What Is a Model?
The problem of science will consist precisely in this, to seek the unitary character of physiological and pathological phenomena in the midst of the infinite variety of their particular manifestations.
--Claude Bernard (1865, p. 124 in Eng. Trans.)
The concept of a model seems to have preceded the frequent appearance of the term in biomedical research literature. In his classic work, An Introduction to the Study of Experimental Medicine, Bernard (1865) discussed "the usefulness to medicine of experiments on various species of animals." (See English edition, pp. 122–129.) Krogh (1929) stated, "For a large number of problems there will be some animal of choice, or a few such animals, on which it can be most conveniently studied." Almost half a century later, this became known as the August Krogh principle (Krebs, 1975). Krebs and Krebs (1980) cautioned that "an uncritical application of this principle may lead to fallacious generalizations, because extrapolating findings from one species to another is not invariably valid." Ross (1981) carried this point further, arguing that comparative physiology, rather than achieving its objectives of contributing to knowledge of phylogenetic relationships and of discovering the origins of physiological functions, has in reality dealt with the description of adaptations. On the other hand, Bullock (1984) argued that ''comparative neuroscience is likely to reach insights so novel as to constitute revolutions in understanding the structure, functions, ontogeny, and evolution of nervous systems." Without using the term, these authors were discussing what we refer to today as models.
The various kinds of models and their meanings were discussed by Ransom (1981), who wrote:
In its simplest form, a model is a simplified representation of a structure…. A heuristic model is a model used to discover how a process works rather than being a descriptive model of the process…. The definition of a
heuristic model is in fact rather simple but it is the way in which such models are constructed that gives rise to most difficulty in classification. Static models can be heuristic; for example, the form of a protein molecule is often worked out by trial and error construction of plastic models….
Ransom described a variety of heuristic modelling techniques, such as the following:
Paper and pencil (static) models. Ransom cited D'Arcy Thompson's (1917) Growth and Form as a classic example of the application of this type of modelling to development. Thompson's grid technique analyzed growth in terms of localized asymmetries arising from differential growth rates during early development.
Mathematical models. In this type of modelling, mathematical equations are used to describe a process. The discrete (statistical or probabilistic) model is mentioned as another type of mathematical model. [A report prepared by a committee of the National Research Council (1981a) contains a discussion of mathematical models, including statistical models, simulation models, and both qualitative and semi-quantitative models.]
Computer models. Elements from both pencil and paper models and mathematical models can be combined to produce hybrid models, normally animated as simulations. Ransom proposes that a simulation is "the dynamic representation of a model on a computer." According to this author, "The sequential representation of a process at different states in time is the essential basis of the computer model…."
Substitute system models. Ransom includes the use of living organisms as models, pointing out the frequent advantage of providing simpler systems than the ones in which our interest might be centered. Used in this sense, the model is often referred to as a surrogate. Russell and Birch (1959) discuss fidelity and discrimination as factors governing the way in which the model differs from the original.
This report is not intended to be an exhaustive survey of either the uses of the term model or of the organisms, preparations, and mathematical procedures that have served as models or model systems. Studies that review the use or potential use of biological materials as model systems are fairly numerous, including several conducted by the National Research Council:
Mammalian Models for Research on Aging (National Research Council, 1981a);
Marine Invertebrates, a volume in the Laboratory Animal Management Series (National Research Council, 1981b);
The Future of Animals, Cells, Models, and Systems in Research, Development, Education, and Testing (National Research Council, 1977);
Animal Models of Thrombosis and Hemorrhagic Diseases (Department of Health, Education, and Welfare, 1976);
Psychopathology: Experimental Models (Maser and Seligman, 1977);
Animals and Alternatives in Toxicity Testing (Balls et al., 1983);
Species-Specific Potential of Invertebrates for Toxicological Research (Kaiser, 1980);
Trends in Bioassay Methodology: In Vivo, In Vitro and Mathematical Approaches (National Institutes of Health, 1981); and
Invertebrate Models in Aging Research (Mitchell and Johnson, 1984).
The proceedings of a symposium sponsored by the Society for Experimental Biology to examine the use of models and analogs in biology provides an illustration of the various applications of the term model in the life sciences (Beament, 1960). Included in the topics covered in this volume are mechanical models, electrical analogs, computers, kinetic models, models in cybernetics, psychological models, and educational models.
As used in biology, the concept of a model has not always been consistent and involves two broad classes, determined by whether the modelling is based on analogy or on homology. Modelling based on analogy is used extensively in the physical as well as in the biological sciences. Homology-based modelling appears to be uniquely biological, reflecting evolution and the genetic fixing of historical events into DNA sequences.
