The second cell membrane: The basal lamina and the tissue cell theory of metazoa

The second cell membrane: The basal lamina and the tissue cell theory of metazoa

J. theor. Biol. (1979) 78,143-165 The Second Cell Membrane: The Basal Lamina and the Tissue Cell Theory of Metazoa DONALDO.RUDIN Department of Molecu...

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J. theor. Biol. (1979) 78,143-165

The Second Cell Membrane: The Basal Lamina and the Tissue Cell Theory of Metazoa DONALDO.RUDIN Department of Molecular Biology, Eastern Pennsylvania Psychiatric Institute, Henry Avenue and Abbottsford Road, Philadelphia, Pennsylvania 19129, U.S.A. (Received 21 July 1978, and in revised form 27 November


We suggest that the basal lamina is essentially a second plasma or cell membrane appearing at the next higher level of biological organization ; that together with associated cell monolayers it creates a tissue level membrane which is used to form multicellular cells and that collections of these provide the essential structure of metazoa. Thus when the histological structure of multicellular organisms is viewed in a topologically simplified form such organisms appear to be sets of multicellular cells (m-cells) formed by a unit tissue membrane built around the basal lamina. Not only are mcells in this way structurally isomorphous (homeomorphic) to unit or classical biological cells (u-cells) but the two cellular levels are also functionally isomorphous. This suggests a “General Principle of Hierarchical Isomorphism or Iteration”, i.e. that multicellular evolution recapitulates unicellular evolution. This principle of structural and functional isomorphic mappability of unicellular onto multicellular organisms then governs the organization of matter all the way from molecules to man. Just as cytoplasm precipitates the bimolecular plasma membrane to form u-cells for the purpose of achieving reaction sequestration, in turn, these u-cells precipitate a common basal lamina to form m-cells, the histologist’s acini, to produce sequestered “tissue plasms”. Thus, the “generalized acinus” with its basal laminar complex seem to constitute a second level (multicellular) cell and cell membrane, respectively. Four operators, ultimately under genetic control, can generate both Uand m-cells from planar configurations of their respective unit membranes therewith providing the essential structure of all cells, tissues, organs and organisms. These are the ply, permeability vector, topological and stratificational operators. They are collected into a set of “organ formulae”. Both the plasma membrane and the basal lamina act as covering membranes and, again, as membranes for subcells so that a complete multicellular organism is a tetrahierarchical cell in which the molecule is the element of the first two cellular domains and the cell is the element of the last two. The analysis identifies a new transport organ group which together with the classical endocrine and exocrine groups comprises nearly the whole 0022-5193/79/090143+23 $02.00/O


0 1979 Academic Press Inc. (London) Ltd


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of the soft tissue organs. In a major reduction, all these organs are continuously (topologically) transformable into each and into hollow spheres, cells or acini thus greatly simplifying the histology of metazoa. Given this emphasis on cellularization it would seem that life, i.e. the autonomous chemoservo, results from the cooperation of cellularization and replication operations on the catalyzation process. Through cellularization, the lipid bilayer and basal laminar membranes provide the essential catalytic reaction sequestration demanded by chemical reaction theory while through complementary base pairing the DNA double helix provides the essential memory which stores the patterns of the variations of the sequestered reactions. 1. Introduction The Schwann cell theory of biology has established that life comes in microscopic globular units. This fact is necessitated by chemical reaction theory which requires that finite concentrations of selected reactants and products be attained against the inevitable tendency to go to infinite dilution. The reactions must also be isolated from interfering reactions or other changes in the reaction conditions which are inherent in a world with the large free energy gradients and thermodynamic variances capable of generating locally negentropic processes leading to life. Schwann himself thought the cell was probably formed by a membrane enclosing a normal reaction space rather than resulting from an adsorptive coacervate which would place severe constraints on chemical activity coefficients. This long controversial membrane theory of the cell has been established in the past 40 years. Crucial analytical work revealed that the membrane had a bimolecular lipid structure modified by protein (Davson & Danielli, 1952; Schmitt, 1959). Subsequently this theory was confirmed by synthesis of the bimolecular lipid membrane as a free standing entity by Rudin and his colleagues (Mueller, Rudin, Tien & Wescott, 1962). Action potentials have been synthesized in it (Mueller & Rudin, 1968) (confirmed by Kalkwarf, Frasco & &attain, 1970) as well as other functions such as active transport (Racker, 1976). But exactly the same principles of reaction theory can, and probably must, operate at the next hierarchical level of evolution in which cells cooperate to form multicellular organisms, the metazoa. To act as autonomous organisms at this level the cells must partition among themselves in specialist organ groups all the functions previously performed by the individual autonomous cell. But this would make each cell group a potentially interfering environment for all the others unless a new level of reaction sequestration were achieved which could be controlled to permit net cooperative interaction. In fulfilment of this requirement we will try to show here that biology does

145 once again what it did before: it discovers a new analogue of the plasma membrane in the form of a tissue membrane this time composed of cell sheets built around the basal lamina this new membrane then being used, once again, to construct a new multicellular cell level composed of “tissue cells” which are just the histologist’s acini. Much of the vast complexity of the histology and cytoarchitecture of metazoa, at both light and electronmicroscopic levels, can thus be reduced to a few simple principles using topology under what amounts to a (tissue) cell theory of metazoa. By applying the principles of topology systematically to both the unit cell and the tissue cell similar underlying principles are revealed which strip away the vastly confusing but essentially trivial geometrical complexity of histology. The crucial concept here is that of a homeomorphism, also called topological equivalence or 1 : 1 bicontinuous transformation. Aside from this mathematical aspect progress towards a cell theory of metazoa is possible only because of new understanding acquired in the past few decades concerning the nature of the cell membrane, histological cytoarchitecture, and the basal lamina. To avoid repetitious referencing we note at this point that crucial background on topology can be found in Lietzmann (1969), Chinn & Steenrod (1966) and the Encyclopedia Brittanica ; on electron microscopy of cells and tissue in Robertson (1960), Farquhar & Palade (1963), Fawcett (1966), Porter & Bonneville (1968) and Rhodin (1974). The basal lamina has been extensively reviewed by Krakower & Greenspon (1951), Kurtz & Feldman (1962), Vracko (1974), Romen et al. (1976) and Ligler & Robinson (1977). Its general pathology has been reviewed by Read (1974) and its specific pathology in relation to brain function, the choroid plexus and “combined transport organ dysfunction” by Rudin (1978). Reviews on the structure, function and synthesis of the lipid bilayer and cell membrane can be found in Davson & Danielli (1952), Schmitt (1959), Rothfield & Finkelstein (1968), Mueller & Rudin (1969), Danielli (1975), Chapman (1975) and Bangham (1975). The rediscovery of the liquid-crystalline phase anisotropy and heterogeneity of the bilayer dependent cell membrane is to be found in Singer (1975). MULTICELLULAR

