What frequencies are important to the interaction of real materials? It is best to learn from example. If we can develop an intuition to know the significant frequencies of fluctuation, our partial ignorance of absorption spectra need not daunt us in computation or, better, this intuition might give us some idea about the accuracy of computation. Differences in dielectric response create the force; sampling-frequency density weights the contribution from higher frequencies; retardation snuffs out the highest frequencies first. These general features show up in specific examples. Water, hydrocarbon (liquid tetradecane), gold, and mica are not only popular materials in van der Waals force measurement but, as a group, they also display a wide variety of dielectric response. (See, e.g., tables in SubSection L2.4.D).

Their detailed energy-absorption spectra as functions of radial frequency ωR translate into smooth functions ε(iξ) of imaginary frequency. This blurring of details in ε(iξ) is one reason why it is often possible to compute van der Waals interactions to good accuracy without full knowledge of spectra (see Fig. L1.21).

To see how these different ε(iξ) functions combine to create an interaction, consider the case of two hydrocarbon half-spaces A = B = H across water medium m = W. First plot εH(iξ) and εW(iξ) as continuous functions [see Fig. L1.22(a)].

In previous chapters we found that, by virtue of their internal dynamics, cells could assume distinct states and thereby follow alternative developmental pathways. This process ultimately generated various types of terminally differentiated cells (Chapter 3). We also found that tissues made up of multiple cells, linked together directly (Chapters 4 and 5) or via an extracellular matrix (Chapter 6), could undergo alterations in shape and form (morphogenesis), leading to the development of new structures. Although developing tissues need not contain different cell types in order to undergo morphogenesis, differentiation often sets this process in motion. For example, sorting and tissue engulfment, which together comprise one of the classes of morphogenetic phenomena discussed earlier, require at least two populations of cells that are differentiated with respect to their cell-surface adhesivity.

Cell sorting, however, is unusual among the morphogenetic processes dependent on differentiation in that the initial differentiation event need not be spatially controlled. Recall that the random mixing of two cell types and the fusing of fragments of the tissues from which they were derived ultimately achieved the same morphological outcome (Fig. 4.5). Thus, if differentiation in a developing cell mass occurs in a spatially random manner, so that two cell types with differing adhesive properties come to be dispersed in a salt-and-pepper fashion, the final configuration of the eventually phase-separated tissues will always be the same. A case in point is Hydra, a diploblastic, i.e., two-germ-layered, organism (see Chapter 5), which starts out as a single-layered blastula.

As a consequence of generating and reshaping the epithelia of their ectodermal and endodermal germ layers and (for those species that have them) the mesenchymes that make up the mesodermal germ layer and neural crest, embryos take on one of approximately three dozen stereotypical “body plans.” These body plans can be asymmetric (sponges), radially symmetric (e.g., hydra and sea urchins), bilaterally symmetric (e.g., planaria, insects), or “bilaterally asymmetric” (vertebrates; see the last section of Chapter 7). While it is obvious that nothing in development, or in any other domain of biology for that matter, can occur without the participation of physical mechanisms, the high degree of structural and dynamical complexity of most living systems makes it exceedingly difficult, in general, to follow the workings of basic physical principles or appreciate their roles in generating characteristic biological phenomena. It is therefore remarkable to how great an extent (as the preceding chapters have shown) the tissue generation and reshaping processes leading to embryonic body plans can be accounted for by physical forces and properties – adhesion, viscoelasticity, dynamical multistability, network formation, positive and negative feedback dynamics, diffusion – that also govern the behaviors of nonliving condensed materials, that is, by “generic” physical mechanisms.

The ability to understand aspects of early development in generic physical terms can be attributed, in part, to the likelihood that the original multicellular organisms were simple, loosely organized, cell masses, whose forms were determined to a great extent by their inherent physical properties (see Chapter 10).

In Chapter 2 we followed development up to the first nontrivial manifestation of multicellularity, the appearance of the blastula. To describe the mechanism of blastula formation we needed a model for cleavage, as well as for the collective behavior of a large number of cells in contact with one another. We based our model on physical parameters such as surface tension, cellular elasticity, viscosity, etc. and when possible related these quantities to experimentally known information such as the expression of particular genes. However, we have so far not dealt with the fundamental question concerning multicellularity: what holds the cells of a multicellular organism together?

As cells differentiate (see Chapter 3) they become biochemically and structurally specialized and capable of forming multicellular structures, with characteristic shapes, such as spheroidal blastulae, multilayered gastrulae, planar epithelia, hollow ducts or crypts. The appearance and function of these specialized structures reflect, among other things, differences in the ability of cells to adhere to each other and the distinct mechanisms by which they do so. During development certain cell populations need to bind, to varying extents, to some of their neighbors but not to others. In mature tissues the nature of the cell–cell adhesion contributes to their functionality: the manner in which two cells bind tightly to one another in the epithelial sheet lining the gut, for example, must be different from the looser attachment between the endothelial cells lining blood vessels.

