Cytomechanics

PrefaceCytomechanics is a discipline for analyzing the relationship between mechanical forces experienced by cells and their subsequent fates. The challenge of analyzing these forces at the pico-Newton level and deformations at nanometer level can be met by merging mechanical engineering with techniques of modern molecular biology such as immunocytochemistry, optical imaging, and microfabrication. This book presents a mix of tools taken from these scientific disciplines. Emphasis is on the processes whereby cells sense and respond to mechanical signals.

The first 6 chapters present the basic structural plan components, and mechanical maintenance of cells, and tools to examine them. Basic kinematics, statics, and dynamics of cells are covered in Chapters 7 -9. Finally chapters 10-13 cover complex cell behaviours of adhesivity, signaling, moving, and growth. Quantitative examples and exercises based on traditional biomechanics applied to cells are provided. Software, such as Matlab and Excel will enhance understanding, and specific examples using them are given.

This book is introductory to the huge and growing field of cell mechanics, and assumes the reader has background in basic cell biology, biochemistry, and Physics. Companion books in those areas are recommended as reference. For more in-depth texts please read, “The mechanics of the cell”, by David Boar, and Biomechanics, by Y.C. Fung. This book has liberally adapted ideas from those two. Please note that this book is a first draft written for the class, which will inevitably contain mistakes, so corrections and comments will be appreciated.

1.1 Table of Contents1.2 Preface

Chapter 1. Introduction1.1 Why study Cytomechanics?1.3 Basic Cell Components 1.4 What forces holds the cell together ?1.5 How does the CSK provide structure?1.6 How smart is the CSK?1.7 What are possible applications of cytomechanics?1.8 Exercises1.9 Bibliography

Chapter 2. Basic Materials of the Cytoskeleton and Matrix

2.1 Basic Cellular Constituents 2.2 Arrangement of Cellular Materials2.3 CSK Components

2.4 Cytogel2.5 Exercises2.6 references

Chapter 3 Selected Cell Types 3.1 A Generic Cell3.2 Red Blood Cells3.3 White Blood Cells3.4 Endothelial Cells3.5 Myocytes3.6 Exercises3.7 References

Chapter 4. Measuring Cell Mechanics

4.1 Overview 4.2 Atomic Force Microscopy (AFM)4.3 Magnetic Tweezers 4.4 Micropipet Aspiration 4.5 Optical Tweezers4.6 Shear flow4.7 Hydrostatic loading4.8 Cell Stretching4.9 Microelectromechanical Systems4.10 Video Tracking4.11 Exercises4.12 References

Chapter 5 Visualizing the cytoskeleton

5.1 Light Microscopy, 5.2 Flourescent labelling5.3 Scanning microscopy5.4 Flow Cytometry.

Chapter 6. Energetics

6.1 Boltzmann relationships 6.2 Membrane Transport and difffusion6.3 Electrical potentials6.4 Molecular electromechanics6.5 Electrokinesis6.6 Fuel6.7 Thermal processes

6.8 Markov processes

Chapter 7. Geometric and Mechanical Properties

7.1 Two Dimensional metrology7.2 Three Dimensional metrology 7.3 Deformations 7.4 Poisson’s Ratio7.5 Viscoelasticity 7.6 Bending, buckling and squishing7.7 Linear elasticity hardness7.8 Entropic elasticity,

,

Chapter 8. Mechanical Behaviour: Statics 7.7 8.1 7.8 Laplace’s Law, 7.9 Stress Tensor7.10 Cell Internal Forces 7.11 Simulating V-E 7.12 Strain tensors in two and three Dimensions

Chapter 9 Mechanical Behaviour: Dynamics

9.1 Tension field theory9.2 Thermal motion9.3 Flowing blood.

Chapter 10 Adhesivity and Cohesivity

10.1 Cell binding to surfaces10.2 Surface Tension theory 10.3 Rolling, adherence, binding

Chapter 11 Mechanical Signalling

11.1 CSK signal Transmission 11.2 Cellular Mechanotransduction11.3 Phase transitions of gels, 11.4 11.5 Cell volume regulation

