Mechanochemical Model Research Articles

A Multicellular Mechanochemical Model to Investigate Tumor Microenvironment Remodeling and Pre-Metastatic Niche Formation

A Multicellular Mechanochemical Model to Investigate Tumor Microenvironment Remodeling and Pre-Metastatic Niche Formation

A tensegrity-based mechanochemical model for capturing cell oscillation and reorientation

A tensegrity-based mechanochemical model for capturing cell oscillation and reorientation

Mechanical characterization of regenerating Hydra tissue spheres

Hydra vulgaris, long known for its remarkable regenerative capabilities, is also a long-standing source of inspiration for models of spontaneous patterning. Recently it became clear that early patterning during Hydra regeneration is an integrated mechanochemical process whereby morphogen dynamics is influenced by tissue mechanics. One roadblock to understanding Hydra self-organization is our lack of knowledge about the mechanical properties of these organisms. In this study, we combined microfluidic developments to perform parallelized microaspiration rheological experiments and numerical simulations to characterize these mechanical properties. We found three different behaviors depending on the applied stresses: an elastic response, a viscoelastic response, and tissue rupture. Using models of deformable shells, we quantify their Young’s modulus, shear viscosity, and the critical stresses required to switch between behaviors. Based on these experimental results, we propose a description of the tissue mechanics during normal regeneration. Our results provide a first step toward the development of original mechanochemical models of patterning grounded in quantitative experimental data.

Mechanochemical modeling of morphogenesis in cell polarization for budding yeast

Cell polarization is a multiphysics problem resulting from coupling protein pathways and cell morphological evolution. The most common example is asexual reproduction in budding yeast through Cdc42 and septin signals. However, how the interaction between the Cdc42-septin systems and the mechanical deformation of the cell surface is not well understood. To explore the interaction, we build a three-dimensional mechanochemical coupling framework to investigate the Cdc42-septin systems and elucidate how morphogenesis at the cell scale enhances the robustness of cell polarization in budding yeast. We utilize the viscous active shell model to describe the moving boundary of the cell surface, and the mechanochemical coupling is achieved through the introduction of cell surface mean curvature and active contraction-growth effects. With a normal effect of septin, numerical results demonstrate the budding processes with different transition shapes of budding profiles. On the other hand, the mechanochemical coupling problem with a weak effect of septin drives the emergence of wrinkles on the cell surface. We also apply linear perturbation analysis of the cell surface deformation to show how cell shape evolution is subjected to active contraction-growth effects. Our results show that a 3D coupled mechanochemical model can reproduce the budding morphology in yeast. Such a model provides a more comprehensive portrait of cell polarity and can be used to characterize both wild-type and mutant phenotypes such as septin mutants.

Corrosion-induced fracture of Cu–Al microelectronics interconnects

We present a mechano-chemical model that couples corrosion, mechanical response, and fracture. The model is used to understand the failure of Cu wires on Al pads in microelectronic packages using a multi-phase field approach. Under high humidity environments, the Cu-rich intermetallic compounds (IMC), Cu9Al4, formed at the interface between Cu and Al, undergo a corrosion degradation process. The IMC expands while undergoing corrosion, inducing stresses that nucleate and propagate cracks along the interface between the Cu-rich IMC and Cu. Furthermore, the volumetric expansion of the IMC may cause damage to the passivation layer and enhance the nucleation of new corrosion pits. We show that the presence of a crack accelerates the corrosion process. The model developed here can be extended to other systems and applications.

Mechano-chemical model for microtubule assembly: Integrating conformational dynamics of tubulins

Mechano-chemical model for microtubule assembly: Integrating conformational dynamics of tubulins

