A Half-Century Adventure in the Dynamics of Living Systems

The Thermodynamic Flow-Force Interpretation of Root Nutrient Uptake Kinetics: A Powerful Formalism for Agronomic and Phytoplanktonic Models

The ion influx isotherms obtained by measuring unidirectional influx across root membranes with radioactive or stable tracers are mostly interpreted by enzyme-substrate-like modeling. However, recent analyses from ion transporter mutants clearly demonstrate the inadequacy of the conventional interpretation of ion isotherms. Many genetically distinct carriers are involved in the root catalytic function. Parameters Vmax and Km deduced from this interpretation cannot therefore be regarded as microscopic parameters of a single transporter, but are instead macroscopic parameters (Vmapp and Kmapp, apparent maximum velocity and affinity constant) that depend on weighted activities of multiple transporters along the root. The flow-force interpretation based on the thermodynamic principle of irreversible processes is an alternative macroscopic modeling approach for ion influx isotherms in which macroscopic parameters L_j (overall conductance of the root system for the substrate j) and π_j (thermodynamic parameter when J_j = 0) have a straightforward meaning with respect to the biological sample studied. They characterize the efficiency of the entire root catalytic structure without deducing molecular characteristics. Here we present the basic principles of this theory and how its use can be tested and improved by changing root pre- and post-wash procedures before influx measurements in order to come as close as possible to equilibrium conditions. In addition, the constant values of Vm and Km in the Michaelis-Menten (MM) formalism of enzyme-substrate interpretation do not reflect variations in response to temperature, nutrient status or nutrient regimes. The linear formalism of the flow-force approach, which integrates temperature effect on nutrient uptake, could usefully replace MM formalism in the 1-3-dimension models of plants and phytoplankton. This formalism offers a simplification of parametrization to help find more realistic analytical expressions and numerical solution for root nutrient uptake.

Plant memory: a tentative model

All memory functions have molecular bases, namely in signal reception and transduction, and in storage and recall of information. Thus, at all levels of organisation living organisms have some kind of memory. In plants one may distinguish two types. There are linear pathways from reception of signals and propagation of effectors to a type of memory that may be described by terms such as learning, habituation or priming. There is a storage and recall memory based on a complex network of elements with a high degree of integration and feedback. The most important elements envisaged are calcium waves, epigenetic modifications of DNA and histones, and regulation of timing via a biological clock. Experiments are described that document the occurrence of the two sorts of memory and which show how they can be distinguished. A schematic model of plant memory is derived as emergent from integration of the various modules. Possessing the two forms of memory supports the fitness of plants in response to environmental stimuli and stress.