2. The “Unit


Tissue Membrane”

Functionally, there are only two cell types in the multicellular organism, mesenchymal and parenchymal. The first consists of fibroblasts and their secretory collagenous products which act as weight carrying structural and mortar-like elements. The second carries out the specific functions necessary to a chemical servomechanism and, therefore, varies from organ to organ. While the mesenchyme is of mesodermal origin the parenchymal cells may

D. 0. RUDIN 146 come from any of the three embryological tissue layers and, depending on their geometric disposition, are classified as ecto-, endo- and meso-thelium. The endothelium is the parenchyme of the vascular tree which is an invasive tissue permeating every organ. The basic inventory of elementary parts of a multicellular organism is completed by adding to parenchymal and mesenchymal cells a third noncellular element, the basal lamina. From the perspective of cellular biology the basal lamina looks remarkably like the plasma membrane of tissues. It is a tough independently stable membrane which always lies between parenchyme’and mesenchyme as plasma membrane lies between cytoplasm and extracellular supporting structures. It is secreted by the parenchymal cells-as the plasma membrane is precipitated by cytoplasm-to provide a geometric substratum upon which the cells can organize themselves in space as a cellular monolayer sheet. In this way, parenchymal cells also protect themselves from invasion by the mesenchymal cell line which forms invasive scar tissue whenever the basal lamina is destroyed. Because of its toughness the basal lamina often survives destruction of the two adjacent cell lines and then provides a scaffold for their spatially organized regeneration, the cells otherwise growing in a scrambled manner. In all this the similarity with the plasma membrane is evident. Like the cell membrane, the basal lamina is also chemically specialized so that parenchymal cells of one organ will not regenerate along the lamina of another organ. This maintains organ distinctions in the face of cell turnover. Both the cell and tissue (i.e. basal lamina) membranes have a discernable turnover. Fibroblasts apparently slowly remove the basal lamina from the “outside” (Kurtz & Feldman, 1962; Vracko, 1974; Romen et al., 1976). In various proliferative laminopathies, e.g. in diabetes mellitus, production exceeds removal and the lamina thickens. The cell membrane and basal lamina also have similar scaling factors. The basal lamina is about lo2 times thicker than the lipid bilayer and is associated with tissue volumes (see later) which are about 106-7 times greater than the cytoplasmic volume. Both structures were long ignored by scientists after being recognized. In the case of the cell membrane the field was mostly dormant until clear analysis in situ of molecular structure was provided by Davson & Danielli (1952) and Schmitt (1959) followed by proof of independent stability through synthesis of the essential structural element, the bimolecular lipid membrane, by Rudin and his colleagues (see Mueller et al., 1962) followed by proof of functional capacity through peptide induction in the bilayer of action potentials having all the properties of the nerve impulse as found in certain plant cells (Mueller & Rudin, 1968).




From the viewpoint of physical chemistry the lipid bilayer turned out to be the thinnest stable structure as well as one of the most remarkable states of matter known. As the limiting unit of the mesomorphic or liquid-crystalline state it exhibits “phase anisotropy”, i.e. it acts as a liquid in one direction (in the plane of the bilayer) and a solid in the other (across the plane). Finally, it spontaneously forms a cellular or soap bubble-like structure creating an internally protected milieu in which chemical evolution can proceed at finite concentration with activity coefficients unmodified by adsorption. The lipid bilayer is thus responsible for making a modern biological cell into a cell or compartment above all retaining small water-soluble high energy compounds which would leak from pure protein membranes. In the case of the basal lamina proof of independent stability was achieved by Krakower & Greenspon (1951) through isolation and purification. This also set into motion a great deal of work (see citations at the opening of this section). The similarity between the two membranes goes one significant step further into the realm of their topological and geometrical roles. Examination of this similarity provides a major clue to the nature of the processes underlying tissue organization. To develop this matter we adopt Robertson’s (1960) useful concept of the “unit cell membrane” and extend it to the tissue and organ level introducing the notion of a “unit tissue (multicellular) membrane”. The renaming of the bimolecular lipid membrane as the “unit membrane” by Robertson helped to clarify the nature of complex geometric and topological relations involving doublings and folding of the bilayer such as Geren’s “jelly role” configuration of myelin and Gasser’s related “mesaxon” (see Robertson, 1960). We will now show that there is a comparable “unit tissue membrane” and that by formally developing certain geometric operations we can generate from it “tissue cells” which underlie the structure of all the soft organs of the body. This is completely analogous to generating the biological or “unit” cell and its various organelles from the “unit cell membrane”. This analysis also reveals the existence of two blood brain barriers as well as their cytoarchitectural differences and, finally, supplies a new transport organ group. A “tissue” is an aggregate of a single cell type. From the above, we therefore, conclude that there can only be two general tissue types: parenchymal and mesenchymal. But these would not exist in any organized form as a recognizable tissue if there were no basal lamina. Therefore, although the basal lamina might be defined as the “unit tissue membrane”, we prefer to reserve that term for the triplet consisting of the basal lamina together with a layer of mesenchyme and parenchyme on either side


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observing that parenchymal cells always form a monolayer of active cells along the basal lamina. If other (stratified) layers of parenchymal cells are present they will be germinatively inactive as in skin and brain or return to the monolayer only when ready to become active as in the secretory cells of the endocrines and exocrines. Like the unit cell membrane of Robertson the “unit tissue membrane” (with triplet substructure) often forms a double unit through apposition of two units. In the tissue case this comes about by the apposition of one tissue unit from a vascular source and one from an organ specific source, This double unit tissue membrane then consists of a hextuple substructure and constitutes what will be defined as the “standard unit organ” when viewed in the planar topological configuration (see Fig. 1). Tissue organ

ord Organ Blotopolcqy

speuf IC The double unit hssue membrane

The negative tissue cei I (exocrme acms, thyroid fotkle, transport orgon ,V,o?-)

