Weight-watching at the university: the consequences of growth.

We began by pointing out that tools (for example) have size optima that are dictated by function. If we assume that the university has a function, it would seem reasonable to think about the size which will serve that function best. The principle of size optimization is fundamental, but its application to the university at once encounters a difficulty: What is the function of a university? It might take forever to secure general agreement on the answer to this question. The problem is that universities have a number of different functions, to which different individuals will attach different weights, and each function may well have a unique size optimum. Just as it is, in general, mathematically impossible to maximize simultaneously for two different functions of the same variable (29), so it is unsound to conceive of a single optimum for the multiversity. Nonetheless, a range of workable sizes may be defined by analyzing the effect of variation in size on all essential functions. The examples from biological systems illustrate this approach. Cells exist in a variety of sizes, each size presumably representing an optimization to one or another set of constraints, yet there are upper bounds. There are no cells the size of basketballs because essential metabolic functions are limited by the surface-to-volume ratio. We must emphasize that one does not need a grand theory of life in order to identify this limiting condition. If cells could talk, they would no doubt differ on the general philosophy of being a cell, yet all conceptions would be subject to certain physically inevitable limitations on size. In the case of the university, no grand theory of education is needed in order to identify dysfunctions of growth that affect essential activities (for example, the diffusion of individuals through, in, and out of the university) or that affect all activities (for example, overall morale). Balanced against these dysfunctions are such advantages of growth as economy, the achievement of a critical mass, and flexibility in staffing. Our analyis of data from the California system indicates that unit costs of education decline very little above a size of 10,000 or 15,000 students. Moreover, the critical mass for departmental excellence, at least in terms of the ACE ratings of graduate departments, is achieved by a university of about this size. Growth beyond this size range conitinues to provide flexibility in staffing and spares administrators the trouble of having to make difficult decisions. At the same time, the dysfunctions attendant on growth become steadily more severe. Our impression is that the dysfunctions have not been seriously considered, while the advantages have been greatly oversold. The idea of dysfunctional growth, although fundamental in biology, contradicts one of America's most cherished illusions. Particular dysfunctions of growth are rarely formulated, set down, and explicitly weighed against the potential advantages. Rather, the American prejudice has been to assume that growth is always good, or at least inevitable, and to treat the dysfunctions (which are inevitable) as managerial problems to be ironed out later or glossed over. There has also been a remarkable failure to think in terms of optima and to distinguish in this way between what we have termed functional and dysfunctional growth. Rather, the tendency has been to extrapolate functional growth into the dysfunctional range: If a university population of 10,000 confers certain advantages as compared with a population of 1,000, then it is assumed that a population of 100,000 must confer even more advantages. We suggest that it is time, in fact past time, to subject university growth to a more searching scrutiny. Functional and dysfunctional consequences need to be spelled out. Scale effects ought to be considered in connection with every plan for expansion. Ideally, one might expect a farsighted and tough-minded administration to carry out this function. This has rarely been the case. Too often administrators regard their function as simply that of broker among competing expansionist tendencies. Such a conception replaces philosophy by politics and often encourages mindless growth. Perhaps it is time for faculties to involve themselves in long-range planning and to pay the price of a more satisfactory environment by giving up some individual dreams of empire. The first step for every large university ought to be a careful analysis of scale effects (30). If analysis indicates that continued growth of a university will be, on balance, dysfunctional, we suggest that plans be formulated to establish an absolute limit on further enrollment increase, and an absolute limit on further building expansion. If further analysis indicates that a university is already well into the dysfunctional size range, then the obvious solution is to cut back. If this turns out to be the case, then we suggest that a program for the gradual reduction of the campus population be undertaken. There are two distinct ways to accomplish this: (i) the establishment of a new university and (ii) the decentralization of the existing university into two or more campuses. Decentralization strikes us as an attractive idea, worthy of careful study. One of the recommendations of the Scranton commission was, "Large universities should take steps to decentralize or reorganize to make possible a more human scale" (18, p. 14). Returning to the natural world, we note again that cells do not grow indefinitely. Instead, they divide.

Evidence for a universal process underlying clonal attenuation.

It is shown by computer simulation that an established commitment model of clonal attenuation can account for clone size distribution data obtained from three vertebrate species--chick, hamster and human--from two evolutionarily divergent classes. The different in vitro replicative lifespans of each cell strain can be explained by differences in cell kinetics. These results suggest that the process of clonal attenuation is qualitatively similar in fibroblasts from all vertebrate species.

A model of alpha-helical distribution in proteins.

It is shown that alpha-helical content of eleven proteins is well correlated with alanine plus leucine content. These residues, taken singly or together, are to a first approximation randomly distributed in the four proteins whose tertiary structures have been determined (i.e., myoglobin, lysozyme, ribonuclease, alpha-chymotrypsin). A model based on the concept that certain randomly distributed residues specifically participate in helix nucleation is shown to be in reasonable agreement with the presently published structures.

Organ scaling in mammals: the liver.