Modelling by analogy involves a point-by-point process relating one structure to another or one process to another (in mathematical terminology, mapping). This means finding correspondences with respect to some features. It requires that there be similarities between the two things being connected by the modelling relationship. Thus, for example, it is possible to model the concentration field in a diffusion problem by the electrostatic voltage field, provided that the geometries and boundary conditions are approximately set. This is possible because both phenomena follow the same differential equation.
All analog computers operate because the computer hardware elements exist in some kind of modelling relationship to the elements in the problem being solved. This accounts for the rigid, high specificity of analog computers and is the reason for their replacement by digital computers, which can model any mathematical structure, according to
Turing's theorem about the existence of a universal computer (Turing, 1936).
In naval architecture, studies using model basins are made possible by the same hydrodynamic equations, once the scaling factors have been taken into account. Here the structural features in common to the model and the object being modelled are quite apparent.
Both physics and engineering commonly use analog models. Indeed modelling, if we include similar mathematical features as one of its bases, is a major part of the activity of those sciences. We can therefore formalize the idea of relationships by analogy within the structure of physical sciences.
The idea of reasoning by analogy goes far back in the history of science. Kant (1790) wrote, "Analogy, in a qualitative sense is the identity of relations subsisting between grounds and consequences-causes and effects -- so far as such identity subsists despite the specific differences of the things, as of those properties, considered in themselves (i.e., apart from this relation), which are the source of similar consequences." This idea has persisted in slightly modified form.
Analogies and models as they relate to the physical sciences have been reviewed by Achinstein (1968). He writes:
In all of the cases considered we might describe the model or analogy as (or as containing) (1) a representation of X; but (2) one that is either not literal, or not faithful in all respects, or not complete, and may represent X in some "indirect" manner; and (3) one that utilizes something more or less familiar, known, understood, readily grasped, or easily experimented upon. Thus, a representational model represents X, but not completely and not necessarily literally, by utilizing something Y that is familiar or more readily grasped. In a theoretical model we represent X, but only approximately and not completely, by bringing it under, or at least utilizing parts of, some more basic theory or theories that are familiar and understood. In an imaginary model we represent X but not in a way intended to be literal, by imagining how X could satisfy certain conditions, where either the set of conditions or the way we represent X is more or less familiar and understood. In an analogy X is represented in an indirect way by being shown to be similar in some though not all respects to a distinct item more familiar or more readily grasped.
These notions have been presented in a somewhat different way by Margenau (1977). He presents what is in many ways a consensus view of how physics is methodologically structured at the most general level. Because of its generality, it applies to all of science, including biology. According to this view, science starts with observation, phenomena, sense perceptions, the raw material of our knowledge of the world. By rules of correspondence we now move to the existence of objects (reification) and the behavior of those objects. We then construct an elaborate set of theoretical devices: laws, definitions, theories, postulated entities (e.g., atoms and electrons), which are connected by logical and mathematical relationships. The validity of this structure is tested by the agreement of statements or predictions with the observed phenomenological world.
Margenau introduced the general term "constructs" to apply to all the theoretical conceptual devices listed above. Physical reality for him, which we generalize to scientific reality, consists of a cycle in which we continuously go from the world of observation through understanding by constructs back to observation.
Next consider two independent sets of observations on different entities. These can be connected insofar as some of the same constructs are used in the understanding of each of them. Analogies then exist between the two systems with respect to the overlapping constructs and the two systems model each other. The more frequently constructs are used in gaining an understanding of independent sets of observables, the stronger is the analogical relation between them.
Modelling by analogy is also used in the biological sciences. For example, since flight in bees, birds, and bats has certain aerodynamic features in common, a modelling relationship is possible (although the differences in these particular systems may be of more interest than the similarities). In the same sense modelling between a goose and an airplane is possible. Here the modelling can have unusual features. For example, both bird and airplane carry their fuel as saturated hydrocarbons, although it is esterified to glycerol in birds. This maximizes the energy-to-weight ratio of fuel in an oxidizing atmosphere.
Biology is characterized by a second type of modelling, i.e., modelling by homology, which seems unique to that field of study. The objects of biology -- organisms -- have an evolutionary history that is embedded in their genomes. As a result of evolution from a common origin, there are many shared genetic sequences and common functions between organisms. In general, species that have diverged most recently have the closest resemblances in DNA sequences and functions of protein and RNA derived from these sequences. The relationships between organisms resulting from their shared evolutionary history and matching DNA sequences form the basis of models by homology. Thus, for example, livers of the rat, pig, and human are homologously related in an evolutionary sense, and we would suspect and indeed do find similarities that make them
suitable for an analogous modelling relationship. On the other hand, the bat wing, the foreleg of the horse, and the porpoise flipper are homologously related to the human arm, as revealed by comparative anatomy and the fossil record, but they provide poor analog models for human arm function.
