Water transport in plants obeys Murray's law

Abstract

The optimal water transport system in plants should maximize hydraulic conductance (which is proportional to photosynthesis) for a given investment in transport tissue. To investigate how this optimum may be achieved, we have performed computer simulations of the hydraulic conductance of a branched transport system. Here we show that the optimum network is not achieved by the commonly assumed pipe model of plant form, or its antecedent, da Vinci's rule. In these representations, the number and area of xylem conduits is constant at every branch rank. Instead, the optimum network has a minimum number of wide conduits at the base that feed an increasing number of narrower conduits distally. This follows from the application of Murray's law, which predicts the optimal taper of blood vessels in the cardiovascular system. Our measurements of plant xylem indicate that these conduits conform to the Murray's law optimum as long as they do not function additionally as supports for the plant body.

Linking phloem function to structure: Analysis with a coupled xylem–phloem transport model

“…This vertical tapering and developmental changes may be similar to those already documented for the xylem (e.g. Anfodillo et al, 2004;Mencuccini et al, 2007;McCulloh et al, 2003;West et al, 1999), at least partially. In the xylem, conduit tapering is predicted to reduce the adverse effects of growing transport distance on the whole xylem pathway conductance (West et al, 1999).…”

Partitioning hydraulic resistance in Sorghum bicolor leaves reveals unique correlations with stomatal conductance during drought

“…This matches model simulations of leaves where increasing major vein density led to a linear decrease in xylem resistance (McKown et al 2010). Decreasing r * LV through changes in the number of vascular bundles rather than the size of vessel elements is expensive to plants as cost of xylem construction is fairly high (McCulloh et al 2003). We found no significant correlations between any anatomical characteristics (D m or vein density) and r * OLV , which suggests that the hydraulic resistance outside the large longitudinal veins may have been controlled by other mechanisms.…”

Electrical admittance of piezoelectric parallelepipeds: application to tensorial characterization of piezoceramics

“…20 Also, it has been shown that most of the branching systems in the nature such as vasculatures and plants obey Murray's law. [21][22][23] Murray's law is also in agreement with the constructal theory which states "For a finite-size flow system to persist in time (to survive) its configuration must evolve (morph) in time in such a way that it provides easier flow access to its currents". 24 Moreover, some studies have tried to generalize Murray's law to obtain a general rule for designing microfluidic networks.…”