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Briefings in Bioinformatics Advance Access originally published online on June 25, 2007
Briefings in Bioinformatics 2007 8(4):258-265; doi:10.1093/bib/bbm025
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© The Author 2007. Published by Oxford University Press. For Permissions, please email: journals.permissions@oxfordjournals.org

An integrative approach to understanding mechanosensation

Christopher C. Poirier and Pablo A. Iglesias

Corresponding author. Pablo A. Iglesias, Department of Electrical & Computer Engineering, The Johns Hopkins University, 3400 North Charles Street, Baltimore, MD 21218, USA. Tel: +1 410 516 6026; Fax: +1 410 516 5566; E-mail: pi{at}jhu.edu


    ABSTRACT
 TOP
 ABSTRACT
 INTRODUCTION
 MECHANISMS OF MECHANOSENSATION
 EXPERIMENTAL APPROACHES
 MODELING STRATEGIES
 CONCLUSIONS
 FOOTNOTES
 Acknowledgements
 References
 
The ability for a living organism to sense and respond to its external environment is crucial to its survival. Understanding mechanosensation, the mechanism by which organisms react in response to mechanical stimuli, presents many interesting and challenging problems for both experimental and computational biologists. A major difficulty in studying mechanosensors is their inherent multiscale nature. The systems involved in mechanosesnsing can span eight orders of magnitude in length scale and up to 10 orders of magnitude in time scale. Trying to ascertain information across these length and time scales simultaneously is challenging. This problem has led to the need to approach these types of problems using an integrative approach, combining both computational and experimental biology. This review classifies the major types of mechanosensors and explains methods that have been employed in understanding their behavior, both using modeling and experimental techniques. Multiscale modeling methods combined with experimental techniques in an integrative approach are suggested as ways of undertaking the study of such systems.

Keywords: ion channels, finite element methods, mechanosensation, multiscale modeling


    INTRODUCTION
 TOP
 ABSTRACT
 INTRODUCTION
 MECHANISMS OF MECHANOSENSATION
 EXPERIMENTAL APPROACHES
 MODELING STRATEGIES
 CONCLUSIONS
 FOOTNOTES
 Acknowledgements
 References
 
The ability to perceive and respond to mechanical stimuli is one of the most basic cellular physiological responses, being found in all organisms and in nearly all cell types [1–6]. Bacterial cells rely on mechanosensation to counteract the effects of osmotic shock [7, 8]. In vertebrates, force-driven displacements in the hair bundles control the opening of electrical channels, thus transducing mechanical forces into electrochemical signals and enabling hearing [9]. Disruptions in the cellular ability to sense mechanical forces can lead to severe consequences. For example, polycystin-1 and polycystin-2 (encoded by the genes PKD1 and PKD2, respectively) are molecules which colocalize to cilia of renal epithelial cells [10, 11]. There, they help to sense and transduce shear stress during fluid flow. Defects in either PKD1 or PKD2 lead to polycystic kidney disease and kidney failure, likely because of an inability to sense and respond to mechanical stimuli properly.

Recent experiments have revealed new roles for mechanosensitive pathways. For example, Engler et al. demonstrated that naive mesenchymal stem cells can commit to a particular lineage based on the elasticity of the surrounding matrix [12]. Meanwhile, Effler and colleagues, using mechanical perturbations during cytokinesis, identified a mechanosensory-based feedback system that regulates cell shape progression [13, 14].

Remarkably, mechanosensitive channels have evolved to discriminate specific stimuli with exquisite selectivity over ranges of pressure spanning eight orders of magnitude [15]. Moreover, owing to the nature of the environment in which they reside, these sensors are subject to many types of external perturbations.

