Mechanochemical Model Research Articles

Role of membrane-tension gated Ca2+ flux in cell mechanosensation.

Eukaryotic cells are sensitive to mechanical forces they experience from the environment. The process of mechanosensation is complex, and involves elements such as the cytoskeleton and active contraction from myosin motors. Ultimately, mechanosensation is connected to changes in gene expression in the cell, known as mechanotransduction. While the involvement of the cytoskeleton in mechanosensation is known, the processes upstream of cytoskeletal changes are unclear. In this paper, by using a microfluidic device that mechanically compresses live cells, we demonstrate that Ca2+ currents and membrane tension-sensitive ion channels directly signal to the Rho GTPase and myosin contraction. In response to membrane tension changes, cells actively regulate cortical myosin contraction to balance external forces. The process is captured by a mechanochemical model where membrane tension, myosin contraction and the osmotic pressure difference between the cytoplasm and extracellular environment are connected by mechanical force balance. Finally, to complete the picture of mechanotransduction, we find that the tension-sensitive transcription factor YAP family of proteins translocate from the nucleus to the cytoplasm in response to mechanical compression.

Mechanochemical Modeling as an Explorative Tool to Study Tissue Morphogenesis

Dorsal closure is a morphogenetic process in Drosophila embryogenesis, whereby an epidermis opening closes. The epidermal opening is filled with the Amnioserosa (AS) tissue, which drives dorsal closure by apical constriction of its individual cells. Apical constriction in turn is driven by apical surface area oscillations of AS cells, which are the result of periodically forming, transient actomyosin foci. It is currently unclear whether neighboring cells coordinate their oscillations and how the cell scale behavior leads to tissue scale dynamics. To better understand these aspects, we developed a coupled finite element simulation of actomyosin dynamics, force generation, and material behavior. Thereby, we model the dynamics of the actomyosin network in AS cells with reaction-diffusion equations at the subcellular level in 2D. The actomyosin concentration determines the strength of local contractions within the AS cell surfaces. Based on our in vivo observations, we model the dynamics of actin binding proteins (eg. Arp2/3) as an activator-depleted substrate system, and couple it to actin network formation. Analytical methods describe the system behavior in the absence of mechanical deformation, and predict how the system will evolve in coupled simulations. We model the surrounding epidermis as a linear viscoelastic material, so that it adapts in response to the pulling force of the AS tissue, as shown experimentally. Our simulations reproduce dorsal closure and make clear predictions that ask for experimental testing. In particular, a sequential arrest of cellular oscillations simply emerges, similar to what was observed in vivo. So far, a dpp-signaling gradient was thought to control this phenomenon. Addressing this experimentally provides support for the model prediction. Interestingly, 3D finite element simulations predict that the emerging sequential pulsation arrest generates a contractility gradient, which controls AS tissue morphogenesis.

Theory of Epithelial Cell Shape Transitions Induced by Mechanoactive Chemical Gradients

Cell shape is determined by a balance of intrinsic properties of the cell as well as its mechanochemical environment. Inhomogeneous shape changes underlie many morphogenetic events and involve spatial gradients in active cellular forces induced by complex chemical signaling. Here, we introduce a mechanochemical model based on the notion that cell shape changes may be induced by external diffusible biomolecules that influence cellular contractility (or equivalently, adhesions) in a concentration-dependent manner—and whose spatial profile in turn is affected by cell shape. We map out theoretically the possible interplay between chemical concentration and cellular structure. Besides providing a direct route to spatial gradients in cell shape profiles in tissues, we show that the dependence on cell shape helps create robust mechanochemical gradients.

Membrane shape-mediated wave propagation of cortical protein dynamics

Immune cells exhibit stimulation-dependent traveling waves in the cortex, much faster than typical cortical actin waves. These waves reflect rhythmic assembly of both actin machinery and peripheral membrane proteins such as F-BAR domain-containing proteins. Combining theory and experiments, we develop a mechanochemical feedback model involving membrane shape changes and F-BAR proteins that render the cortex an interesting dynamical system. We show that such cortical dynamics manifests itself as ultrafast traveling waves of cortical proteins, in which the curvature sensitivity-driven feedback always constrains protein lateral diffusion in wave propagation. The resulting protein wave propagation mainly reflects the spatial gradient in the timing of local protein recruitment from cytoplasm. We provide evidence that membrane undulations accompany these protein waves and potentiate their propagation. Therefore, membrane shape change and protein curvature sensitivity may have underappreciated roles in setting high-speed cortical signal transduction rhythms.