Chapter 12. Micromotors and Locomotion

12.1 Muscular contraction12.2 F1 ATPase

12.3 Cell crawling12.4

Chapter 13. Growth regulation

13.1 Wolff's law for bone cells13.2 DNA regulation13.3 Tumor regulation13.4 Cell-matrix interactions in vascularization

Chapter 14Angiogenesis

Appendix 1 Matlab & SimulinkAppendix 2 Units Appendix 3 abbreviations

Chapter 1 Introduction

1.1 Why study Cytomechanics?Biological cells are structures that self-assemble from basic components, adapt their shapes, sizes and strengths to their ongoing needs, and travel to and settle in appropriate locations using their own renewable energy. Much of these abilities result from sensory/reflex systems possessed by cells that respond to mechanical forces. Mechanical stresses and strains that cells experience throughout their lives are in fact crucial to the proper functioning and growth of cells. Cell function and growth are adversely affected when stresses are outside the proper range, either too large or too small.

The interdependence of stress and function by cells implies a unique design whose principles would be highly useful to engineers. Cytomechanics seeks to uncover those principles using the tools of molecular biology, imaging, biomechanics, and computer modeling. By analyzing forces and deformations on the piconewton and nanometer levels, cytomechanics seeks to explain and possibly manipulate the growth, structure and function of cells. A prominent example of the application of cytomechanics is accelerating the growth of cells and tissues by exposing them to forces from fluid flow in bioreactors. Specifically, growth of nerves, skin, muscles, bone, and probably all biological tissues can be stimulated by proper application of forces. Other technology exploits the highly efficient molecular motors found in bacteria to make nano-scale motors.

1.2 How are cells put together? The architecture of biological cells is highly complex, and its elegance can be appreciated in comparison with that of buildings. Building design must meet certain minimum standards: (1) a foundation anchoring it to the correct address (2) sufficient strength to stand against all expected forces, (3) comfortable internal environment, (4) access portals for incoming and outgoing traffic, (5) food and waste processing . Using well-established formulae from mechanical and civil engineering, the architect can select the type and sizes of structural components, their arrangement, connections, and all the functional components needed to satisfy the building standards. Before construction begins, she knows every line, arc, angle, and load that the building will have. Architecture of buildings is thus laid out as a clearly understood blueprint.

Architecture of biological cells, on the other hand, is laid out by a blueprint that is not so clearly understood, in the form of codes on DNA molecules; structurally, cells are squishy, wiggly, and willful. Nevertheless, cellular architecture not only must satisfy all the same standards as buildings, it must be self-renewable. Cells solve the mechanical and civil engineering problems they face in a myriad of elegant ways, using any and every way to live. In fact, cells have much more intelligence than buildings: they can modify their structure to meet changing demands and conditions. Cytomechanics seeks to learn and apply the rules of cellular architecture. While it may never be possible for us to build cells from scratch, we can expect to learn tricks from them that can help us solve many technological problems.

1.3 Basic Cell ComponentsBasic planThe basic plan of all animal cells is the same: they have a membrane, skeleton, and internal structures. Unlike the components of buildings, which are divided into purely structural or purely functional categories, all cellular components can serve both categories in elegant ways. The membrane is very weak structurally, but nevertheless is a barrier wrap and portal to the outside, as well as a smart skin with sensory and reflex capabilities. Mechanical strength is provided by the cell skeleton, i.e. ‘cytoskeleton,’ (CSK), that supports the membrane and maintains cellular shape. The CSK not only is the backbone and limbs of the cell, it is also a communication network. Within the gel-like cytosol, internal structures include the nucleus, mitochondria, and other organelles Together the 3 components, membrane, CSK, and cytosol provide all the structure and function of the cell.

The Cytoskeleton Two views of the CSK shown below illustrate its architectural complexity. On the left is a scanning electron microscope view from outside of a cell. The dense net is composed entirely of the protein, actin. Note the random crisscrossing of the fibers, and the nodes where 2 or more branches connect. Actin filaments, about 10 nM in diameter, run fairly straight between nodes, or connections, and form a thick tangled 3 dimensional mat at this scale. At a more distant (less

Figure 1.1100 nM100 nM

magnified) view, the network resembles a gossamer spider web as shown in Figure at right, a cartoon of a cross section of a segment of the cell border. The extracellular matrix intimately surrounds cells, and is attached at specific sites.