Despite their importance and much recent progress, relatively little is known about the molecular mechanisms by which mechanosensation is effected in cells. This is especially true when compared with our understanding of other senses that are primarily modulated by receptor–ligand interactions. By its very nature, understanding mechanosensation requires a combination of traditional biological approaches (e.g. genetic, biochemical and pharmacological) and biophysical techniques that can probe the mechanical nature of the stimuli. These experimental techniques are coupled to computational and biophysical models that can test conceptual models. In this review, we illustrate how mathematical models over multiple scales have been used to study mechanosensation.


    MECHANISMS OF MECHANOSENSATION
 TOP
 ABSTRACT
 INTRODUCTION
 MECHANISMS OF MECHANOSENSATION
 EXPERIMENTAL APPROACHES
 MODELING STRATEGIES
 CONCLUSIONS
 FOOTNOTES
 Acknowledgements
 References
 
Most known mechanosensors are believed to act by changing the conformational state of an associated ion channel in response to an applied external force. Assuming a two-state model in which the inactive channel is closed with probability pc, and active open with probability po, the Boltzmann function provides the ratio.


Formula

where {Delta}G is the difference in free energies between the closed and open conformations. The change in free energies {Delta}G has to be generated by the applied mechanical stimuli. There are two broad models by which this mechanotransduction is achieved, either by changes induced by the lipid bilayer [16, 17] (Figure 1A), or through some mechanical tethering (Figure 1B).


Figure 1
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Figure 1: Mechanisms for triggering mechanosensitive ion channels. Cartoon describing the two basic models by which mechanosensitive ion channels are opened. In membrane-activated channels (A), tension in the membrane effects a conformational change which opens the channel. In mechanically gated channels (B), a spring-like tether is attached to an extracellular appendage which, when deflected, opens the channel.

 
To understand how membrane-activated ion channels work, we first consider some relevant features of the lipid bilayer [18, 19]. Compression tests have revealed that the membrane can be assumed to be volumetrically incompressible under physiological conditions, so that mechanical perturbations that increase its surface area—such as a stretching induced by changes in osmotic pressure—result in a localized thinning of the membrane. This thinning causes a corresponding conformational change in the ion channel; computations have demonstrated that the energy required for the membrane deformations is of the same order as the measured free energies of known channels [20].

Of the class of membrane activated mechanosensitive channels, the best understood is MscL (mechanosensitive channel of large conductance) found in bacteria [21]. MscL is one of the few channels for which a crystal structure is known, though only for one conformation, which is assumed to be the inactive closed state (Figure 2). The available crystal structure makes it of particular interest to researchers who wish to model the characteristics of these channels mathematically [22]. Unfortunately, it shows no significant sequence homology to other known voltage channels and has no eukaryotic counterpart [23].


Figure 2
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Figure 2: Structure of the bacterial MscL channel. Side (A1) and top (B1) views of a ribbon model of the Mycobacterium tuberculosis MscL in its closed configuration. This model was obtained using the crystal structure of MscL [22], using Pymol [66]. The model does not show any explicit solvents or lipid molecules. This MscL is a homopentamer. Each of the five monomeric subunits, which contain 136 residues, consists of two transmembrane –{alpha} helices, as well as a cytoplasmic helix which is not believed to be involved in mechanosensation. Panels A2 and B2 show finite element models of the MscL transmembrane helices. This model, similar to that of Tang et al. [65], was obtained by fitting a cylinder along the helical axes of the MscL crystal structure.

 
A large class of mechanosensors is believed to sense forces through the deflection of spring-like extracellular tethers that are coupled to membrane ion channels (Figure 1B). When deflected, these tethers induce a conformational change in the ion channel—either directly, or by opening a gate, thereby altering the channel's conductance. A well-known example is found in the hair cells involved in vertebrate hearing, where deflection of the mechanosensitive stereocilia opens ion channels located on adjacent stereocilia, resulting in an influx of Ca2+ or K+ [24–28]. The specific ion channels involved in hair cell mechanotransduction are not known, though a number of likely candidates, including TRPA1, have been considered [29–31].