In the previous chapter we considered the forces leading to subdivision of the fertilized egg and the large-scale morphological consequences of successive cleavages. We followed the processes leading to the generation of the blastula, an important developmental step. In our treatment, however, the blastula was represented as a mass of identical cells. In reality, at the blastula stage not all cells of the embryo are identical: the “totipotent” zygote (with the potential to give rise to any cell type) first generates cells that are “pluripotent”– capable of giving rise to only a limited range of cell types. These cells, in turn, diversify into cells with progressively limited potency, ultimately generating all the (generally unipotent) specialized cells of the body. At the same time, in the life of each dividing cell, regardless of its level of developmental potency, there are transitions from state to state as the cell performs various functions of the cell cycle.

It is the purpose of this chapter to provide a framework for understanding how genetically identical cells can change their physical states in reliable and stable ways in time and space. We will also explore how these states, in turn, can provide a physical basis for a cell's performance of different tasks at different phases of its life cycle and for its descendants' performance of different specialized functions in different parts of the developing and adult organism.

The transition from wider to narrower developmental potency is referred to as determination.

For the biologist the cell is the basic unit of life. Its functions may depend on physics and chemistry but it is the functions themselves – DNA replication, the transcription and processing of RNA molecules, the synthesis of proteins, lipids, and polysaccharides and their building blocks, protein modification and secretion, the selective transport of molecules across bounding membranes, the extraction of energy from nutrients, cell locomotion and division – that occupy the attention of the life scientist (Fig. 1.1). These functions have no direct counterparts in the nonliving world.

For the physicist the cell represents a complex material system made up of numerous subsystems (e.g., organelles, such as mitochondria, vesicles, nucleus, endoplasmic reticulum, etc.), interacting through discrete but interconnected biochemical modules (e.g., glycolysis, the Krebs cycle, signaling pathways, etc.) embedded in a partly organized, partly liquid medium (cytoplasm) surrounded by a lipid-based membrane. Tissues are even more complex physically – they are made up of cells bound to one another by direct adhesive interactions or via still another medium (which may be fluid or solid) known as the “extracellular matrix.” These components all have their own physical characteristics (elasticity, viscosity, etc.), which eventually contribute to those of the cell itself and to the tissues they comprise. To decipher the working of even an isolated cell by physical methods is clearly a daunting task.

In the previous chapter we saw how the simple physical assumption that the cell is a droplet of liquid comes into conflict with experimental evidence when the transport of molecules in its interior or the response of an individual cell to mechanical stress are considered. By adding more physics to the default concept of diffusion (external forces, viscosity, elasticity) we were able to approach the biological reality of cell behavior more closely. This analysis also had the premium of helping us to identify levels of organization (e.g., chemotaxis in a colony of bacteria or amoebae) at which physical laws that are too simple to explain individual cell behavior may nonetheless be relevant.

In this chapter we will describe the transition made by a developing embryo from the zygotic, or single-cell, stage to the multicellular aggregate known as the blastula. Here again the simplest physical model for both the zygote and the early multicellular embryo that arises from it is a liquid drop. As in the examples in Chapter 1 our understanding of real developing systems will be informed by an exploration of how they conform with, and how they deviate from, the basic physical picture.

The cell biology of early cleavage and blastula formation

The blastula arises by a process of sequential subdivision of the zygote, referred to as cleavage. Cleavage, in turn, is a variation on the process of cell division that gives rise to all cells.

During both gastrulation and neurulation certain tissue regions that start out as epithelial – portions of the blastula wall and the neural plate – undergo changes in physical state whereby their cells detach from one another and become more loosely associated. Tissues consisting of loosely packed cells are referred to as “mesenchymal” tissues, or mesenchymes. Such tissues are susceptible to a range of physical processes not seen in the epithelioid and epithelial tissues discussed in Chapters 4 and 5. In this chapter we will focus on the physics of these mesenchymal tissues.

We encountered this kind of tissue when we considered the first phase of gastrulation in the sea urchin, the formation of the primary mesenchyme, in which a population of cells separate from the vegetal plate, and from one another (except for residual attachments by processes called filopodia), and ingress into the blastocoel (Fig. 5.7). The secondary mesenchyme forms later, at the tip of the archenteron, and these newly differentiated cells help the tube-like archenteron to elongate by sending their own filopodia to sites on the inner surface of the blastocoel wall. In other forms of gastrulation, such as that occurring in birds and mammals, there is no distinction between primary and secondary mesenchyme: cells originating in the epiblast, the upper layer of the pregastrula, ingress through a pit (the “blastopore”) and the “primitive streak” that forms behind it as the mound of tissue (“Hensen's node”) surrounding the blastopore moves anteriorly along the embryo's surface (Fig. 6.1).

