Author response: Computational modeling and quantitative physiology reveal central parameters for brassinosteroid-regulated early cell physiological processes linked to elongation growth of the Arabidopsis root
2022-05-19

Article Figures and data Abstract Editor's evaluation Introduction Results Discussion Methods and materials Appendix 1 Data availability References Decision letter Author response Article and author information Metrics Abstract Brassinosteroids (BR) are key hormonal regulators of plant development. However, whereas the individual components of BR perception and signaling are well characterized experimentally, the question of how they can act and whether they are sufficient to carry out the critical function of cellular elongation remains open. Here, we combined computational modeling with quantitative cell physiology to understand the dynamics of the plasma membrane (PM)-localized BR response pathway during the initiation of cellular responses in the epidermis of the Arabidopsis root tip that are be linked to cell elongation. The model, consisting of ordinary differential equations, comprises the BR-induced hyperpolarization of the PM, the acidification of the apoplast and subsequent cell wall swelling. We demonstrate that the competence of the root epidermal cells for the BR response predominantly depends on the amount and activity of H+-ATPases in the PM. The model further predicts that an influx of cations is required to compensate for the shift of positive charges caused by the apoplastic acidification. A potassium channel was subsequently identified and experimentally characterized, fulfilling this function. Thus, we established the landscape of components and parameters for physiological processes potentially linked to cell elongation, a central process in plant development. Editor's evaluation The manuscript by Grosseholz et al. addresses a so far much overlooked aspect in plant hormone signalling systems, namely how components primarily identified by genetic means jointly regulate plant root physiology. The authors demonstrate a relevant effect of Brassinosteroid signalling on the control of root cell elongation in Arabidopsis. They used an elegant combination of (electro)physiology, computer modelling and confocal microscopy to reveal molecular candidates linking BR perception to fine-tuning of cell elongation through ion fluxes. https://doi.org/10.7554/eLife.73031.sa0 Decision letter Reviews on Sciety eLife's review process Introduction Brassinosteroids (BRs) are plant steroid hormones that regulate a great variety of physiological and developmental processes including elongation growth as well as environmental adaptations (Müssig et al., 2002; Clouse, 2002; Lv and Li, 2020; Wolf, 2020). To achieve this, BR signal transduction is closely linked with a multitude of other signaling pathways (Lv and Li, 2020). The canonical sequence of BR perception and signal transduction, which also leads to cell elongation, is mediated by the plasma membrane (PM)-resident, nanoscale-organized receptor kinase brassinosteroid-insensitive 1 (BRI1) and its co-receptor BRI1-activating kinase 1 (BAK1) as central elements (Bücherl et al., 2013; Bücherl et al., 2017; Lv and Li, 2020; Wolf, 2020). The binding of BR to the receptor's extracellular domain results in the re-arrangement of several BRI1-associated proteins. This involves the release of inhibitory mechanisms that include BRI1 kinase inhibitor 1 (BKI1) and BAK1-interacting receptor like kinase 3 (BIR3) and leads to the stabilization of BRI1/BAK1 association followed by a variety of auto- and trans-phosphorylation events of their cytoplasmic domains. This cascade of events eventually results in the establishment of the fully active BRI1 receptor complex (Bücherl et al., 2013; Bücherl et al., 2017). Once the active complex is established, the BR response is proposed to divide into two distinct downstream pathways to trigger molecular and physiological processes, which can be linked to cell elongation and differ in their kinetic properties (Clouse, 2002; Clouse, 2011; Vukašinović et al., 2021): A long-term (hours to days) gene regulatory pathway leading to extensive transcriptional reprogramming that is realized via the kinase Brassinosteroid Insensitive 2 (BIN2), the key transcription factors brassinazole resistant 1 (BZR1) and BR insensitive EMS suppressor 1 (BES1). The gene regulatory pathway is linked to cell wall remodeling as well as the extent and correct timing of anisotropic cell growth (Lv and Li, 2020; Fridman et al., 2021; Graeff et al., 2021). Physiological work in the past