TRPA1 is a member of the superfamily of transient receptor potential (TRP) channels that have been proposed to have a role in mechanosensation amongst many other functions [32]. The original member of the family, Drosophila trp, was first identified in flies that were defective in vision [33]. TRP channels, which are categorized by their homology rather than ligand function, are responsible for various functions within living organisms. These channels are used to sense and respond to hypertonicity in yeast [34], enable touch and osmosensing in C. elegans [35], are involved in detecting fluid flow in primary cilia of the kidney epithelial cells [10, 11], and are used to sense taste in humans [36]. In humans, 28 TRP genes have been identified and are grouped into seven subfamilies of cation-selective channels [32]. TRP proteins have six transmembrane domains and a pore loop; in membrane topology, they are similar to some voltage and cyclically gated channels.

Another family of putative mechanosensitive ion channels, the Degenerin/Epithelial Sodium Channels (DEG/ENaC), were first discovered through genetic screenings in C. elegans seeking proteins required for touch sensitivity [37]. Interestingly, though they do not have sequence homology, they do show some structural similarity to MscL. The C. elegans touch receptor contains several subunits [38]. Proteins MEC-4 and MEC-10 are members of the family of DEG/ENaC channels and form the pore of the channel complex [37]. MEC-2, which is homologous to stomatin, an integral membrane protein found in many cell types, is thought to connect the channel to microtubules in the cytoskeleton. Activation is believed to be through the connection between the membrane and an external force sensor via the extracellular MEC-9 protein, which acts like a gating spring.

Unfortunately, though TRP and DEG/ENaC channels are believed to be the primary channels involved in mechanosensation in eukaryotic cells, the molecular means by which external forces mediate the required changes in the conformation of the ion channel remain unknown. Research is hampered in part by the lack of an available crystal structure.

So far, we have only considered schemes in which mechanosensation is achieved via direct activation of ion channels. It has also been suggested that cells can sense force through coupling, via transmembrane proteins such as integrins, between the extracellular matrix and the cytoskeleton [4]. Under stress, the cytoskeleton undergoes rearrangement of its interlinked actin and intermediate filaments as well as microtubules [39]. Note that the transmembrane receptors and cytoskeletal filaments may also activate stress-sensitive ion channels on the cell surface.

Mechanosensing may also be mediated by force-driven conformational changes in cytoskeletal proteins that can affect protein function [6]. It is well established that molecular motors, such as myosin [40] and dynein [41], alter their duty cycle and efficiency in a load dependent manner, thus making them good candidates for this mechanism of mechanosensation [6, 13]. In fact, myosin-1c is believed to mediate slow adaptation in hearing [42].


    EXPERIMENTAL APPROACHES
 TOP
 ABSTRACT
 INTRODUCTION
 MECHANISMS OF MECHANOSENSATION
 EXPERIMENTAL APPROACHES
 MODELING STRATEGIES
 CONCLUSIONS
 FOOTNOTES
 Acknowledgements
 References
 
An integrative approach to the study of mechanosensation couples experiments tightly to mathematical modeling. A detailed treatment of the related experimental techniques is beyond the scope of this review and can be found elsewhere [43–45]; however, we provide an introduction to the most popular methods and their applications.

To gather meaningful data on the cellular response to mechanical loads, it is necessary to apply forces and stresses in a physiologically relevant context. These forces are in the order of pN, when studying single molecule responses, to nN at the cellular level.

At the smallest scale, force can be applied to embedded particles (beads) by optical or magnetic means. These forces, which can be either fixed or time varying, are precisely generated and result in highly controlled bead displacement. Optical tweezers generate force by transferring momentum from photons to the beads as the light is bent [44]. This method provides exquisite precision, but can only target one bead at a time unless multiple optical traps are used concurrently [46]. Alternatively, magnetic fields can be used to generate force on paramagnetic beads over a larger sample. Magnetic twisting is similar to magnetic trapping, but uses a magnetic field to generate a rotational force on the attached bead. Upon removal of the magnetic field the resulting motion of the bead can lead to an understanding of the underlying mechanics of the system.

