Transductions to generate plant form and pattern: an essay on cause and effect

Many complex processes can be broken into transduction steps where one state is converted to another by a well defined activity. One difficulty for analysis is that transductions occur in chains or networks. Another, of primary concern here, is that a single transduction can be complex. Some such transductions can efficiently explain phenomena often thought to be summations or orchestrations of many simple transductions. Pattern formation is in this category. For a wide range of transductions one can define cause and effect in a differential equation. In its integral one can define the before and after states. The main experimental tactic to characterize unknown transductions is co-variation. The before state (input) is altered, change in the after state (output) is assayed. Thus an unknown transduction, with cause and effect embodied in the differential, is investigated through long-term changes in its integral. This is fully practical when all of the integral is known or readily surmised, as in simple discrete biochemical transductions. As causal differential expressions become complex, their integrals become more versatile in generating output because this changes not only with variation in the expression itself but also with boundary conditions and limits. These very features, however, make such a function increasingly intractable to discovery by co-variation. Only a small part of the integral is embodied in the before and after states; the remainder is not readily surmised. Accordingly, in contrast to reliance on the role of controls to deduce unknown simple transductions, the complex ones are generally established through formalization of the differential nature of the process itself.