already suggested the second, short-term pathway is proposed to occur in PM-resident, nano-organized BRI1 complexes (Cerana et al., 1983; Cerana et al., 1984; Romani et al., 1983; Mandava, 1988). The response takes place in a matter of a few minutes and leads to the upregulation of the major proton pumping ATPases (AHA1, AHA2) (Figure 1; Elgass et al., 2009; Caesar et al., 2011). The activation of AHAs involves their interaction with BRI1 and BAK1, is BRI1 kinase activity-dependent (Caesar et al., 2011; Ladwig et al., 2015) and occurs very likely via rapid phosphorylation (within 5 min) of threonine and serine residues in the AHAs' large cytoplasmic domain (Lin et al., 2015; Witthöft et al., 2011). The BR-enhanced activity of AHAs induces the acidification of the apoplastic space, hyperpolarization of the PM's membrane potential (Em) and cell wall swelling within 10 min after BR application (Elgass et al., 2009; Caesar et al., 2011; Witthöft et al., 2011; Witthöft and Harter, 2011). The functional link between these BR-regulated cellular responses and AHA activity was proven by the inhibition or constitutive activation of the pump, leading either to the blocking of the reactions or their activation in the absence of BR (Caesar et al., 2011). Figure 1 Download asset Open asset Schematic overview of the key constituents and processes of the plasma membrane-associated fast BR response pathway initiating early steps in cell elongation, here represented by brassinolide (BL). (A) Inactive state: Co-localizing in a preformed nano-orgnaized complex, the inhibitors BKI1, BIK1 and BIR3 suppresses the activity of BRI1 in the absence of BL keeping the activity of H+-ATPases AHA1 and 2 at basic levels. By interaction with BAK1, BIR3 blocks the access of the co-receptor to BRI1. (B) Active state: Upon BL-binding to the receptor, the inhibitory mechanisms of BKI1, BIK1 and BIR3 on BRI1 and BAK1 are released causing the formation of the active BRI1/BAK1 complex. The complex enhances the AHA activity resulting in cell wall acidification, plasma membrane hyperpolarization and eventually onset of cell elongation. These key constituents and qualitatively described processes were used for the initial establishment of the computational model at cellular. The cell wall swelling, thus the incorporation of water in the wall matrix, is mediated by the loosening of the walls rigidity via the activation of acidic pH-dependent, apoplast-resident enzymes regulating wall extensibility (Cosgrove, 2000). According to the acid-growth theory (Hager, 2003), the low pH-induced enzymatic loosening of the cell wall, often paralleled by the accumulation of osmotically active substances inside the cell, causes a water potential difference between the extracellular space and the protoplast, the uptake of water and eventually the onset of cell elongation (Palmgren et al., 2009; Regenberg et al., 1995; Baekgaard et al., 2005; Phyo et al., 2019). This sequence of short- and long-term signaling and reaction pathways allows for instance root cells in the elongation zone (EZ) to grow four times their size in the meristematic zone (MZ) with a growth rate of up to 0.7 μm min–1(Fasano et al., 2001; Verbelen et al., 2006). Comparable growth rates were reported for hypocotyl cells of dark-grown Arabidopsis seedlings upon application of BR (Minami et al., 2019). While the activation of the pathway is well understood qualitatively, the information on the inactivation of the pathway is currently still sparse. The receptor BRI1 autophosphorylates at the residue S891, which inhibits the receptor activity (Oh et al., 2012). However, the time-scale of this phosphorylation is very slow, as it increases over the course of 12 h after stimulation with BR. The dephosphorylation of this site is even slower, as residual phosphorylations can be detected 5 days after inhibiting BR synthesis using brassinazole (Oh et al., 2012). Despite the qualitative knowledge on the constituents, the BR perception and the canonical signaling events, the dynamics of the system as a whole have yet to be examined quantitatively in detail (Sankar et al., 2011; van Esse et al., 2013a; van Esse et al., 2012; van Esse et al., 2013b; Allen and Ptashnyk, 2017). Therefore, we employed computational modeling in combination with quantitative experimental data on the fast BR response pathway in the PM, focusing on the epidermal cells of the Arabidopsis root tip as the epidermis limits the rate of elongation (Hacham et al., 2011). The root tip is an excellent model system for such a combined study because cells there first undergo a phase of