Frequency sensitive mechanism in low-intensity ultrasound enhanced bioeffects.

This study presents two novel theoretical models to elucidate frequency sensitive nuclear mechanisms in low-intensity ultrasound enhanced bioeffects. In contrast to the typical 1.5 MHz pulsed ultrasound regime, our group previously experimentally confirmed that ultrasound stimulation of anchored chondrocytes at resonant frequency maximized gene expression of load inducible genes which are regulatory markers for cellular response to external stimuli. However, ERK phosphorylation displayed no frequency dependency, suggesting that the biochemical mechanisms involved in enhanced gene expression is downstream of ERK phosphorylation. To elucidate such underlying mechanisms, this study presents a theoretical model of an anchored cell, representing an in vitro chondrocyte, in an ultrasound field. The model results showed that the mechanical energy storage is maximized at the chondrocyte’s resonant frequency and the energy density in the nucleus is almost twice as high as in the cytoplasm. Next, a mechanochemical model was developed to link the mechanical stimulation of ultrasound and the increased mechanical energy density in the nucleus to the downstream targets of the ERK pathway. This study showed for the first time that ultrasound stimulation induces frequency dependent gene expression as a result of altered rates of transcription factors binding to chromatin.

Mechanosensitive Adhesion Explains Stepping Motility in Amoeboid Cells

Cells employing amoeboid motility exhibit repetitive cycles of rapid expansion and contraction and apply coordinated traction forces to their environment. Although aspects of this process are well studied, it is unclear how the cell controls the coordination of cell length changes with adhesion to the surface. Here, we develop a simple model to mechanistically explain the emergence of periodic changes in length and spatiotemporal dynamics of traction forces measured in chemotaxing unicellular amoeba, Dictyostelium discoideum. In contrast to the biochemical mechanisms that have been implicated in the coordination of some cellular processes, we show that many features of amoeboid locomotion emerge from a simple mechanochemical model. The mechanism for interaction with the environment in Dictyostelium is unknown and thus, we explore different cell-environment interaction models to reveal that mechanosensitive adhesions are necessary to reproduce the spatiotemporal adhesion patterns. In this modeling framework, we find that the other motility modes, such as smooth gliding, arise naturally with variations in the physical properties of the surface. Thus, our work highlights the prominent role of biomechanics in determining the emergent features of amoeboid locomotion.

ASYMPTOTIC DYNAMICS OF A NEW MECHANOCHEMICAL MODEL IN BIOLOGICAL PATTERNS

In this paper, we prove the existence of attractor for a new mechanochemical model with Neumann boundary conditions on a bounded domain of space dimension n ≤ 3. Based on the regularity estimates for the semigroups and the classical existence theorem of global attractors, we prove that the mechanochemical model possesses a global attractor and Hk attractor.

Characteristics of Myosin V Processivity.

Myosin V is a processive doubled-headed biomolecular motor involved in many intracellular organelle and vesicle transport. The unidirectional movement is coupled with the adenosine triphosphate (ATP) hydrolysis and product release cycle. With the progress of experimental techniques and the enhancement of measuring directness, detailed knowledge of the motility of myosin V has been obtained. Following the ATPase cycle, the 4-state mechanochemical model of the myosin V's processive movement is used. The transitions between various states take place in a stochastic manner. We can use the master equation to analyze and calculate quantitatively. Meanwhile, the effect of the reverse reaction is taken fully into account. We fit the mean velocity, the mean dwell time, the mean run length, and the ratio of forward/backward steps as a functionof ATP, ADP, and Pi concertration. The theoretical curves are generally in line with the experimental data. This work provides a new insight for the characteristic of myosin V.

A 2D mechano-chemical model for the simulation of reinforcement corrosion and concrete damage

This paper presents a comprehensive model for the prediction of the process of steel reinforcement corrosion and concrete damage in two dimensions. The ingress of chloride ions, carbonation, electrochemical reaction and corrosion-induced mechanical damage are coupled in this model. The evolution of the active zone on the reinforcement is determined automatically. Using this model, we can predict the non-uniform distribution of the corrosion product, the expansive pressure, and the growth of corrosion-induced cracks.