A mechanical modeling framework to study endothelial permeability

The inner lining of blood vessels, the endothelium, is made up of endothelial cells. Vascular endothelial (VE)-cadherin protein forms a bond with VE-cadherin from neighboring cells to determine the size of gaps between the cells and thereby regulate the size of particles that can cross the endothelium. Chemical cues such as thrombin, along with mechanical properties of the cell and extracellular matrix are known to affect the permeability of endothelial cells. Abnormal permeability is found in patients suffering from diseases including cardiovascular diseases, cancer, and COVID-19. Even though some of the regulatory mechanisms affecting endothelial permeability are well studied, details of how several mechanical and chemical stimuli acting simultaneously affect endothelial permeability are not yet understood. In this article, we present a continuum-level mechanical modeling framework to study the highly dynamic nature of the VE-cadherin bonds. Taking inspiration from the catch-slip behavior that VE-cadherin complexes are known to exhibit, we model the VE-cadherin homophilic bond as cohesive contact with damage following a traction-separation law. We explicitly model the actin cytoskeleton and substrate to study their role in permeability. Our studies show that mechanochemical coupling is necessary to simulate the influence of the mechanical properties of the substrate on permeability. Simulations show that shear between cells is responsible for the variation in permeability between bicellular and tricellular junctions, explaining the phenotypic differences observed in experiments. An increase in the magnitude of traction force due to disturbed flow that endothelial cells experience results in increased permeability, and it is found that the effect is higher on stiffer extracellular matrix. Finally, we show that the cylindrical monolayer exhibits higher permeability than the planar monolayer under unconstrained cases. Thus, we present a contact mechanics-based mechanochemical model to investigate the variation in the permeability of endothelial monolayer due to multiple loads acting simultaneously.

Coupling of Perinuclear Actin Cap and Nuclear Mechanics in Regulating Flow-Induced Yap Spatiotemporal Nucleocytoplasmic Transport.

Mechanical forces, including flow shear stress, govern fundamental cellular processes by modulating nucleocytoplasmic transport of transcription factors like Yes-associated Protein (YAP). However, the underlying mechanical mechanism remains elusive. In this study, it is reported that unidirectional flow induces biphasic YAP transport with initial nuclear import, followed by nuclear export as actin cap formation and nuclear stiffening. Conversely, pathological oscillatory flow induces slight actin cap formation, nuclear softening, and sustained YAP nuclear localization. To elucidate the disparately YAP spatiotemporal distribution, a 3D mechanochemical model is developed, which integrates flow sensing, cytoskeleton organization, nucleus mechanotransduction, and YAP transport. The results unveiled that despite the significant localized nuclear stress imposed by the actin cap, its inherent stiffness counteracts the dispersed contractile stress exerted by conventional fibers on the nuclear membrane. Moreover, alterations in nuclear stiffness synergistically regulate nuclear deformation, thereby governing YAP transport. Furthermore, by expanding the single-cell model to a collective vertex framework, it is revealed that the irregularities in actin cap formation within individual cells have the potential to induce topological defects and spatially heterogeneous YAP distribution in the cellular monolayer. This work unveils a unified mechanism of flow-induced nucleocytoplasmic transport, providing a linkage between transcription factor localization and mechanical stimulation.

Multiscale Mechanochemical Modeling of Spiropyran–Merocyanine Isomerization in Linear PMMA Polymers

Multiscale Mechanochemical Modeling of Spiropyran–Merocyanine Isomerization in Linear PMMA Polymers

Force-dependent focal adhesion assembly and disassembly: A computational study.

Cells interact with the extracellular matrix (ECM) via cell-ECM adhesions. These physical interactions are transduced into biochemical signals inside the cell which influence cell behaviour. Although cell-ECM interactions have been studied extensively, it is not completely understood how immature (nascent) adhesions develop into mature (focal) adhesions and how mechanical forces influence this process. Given the small size, dynamic nature and short lifetimes of nascent adhesions, studying them using conventional microscopic and experimental techniques is challenging. Computational modelling provides a valuable resource for simulating and exploring various "what if?" scenarios in silico and identifying key molecular components and mechanisms for further investigation. Here, we present a simplified mechano-chemical model based on ordinary differential equations with three major proteins involved in adhesions: integrins, talin and vinculin. Additionally, we incorporate a hypothetical signal molecule that influences adhesion (dis)assembly rates. We find that assembly and disassembly rates need to vary dynamically to limit maturation of nascent adhesions. The model predicts biphasic variation of actin retrograde velocity and maturation fraction with substrate stiffness, with maturation fractions between 18-35%, optimal stiffness of ∼1 pN/nm, and a mechanosensitive range of 1-100 pN/nm, all corresponding to key experimental findings. Sensitivity analyses show robustness of outcomes to small changes in parameter values, allowing model tuning to reflect specific cell types and signaling cascades. The model proposes that signal-dependent disassembly rate variations play an underappreciated role in maturation fraction regulation, which should be investigated further. We also provide predictions on the changes in traction force generation under increased/decreased vinculin concentrations, complementing previous vinculin overexpression/knockout experiments in different cell types. In summary, this work proposes a model framework to robustly simulate the mechanochemical processes underlying adhesion maturation and maintenance, thereby enhancing our fundamental knowledge of cell-ECM interactions.