The positwe ovaa” cell (endocrme ocinus T vy r+)

FIG. 1. Global biotopology at the tissue level. At the top is a reference five-ply “unit organ” or double “unit tissue membrane” composed of two three-ply units fused back-to-back. The permeability vector is positive. From this structure we can obtain the structure of the endocrines (right) or exocrines and transport organs (left) by curving and joining the ends of the unit organ in either the positive or negative sense to form either positive or negative multicellular “tissue cells” the multicellular membranes of which regulate the composition of the enclosed, or quasienclosed, fluid space-the “tissue plasm”. The symbols are “organ formulae” in which the ply number is in roman numerals (in this case V), the permeability vector is given by the subscript and the superscript gives the topological genus rank, the shape/dimensionality and the sense of the membrane curvature taken with respect to the permeability vector.

149 To obtain the actual structure of a complete simple organ (or at least its essential acinar structure) we then introduce three operators to act upon the “standard unit organ”. These are the “ply”, “permeability vector” and “topological” operators, a “stratificational operator” being considered briefly. As will be seen application of these same operators to the planar unit cell membrane similarly generates the “unit” or biological cell together with its organelles. The transport organs (see later) are all simple organs in the sense that they consist of one “acinus”. The exocrines and endocrines are compound organs composed of simple aggregates of acini. They are then often compounded once again by adding exocrine and endocrine acini together to form double compounded organs. We will not bother further with these complexities since it is the acinus which is the working entity the compound structures being derived by simple additions. To avoid terminological confusion it helps to be very explicit. The classical biological cell should now be called the “unit cell” or simply the “u-cell”. The “unit membrane” is then, strictly, the “unit cell unit membrane” which can be most simply referred to as the “u-membrane” or as “the bilayer”. Then at the next level of organization we have, it turns out, the corresponding multicellular terms. The “multicellular cell” may be called the m-cell and the “multicellular membrane” the m-membrane. But, as with the u-cell level, these can come in either unit or double unit form, In unit form the m-cell with its m-membrane will be called the “tissue cell” with its enveloping “tissue membrane”, that is, a “r-cell’ has a “t-membrane”. In double unit form these can be called the organ cell with its organ membrane, i.e. the “o-cell” has its “o-membrane”. MULTICELLULAR


3. The Plexial Blood Brain Barrier (IIBBB)

and the Ply Operator

In Fig. 2 is given the cytoarchitecture of the access routes to the neuropile. All folds have been smoothed out to give the locally planar approximation making it feasible to compare the detailed structure and topological relationships of what amount to two blood brain barriers-one with an enlarged extracellular space, the CSF. These two primary barriers (I & IIBBB) are in parallel with each other thereby constituting “patches” on one continuous but heterogeneous multicellular membrane surface. Moving up the artery to the choroid plexus we find that to get to the brain we must first traverse the endothelium-the parenchymal monolayer of the vascular tissue. These endothelial unit cells are joined only adsorptively through their extracellular coats and are, therefore, “open” to passive intercellular diffusion for compounds of M.W. in excess of about lo6 daltons such as ferritin (Brightman, 1968) and probably up to 10’.





CytwrchWcture of Four Ttssue Transport Regulating the CNS enwronment (I) Blood braln bowler P” c 00



PIA Intlmo (4) CSF P~cqha braln barrier= < P’L’PS>P” 0 0 0


GIla (Ohgo) (3) CSFE~endvmal



(2) Ctxxoid plexus CSF bower = 0 .c


. Fofofr3eof


fd 1 1

M” ,jI






FIG. 2. Geometrical relations and cytoarchitecture of the four tissue membranes regulating the brain environment. The choroid plexus (II blood brain barrier) is in series with the ependymal and piaglial membranes which are in parallel with each other via the Foramina of Luschka and Megendie. The regular vascular or I blood brain barrier is in parallel with the IIBBB and in series with the other two. P = parenchyme, L = basal lamina, M = mesenchyme. Superscript “v” = vascular, superscript “s” = specific organ. Subscripts indicate if the cell layer is diffusionally “open” (0) or “closed” (c) by circumferential tight junctions (zona occludens). Pointed brackets enclosing the tissue membrane elements signify an ordered set reading from blood to tissue on going from left to right. They also separate the barrier from stratified or other elements which the tissue membrane guards. Pz stands for the neuropile parenchyme which is itself “open”. Note the different numbers of plys and the inverted relation of the tight junctions to the basal lamina in the I and IIBBB. This masks the basal lamina in the former creating an exclusionary configuration while in the latter it both exposes the basal lamina to the bloodstream and backstops it to form a dead-end entrapping configuration for molecules between about lo’-lo7 daltons.

We next encounter the vascular basal lamina which will pass compounds of M.W. 10sP6. Next comes the mesenchyme. Here the vascular and organ specific contributions have fused into a single layer. We may view this as the deletion of one ply from the standard organ hextuple or six-ply. This mesenchymal layer is neither rate nor size limiting as a diffusional barrier. Next comes the organ specific basal lamina. Its diffusional properties are similar to the vascular basal lamina. Finally, comes the organ specific parenchymal monolayer, the choroid epithelium. This unit cell layer is “closed” by circumferential “tight junctions” or zona occludens (Farquhar

