On the Association Between Genes and Complex Traits

M ost diseases are complex in that they have multiple causes that interact in nonintuitive ways. Complex traits can be inherited, but they do not follow Mendel’s rules of inheritance because they are in£uenced by many independent genetic and environmental factors, and thus exhibit incomplete penetrance and variable expressivity. Empirical approaches to understanding the causes of complex diseases typically attempt to isolate one factor at a time, and proceed to ascribe the manifestation of disease to some kind of additive or combinatorial eiect of these many independent factors. Recent developments in our understanding of regulatory mechanisms in genetics and development reveal that almost all the processes that lead to normal as well as abnormal phenotypes are nonlinear. It is the nonlinearity of interacting eiects, not their diversity, that makes complex traits di⁄cult to analyze and understand. One of the consequences of this nonlinearity is that the correlation of a complex trait with any one gene, or with any given environmental factor, varies from population to population. Moreover, when any one of these factors is altered in a given population (due to mutation or a change in environment), the correlations of other factors with the trait will also change. Thus the eiects of any one of the factors that aiects a complex trait cannot be understood except in the context of all other factors. A visualization of how this context-dependency arises can be obtained from the study of relatively simple biochemical mechanisms, such as a linear enzymatic pathway (Fig 1). The rate of product accumulation, or £ux through such a pathway, is a function of the activity of the enzymes in the pathway. The exact quantitative eiect of variation in any one of the enzymes depends on the length of the pathway (Kacser and Burns, 1981). For a one-step pathway the £ux is a linear function of enzyme activity, but for a multistep pathway the eiect of variation of any one enzyme is nonlinear, and this nonlinearity becomes progressively more severe as the length of the pathway increases (Fig 2). The consequence of this nonlinearity is not impressive if only one enzyme varies. But if there is variation of two or more of the enzymes in a multistep pathway the situation becomes quite complicated. Figure 3 illustrates the eiect of simultaneous variation in two of the enzymes in a three-enzyme pathway on the £ux through the pathway. The simultaneous eiect can be represented as a surface, called the phenotypic surface. This surface is simply a graph of the joint eiects of two independent variables, just as Fig 2 describes the eiect of a single variable. The independent variable axes in this ¢gure describe the range of possible activities that each enzyme can have. In a natural population there may be allelic variation in the genes that code for these enzymes that results in slight diierences in the activity of the encoded enzymes. Thus the axes of Fig 3 can also be taken to represent a range of allelic variation. Diierent individuals in a population will have their genotypes along the axes, and their phenotype at the corresponding coordinates on the phenotypic surface. Points X and Y in Fig 3 represent two individuals with diierent genotypes for the two alleles. These two individuals have identical phenotypes. Although they look the same, the two individuals will respond very diierently to mutation in gene A. A mutation in gene A changes its allelic value, and can thus be represented by a shift along the corresponding axis. It can be seen by inspection of Fig 3 that such a shift will have little or no eiect on the phenotype (£ux) of individual X, but will have a great eiect on the phenotype of individual Y. The exact reverse is true for a mutation in gene B. Thus an observer of individual Awould call gene A‘major gene’ for the trait, and gene B a modi¢er gene. By contrast, an observer of individual Y would call gene B the major gene for the trait and gene A a modi¢er. Thus, even though both genes contribute equally to the phenotype (as indeed they must in a linear pathway), the eiect variation in one gene has on the trait is conditioned by the particular alleles that exist at the other gene. This illustrates what is meant by the ‘context-dependency’ of the eiect of a gene. This contextdependency would not exist if the eiect of genetic variation on the trait were linear and additive, because then the phenotypic surface would eiectively be a £at plane. Context-dependency arises from nonlinearities of the eiect of individual genes and the resulting nonlinearity of their interactions (this phenomenon is also known as epistasis and results in a curvature of the phenotypic surface). This relatively simple complex system provides a foundation for understanding the nonintuitive eiects of non-linear interactions. A short biochemical pathway is a part of almost every cellular and physiological control mechanism, and thus the properties described in Fig 3 are likely to be extremely common. More complex mechanisms, with more independent variables, will behave in exactly the same way (Nijhout and Paulsen, 1999; Gilchrist and Nijhout, 2001), except that they cannot be easily visualized on paper because each independent variable must be represented as an axis of variation that is orthogonal to all other axes. Thus with more than two independent variables, the space of the phenotypic surface is multidimensional (Nijhout, 2002). There is nothing magical or abstract about this, if we remember that the phenotypic surface is nothing more than a graph. It is a description of the mathematical relationships among the independent and dependent variables. Because the surface is a description of a mechanism, we can only construct such surfaces for complex traits where the underlying generative mechanism is known. This is possible for most metabolic and biochemical systems, for a great many physiological systems, and for a number of cellular and molecular mechanisms. An exploration of the properties and implications of one such set of landscapes is given in Nijhout et al, 2003. Correspondence to: H.F. Nijhout, Duke University Dept of Biology, Durham, NC 27708, USA. Manuscript received December 30, 2002; revised May 12, 2003; accepted for publication May 12, 2003