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Measurement of cell and tissue deformation

Two approaches are worth highlighting because they have already had some success and are providing experimental ways to manipulating biological cells. On the one hand, several authors propose using nanoribbons made of piezoelectric lead zirconate titanate (PZT) for electrical stimulation of cell membrane and detection of cellular deformation. 38 The aim is to characterize the mechanical response of neuronal cells to applied voltages. Depolarization caused by an applied voltage induces a change in membrane tension.
Charges on opposing sides of a membrane repel to each other laterally, creating a local pressure, thus changing the net surface tension. This has the effect of altering the cell radius so that the pressure remains constant across the membrane. A preliminary setup calibration (without cells) by making use of AFM is required. Then, neuronal cells are cultured on PZT nanoribbons and a standard whole-cell patch-clamp technique is used to stimulate membrane voltages in cells while recording the electrical response in PZT nanoribbons. The generated electrical response was characterized by a whole-cell patch clamp technique using 1 micron diameter micropipette through which a current is supplied to the membrane to evoke a sharp increase in membrane potential after a certain threshold. This suggests the presence of voltage gated ion channels and cell perforation. A current pulse of up to 200 pA was used which raised the membrane potential up to 20mV from a resting potential of 50mV for roughly about the duration of the pulse and thereafter relaxing gradually. The electrical response was accompanied with a change in surface tension of cell and a small change in shape. Correspondingly, the altered force exerted by the cell on the suspended piezoelectric nano-ribbon produced a detectable FIG. 3. Human bone marrow mesenchymal stem cells (top row) stained with blue color for nucleus and red color for actin fibers (top) showing a control image (no stimulation) and selected images from controlled electrical stimulation (biphasic square-wave pulse of 61.2V for 1ms at 1Hz repetition is applied that delivers an average electric field of 5V/cm), mechanical stimulation (the entire base is stretched along the y axis as shown on right by double arrow), and electromechanical stimulation; scale bars are 100 lm each. Subsequent orientation analysis (bottom) for selected stimulation scenarios: In each image, several actin fibers are identified along with their orientation angle and a histogram of percentage orientation is plotted [Reproduced with permission Pavesi et al., Sci. Rep. 5, 11800 (2015). Copyright 2014 Author(s), licensed under a Creative Commons Attribution 4.0 License.].42 deflection. From the analytical model relating the cell radius to the magnitude of the force, the authors are able to show that a change of 120mV of the cell membrane voltage induces a force of about 1.6 nN on the suspended nanoribbons corresponding to a 1 nm deflection (Fig. 6). Several benefits of this method are worthy to note. Firstly, it turns out that PZT nanoribbons are thin and flat and can therefore conform to or even buckle onto curvilinear surfaces. Secondly, they can be fabricated using standard microfabrication techniques and are easily scaled. They can be bio-interfaced directly with tissues for measuring macroscopic electromechanical properties.


It has been established above that the mechanical forces between cells generated by an electric field are so far poorly appreciated and consequently under-exploited. Over the past few years, a variety of numerical modelling techniques have been designed to overcome the severe limitations of analytical models used to quantify intercellular forces, such as the inclusion of arbitrary shape for cell and the distribution of material properties, and offer much more versatile analysis. One of the major goals of such theoretical modelling is to predict quantities which are physically measurable at cellular and subcellular levels. However, due to the mismatch between theoretical assumptions and experimental realities, disagreements are quite common. Ab initio classical molecular dynamics (MD) of biomolecules which can simulate the coupling between electrical and mechanical properties have not yet been published in the archival literature. On the other hand, continuum (homogenized) medium approaches such as FIG. 6. Sensing nanometer scale deformations in excitable cells on a scalable substrate: SEM image of the device showing (a) piezoelectric nanoribbons as part of the substrate and (b) a neuronal cell adhering over it; scale bars are 15 lm. (c) Calculated force (blue line) as a function of membrane voltage based on the model presented in Ref. 38 and measured membrane voltage (red data points, error bars include variance of data and fitting errors from the AFM calibration) which increases along with its variance as the voltage across the membrane is increased [Reproduced with permission from Nguyen et al., Nat. Nanotechnol. 7, 587 (2012). Copyright 2012 Macmillan Publishers Ltd.].38 FIG. 7. Near-field optical manipulation of RBC on a substrate as a function of power in the focal plane: (a) stretching is denoted by size qh;v x;y (lm), where the superscript h-v corresponds to RBC trapped in horizontal or vertical plane on substrate, subscript x-y corresponds to x and y axes; (b) rotation of RBC trapped in horizontal plane, arrows indicate change in the direction of incident laser polarization; (c) folding of RBC trapped in the horizontal plane. The response is reported to be mainly linear in all cases and thus a linear fit is performed [Reproduced with permission from Gu et al., Opt. Express 15, 1369 (2007). Copyright 2007 Optical Society of America].45