1. Values for liver weight, in growing and adult male and female mammals, both terrestrial and aquatic, as well as values for hepatic blood flow, blood volume and oxygen consumption are submitted to linear (log-log) regression analysis. 2. The slope of the regression line for liver weight on adult body weight in adult mammals was found to be 0.886. No statistically significant difference was found between male and female, nor between terrestrial and aquatic mammals (at the 1% confidence level). 3. Over about four orders of magnitude there is (on present evidence) a tendency for the mammalian liver to grow as about the 0.94 power of body weight (pre- and post-natal). 4. The slopes of the regression lines for hepatic blood flow, blood volume and oxygen consumption were found to be 0.91, 0.86 and 0.69, respectively. 5. The mean hepatocyte size in fixed tissue of rats was found to be 7400 micrometers 3. 6. It is argued that the slope of the regression line for hepatic oxygen consumption in mammals generally is likely to fall in the range of 0.67-0.77.

Clonal attenuation in chick embryo fibroblasts. Experimental data, a model and computer simulations.

When cells from mass cultures of chick embryo fibroblasts are grown at very low density, some cells yield large clones while others produce smaller clones, and some cells fail to divide at all. The distribution of clone sizes is related to the number of population doublings which the donor mass culture has undergone: the more doublings which have occurred, the smaller the average clone size. In this report we describe a model which analyses this phenomenon, referred to as 'clonal attenuation', in detail. The model is based on the concept that a cell with hypothetically unlimited replicative potential--i.e. a 'stem' cell--can become 'committed' to a programme of limited replicative potential. This event is assumed to be stochastic and to have a fixed probability per stem cell division. The parameters of the model are: Pc, the probability of commitment; N, the number of differentiative divisions; and Tc, the cell-cycle times. By computer simulation, it is shown that Pc increases roughly exponentially at each successive stem cell division. According to the model, when the daughter of a stem cell becomes committed, its progeny proceed through N obligatory divisions before becoming terminally differentiated (post-mitotic). The best-fit value of N was found to be seven. The simulations also reveal that the absolute number of stem cells in the total population increases for most of the lifespan of the culture. When Pc becomes much greater than 0.5, the number of stem cells declines rapidly to zero, and the culture nears senescence. Sensitivity analysis shows that Pc can assume only a limited range of values at each stem-cell division.

TOPPER, a software package in FORTRAN for scaling studies.

Scaling studies are concerned with the differences in structure, function, behaviour and life-history associated with differences in size in broadly similar organisms. These studies make extensive use of bivariate regression analysis. Often it is of interest to carry out such analyses on many different subpopulations within a given sample population. The programs described here allow these analyses to be carried out efficiently. The output gives a summary of taxonomic parameters in addition to the usual statistical parameters, such as standard deviations and mean percent deviation. Some improvements in the software which are currently being implemented are discussed briefly.

Folding of the cerebral cortex in mammals. A scaling model.

A model of cortical folding in mammals is presented. The model consists of a cube, superimposed on which are straight close-packed gyri, running the length of the cube. The cortex is represented by a thin layer of constant thickness. It proves possible, by adjusting the length, height, and width of the 'gyri' and the thickness of the 'cortex', to obtain a reasonable fit to the available empirical data (which extend over three to four orders of magnitude in brain weight). The model directs attention to possible features of the macroscopic organization of the mammalian brain which are novel and hitherto unremarked.

Three-dimensional reconstruction from serial sections: II. A microcomputer-based facility for rapid data collection.

A microcomputer-based facility is described that permits the data required for three-dimensional reconstructions to be collected quickly and inexpensively from serial sections. The facility consists of a microcomputer, a digitizer tablet, a graphics terminal, a printer, a plotter, and telephone coupler. Images of serial sections are superimposed on the digitizer tablet. Contours of interest on each section are digitized and the coordinates are stored on "floppy" disks. The problems of putting successive sections in correct register and of taking into account magnification factors are discussed briefly. Use of the facility for high-resolution applications is also considered.

Three-dimensional reconstruction from serial sections. IV. The reassembly problem.

In many fields of biology and medicine there is a pressing need for quantitative descriptions of biological structures at a resolution of micrometers. This need is currently met best by three-dimensional reconstruction from serial sections. The preliminary steps in three-dimensional reconstruction include fixation, embedding in plastic, introduction of fiducials, serial sectioning, and staining. At the light microscope level, with which we are chiefly concerned, one will usually want to do photomicrography (or videomicrography) of adjacent fields within individual tissue sections. The resultant images are projected onto a digitizer pad and the contours of interest manually digitized. From the digitized coordinates generated thereby, one wishes to generate a likeness of the original object, using computer graphic displays, and to then do interactive morphometrics. The problem of combining the digitized coordinates so as to produce a numerically faithful representation of the original object (i.e., the reassembly problem) is, as a practical matter, nontrivial. A technical description of the reassembly problem is presented. The main factors entering into a solution of the problem are discussed and a mathematical statement of the solution is given.

Three-dimensional reconstruction from serial sections. V. Calibration of dimensional changes incurred during tissue preparation and data processing.