Models by homology are thus of heuristic value in the search for analogs, but they become functionally useful only when they are also good models by analogy for the phenomenon or structure being studied. Thus, if one is investigating lipid solubilization in mammalian metabolism, the rat-pig-human liver homology transfers to a very useful analogous modelling system for research. If one is interested in flight, the bat-horse-porpoise homology may be of limited value for special questions.
The reason that homolog models sometimes fail to be good analog models is twofold. First, individual physiological adaptations may make homologs poor analogs. Ross (1981) illustrated this by describing the phylogenetic irregularities in the distribution of respiratory pigments in invertebrates.
Second, convergent evolution may make good analogs out of genetically very distant structures and processes. A commonly cited example for convergent evolution is the mammalian eye and the cephalopod eye. They are good optical analogs, which would have been entirely unanticipated on the basis of their weak homologous relationship. In another example, the Australian dingo (a placental mammal) and the Tasmanian wolf (a marsupial) are good ecological analogs, although the latter would be a very poor model if one were studying typical late embryological development in mammals. In any case, because modelling is based on relationships between organisms, it necessarily has reciprocal features: if A is a model of B, then B is a model of A.
In biomedical research, model selection generally begins with a search for close homologs that were judged at the outset of the research to be good analogs. Thus the spontaneously diabetic Wistar BB rat (discussed in the workshop on disease and aging, which is summarized in Appendix E) turns out to be an excellent model in the study of juvenile-onset diabetes, because the rat is a relatively close homolog of the human in terms of organ function, and between the ages of 60 and 120 days this strain develops diabetes with pathological characteristics almost identical to those of humans with the disease. Although other animals may be more closely homologous to humans, diabetic strains are not available and, therefore, cannot serve as models for this disease in humans. The use of Watanabe rabbits in the study of atherosclerosis and a strain of New Zealand black mice in the study of lupus erythematosus are additional examples of this principle. The search for animals with the same clinical manifestation of a disease as humans is an obvious route to the identification of animal models for biomedical research. Such systems seem so obviously useful as to require little further justification, but for purposes of completeness we elaborate on one such case.
For many years there were no adequate models to study human familial hypercholesterolemia and the attendant arteriosclerosis. Human skin fibroblast cells in culture possess a specific receptor for low density lipoprotein (LDL), which is lacking in cells from subjects with homozygous familial hypercholesterolemia. Thus, although certain biochemical aspects of the disease were studied in cell culture, no satisfactory animal models were available prior to 1975 to study the clinical aspects of the genetic defect. Then Kondo and Watanabe (1975) reported on a hyperlipidemic rabbit, which had been a spontaneous mutant. A homozygous strain that was subsequently bred has become known as the WHHL (Watanabe-heritable-hyperlipidemic) rabbit. The WHHL rabbits have been shown by analogy to be extraordinarily good models of humans with familial hypercholesterolemia insofar as the disease process is concerned. They have an LDL receptor deficiency in skin fibroblasts which the authors suggest will be a powerful tool for finding a significant role of LDL receptor-deficiency in the occurrence of the clinical syndrome of hyperbetalipoproteinemia (Tanzawa et al., 1980).
By virtue of having a genetic lesion similar to that in humans with hypercholesterolemia, the WHHL rabbit is a fairly close model by homology of a circulatory system disorder. Studies over the past few years have shown many striking analogs between the disease process in WHHL rabbits and afflicted humans. Buja et al. (1983) described recent examples of modelling with the WHHL rabbit.
Cultured human skin fibroblast cells are models by homology (they possess the same genome and express some but not all of the same genes), and in the domains of biochemistry and cell physiology, they have proven to be good analogs for lipid binding. Thus, the WHHL rabbit and human cell cultures are providing excellent models for the study of a major disease and illustrate how one-to-one modelling can be extremely important.
In the process of developing the concepts of this report, it has been necessary to define two types of surrogate modelling, described as one-to-one and many-to-many.
One-to-one modelling. If in the study of a normal or pathological process or structure we find analogous behavior with respect to several features in two groups of organisms and no negative features, the organisms are models for each other with respect to those processes or structures, and studies of one are considered to have a high probability of yielding useful information about the other. For example, in a disease state of humans, if we can locate another organism that has the same range of symptomatic behavior, we are encouraged to use that organism as a model for studying the etiology, pathology, and therapy of the disease in humans.