The interfaces of applied physics and biology have both precedence and promise.57 The quantitative study of living matter, trying to understand the living part of the world with the same precision as we understood the inorganic world is eventually one of the most fascinating challenges of our time. We hope that this comprehensive report will serve to motivate newcomers who have never been exposed to the field of electromechanobiology. In the present perspective, we focused on a few fundamental points emphasizing how the quantitative analysis of forces can be controlled by various stimulation parameters. A single multiscale theoretical model or experimental platform which would include subcellular, cellular and tissue details is still lacking. Such analysis can be envisioned through a hybrid continuum approach that takes into account coarse-grained biomolecular details as well as larger length scales up to hundreds of cells. While biochemical reactions were not considered in this report it should be noted that the physical responses are often coupled with specific biochemical reactions during regular biological processes that eventually impact physical models.

Theoretical perspectives

A physics perspective in this field will likely be to imagine numerical tools that lower the level of complexity of living BM by keeping only the relevant and most important structural features, and how to think about the collective mechanics of individual cells organized in a hierarchical structure which is stimulated with an electric field. Though simplifications must be made to any simulation, the trend of increasing computer power and performance enables many of these inhibitions to be overcome by simulations that achieve a greater predictive capacity and come ever closer to simulating precise experimental and clinical conditions. Immediate challenges are as follows: (i) develop a multiscale multiphysics analysis of BM.58 What is needed is a way to gradually increase the BM complexity so that over complexity can be avoided but with the necessary physical features retained, for instance, linking the cell scale (continuum) electroporation model discussed earlier in Sec. VB and tissue model and then linking the biomolecular reactions database to it to test further responses.59 To truly capture and explore physical phenomena in 3D systems requires accounting for more of the complexities of a biological cell, such as its irregular geometry and their inhomogeneous and anisotropic material properties, i.e., meaning that the material’s mechanical properties do depend on the direction of the force; (ii) consider the behavior and self-assembly of cell collections. Out of thermodynamic equilibrium selforganization mechanisms can emerge and their understanding can open up paths to control emergent tissue patterns under external mechanical and electromagnetic fields; and (iii) analyze the role of ECM that surrounds and supports cells which is known to strongly affect cell/tissue organization; in particular the full exploitation of the interfacial properties will require an evaluation of the distance over which forces propagate by multiscale tissue modeling and to compare with experimental observations suggesting that long distance signals (typically, on the order of ten micrometers) are dependent on the inherent tension in the cytoskeleton.60

Table of contents :

List of publications
Overview of publications
1. Introduction
2. State-of-the-art and current issues of ED and EP
2.1 Prior to application of electrical stimulus
2.2 After application of electrical stimulus
Shamoon et al. (2018)
2.3 A closer context on ED and EP
3. Modelling cells and tissues
3.1 Introduction
3.2 Finite Element Method
3.3 COMSOL Multi physics and computational resources
3.4 Electric field fluctuations
Shamoon et al. (2017)
3.5 Numerical protocol
3.6 Geometry and meshing
3.7 Modelling coupled physics
3.7.1 Electrical model
3.7.2 Structural model
3.7.3 Pore model
3.8 Problem size and solver techniques
4. Results and discussion: ED and EP of cell assemblies
4.1 Time-dependent analyses
4.1.1 Small number of deforming cells
Shamoon et al. (2019-a)
Shamoon et al. (2019-b)
4.1.2 Large number of deforming cells (unpublished work)
4.2 Frequency analyses
4.2.1 Effect of relative orientation among two cells on total force
4.2.2 Effect of introducing next-nearest neighbors
5. Conclusion and Perspectives


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