Homeostats are important to control homeostatic conditions. Here, we have analyzed the theoretical basis of their dynamic properties by bringing the K homeostat out of steady state (i) by an electrical stimulus, (ii) by an external imbalance in the K+ or H+ gradient or (iii) by a readjustment of transporter activities. The reactions to such changes can be divided into (i) a short-term response (tens of milliseconds), where the membrane voltage changed along with the concentrations of ions that are not very abundant in the cytosol (H+ and Ca2+), and (ii) a long-term response (minutes and longer) caused by the slow changes in K+ concentrations. The mechanistic insights into its dynamics are not limited to the K homeostat but can be generalized, providing a new perspective on electrical, chemical, hydraulic, pH and Ca2+ signaling in plants. The results presented here also provide a theoretical background for optogenetic experiments in plants.

Ion homeostasis is a crucial process in plants that is closely linked to the efficiency of nutrient uptake, stress tolerance and overall plant growth and development. Nevertheless, our understanding of the fundamental processes of ion homeostasis is still incomplete and highly fragmented. Especially at the mechanistic level, we are still in the process of dissecting physiological systems to analyse the different parts in isolation. However, modelling approaches have shown that it is not individual transporters but rather transporter networks (homeostats) that control membrane transport and associated homeostatic processes in plant cells. To facilitate access to such theoretical approaches, the modelling of the potassium homeostat is explained here in detail to serve as a blueprint for other homeostats. The unbiased approach provided strong arguments for the abundant existence of electroneutral H+/K+ antiporters in plants.

The idea that plants would be efficient, frugal or optimised echoes the recurrent semantics of ‘blueprint’ and ‘program’ in molecular genetics. However, when analysing plants with quantitative approaches and systems thinking, we instead find that plants are the results of stochastic processes with many inefficiencies, incoherence or delays fuelling their robustness. If one had to highlight the main value of quantitative biology, this could be it: plants are robust systems because they are not efficient. Such systemic insights extend to the way we conduct plant research and opens plant science publication to a much broader framework.

The United States National Science and Technology Council has made a call for improving STEM (Science, Technology, Engineering, and Mathematics) education at the convergence of science, technology, engineering, and mathematics. The National Science Foundation (NSF) views convergence as the merging of ideas, approaches, and technologies from widely diverse fields of knowledge to stimulate innovation and discovery. Teaching convergency requires moving to the transdisciplinary level of integration where there is deep integration of skills, disciplines, and knowledge to solve a challenging real-world problem. Here we present a summary on convergence and transdisciplinary teaching. We then provide examples of convergence and transdisciplinary teaching in plant biology, and conclude by discussing limitations to contemporary conceptions of convergency and transdisciplinary STEM.

Cell-based, mathematical models helpmake sense of morphogenesis—i.e. cells organizing intoshape and pattern—by capturing cell behavior in simple, purelydescriptive models. Cell-based models then predict thetissue-level patterns the cells produce collectively. The firststep in a cell-based modeling approach is to isolatesub-processes, e.g. the patterning capabilities of one or afew cell types in cell cultures. Cell-based models can thenidentify the mechanisms responsible for patterning in vitro.This review discusses two cell culture models of morphogenesisthat have been studied using this combinedexperimental-mathematical approach: chondrogenesis (cartilagepatterning) and vasculogenesis (de novo blood vessel growth). Inboth these systems, radically different models can equallyplausibly explain the in vitro patterns. Quantitativedescriptions of cell behavior would help choose betweenalternative models. We will briefly review the experimentalmethodology (microfluidics technology and traction forcemicroscopy) used to measure responses of individual cells to theirmicro-environment, including chemical gradients, physical forcesand neighboring cells. We conclude by discussing how to includequantitative cell descriptions into a cell-based model: theCellular Potts model.