151 & Palade, 1963). This restricts diffusion at least one more order of magnitude and constitutes the final guardian of the ecology of the brain by this route. While the tight junctions in some tissues, such as kidney, may only reduce permeability to about 1O4-5 daltons, they use reverse active transport to reduce final concentrations of compounds below this weight. In the brain, however, compounds as low as 300 daltons (proflavine) seem to be directly excluded by the diffusional barrier of the tight junctions in both I and IIBBB there being no evidence of intracellular staining by such dyes (Rodriguez, 1955; Rodriguez-Peralta, 1957). Filtration limits, therefore, seem to lie between 10ze3 daltons in the I and IIBBB. We now have a five-ply structure resulting from the apposition back-toback of two unit tissue membrane triplets followed by one deletion through fusion. This is the most common ply state found in various organs of the body. However, biology has, in fact, come to “occupy” all ply numbers. Around the corner in the IBBB the mesenchyme is also fully deleted to give a four-ply, In the glomerulus, where filtration is at a premium, the two basal lamina are further “fused” into one to give a three-ply structure. In the liver, which chemically isolates the bowel output in the hepatic portal system from the rest of the body, there is a further deletion of the remaining basal lamina in approach to liver sinuses. This gives a two-ply. Finally, in the full liver sinuses even the endothelium is deleted so the blood courses directly against the liver cell plasma membranes-a relation identical to that between secretory products and exocrine ducts discussed later. The variations of ply number may be viewed as a “ply operator” under control of the genes. An analogous operator exists at the bilayer level. Let the bilayer correspond to the basal lamina, adhering cytoplasm to the parenchymal cell monolayer and adhering extracellular coats to the mesenchymal layer. Then the ordinary double unit membrane found in nuclei, mitochondria and chloroplasts corresponds to the five-ply configuration in the choroid plexus. In the zona adherens where the two bilayers come together to exclude extracellular space we have the four-ply analogue of the IBBB. In the zona occludens there is a seeming fusion of the two outer halves of the lipid bilayer into a single layer creating a three-ply analogue of the glomerulus. MULTICELLULAR


4. The Permeability Vector Operator: Exclusionary and Entrapping Tissue Membrane Configurations We come now to the second or permeability vector operator. Except for trivial cases, it is independent of the ply operator. Looking at the choroid plexus permeability, we may characterize the




results, to an order of magnitude, by saying that as we go from blood to brain the filtration efficacy increases in steps from about lo6 to 104 to 102 daltons at the endothelium, basal lamina and epithelium, respectively, Most organs probably run nearer 6,5,4 using a pP notation analogous to pH or pK. But in either case this is a deadend or backstopped entrapping configuration putting at risk for entrapment molecules of M.W. between about lo2 and lo6 daltons. In contrast we will find that in the IBBB just the opposite order holds which, therefore, constitutes an exclusionary situation for all molecules in excess of about lo2 daltons. To characterize this variable we introduce a “permeability vector operator” at right angles to the ply planes. If the filtration degree increases on going from blood to organ specific parenchyme, as it does in the IIBBB, we define this entrapping configuration by a positive permeability vector. The exclusionary configuration of the IBBB is then represented by a negative vector. All organs of the body have a positive vector except for the thymus cortex and the IBBB, although the latter has certain “windows”. Finally, we may let the length of the permeability vector represent the steepness of the permeability gradient just as we let its sign represent the direction of the gradient. For example, the permeability vectors of the piaglial (see next section) and ependymal membranes are zero while their pP’s are about 6. Given the positive permeability vector or entrapping cytoarchitectural configuration immune complexes having M.W. about 1O5-7 daltons can be precipitated, adsorbed or entrapped in or near the basal lamina. By making antibody to the antibody in the complex and putting fluorescent ligands on the anti-antibody the lamina will be lighted up against a black background if there is entrapped antibody present as shown in Plate I which gives a good demonstration of the basal lamina. In finishing this section on the plexial barrier it is now useful to carry out an explicit comparison of its cytoarchitecture with that of skin. The two can, in fact, be “mapped 1 : 1 onto” each other, i.e. they are isomorphous if we let the skin develop a blister fluid along the dermoepidermal junction as the counterpart of the CSF and then also let the basal cell layer grow around the cavity so formed to provide an ependymal analogue. Then the structure of the skin from blood to blister fluid is the same as that from blood to CSF across the choroid plexus. The basal cell layer and choroid epithelium are homologues, the blister fluid and CSF come next and are analogues. Then comes a monolayer of basal cells as homologue of ependyma and, finally, the stratified layers of the skin form the blister dome ‘as homologue of the neuropile. For purposes of pathology we have evidently found in the choroid plexus a structure which provides the CNS with a

PLATE I. (Upper). An actual anti-IgG immunofluorescent photomicrograph from uninvolved skin of an SLE patient (reprinted by permission of the Annals of Internal Medicine & Kay & Tuffanelli, 1969). This corresponds to the upper left schematic drawing, i.e. a “positive band test”. Note the basal cell or germinative layer immediately above the fluorescing basal lamma. This layer is homologous with the ependyma lining the ventricles of the brain. Above it lies the stratified epithelium including an outer keratinized layer these being homologous with the neuropile. facing p. 1521




homologue of structures in skin and bowel all three exhibiting positive permeability vector or (entrapment) sequence. 5. The Conventional

or Vascular Blood Brain Barrier

a five-ply


As we turn to consider the structure of the conventional or IBBB we note that our terminology seeks to avoid asymmetry in the treatment of the I and IIBBB. We do not normally call the ordinary or IBBB the “bloodextracellular space-brain barrier” as we should to be complete. And yet the convention is to break the plexial CSF route down in this way by referring separately to the plexial-CSF barrier and then the CSF-brain barrier. This is not improper but should not be applied to one barrier and not the other given the fact that the CSF is merely an extended extracellular space (see Davson, 1976). Therefore, we have simply dropped the CSF or extracellular space terms in both cases to give proper emphasis to the fact that there really are two parallel blood brain barriers. If we now follow the artery along the parallel path we come to a region of direct contact between the blood vessels and the oligodendroglia, these latter constituting the analogue of the ependymal layer of the ventricles. To get to the brain we must now first cross an endothelium with tight junctions. Then, masked behind this, comes the vascular basal lamina as shown in Fig. 2. The Iamina is thus protected from normal contact with immune complexes. Next comes the organ specific basal lamina which forms a double thickness basal lamina since the mesenchyme has been deleted. Finally, comes the layer of “open” oligos with their “podocytes” designed to reduce transcellular structure and increase filtration as also found in the glomerulus. Beyond these barriers comes the extracellular space and then the stratified “open” neuropile itself. Thus the classical or IBBB is a four-ply structure with inverted or negative permeability vector creating an exclusionary rather than an entrapment configuration. This presentation of tight junctions directly to the blood stream, together with the double thickness basal lamina and very low rates of pinocytotic active transport all constitute what is meant by the ordinary blood brain barrier. 6. Biotopology : Transport, Endocrine and Exocrine Organs as Tissue Cells Generated by Topological Operations on the Tissue Membrane