Three types of filaments make up the CSK, schematized below. The CSK is a network connecting the outside of the cell directly to points within, including the nucleus. Note that actin is the thinnest of the 3 filaments and forms a dense peripheral shell. Intermediate filaments are larger, and connect through the membrane at distrete points. Microtubules are straight hollow tubes with diameter 100 nM, and traverse across the cell and between the cell membrane and the nucleus.

Figure 1.2: Major CSK components

TissuesWhen cells aggregate to form tissues, things become more complicated as shown in the schematic view of 3 skin cells below. Many different types of connections, each with their own biochemical traffic patterns, are made among the various cells and extracellular components.

1.2.1 Figure 1.3

1.4 What forces holds the cell together ?

From the above sketches of cells, it is apparent that understanding cell structure starts with a look at its basic structural plan. At one level, it appears that the basic architecture of the cell is the same as the geodesic dome, designed by Buckminster Fuller. Geodesic is a highly efficient building, whose structural elements traverse the shortest distance required to hold it up. Many other structures, including

viruses, enzymes, organelles and even small organisms, all exhibit geodesic forms. Stick models of the structure are shown in Figure 1.4, left, and the CSK of a living cell is shown at right.

Tensegrity models can be made from sticks and rubber bands. Their integrity relies on the tension applied to the sticks by the elastic elements; hence the structure has ‘tensegrity’. In engineering terms, the sticks represent struts, since they sustain compression and the rubber bands represent ties (or ropes) since they hold tension. While the geodesic dome has a characteristic spherical shape, many other shapes are held together by tensegrity, not the least of which is standing bipeds (see below). Your bones are struts compressed by gravity, while your skeletal muscles apply tension to maintain the posture. Another structure is the loaded bow, shown below: Figure 1.5 Biped and Bow tensegrity structures

Cellular tensegrity is accomplished by the network of contractile micro-filaments pulling the cell membrane and all its internal constituents toward the nucleus at the core; Opposing this centrifugal tensile pull are two types of compressive elements, one of which is outside and the other inside the cell. The component outside the cell is the extracellular matrix (ECM); the compressive "girders" inside the cell are microtubules and/or bundles of cross-linked micro-filaments. The third component of the CSK, the intermediate filaments, link microtubules and contractile micro-filaments to each other as well as to the surface membrane and the cell's nucleus. In addition, they act as guy wires, stiffening the central nucleus and securing it in place. Although the CSK is surrounded by membranes and lies within a viscous fluid resembling a gel, it is this hard-wired network of molecular struts and cables that stabilizes cell shape. Thus the cell uses ropes to tightly bind compression-resistant struts together.

1.5 How does the CSK provide structure?Now that we have the basic structural principal of the cell (whose mechanical details are discussed in Chapters 7 & 8), we can begin to tease out more of the story, since the most interesting story is in the details. In later chapters will ask more probing questions, such as, ‘what other roles does the CSK play’? how does it interact with the nucleus? ‘how is it formed and maintained?

If in fact the CSK can be compared to (or modelled as) a geodesic dome, lets’ test its validity. For example, when you hit one of its struts, the mechanical energy quickly reverberates throughout the structure. Does the cell have a corresponding behaviour? The answer is yes, since when the CSK

Figure 1.4

is perturbed at a single site, either by a specific binding event, or experimental poking, the entire structure ‘feels’ it, as the energy is dissipated throughout at the speed of sound.

Next compare dome behaviour with another cell behaviour:cell spreading. Many cells can spread and flatten without microtubules, the major compression struts in the CSK. This is known from experiments in which microtubules were removed either through drugs or gene knockout. Many stimuli can change cell shape, such as stress applied by the ECM, as depicted in Figure 1.6 below. If living cells can remain spherical, and then change from spherical to flat without these struts, how does tensegrity apply? For example, imagine removing most of the sticks from the geodesic dome- it would collapse. Thus the CSK must have built-in redundancy, and it is known that the microfilament network by itself is a tensegrity structure. This ability of microfilaments to substitute functions could relate to its ability to adapt to stress, by ‘stress-stiffening.’ (see Chapter 10). In fact, redundancy of the CSK is to be expected, since its construction can be characterized as fractal, i.e. structural forms are self-similar at different scales; stated another way, the network weight is not proportional to its volume. Thus the simple geodesic dome model falls short of predicting some cell capabilities.