Allosteric control of olefin isomerization kinetics via remote metal binding and its mechanochemical analysis

Allosteric control of reaction thermodynamics is well understood, but the mechanisms by which changes in local geometries of receptor sites lower activation reaction barriers in electronically uncoupled, remote reaction moieties remain relatively unexplored. Here we report a molecular scaffold in which the rate of thermal E-to-Z isomerization of an alkene increases by a factor of as much as 104 in response to fast binding of a metal ion to a remote receptor site. A mechanochemical model of the olefin coupled to a compressive harmonic spring reproduces the observed acceleration quantitatively, adding the studied isomerization to the very few reactions demonstrated to be sensitive to extrinsic compressive force. The work validates experimentally the generalization of mechanochemical kinetics to compressive loads and demonstrates that the formalism of force-coupled reactivity offers a productive framework for the quantitative analysis of the molecular basis of allosteric control of reaction kinetics. Important differences in the effects of compressive vs. tensile force on the kinetic stabilities of molecules are discussed.

Investigation of non-uniform oxidation based on a mechanochemical phase field model with nonlinear reaction kinetics and large inelastic deformation

A mechanochemical model is proposed to investigate the non-uniform oxidation of thermal barrier coatings (TBCs) that involves large inelastic deformation and nonlinear reaction kinetics. The large-deformation theory incorporates the higher-order term of geometric nonlinearity for a more precise description of the deformation and stress evolution in an oxide layer. The effect of stresses on the reaction kinetics is considered, which is expressed as the Eshelby stress tensor to account for the conformational volume change and deformation energy. A nonlinear reaction kinetics is adopted for a more accurate description of the nonequilibrium thermodynamic processes. The 2D simulations reveal a non-uniform oxide growth, three modes of oxide-metal interfacial morphology evolution, and tensile stress concentrations in the oxide scale. These simulation results agree with the experimental observations that cannot be described by the previous models. With the model, it is further demonstrated that a stable interfacial morphology and a significantly reduced tensile stress can be achieved by increasing the creep rate of the oxide and the flatness of the oxide-metal interface. This model thus provides an approach to extend the service time of TBCs.

Local and Global Bifurcations in a Mechanochemical ODE Model for Cell Behavior

Local and Global Bifurcations in a Mechanochemical ODE Model for Cell Behavior

A deep learning approach for solving diffusion-induced stress in large-deformed thin film electrodes

Understanding the effects of large deformation on electrochemical performance of electrodes, such as silicon and tin, in lithium-ion battery has stimulated great interest in analyzing stress evolution during electrochemical cycling and in developing mechanochemical models for the stress analysis. As the complexity of mechanochemical models continues to increase, there is an urgent need to develop computational methods to reduce computational costs and increase computational efficiency. In this work, we propose a physics-inspired neural network (PINN) based on the DeepXDE deep learning library in analyzing diffusion-induced stresses (DIS) in a thin film electrode with large deformation, in which a loss function, which is associated with the loss functions of partial differential equations (PDEs) in the domain and the initial/boundary conditions for the mechanochemical problem, is introduced. Using the proposed physics-inspired neural network, the mechanical equations, including geometric, constitutive and equilibrium equations, in the framework of finite deformation theory as well as the mass transport equation are solved to obtain the stress evolution in the large-deformed thin-film electrode. The numerical results are in accord with the results obtained from finite element method. This work provides a unique approach for deep learning to solve the coupling mechanochemical problems in energy storage.