Introducing the topological operator we now deform either the unit tissue membrane or the unit organ (i.e. the double unit tissue membrane) of any ply and any permeability vector to obtain the actual configuration of several


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types of soft tissue organs. The matter is best considered from the global topological viewpoint adding details of local geometry later. Topology or “rubber” (better, plastic) math (see Chinn & Steenrod, 1966; Lietzmann, 1969) systematizes the analysis of geometric continuity and discontinuity. Given a specified dimensionality and number of independent degrees of continuity topology treats all objects obtained by continuous deformations as equivalent. Line, plane and solid have one degree of continuity since one break or continuous cut will divide them in two. They can also continuously generate each other. A torus or doughnut has two independent degrees of continuity and must be cut through twice to divide it in two since it is generated from a plane (or a disc) carried face forward in a loop to form a discontinuous “join” with itself thus adding one new independent degree of continuity to the plane. Such a torus is continuously deformable into a coffee cup (a single handled mug) by letting the hole become the handle ring and placing a depression in the rim to form the mug. A torus also happens to be continuously deformable into a man since (neglecting nasal passages) he is a solid object with a hole through his center. We may, therefore, say (1) that a man, a doughnut and a coffee cup are topologically equivalent, homeomorphic or 1 : 1 bicontinuously transformable into each other, (2) that they all have two independent degrees of continuity and (3) that, in the limit, they are reducible to a plane with a single hole in it. If we add the final detail of two nasal passages man becomes homeomorphic with a pillory board (for head and hands). Evidently, we can build up the number of independent degrees of continuity by making various “joins” and counting either these or the number of continuous “cuts” needed to separate the figure into two parts. Alternatively, we can punch holes in some starting object. It is convenient in the present context to take a sphere (solid or hollow) as a standard object and punch holes in it or, equivalently, put “handles” on it. Thus a simple torus is a standard (spherical) figure with one handle. The pillory board is a sphere with three handles. It is also convenient to define the “genus” as the number of independent degrees of continuity reduced by one so that a solid sphere having one degree of continuity has a genus of rank 0, i.e. there is no cut which can be made without dividing the figure in two. Let us now proceed generatively one step further by taking the solid torus above and pass it, face forward, in another loop to join discontinuously with itself. This produces an inner tube. It has three independent degrees of continuity or a genus of rank II (since two cuts can be made which will not divide it in two). We may also view it as a hollow sphere with one handle. Its dimensionality is three since its hollows are at right angles to each other, i.e. it cannot be reduced to a plane figure with holes in it.




Again, neglecting nasal passages, this hollow torus or inner tube is topologically equivalent to the covering organ of the body; namely, the mucoso-cutaneous organ. The columnar epithelium of the mucosa lies along the inner rim of the hollow torus, the skin everywhere else and the basal lamina is continuous overall. Moreover, the mucosa may be said to “work into” or regulate the composition of a subsector within the inner tube-the hepatic portal system-while the basal cells of the skin work into the outside stratified layers. Because the mucosocutaneous organ is a multicellular membrane we may view the entire hollow torus as an oddly-shaped toroidal multicellular or m-cell the membrane of which performs the same active and passive transport functions performed by the plasma membrane of regular (unit) biological cells, “u-cells”. Although in “unit cellular biology” such unusually-shaped cells are not known it is useful to view this as an m-cell having isolated fluid regions called the “tissue plasm” analogous to the “cytoplasm” of the unit cells. We will next fill the hollow toroidal m-cell with hollow spherically shaped m-cells, i.e. m-cells of genus rank 0 having no “handles”. These can be generated from the planar unit tissue (or organ) membrane by curving it into a closed sphere as shown in Fig. 1. One example of this topological class of mcells would be the synovial membranes and their joint spaces which contain a lubricating fluid the composition of which is regulated by the synovial membrane (in this case secondary secretory synthesis is also operating to produce “lubricating molecules”). We observe that as we move from the blood stream inside an associated blood vessel towards the synovial space we would cross exactly the same fiveply cytoarchitectural sequence found in the choroid plexus. The permeability vector would also be positive. The same is true of the serosal membranes which regulate the composition of lubricating fluids in the peritonial, pericardial and pleural spaces. All these are homeomorphic with hollow spheres having five-ply membranes, a positive permeability vector and membrane regulated tissue plasms primarily involving bidirectional transport and not synthetic secretory processes. This statement defines a “transport organ”. To this transport organ group belong also the anterior chamber of the eye with its ciliary “body” (or membrane) and, of course, the I and IIBBB which constitute patches on a heterogenous m-cell surface the properties of which change along the plane of the surface. If we reduce the ply number to three then the kidney can be entered into the group since it acts to regulate the composition of the urine largely by mmembrane active and passive transport. This membrane is also heterogeneous since passive transport occurs over one patch (the glomerular) and active transport over another (tubular).


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We may view the vascular system as another type of transport organ or “cell” having a very large number of handles which either graze the other tissue cells or penetrate them once in the case of the endocrine acini (see later). If, to all these, we add the skin and mucosa, counted as separate quasicells, we obtain a set of eight transport organ types in the body, some types having many members and a few also performing secondary synthetic secretory functions such as the synovia, as already mentioned, and the sweat glands which secrete various compounds including mucous in some animals. We do not include the bowel secretory immunoglobulin, IgA, in this group since it is synthesized by plasma cells and merely transported across the mucosa (excepting a small “secretory piece”). All the above transport organs may be viewed as organs comprised of a single acinus or multicellular cell to be contrasted later with the multiacinar exocrine and endocrine organs. We count the lung as an atypical member of the transport organ group for although, like all tissues, it performs a transport function, it is restricted to the physical case of gaseous transport which then necessitates a major additional synthetic mucous secretory function placing it simultaneously into the exocrine organ group. In fact, the pathology of this organ suggests a mixed membership since it is often involved in both cystic fibrosis-the prototypical combinatorial exocrinopathy-as well as systemic lupus erythematosus-the prototypical combinatorial transportopathy (see Rudin, 1978). We do not here evaluate the status of the skeletal system in terms of the concept of multicellular cellularization. The exoskeleton of lower animals is merely a secretion of the epidermis analogous to the cornified layers of the stratified epithelium in higher animals. But the endoskeleton will require a separate study for its evaluation. One degree of freedom remains to be specified. The simple sphericallyshaped tissue cells could have been formed either by curving their membranes positively or negatively with respect to the defined permeability vector. We have implicitly been making this curvature negative so that standing on any organ parenchymal cell we see its neighbors climbing over our heads to form a space immersing us in tissue plasm (see Fig. 1). The positively-curved tissue cell is equally possible as depicted on the right side of Fig. 1. Standing now on any specific parenchymal cell its neighbors fall away from us on all sides and the tissue plasm does not immerse us. Instead there is now a blood vessel running down the middle. Starting in the bloodstream a monolayer of endothelium is encircled by a vascular basal lamina outside of which lies a ring of mesenchyme outside of which, in turn,




