in the contexts of asthma and cardiac fibrosis. Recent efforts in understanding how cells sense their physical environment at the micro- and nano-scales have ushered in a new appreciation that the substrates on which the cells adhere provide not only passive influence, but also active stimulus that can affect fibroblast activation. These studies suggest that mechanical interactions at the cell-substrate interface play a key role in regulating this phenotype transition by changing the mechanical and morphological properties of the cells. Here, we briefly summarize the reported chemical and physical cues regulating fibroblast phenotype. We then argue that a better understanding of how cells mechanically interact with the substrate (mechanosensing) and how this influences cell behaviors (mechanotransduction) using well-defined platforms that decouple the physical stimuli from the chemical ones can provide a powerful tool to control the balance between physiological tissue regeneration and pathological fibrotic response.

Tools for computational analysis of moving boundary problems in cellular mechanobiology

A cell's ability to change shape is one of the most fundamental biological processes and is essential for maintaining healthy organisms. When the ability to control shape goes awry, it often results in a diseased system. As such, it is important to understand the mechanisms that allow a cell to sense and respond to its environment so as to maintain cellular shape homeostasis. Because of the inherent complexity of the system, computational models that are based on sound theoretical understanding of the biochemistry and biomechanics and that use experimentally measured parameters are an essential tool. These models involve an inherent feedback, whereby shape is determined by the action of regulatory signals whose spatial distribution depends on the shape. To carry out computational simulations of these moving boundary problems requires special computational techniques. A variety of alternative approaches, depending on the type and scale of question being asked, have been used to simulate various biological processes, including cell motility, division, mechanosensation, and cell engulfment. In general, these models consider the forces that act on the system (both internally generated, or externally imposed) and the mechanical properties of the cell that resist these forces. Moving forward, making these techniques more accessible to the non-expert will help improve interdisciplinary research thereby providing new insight into important biological processes that affect human health. This article is categorized under: Cancer > Cancer>Computational Models Cancer > Cancer>Molecular and Cellular Physiology.

A minimal mechanosensing model predicts keratocyte evolution on flexible substrates

A mathematical model is proposed for shape evolution and locomotion of fish epidermal keratocytes on elastic substrates. The model is based on mechanosensing concepts: cells apply contractile forces onto the elastic substrate, while cell shape evolution depends locally on the substrate stress generated by themselves or external mechanical stimuli acting on the substrate. We use the level set method to study the behaviour of the model numerically, and predict a number of distinct phenomena observed in experiments, such as (i) symmetry breaking from the stationary centrosymmetric to the well-known steadily propagating crescent shape, (ii) asymmetric bipedal oscillations and travelling waves in the lamellipodium leading edge, (iii) response to remote mechanical stress externally applied to the substrate (tensotaxis) and (iv) changing direction of motion towards an interface with a rigid substrate (durotaxis).