So far we have followed early development from the first cleavage of the zygote (fertilized egg) to the appearance of fully developed organs. We have reviewed the biology of the most fundamental processes along this path, introduced relevant physical concepts, and used them to build models of the same processes. As the organism matures it eventually arrives at the stage where it is ready to reproduce. At this point the female and the male possess the fully developed sex cells or gametes (i.e., egg and sperm), the fusion of which, termed fertilization, sets the developmental process in motion. Fertilization thus can be viewed both as an end and a beginning, the process that simultaneously terminates and initiates the developmental cycle.

The major activities during fertilization that apply generally to any sexually reproducing organism are: (i) contact and recognition between the sperm and the egg; (ii) the regulation of sperm entry into the egg; (iii) fusion of the sperm's and egg's genetic material; and (iv) activation of the zygotic metabolism.

It is clear from this list that fertilization is among the most complicated and spectacular of all developmental processes. It must also be clear that highly sophisticated machinery is needed to carry out the tasks associated with fertilization. The sperm must often travel over great distances relative to its size, it must distinguish between eggs of different related species (in certain marine organisms, sea urchins and abalone for example).

Physics deals with natural phenomena and their explanations. Biological systems are part of nature and as such should obey the laws of physics. However correct this statement may be, it is of limited value when the question is how physics can help unravel the complexity of life.

Physicists are intellectual idealists, drawing on a tradition that extends back more than 2000 years to Plato. They try to model the systems they study in terms of a minimal number of “relevant” features. What is relevant depends on the question of interest and is typically arrived at by intuition. This approach is justified (or abandoned) after the fact, by comparing the results obtained using the model system with experiments performed on the “real” system. As an example, consider the trajectory of the Earth around the Sun. Its precise details can be derived from Newton's law of gravity, in which the two extensive bodies are each reduced to a point particle characterized by a single quantity, its mass. If one is interested in the pattern of earthquakes, however, the point-particle description is totally inadequate and knowledge of the Earth's inner structure is needed.

An idealized approach to living systems has several pitfalls – something recognized by Plato's student Aristotle, perhaps the first to attempt a scientific analysis of living systems. In the first place, intuition helps little in determining what is relevant. The functions of an organism's many components, and the interactions among them in its overall economy, are complex and highly integrated.

The view of embryonic development presented in the preceding nine chapters is rather different from accounts to be found in other modern developmental biology textbooks. We have focused on the phenomena of transitions between cell types, changes in the shape of tissues, and the generation of new arrangements of cells and have approached them as problems in physics. In contrast, when these subjects are dealt with in most contemporary treatments of development it is primarily as problems in regulated differential gene expression. While we have by no means ignored the roles of gene products and gene regulatory systems in our account of development, and while the notion of the embryo as a physical system is not entirely absent from the more standard accounts, the different emphases of the two perspectives could not be clearer.

Developmental biology has advanced to its current high level of sophistication with little explicit analysis of the physical dimension of the questions it treats. This is changing, however. The DNA sequencing initiatives of the last decade of the twentieth century confirmed that genes number in the range 10,000–50,000 in all the species traditionally studied by developmental biologists. Analysis with microarrays (computer-interfaced devices for quantifying the abundance of mRNAs in tissue samples) has shown that many genes are simultaneously expressed during any significant developmental event (Bard, 1999; Montalta-He and Reichert, 2003).

In the previous chapters we have followed the process of rapid cell divisions in the early embryo until the formation of the blastula, initially a solid mass of cells poised to develop into the structurally and functionally differentiated organism. Adhesive differentials along the surfaces of individual cells of the early blastula, the blastomeres, drive the formation of spaces or lumens (see Fig. 4.2) within the embryos of most species. As a result, the typical blastula acquires a geometrically simple closed spheroidal structure that consists of a single cell layer enclosing the hollow blastocoel.

By the time the blastula has developed, the embryo already contains, or begins to generate, a number of differentiated cell types (see Chapter 3). Insofar as these cell types have or acquire distinct physical (adhesive, contractile) properties, compartmentalization or other forms of regional segregation start taking place. This regionalization, accompanied by the collective movement of the resulting cell masses, gives rise in most cases to embryos consisting of two major cell layers, referred to as “germ layers,” along with some subsidiary populations of cells.

The various modes of cell rearrangement by which a solid or single-layered blastula becomes multilayered are known collectively as gastrulation. In “diploblastic” animals, such as sponges and coelenterates (hydra, jellyfish), gastrulation is complete when the two germ layers, the outer ectoderm, and inner endoderm, are established. Further cell specialization occurs within these two main layers and any subsidiary cell populations.