Atomic force microscopy can be used to probe the mechanical properties of the membrane [43]. In this method, the deflections of a small tip connected to a cantilever arm can be tracked as it scans the surface of an object, such as the cellular membrane, thereby providing a detailed map of the surface geometry and local membrane stiffness.

A classical and still popular technique is micropipette aspiration [14]. Here, suction pressure is applied to cells through needles that are placed in contact with the cell surface. The corresponding cellular deformations can be used to determine the mechanical properties of the cell cortex.

The approaches discussed so far apply primarily to single cell measurements. To determine the mechanical properties of cellular ensembles, such as a layer of endothelial cells, it is customary to grow a monolayer in culture and to apply shear stress by flow [47]. Recent advances in development of microenvironments and microfluidics may expand the range of applications of such techniques [48].


    MODELING STRATEGIES
 TOP
 ABSTRACT
 INTRODUCTION
 MECHANISMS OF MECHANOSENSATION
 EXPERIMENTAL APPROACHES
 MODELING STRATEGIES
 CONCLUSIONS
 FOOTNOTES
 Acknowledgements
 References
 
Because of the large number of unknown questions regarding the mechanics of mechanosensation, an integrative approach, combining both experimental measurements and mathematical modeling, offers insight that is not available based only on traditional genetic, pharmacological and biochemical approaches. Mathematical models, once verified with experimental data, can be used to discern mechanistic behavior, largely due to their ability to test a large variety of hypotheses. One of the major problems in modeling biological systems, such as those involved in mechanosensation, is their inherent multiscale nature, both in time and space. The dynamics of the systems can range from nanoseconds to minutes and across length scales from nanometers to meters; models have been proposed and used to study mechanosensation at all of these levels.

At the finest scale, molecular mechanics may shed light on the underlying mechanism by which channels function. Molecular dynamics simulations begin with the protein's crystal structure as well as the underlying membrane and solvent landscape and attempt to solve Newton's equations for every atom in the system, from which atomic trajectories can be determined. For example, molecular dynamic simulations of MscL proteins in fully hydrated lipid bilayer have been made [49–52]. Using a model in which external steering forces are applied near the lipid/water interface, thereby emulating the effect that an external force may have on the channel, a gating transition occurred within 10 ns. The MscL was seen to open in an iris-like manner. In this particular simulation, however, forces much larger than physiologically possibly were used in order to see the gating transition [51]. A related approach, involving targeted molecular dynamics—a method for computing transition pathways between two known protein conformations—has been used to study the MscL gating mechanism [53]. Structural modeling has also been used to determine the gating mechanism of the MscL, where external constraints are placed on the allowable transitions. In this way, intermediate gating conformations in MscL were obtained [54, 55].

Though molecular dynamic simulations provide an accurate technique for determining the atomic fluctuations of systems, several challenges limit their use. The first is that the time evolution of the system is highly dependent on the initial condition. An all-atom simulation of a channel along with a segment of the associated membrane and solvent can constitute a simulation of tens to hundreds of thousands of atoms. To gather relevant information about the system, the time step used in the calculation of the atoms’ trajectories must be small enough to capture the fastest dynamics of the system. This necessitates femtosecond time steps. Combining a large number of atoms, along with the small time step intervals needed means that simulations can only realistically cover tens to hundreds of of nanoseconds—only a fraction of the total gating transition time of mechanosensitive channels like MscL. Moreover, because they are so computationally expensive, both in time and the computational resources needed, it is difficult to examine a broad range of hypotheses, negating one of the advantages of modeling. Steered molecular dynamics can ameliorate these problems, but to get the expected channel transition in the limited amount of simulation time, it may be necessary to apply physiologically unrealistic forces.