1.2.2Figure 1.6

1.6 How smart is the CSK?

The CSK apparently can sense the forces applied to it, and adjust its size, strength, and orientation in order to resist the forces in an efficient manner. When stresses are highly polarized, such as along the axis of muscles or neurons, filaments of the CSK align themselves according to principal stress directions, as shown in Figure 1.7 below. That means the CSK is very smart.

1.2.2.1 Figure 1.7

Besides orienting along stress lines, filaments size themselves according to strength requirements: a conservative architectural practice. Hulls of wooden ships, for example, are made with heavy axial beams, but light cross beams, as shown (an ancient rendering) below in Figure 1.8. This design plan is used in 2-dimensional CSK networks, as shown in the right panel, wherein thin cross struts hold the axially-oriented net together.

1.2.3 Figure 1.8 Ancient hull design 2-D CSK net

While there are many aspects of cellular architecture remaining to be discussed, lets consider one more question: how is the CSK constructed? Surely there are blueprints, ie. genes, for each of the protein components, and an overall blueprint laying out their 3-dimensional arrangement, but how do the ropes and rods connect themselves properly, in the right amount and orientation to form the fantastic structures seen above? This is a fundamental problem of biological development. While there is no simple answer, there are 2 somewhat competing models or theories that provide at least scenarios of how it could happen.

One assembly sequence for the CSK could be similar to that of the geodesic dome, with regular sub-structures such as triangles, being welded one by one into a 3 dimensional network. Tensegrity would hold the structure together, and would allow it to adapt and change. The attractive concept that the CSK represents essentially a “fullerene’ structure was originally proposed by Ingber [] and subsequently supported by many studies [].

While tensegrity and the geodesic dome definitely applies to cells, it is difficult to imagine how the complex CSK structures seen above assemble and maintain their shape. Geodesic models significantly change shape or collapse when a single strut or rope is cut, a behaviour that cells do not share. Thus an alternate theory of the CSK has been proposed, that is based on percolation [Fogacs]. This is a well-known process of network formation whereby individual lines grow somewhat randomly from point to point until sufficient connectivity establishes a network.

A simple example of percolation is the growth of telephone lines linking the East and West coasts of the U.S. There is no direct line connecting NY with Los Angeles, however in the development of lines between intervening cities, eventually a continuous pathway was formed, and as lines continued to link cities, more and more pathways were formed. Thus a large number of redundant pathways link the structure end-to-end. Figure 1.9 below shows a hypothetical telephone network in the U.S. many years ago. Note that lines between cities in the Northern sector do link NY with LA. As more cities are connected, it can be seen that more pathways will connect the 2 coastal cities. Since removal of a single line from the network can disrupt the continuously connected pathway from NY to LA, this network has a just critical number of elements; it is therefore at its, ‘percolation threshold.’

The percolation model is useful in describing network signalling, as well as elasticity, as will be seen in Chapters 7 and 10.

Thus there are at least 2 ways to think of the CSK: as a geodesic dome with regular networks of triangular elements or as random networks of lines tied together by percolation. The theories are not mutually exclusive, and both are useful, however neither tells the complete story.

1..7 What are possible applications of cytomechanics? This topic brings us full circle to the first: why study cytomechanics? The simplest answer is that you may find in cells valuable solutions to engineering problems. One example of a structural solution for a strong, lightweight, and flexible material is shown in figure 1.10 below. Design for this material is taken directly from CSK structure, and is in fact being developed by a company formed by Donald Ingber. Reverse engineering and exploitation of biological structures can be highly profitable, since no patent royalties are required by cells. The material below can absorb impact energy well, because shocks are dissipated thoroughly throughout the structure.