comes the specific laminar ring and, finally, outside all this lies the ring of specific parenchymal cells. Putting aside the exceptional thyroid gland, considered below, this is precisely the structure of all the endocrine acini. In some cases additional stratified layers of specific parenchyme lie still further outside (a stratificational operator is here added) but these are not actively secreting and move into the functional monolayer only when ready to do so. In these endocrine “tissue cells” of positive curvature the “tissue plasm” which is being regulated is just the blood stream. Precursors are picked up from the central blood stream, synthetically converted into secretory product and released by exocytosis from the base of the specific parenchymal cells back into the blood stream after crossing the sequence of layers just given. Chemically, this is a synthetic secretory and not a simple transport secretory function. It is interesting to note that the permeability vector as well as the ply number has remained constant. This happens to dispose the tight junctions properly to prevent regurgitation of the synthetic secretory product while still leaving the diffusional path to the blood stream “open”. Returning now to the reference planar organ membrane at the top of Fig. 1 we can once more use positive curvature. This time we restrict the operation to the vascular tissue membrane and then use negative curvature on the specific tissue membrane to generate the tissue cell on the left. Now the apices of the specific parenchymal monolayer form an enclosing ring at the center. Outside of it the other layers follow in order as we progress toward the blood stream. This negatively curved tissue cell provides not only the transport organ structure, as already discussed, but is also identical to the structure of all the exocrine glands. In this latter case the central space is just the exocrine gland duct and the composition of this space may be said to be regulated synthetically by the tissue membranes of this type of “negative” multicellular cell. Precursors now come from the outlying blood vessel and the product is released on the central side. The ply number stays the same and so does the permeability vector which again just happens to dispose the tight junctions properly to prevent regurgitation without interfering with secretion. This topological analysis reveals the thyroid to be an instructive exception. It is an endocrine with the structure of an exocrine. This can be explained if we suppose that it was once an exocrine which discovered how to close off its duct to use as a storage depot-the thyroid follicle-and was then forced to resecrete into the peripherally located blood vessels. There is some evidence for this view since the thyroid has an exceptional embryological development originating from a pharyngeal groove in protochordates called the endostyle. We may analogize this evolution with that of Castle’s intrinsic factor (lack of which causes pernicious anemia). Castle’s factor is a protein secreted by

D. 0. RUDIN 158 exocrine glands , . in the stomach which adsorbs to an ingested organic molecule, vrtamm B,,, to aid its absorption lower down in the bowel. The thyroid may have also once secreted thyroglobulin as an exocrine aid to the absorption of ingested iodine containing organic molecules. The transition to land then necessitated endogenous synthesis of iodothyroxin but not BIz. One exocrine then converted to an endocrine while the other remained an exocrine. Whatever its origin, we place the thyroid with the exocrines and the transport organs in a common topological or cytoarchitectural group, the group of “negative” tissue cells. From the viewpoint of neurophysiology this means that if. we place the brain in the joints, major body cavities, the anterior chamber of the eye, the thyroid follicle or any of the exocrine gland ducts it will have the same cytoarchitectural environment that it has in its usual space. Moreover, an appropriate “cut” and “join” operation, allowed in topology, inverts the negative tissue cell, much as one turns his socks inside out, to give the positive cell and thus the endocrines. We may thus conclude that simple transformations can convert all the soft tissue organs of the body into each other. We can briefly summarize the above by means of the organ formula:

% = Ex, = thyroid = V”:which says that the global organ structure for the transport group, Tr,, the exocrine group, Ex,, and the thyroid all consist of a five-ply structure (V), with entrapping or positively directed permeability vector (the -t subscript) and a topological genus rank of 0, spherical shape (s) and opposite (negative) curvature with respect to the permeability vector taken as radius of curvature. The endocrine organ formula is given by substituting a positive sign for the negative sign in the superscript. The global mucoso-cutaneous organ formula is : MC,




which indicates that the genus is two, the limiting dimensionality curvature both positive and negative with saddle point. The glomerulus is: G = IIIos-. +

3, and the

Approached from the global end little need be said now about the local topology for it can be produced simply by adding local deformations such as the various (positive) villiform and papilliform invaginations which characterize the transport organ group. The local topology of the renal glomerulus and tubule can be obtained




from the left side of Fig. 1 by the appropriate ply deletions discussed above, placing handles on the vessel and then letting these invaginate into the negative tissue cell, taken to be closed off at the top to form the glomerulus and stretched out below to form the tubule (with vessels running alongside). In passing we note that nearly all the exocrines operate functionally like the renal tubule by letting a serum ultrafiltrate enter at their beginning end (equivalent to the glomerulus) and then carrying out salt resorption further down the duct (equivalent to renal tubule resorption). The exocrines, however, also secrete synthesized mucoproteins at the head end. We may conclude this section by observing that just as unit cells have organelles within them to create a cellular hierarchy we have a similar hierarchy at the m-cell level. We may, therefore, describe man, approximately, as a tetrahierarchical cell. Starting at the top we have a hollow toroidal m-cell (one handle) the covering mucoso-cutaneous-cell filled with many positive and negative hollow spherical m-sub-cells (no handles jthe various transport, exocrine and endocrine acini-which are interconnected or penetrated once by a filamentous m-cell (many handlesk the vascular system. Then the membranes of all of these m-cells are composed of many unit cells having no handles and themselves containing many sub “u-cells” or organelles. In brief, man is a cell (m-toroidal) containing cells (mspherical with none or many handles) containing cells (unit) containing cells (organelles). In this scheme the organs of metazoa are analogous to organelles of “unizoa”. Moreover, two kinds of membranes provide the basis for these four levels of cellularization or sequestration. At the two lower levels it is the lipid bilayer membrane; at the two higher levels it is the basal lamina-the fundamentally new element in the m-membrane. 7. General Discussion