Thermodynamic properties of three-dimensional radical polymerization of dimethacrylates and their relation to the structure and properties of network polymers

For the polymerization of dimethacrylates, thermodynamic properties related to effect of the formed network polymer on the reaction between pendant methacrylate groups and free radicals have been studied. The polymer matrix creates steric hindrances for this reaction and impedes the shrinkage process accompanying the opening of С=С bonds. As a result, internal stresses develop in the polymer, the heat of polymerization of methacrylate groups decreases compared with the polymerization of methyl methacrylate, and the full conversion of double bonds is prevented. The relaxation of internal stresses and of excess free volume leads to the spontaneous cracking of network polymers and causes formation of regular adhesive-shrinkage patterns. The process of superslow relaxation of internal stresses in polymer films has been ascertained, and the mechanochemical model of this process has been advanced. The effect of internal stresses on the physicomechanical properties of polydimethacrylates has been discussed.

Effect of fuel concentration on cargo transport by a team of Kinesin motors

Eukaryotic cells employ specialized proteins called molecular motors for transporting organelles and vesicles from one location to another in a regulated and directed manner. These molecular motors often work collectively in a team while transporting cargos. Molecular motors use cytoplasmic ATP as fuel, which is hydrolyzed to generate mechanical force. While the effect of ATP concentration on cargo transport by single Kinesin motor function is well understood, it is still unexplored, both theoretically and experimentally, how ATP concentration would affect cargo transport by a team of Kinesin motors. For instance, how does fuel concentration affect the travel distances and travel velocities of cargo? How cooperativity of Kinesin motors engaged on a cargo is affected by ATP concentration? To answer these questions, here we develop mechano-chemical models of cargo transport by a team of Kinesin motors. To develop these models we use experimentally-constrained mechano-chemical model of a single Kinesin motor as well as earlier developed mean-field and stochastic models of load sharing for cargo transport. Thus, our new models for cargo transport by a team of Kinesin motors include fuel concentration explicitly, which was not considered in earlier models. We make several interesting predictions which can be tested experimentally. For instance, the travel distances of cargos are very large at limited ATP concentrations in spite of very small travel velocity. Velocities of cargos driven by multiple Kinesin have a Michaelis–Menten dependence on ATP concentration. Similarly, cooperativity among the engaged Kinesin motors on the cargo shows a Michaelis–Menten type dependence, which attains a maximum value near physiological ATP concentrations. Our new results can be potentially useful in controlling artificial nano-molecular shuttles precisely for targeted delivery in various nano-technological applications.

Impact of anomalous transport kinetics on the progress of wound healing

This work focuses on the transport kinetics of chemical and cellular species during wound healing. Anomalous transport kinetics, coupling sub- and superdiffusion with chemotaxis, and fractional viscoelasticity of soft tissues are analyzed from a modeling point of view. The paper presents a generalization of well stablished mechano-chemical models of wound contraction (Murphy et al., 2012; Valero et al., 2014) to include the previously mentioned anomalous effects by means of partial differential equations of fractional order. Results show the effect that anomalous dynamics have on the contraction rate and extension and on the distribution of biological species, and indicators of fibroproliferative disorders are identified.

Dynamic Instability Emerges from Micromechanics and Chemical Kinetics of Microtubule Protofilaments

Microtubules are crucial for various cellular processes like chromosome segregation, intracellular transport, and cell motility. They are known to display cycles of consistent growth and rapid shrinkage in a phenomenon called dynamic instability. The dynamic instability is attributed to the coupling between chemical kinetics and mechanics of its constituent protofilaments. To develop a mechanistic understanding of the microtubule dynamics and its regulation, we study a mechanochemical model that takes into account a coarse-grained description of the mechanics of microtubule protofilaments in the presence of thermal fluctuations along with association-dissociation kinetics and hydrolysis of tubulin subunits. Our simple model allowed us to simulate and evaluate various mechanisms of catastrophe and rescue in microtubules for a large range of parameters. We found a range of parameters for which the characteristics length- and time-scales associated with microtubule dynamics naturally emerge from our mechanochemical model. Furthermore, our analysis provides novel insights into how the distribution of GTP subunits along the microtubule influences catastrophe and rescue during the dynamic instability.

