THEORETICAL AND MATHEMATICAL DEVELOPMENTAL BIOLOGY 



Treatises 



3. 



R.ROSEN, ed. 1972. FOUNDATIONS OF MATHEMATICAL BIOLOGY. Vol.11 



Cellular systems 



Academic Press, New York, etc. XVIII, 330 pp., 116 figs., 3 tabs. 



author and subject indexes. $ 16.00 



This is the second volume of a three-volume series, the other 

 two being entitled "Subcellular Systems" and "Supercellular 

 Systems". The book consists of five chapters, and with possibly 

 one exception, is not of much use to people working on problems 

 of development. 



The exception is Arbib's essay on automata theory. To put it 

 simply, the approach is to regard the cell as a spatially dis- 

 crete unit which has access to a number of states under the in- 

 fluence of its neighbours. The contrast with the usual conti- 

 nuum models employed by theorists is obvious. It is very inter- 

 esting, for instance, to see how the problem of the regulation 

 of pattern in multicellular systems is posed. Readers without a 

 background in mathematics (especially formal logic) can safely 

 skip sections 4 and 5 and still get the flavour of the attempt. 

 In particular, no one should miss the evaluation on page 208 of 

 Wigner's old (wrong) claim that the laws of physics make it 

 highly unlikely that self-reproducing beings can exist. 



Rescigno and Beck contribute a chapter on compartment analy- 

 sis. As the word might suggest, this is a study of the dynamics 

 of exchange of substances between different units (composed of 

 cells). A typical problem - mentioned by the authors - is the 

 distribution (at different times) of radioactivity in the blood, 

 the lipid of the liver, and the skeleton of rats fed radioac- 

 tive phosphate. 



The remaining chapters are all by Rosen. "Morphogenesis" con- 

 siders strategies for assembling a whole out of a large number 

 of subunits, allowing for errors. A survey of theories of cell 

 sorting-out follows; readers must remember that the problem is 

 posed as one static in time, and is essentially restricted to 

 minimizing the configuration energy. Then there is a summary of 

 the attempts of Turing, and of Keller and Segel to look at mor- 

 phogenesis (in particular, the formation of spatial pattern) as 

 a phenomenon in which a system "switches" from one steady state 

 to another when external parameters are suitably varied. On 

 page 58, a misleading aside on entropy and order intervenes; 

 this is best totally disregarded. "Mechanics of epigenetic con- 

 trol" yields quite a few misprints even on first sight; and 

 more dangerously, wrong mathematics right at the beginning, in 

 the study on open systems with chemical kinetics (page 87). And 

 there is a reference to a non-existent figure 2a which is sup- 

 posed to show a stable point in phase space, whereas both fig- 

 ures 2 show instabilities However, the varieties of chem- 

 ical kinetics considered can make this chapter useful as a 

 source of ideas, if one is careful not to take the results on 

 faith. "Metabolism-repair systems" is a super-formalised ac- 

 count of input-output systems representing cells, and might 

 suit the reader who demands no biology in her mathematics. 



On the whole, this is a book quite dispensable to developmen- 

 tal biologists. 



V.Nanjundiah 



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