Many-to-many modelling. If we have some process or state in an organism of interest and analyze it from a reductionist viewpoint into component features at several hierarchical levels, e.g., system, organ,
tissue, cellular, or subcellular levels, we may then at each level note all the taxa in which analogous features appear. Each of these species is a model for the other with respect to those features. This is many-to-many modelling, the first many referring to the many features at various hierarchical levels that have emerged from the analysis and the second many referring to the many taxa at each level in which the features appear.
The usefulness of one-to-one modelling is illustrated by Brinkhous and Bowie (1977), who reviewed studies on the pigeon, dog, rabbit, pig, and nonhuman primates. They have shown how difficult it has been to develop good models of atherosclerosis, although pigs with von Willebrand's disease have been valuable in the study of spontaneous atherosclerosis. The search clearly relies on one-to-one modelling. Further exposition of the general approach can be found in a publication of the Department of Health, Education, and Welfare (1976).
One-to-one modelling describes the view of models that dominated the committee's initial discussions. The workshops and their subsequent analyses led to the adoption of many-to-many modelling-- a more general view of models that is introduced in the following paragraphs and developed in Chapter 5.
Investigators studying a phenomenon may analyze its various components at the organ, tissue, cellular, or subcellular levels and seek models for its different parts from the entire corpus of biological knowledge. This then allows them to study one organism or system in terms of related features from a variety of other organisms and other systems. In the new kind of epistemic structure that emerges, the matrix of biological knowledge replaces the one-to-one model as a source of analogs for reaching an understanding of problems. Within the matrix, homology and analogy still exist, analogy arising out of common strategies and common functional groups, and all the analogical behavior derived by using the same hardware and the same physical and chemical laws to solve similar problems or to perform similar functions.
A classical biological model (of the one-to-one type) can now be seen as one relationship within the larger context. If we are investigating some phenomenon in organism A, which has a certain relationship to the overall matrix, and in organism B, which has the same or very similar relationship to this matrix, then B is a good model for A for that specific study. Furthermore, experiments on B are likely to produce results that will be of great assistance in understanding A. Therefore, the modelling relationships are reciprocal. The associations need to be relevant only to the problem under study and need not be more general.
The body of biological knowledge is beginning to form a coherent and interrelated structure, but it lacks the tight theoretical formulation of physical science. As noted by Baldwin (1938) at the biochemical level, a general biology is emerging from our understanding of the vast number of
interrelationships and common features that arose through organic evolution.
In a recent paper describing comparative neuroscience and its potential for advancing knowledge, Bullock (1984) makes a strong case for comparative studies and, thereby, for the use of models to provide data points in a complex matrix. The arguments he put forward for comparative neuroscience have been made for various aspects of the endocrine system (Roth et al., 1983) and for other phenomena, other organisms, and other areas of biology. Because of its particularly cogent presentation, the summary of Bullock's paper is quoted here in its entirety:
The brain has diversified and advanced in evolution more than any other organ; the variety of nervous systems and behaviors among animal species is thus available for our exploitation. Comparative neuroscience is likely to reach insights so novel as to constitute revolutions in understanding the structure, functions, ontogeny, and evolution of nervous systems. This promise requires pursuit on a wide front, in respect to disciplines and in respect to the species, stages and states compared. It also requires deliberate concentration on the differences among animals, in addition to the prevailing concern for the basic and common. Neglect of these challenges would be costly. Without due consideration of the neural and behavioral correlates of differences between higher taxa and between closely related families, species, sexes, and stages, we cannot expect to understand our nervous systems or ourselves (Bullock, 1984, p. 473).
The case for comparative studies in biomedical research is well made in the report of a study on research needs in endocrinology and metabolic diseases (National Institutes of Health, 1981). The report, compiled from the work of 18 task forces, including a committee on comparative endocrinology, contains the following statement:
When viewed superficially, studies of comparative biology may seem esoteric or irrelevant to the human condition. The report of the task force on comparative endocrinology provides numerous examples which attest strongly to the contrary (National Institutes of Health, 1981, p. 42).
This assertion regarding comparative endocrinology can be applied to comparative studies in other biomedical research areas as well.
The committee's workshops have led inexorably to the conclusion that a theoretical biology or, to use Claude Bernard's phrase, a "theoretical medicine" is beginning to exist (Bernard, 1865). It is different from theoretical physics, which consists of a small number of postulates and the procedures and apparatus for deriving predictions from those postulates. But it is far more than just a collection of experimental observations. The vast array of information gains coherence when organized into a conceptual matrix through empirical generalizations and reductionist laws-- a construct that permits a view of models far more comprehensive than the committee envisioned at the outset of the study. This view is reflected in the concept of many-to-many modelling.
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