Mechano-Chemical Model for the Mechanism of Directed Processive Motility of Cytoplasmic Dynein

Linear motor proteins move along their tracks by performing a mechano-chemical cycle in which the conformational and binding affinity changes are coupled to the ATP hydrolysis cycle. Although the two way coupling between the catalytic site, track binding and lever motion is a universal feature of myosins, kinesins and dyneins, the experiments on mutants with one inactive motor head suggest that the dimeric motor could be functional with a less complex mechanism. In this talk we will discuss the minimal prerequisites for the dimeric motor to move processively in a directed fashion. Without any coupling between the catalytic site and binding domain, asymmetric unbinding of the trail/lead head and/or asymmetric binding in the forward/backward direction can be driven solely by an asymmetry in the force-induced unbinding rate, together with a conformation dependent internal tension of the dimeric motor. However, the stepping efficiency of such motility is much lower than that of a motor with further allosteric coupling. A more specific and complex mechano-chemical model for cytoplasmic dynein reproduces well the observed stepping efficiency, velocity and force production. By changing the strength of the interhead elastic interaction the model accounts both for uncoordinated and coordinated stepping characteristics of yeast and mammalian dyneins, as observed in recent single-molecule studies.

Bacterial growth and form under mechanical compression

A combination of physical and chemical processes is involved in determining the bacterial cell shape. In standard medium, Escherichia coli cells are rod-shaped, and maintain a constant diameter during exponential growth. Here, we demonstrate that by applying compressive forces to growing E. coli, cells no longer retain their rod-like shapes but grow and divide with a flat pancake-like geometry. The deformation is reversible: deformed cells can recover back to rod-like shapes in several generations after compressive forces are removed. During compression, the cell elongation rate, proliferation rate, DNA replication rate, and protein synthesis are not significantly altered from those of the normal rod-shaped cells. Quantifying the rate of cell wall growth under compression reveals that the cell wall growth rate depends on the local cell curvature. MreB not only influences the rate of cell wall growth, but also influences how the growth rate scales with cell geometry. The result is consistent with predictions of a mechanochemical model, and suggests an active mechanical role for MreB during cell wall growth. The developed compressive device is also useful for studying a variety of cells in unique geometries.

In silico Mechano-Chemical Model of Bone Healing for the Regeneration of Critical Defects: The Effect of BMP-2.

The healing of bone defects is a challenge for both tissue engineering and modern orthopaedics. This problem has been addressed through the study of scaffold constructs combined with mechanoregulatory theories, disregarding the influence of chemical factors and their respective delivery devices. Of the chemical factors involved in the bone healing process, bone morphogenetic protein-2 (BMP-2) has been identified as one of the most powerful osteoinductive proteins. The aim of this work is to develop and validate a mechano-chemical regulatory model to study the effect of BMP-2 on the healing of large bone defects in silico. We first collected a range of quantitative experimental data from the literature concerning the effects of BMP-2 on cellular activity, specifically proliferation, migration, differentiation, maturation and extracellular matrix production. These data were then used to define a model governed by mechano-chemical stimuli to simulate the healing of large bone defects under the following conditions: natural healing, an empty hydrogel implanted in the defect and a hydrogel soaked with BMP-2 implanted in the defect. For the latter condition, successful defect healing was predicted, in agreement with previous in vivo experiments. Further in vivo comparisons showed the potential of the model, which accurately predicted bone tissue formation during healing, bone tissue distribution across the defect and the quantity of bone inside the defect. The proposed mechano-chemical model also estimated the effect of BMP-2 on cells and the evolution of healing in large bone defects. This novel in silico tool provides valuable insight for bone tissue regeneration strategies.

Type IV pili mechanochemically regulate virulence factors in Pseudomonas aeruginosa

Bacteria have evolved a wide range of sensing systems to appropriately respond to environmental signals. Here we demonstrate that the opportunistic pathogen Pseudomonas aeruginosa detects contact with surfaces on short timescales using the mechanical activity of its type IV pili, a major surface adhesin. This signal transduction mechanism requires attachment of type IV pili to a solid surface, followed by pilus retraction and signal transduction through the Chp chemosensory system, a chemotaxis-like sensory system that regulates cAMP production and transcription of hundreds of genes, including key virulence factors. Like other chemotaxis pathways, pili-mediated surface sensing results in a transient response amplified by a positive feedback that increases type IV pili activity, thereby promoting long-term surface attachment that can stimulate additional virulence and biofilm-inducing pathways. The methyl-accepting chemotaxis protein-like chemosensor PilJ directly interacts with the major pilin subunit PilA. Our results thus support a mechanochemical model where a chemosensory system measures the mechanically induced conformational changes in stretched type IV pili. These findings demonstrate that P. aeruginosa not only uses type IV pili for surface-specific twitching motility, but also as a sensor regulating surface-induced gene expression and pathogenicity.