To circumvent the scaling problems associated with simulations, thermodynamic models have been used to study mechanosensation, once again, primarily focused on MscL [1, 17, 20, 56, 57]. These computations have the advantage that they can analytically determine the mechanistic properties of the system through analysis of the relevant energies. The energetics associated with the lipid bilayer and channel system have been used to identify potential mechanisms by which channels are activated, showing that the mechanism for MscL gating is a function of the local and global asymmetries in the channel–bilayer interface [16, 20, 56, 57].

Theoretical approaches allow for qualitative understanding of the systems. To determine how mechanosensitive channels respond to different types of local stress–strain fields, continuum mechanics can be used. At this level, the characteristics of individual atoms are ignored in favor of macroscopic physical quantities. The application of continuum modeling to biology is not a new idea, and has been used extensively in the study of cellular mechanics [58]. Significant advantages of a continuum approach include the ability to study time evolution of the system over a much longer time span and the capacity to examine a large parameter space. As well, time dependent inputs can be used to study the transient properties of the system. One of the first applications of continuum mechanics to the study of mechanosensation involves the study of stereocilia and the associated mechanical properties of hair cells [59, 60].

Owing to the complex nature of the ‘real world’, analytical solutions to the continuum model equations are rare. Their numerical solution can be obtained through computation, of which finite element analysis is an appealing choice. Originating in engineering from its use in the stress analysis of beams, it has proven to be a useful tool in dealing with the complex geometries and material properties associated with continuum models of biological systems. A finite element analysis starts with the geometry of the system of interest, which is broken down into a series of discrete nodes and elements through the use of a mesh. For each node and element, a set of equations based on a discretized version of the continuum equations of the system is derived. These equations are then solved simultaneously to determine the dynamics of the system. Owing to the numerical advantages of the finite element method over other algorithms, 3D simulations are possible. The finite element approach has been used to solve for increasingly sophisticated mechanical models of the hair ciliary bundles [61–64]. In these models, the cilia are modeled as deformable beams and their mechanics are analyzed under different force loading conditions.

Finite element methods may also prove attractive for multiscale models of mechanosensation. The idea is to combine some of the computational advantages of continuum models with the fine structure of molecular models. This approach was used to study MscL gating [65]. In this work, the MscL–{alpha} helices in the structure (10 in all) are modeled as homogeneous elastic rods using finite elements. The channel is embedded in a homogeneous elastic solid, thought to be representative of the physical characteristics of the membrane. The conformational change of the channel can then be simulated for various membrane deformations induced by external forces. This multi-scale modeling approach combines some of the best features of molecular dynamic simulations, in that it is based on first principles and allows for the analysis of ion channel conformations at the macroscopic level, while retaining the computational advantages of the continuum formalism.

Techniques analogous to this one may prove useful in study systems at multiple length and time scales. Solving two systems of different length and time scales simultaneously may allow one to probe global system behavior. For example, a finite element model of the entire cell could be used to analyze the cellular level response to external perturbations (Figure 3). Concurrently, the model can be analyzed to determine the localized force profile in the membrane for the given location of a prospective mechanosensitive ion channel. This force profile can then be used in another finite element model of the channel protein and membrane in a multiscale framework similar to that of Tang et al. [65]. This model, on a much shorter length and time scale can be used to determine the average kinetic parameters of the channel in response to force input. These averaged kinetic parameters analyzed from the molecular level model can then be incorporated back into the cellular level model and an analysis of the ion content in the cell can be conducted and compared with experimental results. Through the use of all atom simulations, the dynamics of the molecular level systems can be better determined and used to refine the molecular level finite element model. Though it does present a compromise, we believe this type of analysis is ideal for identifying mechanisms of mechanosensitive behavior that can then be tested experimentally, and provides another tool to gain insight into system behavior.


Figure 3
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Figure 3: Multiscale approach to studying mechanosensation. Here we illustrate how multiscale modeling could be used to study the mechanical response of a cell to micropipette aspiration [14]. In these experiments, suction pressure was observed to recruit myosin II to the site of aspiration which enabled the cell to escape the pipette. A finite element model can be used to determine the cellular deformation to an applied pressure. This simulation can be used to obtain the local membrane force profile (inset) at different points along the cellular membrane, which can then be used to perturb a mesoscale model of mechanosensation in ion channels. The corresponding signaling response can then be used to generate a myosin II profile along the cellular cortex. This profile will generate force and work against the force generated by the micropipette altering the cell shape.

