The miracle that gives life its shape

Originally published 14 June 1993

There is a cer­tain mag­ic moment in the spring woods near my house when the ladys­lip­pers and starflow­ers bloom together.

What­ev­er it is in the sea­son and the soil these flow­ers like, it suits them both. Where you find one, you find the oth­er, in cozy company.

But what dif­fer­ent plants! The ladys­lip­per is large, lush, almost trop­i­cal in its thick-stalked gaudy exu­ber­ance. The two-blos­somed starflower is lithe and pale, with thread­like stems.

Each plant begins life as a sin­gle cell, and there is no mys­tery in biol­o­gy deep­er than the devel­op­ment of mature plants or ani­mals from micro­scop­ic fer­til­ized eggs. What directs the prodi­gious mul­ti­pli­ca­tion of cells into a blos­som­ing ladys­lip­per or starflower? One cell becomes two; two becomes four; four becomes eight. As they split, cells diver­si­fy for spe­cial func­tions: roots, stems, leaves, petals, sta­mens, pistils.

The process is called mor­pho­gen­e­sis, and it seems a miracle.

Aris­to­tle thought a cre­ative spir­it asso­ci­at­ed with the male sperm gave shape to the amor­phous mate­r­i­al of the female egg. Oth­er ancient thinkers imag­ined that every germ cell con­tained a tiny but com­plete repli­ca of the mature plant or ani­mal, that had only to enlarge its size. (The ques­tion of where those micro­scop­ic effi­gies came from caused nat­ur­al philoso­phers con­sid­er­able trouble.)

The rise of mate­ri­al­ist phi­los­o­phy in the 17th cen­tu­ry brushed Aris­totle’s spir­its aside, and the inven­tion of the micro­scope put the minia­ture effi­gy the­o­ry to rest. Which left devel­op­men­tal biol­o­gists dan­gling in the wind. When I was a school kid, they were still doing a lot of hand­wav­ing about genes and the fis­sion­ing of cells, but they did­n’t know much more about mor­pho­gen­e­sis than did Aristotle.

The dis­cov­ery of the struc­ture of DNA by Wat­son and Crick in the 1950s made it clear that this remark­able mol­e­cule was the basis for genet­ics and repro­duc­tion, but huge mys­ter­ies remained about how genes are expressed in space and time in such a way as to lead to the order­ly devel­op­ment of an organism.

One day in the late 1950s, I was eat­ing a brown-bag lunch with a friend in the botan­i­cal gar­den of the Uni­ver­si­ty of Cal­i­for­nia at Los Ange­les. We were sur­round­ed by a won­der­ful pro­fu­sion of plants of every size and shape — trees, shrubs, vines, cac­ti, wild­flow­ers. My friend took it all in and said, “Math­e­mat­ics.”

I asked, “What?”

“The way these things grow,” he replied; “It is all math­e­mat­ics. I don’t know how, but it’s got­ta be mathematics.”

I was­n’t con­vinced. I was too much the poet then, too much agog at the won­der of life to allow my friend to reduce the gor­geous­ness of the botan­i­cal gar­den to mere numbers.

A few years lat­er, I obtained a copy of D’Ar­cy Thomp­son’s On Growth and Form. That 1917 clas­sic had just been re-issued in an abridged paper­back by Cam­bridge Uni­ver­si­ty Press. Thomp­son seemed to agree with my friend. The book offered a huge com­pendi­um of math­e­mat­i­cal pat­terns observed in the struc­ture and growth pat­terns of plants and animals.

“Math­e­mat­ics, it’s all math­e­mat­ics,” Thomp­son seemed to say.

OK, but how does it hap­pen? How can a sin­gle cell unfold a ladys­lip­per or a starflower? Or a human being? Thomp­son’s book has recent­ly been re-pub­lished by Dover in an unabridged ver­sion three times thick­er than the edi­tion I read in 1961 — even more evi­dence that mor­pho­gen­e­sis is strik­ing­ly math­e­mat­i­cal. But Thomp­son did­n’t have the fog­gi­est idea how it happens.

The answer is still uncer­tain, although cell biol­o­gists are mak­ing remark­able break­throughs. Recent stud­ies in the com­put­er mod­el­ing of plant devel­op­ment may offer anoth­er key to the mystery.

Using pro­gram­ming lan­guages espe­cial­ly designed for the pur­pose, com­put­er sci­en­tists are caus­ing col­or­ful gar­dens to flour­ish on mon­i­tor screens. At first, these arti­fi­cial plants were not much more real­is­tic than stick fig­ures drawn by chil­dren, but they grew, branched, and blos­somed in response to their dig­i­tal envi­ron­ment. They even evolved.

In recent years, plants on com­put­er screens have become uncan­ni­ly real­is­tic, almost indis­tin­guish­able from pho­tographs of real plants. Forests of pine trees with nee­dles and cones. Field of sun­flow­ers. Rose gar­dens. Lily ponds. The plants grow, self-repli­cate, respond to exter­nal fac­tors, even mutate, all accord­ing to math­e­mat­i­cal rules.

Math­e­mat­ics, all mathematics.

Call it “vir­tu­al botany.”

We’ll be see­ing more of these vir­tu­al gar­dens soon — in TV com­mer­cials, as spe­cial effects in movies, and in sci­ence doc­u­men­taries. The impor­tant thing to remem­ber is this: The plants we watch grow­ing and devel­op­ing on screen are spec­i­fied by strings of sym­bols — pro­grams — that are far less com­plex than the infor­ma­tion con­tained in a sin­gle cel­l’s com­ple­ment of DNA.

Grant­ed, the vir­tu­al gar­dens on com­put­er mon­i­tors are present­ly no more than arbi­trary mod­els of real plants, but they will almost cer­tain­ly lead to fresh insights into the rid­dle of mor­pho­gen­e­sis. At the very least they make it clear that the devel­op­ment of plants and ani­mals from sin­gle cells is some­thing less than miraculous.