Computational model of collagen turnover in carotid arteries during hypertension.

It is well known that biological tissues adapt their properties because of different mechanical and chemical stimuli. The goal of this work is to study the collagen turnover in the arterial tissue of hypertensive patients through a coupled computational mechano-chemical model. Although it has been widely studied experimentally, computational models dealing with the mechano-chemical approach are not. The present approach can be extended easily to study other aspects of bone remodeling or collagen degradation in heart diseases. The model can be divided into three different stages. First, we study the smooth muscle cell synthesis of different biological substances due to over-stretching during hypertension. Next, we study the mass-transport of these substances along the arterial wall. The last step is to compute the turnover of collagen based on the amount of these substances in the arterial wall which interact with each other to modify the turnover rate of collagen. We simulate this process in a finite element model of a real human carotid artery. The final results show the well-known stiffening of the arterial wall due to the increase in the collagen content.

Mechano-Chemical Model for the Stepping of Cytoplasmic Dynein

Cytoplasmic dynein moves processively along microtubules, but it is still unclear how its heads use the energy from ATP hydrolysis, coupled to a linker swing, to achieve directed motion. We present a theoretical model based on a winch mechanism in which the principal direction of the linker stroke is toward the microtubule rather than along it. When mechanically coupling two identical heads, each with postulated elastic properties and a minimal ATPase cycle, the model reproduces stepping with 8-nm steps and directed processivity. Depending on the strength of the interhead connection, the stepping can either be coordinated (tightly coupled heads) or uncoordinated (loosely coupled heads); in the latter case the stepping pattern shows a greater variability. The uncoordinated motor retains a high level of processivity with a reduced product release rate and at the cost of a reduced velocity. The maximum force is largely limited by the loaded motor's processivity, which depends on the product release rates, and can be as high as 6pN in uncoordinated motors. The results of our model show that the winch mechanism is in itself robust and can account for a high stall force and processivity. Its stepping efficiency, however, can be greatly improved by an attractive interaction that leads to the stacking of the two heads.

Computational Models of Sprouting Angiogenesis and Cell Migration: Towards Multiscale Mechanochemical Models of Angiogenesis

Angiogenesis, the formation of new bloods vessels from the existing vasculature, is a process that is essential during development and regeneration of tissues, and that plays a major role in diseases like cancer. Computational models have been designed to obtain a better under- standing of the mechanisms behind angiogenesis. In this paper we review computational models of sprouting angiogenesis. These models can be subdivided into three categories: models that mainly focus on tip cell migration, models that make a distinction between the role of tip cells and stalk cells, and models that consider cell shape dynamics. Many models combine discrete modeling of individual cells with continuous modeling of the extracellular matrix (ECM) and diffusing solutes, in this way resulting in a hybrid model. We discuss their merits in unraveling the role of certain factors for vascular network formation, such as the role of (chemotactic, haptotactic, contact) guid- ance cues in the dynamics and morphology of vascular network formation, and the role of cell-cell interactions that govern tip cell selection and phenotypic changes in general. At the same time, we identify a need for the inclusion of cell mechanical principles in models of angiogenesis, in partic- ular for the description of cell migration, cell-matrix and cell-cell interaction, as the generation of cellular forces is key to cell migration. To further underline this we review models of single cell migration that incorporate such principles, which could be the starting point for formulating novel models of angiogenesis that respect the fundamental laws of classical mechanics at the cell level. As the generation of cellular forces is strongly mediated by pro-angiogenic signals, such models must couple cell mechanical principles to molecular signaling into multiscale mechanochemical models of angiogenesis. Finally, a tight coupling between models and experiments will be re- quired to facilitate model improvements and the generation of novel insights on the regulation of angiogenesis.