Mechanochemical Felkin-Anh Model: Achieving Forbidden Reaction Outcomes with Mechanical Force.

Anti-Felkin-Anh diastereoselectivity can be achieved for nucleophilic additions to α-chiral ketones upon stretching the ketone with a mechanical pulling force. Herein, a mechanochemical Felkin-Anh model is proposed for predicting the outcome of a nucleophilic addition to an α-chiral ketone. Essentially, the fully stretched chiral ketone has one substituent shielding each side of the carbonyl, in contrast to the Felkin-Anh model, in which free rotation around a bond is required to achieve the two rotamers of the ketone. Depending on the pulling scenario, either Felkin-Anh or anti-Felkin-Anh diastereoselectivity is obtained. The model is entirely based on the distance between the pulling points, which is maximized in the anti-periplanar arrangement. The major diastereomer is associated with the approach with the least steric interactions. The intuitive model is validated by means of mechanochemical density functional theory calculations. Importantly, the ketone is fully stretched in the sub 1 nN force regime, thus minimizing the risk of undesired homolytic bond rupture. Moreover, the mechanical force is not used for lowering the reaction barriers associated with the nucleophilic addition; instead, it is solely applied for locking the conformation of a molecule and provoking otherwise inaccessible reaction pathways on the force-modified potential energy surface.

Review and Stress Analysis on the Lithiation Onset of Amorphous Silicon Films

This work aims to review and understand the behavior of the electrochemical lithiation onset of amorphous silicon (a-Si) films as electrochemically active material for new generation lithium-ion batteries. The article includes (i) a review on the lithiation onset of silicon films and (ii) a mechanochemical model with numerical results on the depth-resolved mechanical stress during the lithiation onset of silicon films. Recent experimental studies have revealed that the electrochemical lithiation onset of a-Si films involves the formation of a Li-poor phase (Li0.3Si alloy) and the propagation of a reaction front in the films. The literature review performed reveals peculiarities in the lithiation onset of a-Si films, such as (i) the build-up of the highest mechanical stress (up to 1.2 GPa) during lithiation, (ii) a linear increase in the mechanical stress with lithiation which mimics the characteristics of linear elastic deformation, (iii) only a minute volume increase during Li incorporation, which is lower than expected from the number of Li ions entering the silicon electrode, (iv) the largest heat generation appearing during cycling with only a minor degree of parasitic heat contribution, and (v) an unexpected enhanced brittleness. The literature review points to the important role of mechanical stresses in the formation of the Li-poor phase and the propagation of the reaction front. Consequently, a mechanochemical model consisting of two stages for the lithiation onset of a-Si film is developed. The numerical results calculated from the mechanochemical model are in good accord with the corresponding experimental data for the variations in the volumetric change with state of charge and for the moving speed of the reaction front for the lithiation of an a-Si film of 230 nm thickness under a total C-rate of C/18. An increase in the total C-rate increases the moving speed of the reaction front, and a Li-rich phase is likely formed prior to the end of the growth of the Li-poor phase at a high total C-rate. The stress-induced phase formation of the Li-poor phase likely occurs during the lithiation onset of silicon electrodes in lithium-ion battery.

A structural mechano-chemical model of microtubule nucleation.

Microtubules (MTs) are the backbone of cytoskeleton and crucial for many essential processes, such as mitosis, morphogenesis and migration. A critical step in the assembly and regulation of cellular MT network is nucleation. There are two types of templates for MT nucleation in cells: existing MT and γ-tubulin ring complex. Both types of nucleations have been reconstituted in vitro, but their mechanisms remain poorly understood. Here, we developed a physically rigorous structure-based mechano-chemical model that provides an unified mechanism for both types of nucleations. For nucleation from seed MTs, the key observations are: 1) the critical tubulin concentration for nucleation is much higher than that for growth, 2) the concentration-dependent time lags. Our model shows that the bottleneck for nucleation is frequent catastrophes (i.e., the switching from MT growth to shortening) that keep removing nascent MTs from the seed, which is reduced as tubulin concentration increases. The observed time lag is due to repeated assembly and removal of nascent MTs, which delay nucleation. For nucleation from γ-tubulin ring, the most intriguing question is the effects of ring closure, a complex-wide conformational change required for the ring complex to match the tube-like geometry of MT. Our model shows that ring closure helps tubulins to first form a sheet, which is then closed into tube with the help of the ring closure process. Because catastrophe cannot develop while sheet is open, MTs more likely grow longer, increasing the chance of nucleation. Thus, ring closure allows more regulated and efficient MT nucleation.