Three-dimensional (3-D) reconstructions from serial tissue sections produce a table of x, y, z coordinates (i.e., a numerical description of the object) that will support 3-D computer graphics displays and morphometric analyses. While measures such as volume or surface area can be generated interactively, almost instantaneously, they are usually of unknown accuracy due to artifacts that may be introduced at two different stages: (1) tissue shrinkage during dehydration and polymerization of a plastic and compression or expansion during sectioning and mounting and (2) geometric and intensity distortions during image capture and data processing. This paper describes simple methods for (1) introducing fiducials (reference marks) that allow measurement of the net distortion incurred during tissue preparation and (2) estimating the amount of geometric distortion arising during image capture and data processing. Application of these methods showed that the net areal change introduced in dog and sheep hearts during tissue processing amounted to +/- 5%. Apparently, the substantial shrinkage that occurs during tissue processing is largely compensated for by the expansion during tissue sectioning and mounting. The methods described may have application to other semisolid tissues.

The blastomere pattern in echinoderms: cleavages one to four.

The results of a longitudinal study of the blastomere pattern in six embryos during the first four cleavages are reported. At each cleavage stage optical sections through an embryo, taken at vertical intervals of 5 or 10 micron, were recorded on 35 mm film: digitization of the blastomere contours and computer analysis allow calculation of the center, radius, surface area and volume of each blastomere. The subjective impression of exquisite regularity seen in normal echinoderm blastulae acquires a quantitative dimension from the present study. For example, the individual angles formed by the various quartets of blastomeres depart from right angles by at most a few degrees. The egg volume was found to be conserved up to the fourth cleavage. At the 16-cell stage, unlike the earlier stages, the blastomere positions cannot be ascribed solely to the position and orientation of the respective cleavage planes. Finally, a few features of a formal model of these early cleavages are sketched.

A model of cell cleavage.

A model is presented which describes, at least to a first approximation, the oserved changes in cell shape and the movement of surface markers associated with cleavage in some types of cells. The model postulates that the constraints governing cell cleavage are minimum surface area and constancy of cell volume. Equations are derived both for the case of symmetric as well as the case of asymmetric cleavage. It is pointed out that the generally symmetric character of cell cleavage is explicable if there is a positive correlation between internal cell pressure and the radii of curvature.

A model of blebbing in mitotic tissue culture cells.

A preliminary study of blebbing in tissue cultures has been made. The tubal epithelium of fetal mouse oviduct was cultured at 37 degrees C in Rose chambers. A cinematographic record was obtained of phase microscope observations of mitotic cells. Measurements of the size of both cells and blebs were made on the film using a "traveling" microscope. The duration and the rise and decay times of blebs were determined simply by counting frames on the film. Detailed observations are reported on blebbing in four cells undergoing mitosis. The results indicate that the frequency of blebbing as well as the duration of individual blebs exhibits a maximum during telophase. A model is proposed to account for blebbing in mitotic cells. The model attributes to local regions of the cell membrane the property of constant tension independent of stretch over some restricted range of stretch. This property implies that the cell membrane is locally unstable. Further assumptions stated explicitly in the model are that (i) cell division occurs at constant volume, (ii) the cell membrane stretches during cleavage, (iii) there is a positive pressure drop across the cell membrane. Evidence is cited in support of these assumptions as well as independent evidence that the cell membrane may be locally unstable. A physical model is described which would be expected to exhibit blebbing given the above assumptions.

Three-dimensional reconstruction from serial sections III. AUTOSCAN, a software package in FORTRAN for semiautomated photomicrography.

A FORTRAN program, called AUTOSCAN, is described. This program permits the collection of photomicrographic data from serial sections to be semiautomated. In essence the user defines a box around a microscopic field of interest. Then the program drives the stage incrementally in the x and y directions, taking photographs of contiguous subfields. The box is defined by the use of a joystick and the "return" key. That is, movements of a joystick cause the stage to translate in the x and y directions. When a corner of the object is reached, as defined by cross-hairs in the microscope eyepiece, the user hits the return key. Repetition of this process at each corner defines a "box" within which photographs are to be taken. AUTOSCAN then calculates the step size and the number of frames to be taken from the user-defined values for the magnification. The actual movements of the stage in the x and y directions and the photography are fully automated. Each frame of film has the x and y coordinates of the center of the subfield being photographed imprinted in one corner, along with other relevant data. The x and y coordinates permit the resultant information to be assembled correctly into a two-dimensional montage.

Evidence for clonal attenuation of growth potential in HeLa cells.

The growth of primary clones and serial subclones of HeLa cells and of diploid human fibroblast-like cells were compared both in the presence and absence of feeder layers; the latter had no significant effects upon the results. Clones and subclones of both cell types displayed great heterogeneity in growth rates, typically with a bimodality of growth distributions. Serial passages of clones selected on the basis of superior rates of proliferation showed attentuation of growth potentials; the extent of such attentuations was much less in the case of HeLa cells, suggesting at least one possible basis for the differences in long-term growth potential between these two classes of cell lines.