Sizing Up Allometric Scaling Theory

Metabolic rate, heart rate, lifespan, and many other physiological properties vary with body mass in systematic and interrelated ways. Present empirical data suggest that these scaling relationships take the form of power laws with exponents that are simple multiples of one quarter. A compelling explanation of this observation was put forward a decade ago by West, Brown, and Enquist (WBE). Their framework elucidates the link between metabolic rate and body mass by focusing on the dynamics and structure of resource distribution networks—the cardiovascular system in the case of mammals. Within this framework the WBE model is based on eight assumptions from which it derives the well-known observed scaling exponent of 3/4. In this paper we clarify that this result only holds in the limit of infinite network size (body mass) and that the actual exponent predicted by the model depends on the sizes of the organisms being studied. Failure to clarify and to explore the nature of this approximation has led to debates about the WBE model that were at cross purposes. We compute analytical expressions for the finite-size corrections to the 3/4 exponent, resulting in a spectrum of scaling exponents as a function of absolute network size. When accounting for these corrections over a size range spanning the eight orders of magnitude observed in mammals, the WBE model predicts a scaling exponent of 0.81, seemingly at odds with data. We then proceed to study the sensitivity of the scaling exponent with respect to variations in several assumptions that underlie the WBE model, always in the context of finite-size corrections. Here too, the trends we derive from the model seem at odds with trends detectable in empirical data. Our work illustrates the utility of the WBE framework in reasoning about allometric scaling, while at the same time suggesting that the current canonical model may need amendments to bring its predictions fully in line with available datasets

Chemical synthesis and biological activities of 3-alkyl pyridinium polymeric analogues of marine toxins

Two new large poly-1,3-dodecylpyridinium salts, APS12 and APS12-2 of 12.5- and 14.7-kDa size, respectively, were synthesised and tested for their pore-forming and transfection capabilities in HEK 293 and undifferentiated mouse ES cells using patch-clamp recording, Ca2+ imaging and flow cytometry. Polymerisation reactions were enhanced by microwaves, and the product sizes were controlled by altering the irradiation time. This method can also be applied to obtain polymers with variable linking chains as shown by the preparation of poly-(1,3-octylpyridinium) salt of 11.9-kDa size. Molecular weights of the final products were determined using ESIMS analysis, which also indicated the products to be amongst the largest macro-cycles ever recorded, up to a 900-membered ring. Anti-bacterial, haemolytic and anti-acetylcholinesterase activities were also reported for the two dodecyl pyridinium polymers. These biological activities are characteristic to the structurally related marine toxin, poly-APS