Mechanism of assembly of an elongation-competent SARS-CoV-2 replication transcription complex.

The development of effective therapeutics against COVID19, caused by SARS-CoV-2, as well as preparedness for possible future coronavirus outbreaks, heavily relies on our mechanochemical knowledge of the viral genome processing machinery. SARS-CoV-2 expresses 16 non-structural proteins (nsp1-16), with most nsp's assembling into the Replication Transcription Complex (RTC), which efficiently synthesizes all viral RNAs in the host cell from the very long coronavirus genome (∼30 kb). The core RTC consists of the nsp12-polymerase and the elongation co-factors nsp7 and nsp8 (1:1:2 stoichiometry), which are sufficient to ensure efficient synthesis. Despite the many structural studies already reported, the precise role of the co-factors and the mechanism of assembly of the core RTC remain unknown. Here, we use high-throughput magnetic tweezers to monitor the kinetics of assembly of the core RTC preceding primer-extension at the single molecule level in different nsp's conditions. Our data demonstrate that the assembly step largely dominates the overall RNA synthesis duration and that the nsp co-factors don’t affect elongation dynamics, but rather speed up the assembly process. Using our data to build a mechanochemical model of assembly we reveal that a rate limiting barrier separates RNA bound complexes from becoming elongating core RTCs. Our findings support a model in which nsp8 recruits nsp12-polymerase at the primer template. We further propose that an RNA bound nsp12-nsp8 competes with nsp7 for the binding of another nsp8, where nsp7 increases the assembly rate by 2- to 3-fold. Our results clearly demonstrate that inhibition of the contacts between nsp7 and nsp12 or nsp8 could serve as an effective strategy to combat viral replication as a whole.

Dynamic instability from nonequilibrium structural transitions on the energy landscape of microtubule.

Microtubules are the backbone of the cytoskeleton and vital to numerous cellular processes. All the functions of microtubules are driven by dynamic instability, but its mechanism has remained unresolved for over 30 years because of conceptual difficulties inherent in the prevalent GTP-cap framework. We present a physically rigorous structural mechano-chemical model: dynamic instability is driven by non-equilibrium transitions between the bent (B), straight (S), and curved (C) structures of tubulin monomers and longitudinal interfaces in the two-dimensional lattice of microtubule. All the different phenomena (growth, shortening, catastrophe, rescue, and pausing) are controlled by the kinetic pathways for B-to-S and S-to-C transitions and their corresponding energy landscapes. Different kinetics of dynamic instability at plus and minus ends are due to different B-to-S and S-to-C pathways necessitated by the polarity of microtubule lattice. This model enables us to reproduce all the observed phenomena of dynamic instability of purified tubulins in kinetic simulations and provide the detailed physical mechanisms behind them.

Time periodic solution to a mechanochemical model in biological patterns

<p style='text-indent:20px;'>In this paper, we consider a mechanochemical model in biological patterns in <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^N $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M2">\begin{document}$ N\geq 5 $\end{document}</tex-math></inline-formula>. We first prove the existence of time periodic solution in <inline-formula><tex-math id="M3">\begin{document}$ BC(\mathbb{R}; L^{N,\infty}(\Omega)) $\end{document}</tex-math></inline-formula>. Then we obtain the existence, uniqueness and regularity of the mild solution of the problem. Finally, we prove that the mild solution can become strong solution in <inline-formula><tex-math id="M4">\begin{document}$ BC(\mathbb{R}; L^{N,\infty}(\Omega)) $\end{document}</tex-math></inline-formula>.</p>