 

    CONCLUSIONS
 TOP
 ABSTRACT
 INTRODUCTION
 MECHANISMS OF MECHANOSENSATION
 EXPERIMENTAL APPROACHES
 MODELING STRATEGIES
 CONCLUSIONS
 FOOTNOTES
 Acknowledgements
 References
 
Despite the importance that mechanosensation plays in regulating many aspects of cellular physiology, it is remarkable that so many questions remain about the mechanisms by which cells can react to external forces. Elucidating these mechanisms will require the combined integrated efforts of researchers in many fields.

In this review, we have outlined different techniques used to study mechanosensation. We have focused on computational approaches and highlighted the need for multiscale models and approaches. At the finest scale, mechanosensation is clearly effected by conformational changes of protein structure, either through ion channels or other proteins. However, in many cases we are interested in cellular responses at more macroscopic levels. The computational burden of the molecular simulations makes studying these responses impractical without some means of integrating multiple scales. New modeling efforts will need to be tightly coupled to the experiments. We believe that this multiscale and integrative approach to uncovering mechanosensation will have a large impact in the understanding of this vital cellular process.


Key Points

  • Though mechanosensation is found ubiquitously in biology, from single cell organisms to humans, there is remarkably little understanding of the molecular mechanisms used to sense mechanical stimuli. Understanding these systems will require the concerted effort of researchers from many disciplines, including biochemistry, genetics, biophysics and computational biologists.
  • Most mechanical sensors are believed to involve the activation of membrane ion channels, either directly through the membrane or by coupled mechanical activation.
  • Mechanical sensors act across a large range of spatial and temporal scales. Many mathematical and computational models exist at discrete scales, but only recently have multiscale models emerged that study mechanosensation. We believe that this class of models will have a large impact in the understanding of this vital physiological process.

 


    Acknowledgements
 TOP
 ABSTRACT
 INTRODUCTION
 MECHANISMS OF MECHANOSENSATION
 EXPERIMENTAL APPROACHES
 MODELING STRATEGIES
 CONCLUSIONS
 FOOTNOTES
 Acknowledgements
 References
 
We thank members of the Iglesias lab for comments on earlier versions of the manuscript, as well as Doug Robinson (JHU School of Medicine) for numerous conversations. The work of our lab is supported by grants from the National Science Foundation (CCF 0621740) as well as the National Institute of General Medical Sciences (71920 and 72024). CPP has been supported by the Institute of Multiscale Modeling of Biological Interactions, under Department of Energy grant DE-FG02-04ER25626.


    FOOTNOTES
 TOP
 ABSTRACT
 INTRODUCTION
 MECHANISMS OF MECHANOSENSATION
 EXPERIMENTAL APPROACHES
 MODELING STRATEGIES
 CONCLUSIONS
 FOOTNOTES
 Acknowledgements
 References
 
Chris Poirier is a PhD student in the Institute for Multiscale Modeling of Biological Interactions at Johns Hopkins University. His interests are in using multiscale modeling to understand mechanical properties of cellular division.

Pablo A. Iglesias is Professor in the Departments of Electrical & Computer Engineering, Biomedical Engineering, and Applied Mathematics & Statistics at Johns Hopkins University. His main research interests are in the use of computational models to study directed cell migration and cell division.

Submitted: March 31, 2007. Received (in revised form): March 31, 2007.


    References
 TOP
 ABSTRACT
 INTRODUCTION
 MECHANISMS OF MECHANOSENSATION
 EXPERIMENTAL APPROACHES
 MODELING STRATEGIES
 CONCLUSIONS
 FOOTNOTES
 Acknowledgements
 References
 

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