cell division in the MZ followed by a phase of growth in the EZ. The boundary from the MZ to the EZ is represented by the transition zone (TZ). The formation of the TZ is characterized by the cytokinin-induced expression of the AHA1 and AHA2 genes as a precondition for cell elongation in the EZ (Pacifici et al., 2018). However, BR is involved in the control of both cell division and cell elongation in the different zones, apparently also adding to the specific functional competence and behavior of the cells along the axis of the root tip. However, the molecular determinants and processes establishing this competence and their link to the cytokinin-caused gradient of growth competence are poorly understood in terms of their quantitative dynamics. This lack of knowledge virtually provokes the implementation of computational modeling. While computational modeling has been used frequently in biomedical research since the early 2000 s, its application to the plant field has started more recently (Hübner et al., 2011; Holzheu and Kummer, 2020). Here, the growth and development of the root tip has been of particular interest (Bruex et al., 2012; Muraro et al., 2016; Di Mambro et al., 2017; Rutten and Ten Tusscher, 2019; Salvi et al., 2020; Rutten and Ten Tusscher, 2021). Further computational studies in plants include the modeling of auxin signaling (Vernoux et al., 2011) and transport pattern (Band et al., 2014), and parts of the BR signaling (Sankar et al., 2011; van Esse et al., 2013a; van Esse et al., 2012; van Esse et al., 2013b; Allen and Ptashnyk, 2017). For instance, the modeling approach by van Esse et al. analyzed the link between the BR dose, gene expression and growth behavior in both the Arabidopsis root and shoot (van Esse et al., 2013a; van Esse et al., 2012; van Esse et al., 2013b). However, none of the previous modeling approaches has been able to truly quantitatively depict cellular responses, make clear predictions about the cellular behavior, limiting constituents or processes. In our study, we were able to determine how the constituents of the PM-resident fast BR response pathway work together and identified its rate-limiting elements applying an ordinary differential equations (ODE) approach. Substantiated by wet lab experiments, our computational approach led to a detailed kinetic model that describes the rapid cellular response and offers an explanation for the initiation of BR controlled differential growth behavior of the root cells on the basis of the differential AHA accumulation and activity. Furthermore, the model predicts the existence of a cation influx across the PM that is crucial for the apoplastic acidification and Em hyperpolarization, which was subsequently narrowed down experimentally. Lastly, the model shows how the extent of the BR response can be fine-tuned by the level of the BIR3 inhibitor. Our model proposes that the specific composition of the PM-resident nano-organized BRI1 complexes determines the competence of the root cells to initiate elongation in response to BR. Results A mathematical model of the fast BR response To analyze the important steps and factors of the cell-specific, fast BR response in the root tip, we developed a detailed mathematical model consisting of ODEs (Figure 2). The model comprises four cell compartments: the cytosol, the cell wall and the vacuole as three-dimensional compartments as well as the PM as a two-dimensional compartment. The explicit inclusion of the PM as two-dimensional compartment was prompted by the fact that most components of the BR perception and initial processes are located in the membrane and the relevance of the membrane as a scaling factor in this kind of system (Holzheu et al., 2021). The compartment sizes were set such that the model initially describes the behavior of a single epidermis cell in the early EZ of the Arabidopsis root (Wilma van Esse et al., 2011) (see Appendix 1—table 1). Figure 2 Download asset Open asset Model structure of the fast BR response pathway of Arabidopsis thaliana. Compartments are indicated by grey boxes. Smaller molecules are indicated by circles, proteins by rectangles. Potential sites for protein modifications are indicated by the small circles on the boundaries of the rectangles. Reactions, including substrates and products, are indicated by the arrows, with the reaction numbers noted in the small box. Reactions, which are required for the model to return to the initial state, are drawn in grey. A bar at the bottom of the circle or rectangle indicates that this entity appears more than once in the scheme. The model captures