Polymer Science and Biology: Structure and Dynamics at Multiple Scales

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New entry by Andrew Capulli, AP225 Fall 2011

Reference

Polymer science and biology: structure and dynamics at multiple scales (Opening Lecture) L. Mahadevan, Faraday Discussions, 139, 9, 2008.

Key Words

Poroelastic, Cell Adhesion, Filament Bundling, Cell Alignment, Actin, Sickle Cell Anemia, Cytoskeleton

Introduction

In this review, Mahadevan gives a brief overview of cell dynamics and the complex behavior what is the simplest unit of life. He begins by addressing the aggregation of cellular filaments and membranous structures into ordered bundles of limited size and further continues by describing potential models that incorporate the response of the entire cell in terms of the complex material properties of the cytoplasm (and extracellular matrix as discussed in the previous entry). Mahadevan states about cells, "These low dimensional objects have a large surface to volume ratio and thus serve as substrates for chemical reactions associated with the dynamical processes underlying life while having the ability to encode function in complex dynamic structures." His comments highlight the complex material behavior of the cell, the smallest known form of life; this review begins to peel away at the complexity into useful models for future study.

Filament Bundling

The body, and the cell for that matter, is full of polymer molecules either arranged in ordered, bundled networks such as actin bundles in muscle, microtubules within the cell, and even collagen/elastin in hair or 'disordered' networks such as the extracellular matrix of many organs/connective tissue or the cascade of thombin proteins in blood clotting for example. In particular Mahadevan describes the bundling of filaments in terms of know polymer physics. Because of the natural curvature of some polymers in the body, bundling is limited in size and geometry. Curvature presents an interesting problem for the bundling of polymers; as the bundle grows in radius, the polymer filaments on the outside are stretched or compressed due to the curvature. This is much like a simple stress analysis problem of a fixed beam being bent: the face of the beam that force is applied to compresses while the opposite face stretches to compensate. As Emily gives in the previous entry, Mahadevan discusses that kinks in the formation of large bundles are necessary to allow for the described curvature limiting bundle girth of a particular filament complex but allowing for bundles of varied shape and length. Filament curvature may explain why certain filament bundles such as actin and sickle cell hemoglobin for kinks in their structure. Interestingly, Mahadevan discusses the consequence of sickle cell hemoglobin formation: essentially the unnatural kinks in the ill-formed hemoglobin cause red blood cells to lose their natural doughnut shape which allows for flow in the capillaries, the misshapen diseased cells cannot readily flow in this small vasculature which can result in clotting-embolism-and eventually stroke or heart attack. At the root of this disease is polymer science of soft matter; the physical shape of the aggregated filaments (in this case the folding of the hemoglobin protein) reduces flow in small capillary beds, in particular in the lungs, which not only inhibits flow causing potential embolism but also reducing gas exchange slowing respiration.

Model for Cytoplasm - Soft Matter

Perhaps where Mahadevan really delves into the complex nature of soft matter is when he discusses 'A micro-structural model for the cytoplasm' in section 3.1 of this review. Traditionally, models of the cytoplasm simplified the material as simple visco-elastic or visco-plastic. More appropriately, the cell can be modeled as poroelastic which allows for a model that includes the many components of the cytoplasm (water, ions, soluble proteins,filamentous structures, membranous structures, organelles etc). While the mathematics is summarized in the previous entry (Polymer science and biology: structure and dynamics at multiple scales), in terms of soft matter, the physical consequences are very interesting. Cell size, membranous pore size, and the viscous nature of the fluid (cytoplasm) in the cell are what control the mechanical response of the cell to an applied stress or strain. In a simplified explanation, as the cytoplasm is stressed as some point on the cell, water flows out of the pores in the membrane and the remaining cell contents are stressed. This propagates throughout the cell until all free water has evacuated and finally the remaining cytoplasm can equilibrate. While we know cells are not always chemically at equilibrium, as Mahadevan points out, they may not be mechanically at equilibrium either. This is why, for example, endothelial cells that line the inside of blood vessels align in the direction of flow; this alignment along the axis of shear stress they experience may keep the cell in a more mechanical equilibrium state. Figure 3 from the review is an example of a cell cultured without the presence of external forces. It is interesting to note the seemingly random microtubule and actin cytoskeleton not in any particular alignment (the cell is seeded in a circular-spread fashion).

MahadevanFIG3.jpg

Studies have shown the cells align along the axis in which they are being stretched. Below is a picture from a study I contributed to of valvular interstitial cells stretched uni-axially (in this case left to right); click to enlarge. As you can see these cells align along the axis of strain, perhaps as Mahadevan suggests, to become more mechanically equilibrated. These valvular interstitial cells (heart valve cells) are subjected to enormous shear stresses as blood flows past and very large pressures during diastole in the heart right before contraction. Like these valvular cells, other cardiac cells such as the myocytes responsible for contraction also align along the axis of strain (direction of contraction). While it is intuitive that cells align for maximum contraction along the axis, it may be the case the this alignment also results in a more uniform mechanical environment within the cell that as we know, has complex composition of soft matter make up.

Grad image 2.jpg

Model for Cell Adhesion - Soft Matter

Cell adhesion to a specific substrate depends on a number of factors such as cell type, substrate type, the presence of adherence proteins as well as membranous receptors, focal adhesions, and/or any other proteins/receptors that "exchange matter, information and energy with the exterior," as Mahadevan reports. Any number of mechanical, chemical, or electrical stimuli can also dictate adhesion (and alignment as discussed early in this entry). Mahadevan presents a model of cell adhesion neglecting exterior adhesive forces with a rate of change of contact of (assuming the cell to be a disk) RdR/dt; consequently the adhesive power is JRdR/dt (J is adhesion energy/area). Where w is the thickness of the 'shell' of the cell dR/wdt to accommodate spreading; assuming flow as a result of the spreading within the shell dominates the model the volume over which the 'dissipation' or spreading occurs is R^2w. u(dR/wdt)^2R^2w represents the energy dissipation rate due to flow (where u is the viscosity of the shell); Mahadevan demonstrates that this balanced with the adhesive power (for short times) results in R=(Jwt/h)^(1/2) - a scaling law for the contact radius. Independent of cell type and substrate, the contact area (radius in the model)grows linearly with time. This simplification of cell adhesion is, as Mahadevan even notes raised more questions than it answers. As he notes, what dictates adhesion energy (J)? Furthermore, upon examining the model, is a model that neglects outside forces such as mechanical stimuli and chemical stimuli even a worthwhile model since they are always variables in vivo? The age of the cell is also important; do neonatal cells behave similarly to adult cells? In modeling the cytoplasm I briefly discussed cell alignment in the axis of stress or strain. Perhaps these forces not only align the cells but also dictate adhesion. It is known that bone cells need a level of compressive stress to survive (necrosis results due to to stress shielding in bone plates for example); is their adhesion to the bone matrix also dependent on this compressive stress? These are all question Mahadevan would surely welcome and not merely to dismiss his model but to suggest improvements to is. It would likely be worth investigating the source of adhesive energy in different cell types due to predetermined factors (such as the environmental stimuli I suggest or chemical stimuli like the presence of fibronectin (adhesive protein).