The evidence suggests that the basal lamina is more than a generalized scaffold for organizing cells as has been recognized. When taken with its associated cell layers and viewed in wide topological perspective it may be viewed more broadly as a universal “unit tissue membrane” permitting vectorial operations between an “inside” and “outside” which it creates by organizing unit biological cells into “tissue cells”-the histologist’s acinijust as molecules of the bimolecular cell membrane organize other molecules to form the unit biological cell. Thus a hierarchical compartmentalization is achieved under the requirements of reaction theory. Once the unit tissue cell has evolved it, in turn, is treated as a new unit to be further elaborated by aggregation and nesting to form much or all of the structure of the advanced (multiorgan) multicellular organism.

D. 0. RUDIN 160 These structural features suggest that we view biological organisms as living in three major superkingdoms which are subsets of each other starting with (1) the Unicellular Group which evolve into (2) the Transitional or Colonial Group and ending with (3) the Multicellular or Metazoan Group. We could then divide the Unicellular and Multicellular Groups into simple and compound forms. In the Unicellular Group these would correspond to the Kingdom Procaryotes (Monera) and the Kingdom Eucaryotes (Protista) the latter being a nested or compound version of the former. The Transitional Superkingdom would consist of Porifera (the sponges) which have only one cell type and no basal lamina. Possibly the lower coelenterates should be put here as well for although they have evolved two cell lines (ectoderm and endoderm) they still have no basal lamina. We would then enter the Multicellular Superkingdom at about the level of the upper coelenterates where mesoglia and basal lamina apparently first arise as in the Hydra (see Hess in Vracko, 1974). Since this group still has no true internal organs it would constitute a simple or single m-cell Metazoan Kingdom while the rest of the plants and animals starting with the Phylum Platyhelminthes (flat worms) would then belong to the Compound Metazoa which would be analogues of the compound Eucaryotes in the Unicellular Superkingdom. Since “Ontogeny (tends to) Recapitulates Phylogeny” we suppose that the morula, blastula and early gastrulation stages of embryogenesis will also be without basal lamina and thus correspond to the Transitional or Colony Superkingdom. During later gastrulation the appearance of mesenchyme and the basal lamina would create the ontological analogues of the true Metazoa. These would, again, begin as simple and, later, develop into compound metazoan forms as internal organ development proceeds. In the present view the Transitional or Colonial stages in both phylogeny and ontogeny might be viewed as analogous to the prebiotic stages in the evolution of the unicellular organism. The principle of “hierarchical cellularization” or hierarchical compartmentalization (sequestration) is thus seen to occur over four levels, two at the cell bilayer level and two at the basal lamina level leading to a “Tetrahierarchical Structural Isomorphism” carrying biology from the molecular to the compound multicellular organism. This extends downward the significance of the proposition that “Ontogeny Recapitulates Phylogeny”. Of course, the evolution of hierarchicalization did not occur serially in time. In addition to the principle of hierarchical structural isomorphism there is a corresponding “Principle of Hierarchical Functional Isomorphism” since the multicellular organism achieves its autonomous living status by partitioning among the set of multicellular cells (i.e. organs) all the molecular

161 functions of the autonomous unit cell. Thus, (cellular) biochemistry maps isomorphously onto (organ) physiology. To put it yet another way, uni and multicellular organisms have essentially the same state variables including transport, synthesis and energy transductions. This partitioning of functions among different cells to form organ specificity is achieved, as we know, by the remarkably simple expedient of differentially derepressing the DNA templates of the multipotential unit cell. To examine this functional isomorphism in more detail we can again use topological simplification to advantage. We bring to the surface of the toroidal mucoso-cutaneous multicellular covering membrane all its invaginations. We evert the lung buds down to their alveoli to create a local pulmonary patch on the upper gastrointestinal mucosa lying on the inner or negatively curved rim of the toroidal figure which is homeomorphic with the overall organism. Similarly, we evert the urethra so the renal tubular and glomerular surfaces come to lie as specialized patches on the middle of the skin on the positively curved surface of the toroid. The sex orifices can be similarly rendered locally planar with the skin thus bringing the gametes immediately under the surface membrane just as DNA is attached to the inner surface of the plasma membrane ready for duplication and transmembrane transport during bacterial conjugation. Finally, we exteriorize all the exocrines up to the tips of their acini to produce several patches on both the mucosa and the skin (the sweat glands) which are analogous to the various exosecretory activities of the plasma membrane of bacteria. Clearly this heterogeneous mucoso-cutaneous covering organ is ‘now analogous to the plasma membrane of the unit cell since both contain the same adsorbed enzymes, channels and interchannel regions performing the same vectorial active and passive transport and secretory functions which regulate the influx and etflux of precursors and products including gases, solvents, solutes and even solids which are transported by endo- and exocytosis. The analogy, in fact, becomes a virtual homology if, at their abutments, we fuse the plasma membranes of all the cells comprising the topologically reduced covering organ. The double plasma membranes then enclose cytoplasm between them and encircle a large central “vacuole” just as occurs in Nitella or Halicystis. The resulting fused plasma membrane would then have specialized functional patches which, given the liquidcrystalline state of the bilayer, would redistribute until only local molecular heterogeneity existed as in the autonomous single cell. Turning to other functions we observe that some cell activities are carried out by every cell in the multicellular organism, i.e. there is some distributive function instead of a total specialization. However, the liver may be viewed MULTICELLULAR