CSK structure is finding applications in other areas. Bioactive geodesic scaffolds for filtration and catalysis are highly efficient due to their high ratio of surface area-to-volume and low mechanical resistance to flow. One spin-off from this technology is an improved face mask with better protection against pathogens. These filters have adapted many features of cell structure, the CSK, and its bioactive nature. The scaffolds thus have large pores (much larger than the pathogens) for easy air flow, but have huge surface area and tortuous path to trap particles. Moreover the scaffolds are coated with a synthetic hydrogel "protoplasm" that soaks up pathogens which are highly hydroscopic (water seeking). The pathogens are killed using solid-state enzymes and other bactericidal agents that are incorporated within the gel.

Such ‘CSK- inspired’ materials can have unusual 3-D characteristics, such as the structures shown below that have zero mean curvature.

The CSK behaviour of stress-stiffening has inspired flexible fabrics that get stiffer when stretched, while maintaining their porosity for critical heat exchange. Development of an "artificial gill" for oxygen production is underway, using the high surface area and efficient solid-state catalysis offered by CSK design.

Biomimicry of cytomechanical design is advancing many other technologies, including tissue engineering, wound healing, microtubular nanostructures, bioprocess optimization, cryogenics mechanoelectrical signalling, tumor therapies, and genetic regulation. Microtubules serve as perfectly straight templates for fabrication of nanowires.

Exercises And Review Questions

1. The cytoskeleton is made of (Select one)a. Filamentous proteinb. Lipidc. Actin, microtubules and microfilamentsd. Extracellular matrix (ECM)e. (a, b and c)f. (a and c)g. (all of the above)2. Integrin is a transmembrane peptide (True or False)

3. State a specific method or technique to "knock out" or remove a component of the cytoskeleton

4. Immunofluorescence is a procedure to visualize specific molecules in a cell. The technique involves shining long wavelength light on the specimen, and seeing or detecting shorter wavelength light fluoresce. (True or false).

5. Red blood cells can increase volume without increasing their surface area. (True or false).

6. How does mechanoelectrical feedback differ from excitation-contraction coupling?

7. How do cells convert mechanical signals into chemical responses?8. Cite a specific pathway for such conversion and label all components of it9. Cite a converse example, i.e conversion of chemical signal into mechanical response.

10. Can you think of other examples that could represent tensegrity structures? Sketch 2 of them and draw their free body diagrams.

11. State 3 differences between cellular and building architecture. 12. Examine and run the MATLAB percolation model. Describe its function, and add

documentation to the program. 13. What are the structural advantages for 14. How many topics within the Biosciences are more interesting than cytomechanics? If

answer > 0 please explain.

Bibliography ON GROWTH AND FORM. REVISED EDITION. D'Arcy W. Thompson. Cambridge University Press, 1942 (reprinted 1992). MOVEMENT AND SELF-CONTROL IN PROTEIN ASSEMBLIES. Donald L. D. Caspar in Biophysical Journal, Vol. 32, No. 1, pages 103--138; October 1980. CLAY MINERALS AND THE ORIGIN OF LIFE. Edited by A. Graham Cairns-Smith and Hyman Hartman. Cambridge University Press, 1986. CELLULAR TENSEGRITY: DEFINING NEW RULES OF BIOLOGICAL DESIGN THAT GOVERN THE CYTOSKELETON. Donald E. Ingber in Journal of Cell Science, Vol. 104, No. 3, pages 613--627; March 1993. MECHANOTRANSDUCTION ACROSS THE CELL SURFACE AND THROUGH THE CYTOSKELETON. Ning Wang, James P. Butler and Donald E. Ingber in Science, Vol. 260, pages 1124--1127; May 21, 1993. GEOMETRIC CONTROL OF CELL LIFE AND DEATH. Christopher S. Chen, Milan Mrksich, Sui Huang, George M. Whitesides and Donald E. Ingber in Science, Vol. 276, pages 1425--1428; May 30, 1997. TENSEGRITY: THE ARCHITECTURAL BASIS OF CELLULAR MECHANOTRANSDUCTION. Donald E. Ingber in Annual Review of Physiology, Vol. 59, pages 575--599; 1997.