Duality, thermodynamics, and the linear programming problem in constraint-based models of metabolism

It is shown that the dual to the linear programming problem that arises in constraint-based models of metabolism can be given a thermodynamic interpretation in which the shadow prices are chemical potential analogues, and the objective is to minimise free energy consumption given a free energy drain corresponding to growth. The interpretation is distinct from conventional non-equilibrium thermodynamics, although it does satisfy a minimum entropy production principle. It can be used to motivate extensions of constraint-based modelling, for example to microbial ecosystems.Comment: 4 pages, 2 figures, 1 table, RevTeX 4, final accepted versio

Otolith shape analysis of Lethrinus lentjan (Lacepède, 1802) and L. microdon (Valenciennes, 1830) from the Red Sea

Otolith shape and morphology are used to identify fish species and population stocks. The aim of this study was to distinguish the Lethrinus lentjan (Lacepède, 1802) and L. microdon (Valenciennes, 1830) (family: Lethrinidae) using otolith shape. The analyses apply the ShapeR package in R which enables to extract the outline and otolith morphology from images and for statistical examining of individual variation. Otoliths of 165 individuals from the two Lethrinus species were collected during 2019 and 2020. The wavelet levels were examined by using 6 wavelets to collect 63 coefficients. The regression between width and fish length were b = -0.03 (t = 2.6, P = 0.01) for L. lentjan and was significantly different (t = 2.120, P = 0.036) for L. microdon (b = 0.018)