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as a functionally specialized organ acting on behalf of all the other organs to perform ribosomal and mitochondrial processes since the liver provides common protein synthesis and energy transductions leading to carbohydrate storage (glycogen). The reticuloendothelial system provides an escalated defense function involving the scavenging of cells by cells, as well as molecular level antibody defense. The endocrines perform multiorgan regulation analogous to allosteric and other molecular level regulatory mechanisms at the unit ceil level. The cardiovascular m-cell (of many handles) supplements the normal diffusional distribution of materials. Mechanical effects in the unit cell are performed by gelation and specific contractile elements of actinomycin as used in locomotion, transport and endo- and exocytotic processes. In metazoa these same mechanisms are elaborated in some cells to become muscular organs working on either an exoskeleton or an endoskeleton. Tubulin could be a functional precursor of the latter. Coordination of the new contractile organs is achieved by using the bilayer gating systems to form action potentials. An early use of these is found in the elevation of the fertilization membrane which is induced by action potential release of mucoprotein in cortical granules this being the precursor to the release of synaptic transmitters by the action potential in neurons. The same amine and peptidergic exocytotic release mechanism is used in the regulation of the inflammatory process. For all these reasons we conclude that a principle of functional hierarchical isomorphism exists and that it does so in conjunction with a principle of structural hierarchical isomorphism. Taken together these two principles constitute a global static (but not dynamical or evolutionary) principle of hierarchical isomorphism in biology. While the concept is well accepted that there must be a memory in the form of DNA (or a protein template precursor for it) to achieve systematic evolution, the present analysis implies that the concept of cellularization is no less important. Cellularization is required by chemical reaction theory as a precondition for life since only a cell can provide efficient reaction sequestration to prevent reactions from going to infinite dilution where they would cease to occur at finite rates. This effect of finite concentration must be achieved either by adsorptive coacervation or by cellularization. But the former imposes a costly adjoint condition on the evolution of every molecule ; namely, an extremely high adsorption energy with correspondingly reduced activity coefficients. Considering in more detail the dynamical or time varying aspects of these isomorphisms we still do not know the early evolutionary history of either the bilayer or the basal lamina. The bilayer and its lipids may have had prebiotic origins along with bases, neucleotides and amino acids especially if




there were “hydrocarbon rains” (Lasaga & Holland, 1971). Alternatively, the bilayer may have come to prominence only biotically (i.e. enzymatically). An earlier protein “bilayer” membrane may have preceded the lipid bilayer. It may even have been essential to permit substrate access to bound enzymes. But, for the same reason it would not evolve far since protein membranes would be unable to prevent free diffusion of high energy compounds once concentrative competition became necessary ; ATP, sugars and polyphosphates being small water-soluble compounds. The same statement holds for most of the structural monomeric building blocks such as amino acids, bases, fatty acids, etc. Thus protein membranes are too “leaky” and adsorption coacervates too chemically restrictive to go far. The evolution of the basal lamina is uncertain. We only know that it is present at least as early as the Hydra. But it could be an adaptation of the secretions of the far more primitive slime molds which have colonial stages. Weiss has developed the theory that oriented adhesion of cells to physical substrates may require that the cells secrete specific proteins or mucoproteins. The spectacular reconstitution of organs and even simple organisms from separated cells may also involve active synthetic secretory processes producing basal laminar-like structures of their precursors in the form of various intercellular matrices (see Trinkaus, 1969, for a review of this subject ). In the shorter time span involving embryogenesis the time of appearance of the basal lamina is uncertain. The best current interpretation concerning the general nature of embryogenesis suggests that the whole process results from a “reaction-diffusion” mechanism in which certain key cells synthesize and release “morphogens”. These may be no more than sets of catalyst activators and inhibitors with different diffusional ranges and rates. These then produce a local activator gradient which triggers local and specific DNA derepression and thus cellular differentiation while at a distance the inhibitor dominates and stops the process. This could form what we would here view as a “diffusional cell”. Such a diffusional cell could then go on to become the adult “tissue or organ cell” of this paper. This process may be serial so that at the edge of any given “cell” the gradient triggers new centers of morphogen production leading to new, adjacent diffusional cells creating segmentation and more complex structuralization. This “reaction-diffusion” mechanism has been discussed by Grossberg (1976) and placed in a much broader context. He notes that it may be only one expression of a broad principle for achieving self-organization. The differentiation of the nervous system seems to involve a related “on-center off-surround” or excitation-inhibition effect systematically reinforcing some and weeding out other synapses formed under more general but not entirely


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random genetic connection rules. This, in turn, is similar to the reciprocal inhibition (lateral activation) mechanism which is probably used to achieve pattern discrimination and enhancement in adult CNS data processing. This broad principle might be known in all its forms as the principle of “lateral countervailing effect”. However, it can be still further generalized as an expression of negational and relational operations in logic known as the “NOR” operation which is a complete logical set from which all other possible logical operations follow. Therefore, we might view this as the “NOR” self-regulation and self-organizing principle. The diffusion-reaction mechanism also operates in a simpler physicalchemical version to form the unit cell itself from the molecular level. Chambers & Chambers (1961) have reported the spectacular result (personally confirmed) that pieces of amoeba cytoplasm denuded of cell membrane precipitate a new bilayer around a clump of dispersing cytoplasm to reform a functioning cell, i.e. “instant life”. This process may be assumed to occur at the radial concentration gradient loci where the variables of the lipid phase diagram cause the lipid bilayer or unit mesomorphic phase to exist. Thus, the reaction-diffusion mechanism may not only form the organism from a cluster of cells such as the blastula, but the cell from the proper molecular (cytoplasmic) mixture. Thus, in the notion of the “diffusion cell” there may lie an ultimate governing principle, holding both dynamically and statically, from molecule to man. Overall, we have found reason to suggest that the notion of a “generalized acinus” together with its associated basal laminar complex may be viewed, respectively, as a second level cell and a second level cell membrane. The aggregation of these second cells then might provide the basis for building multicellular organisms by a straightforward recapitulation of the principles governing the classical or first cell level so that the Schwann cell theory of biology holds twice over. This view permits the great empirical complexity of present-day histology to be reduced to a simple mathematical-topological representation. It also suggests that embryological development and evolutionary “tissue sculpting” in genera1 may obey similar rules of multicellular cellularization. REFERENCES A. D. (1975). In Cell Membranes (Weissman & Claiborne, eds), p. 24. New York : HP Publishing. BRIGHTMAN, M. W. (1968). Prog. Bruin Res. 29, 19. CHAMBERS, R. & CHAMBERS, E. L. (1961) Explorations into the Nature of the Living Cell. Cambridge, Mass. : Harvard University Press. CHAPMAN, D. (1975). In Cell Membranes (Weissmann & Claiborne, eds), p. 13. New York: HP Publishing. BANGHAM,




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