the important components and steps of the fast BR response pathway focusing on protein interactions and post-translational modifications. We decided against the inclusion of data, which are derived from the genetic manipulation of component amounts or activity or are based on long-term incubation of BR biosynthesis inhibitors such as brassinazole. This kind of manipulation or long-term treatment are expected to have considerable effects on the physiological and developmental properties of the plant as a whole. The model is set up in a way that an equilibrium state was reached before the system is stimulated with the hormone by maintaining the system first without the hormone for 24 hr. In this state, only a few crucial reactions occur and carry a flux (v): the interaction between BIR3 and BAK1 (v7) and BIR3 and BRI1 (v6), the proton leak from the cell wall into the cytoplasm (v2) (Appendix 1—figure 1), the basal activity of the ATPases AHA1 and AHA2 (ν1) and the exchange of monovalent cations (here represented by potassium) between cytoplasm and cell wall (v4) and cytoplasm and vacuole (v5). Modeling the basal state as a physiologically plausible steady state ensures that the model describes the inactive state of the BR response pathway accurately and that the interactions of BIR3 with BAK1 and BRI1 are in an equilibrium. The hormone is added to the model by an event triggered at 24 h. According to the current state of knowledge, this initiates a number of molecular processes in the PM that occur almost simultaneously (Figure 2): binding of BL to BRI1 (v9), the loss of BRI1 inhibition by its C-terminus (v12), the release of BKI1 and BIK1 after phosphorylation (v10 and v11, respectively) as well as the release of BIR3 from BAK1, the establishment of the BAK1-BRI1 interaction via BR (v13), and the auto- and transphosphorylation of BAK1 and BRI1 (v14). These spatial rearrangements and post-translational modifications result in the active form of the BRI1 receptor complex, which immediately stimulates the activity of H+-ATPases very likely by phosphorylation (Lin et al., 2015) (v15). Further signaling events occur later in time and include differential gene expression (Lv and Li, 2020). However, these late events were not considered here for our modeling approach. The main cell physiological output of this early sequence of events is the acidification of the apoplastic space, the hyperpolarization of the Em and the swelling of the cell wall. The Em is calculated based on the net change in charge distribution of protons and potassium across the PM, the specific capacitance of the plasma membrane (White et al., 1999) and the membrane surface (Wilma van Esse et al., 2011) (see Appendix 1—table 1). However, combining the available information derived from the literature resulted in preliminary model draft that was not able to reproduce the measured experimental data, for instance regarding the Em hyperpolarization. Without a mechanism to balance out the shift in charge distribution caused by the transported protons, even a modest acidification of the apoplast from a pH of 5.4–5.0 will result in a non-physiological membrane hyperpolarization (Sondergaard et al., 2004) (see: Appendix 1 - example calculation of Em and pH change). Consequently, we postulated a cation influx in the model (here represented by potassium) that starts upon activation of the BRI1 complex (v16) and is driven by the Em (v3). However, in order to accurately model and simulate the fast BR response pathway, we needed more experimental data about the PM-based BRI1 response module. Any remaining unknown model parameters were estimated based on experimental data of the cell wall acidification (this study), Em hyperpolarization (Caesar et al., 2011) and the qualitative overexpression behavior of BIR3 (Imkampe et al., 2017). To account for non-identifiable parameters, we investigated the parameter space by computing several independent model parameterizations that describe the experimental data equally well. All computational analyses were run with each model of the resulting ensemble of structurally identical models (n=10) to ascertain consistent results across parameter space. Quantification of signaling components One experimental challenge for the refinement of the model was to quantify the central components of the pathway comprising predominantly BRI1, BAK1, BIR3 and AHA in the PM of epidermal cells of the root tip. Initially, we drew our attention on their steady-state transcript levels as they were determined by high-throughput single cell RNA-sequencing (scRNA-Seq) of the different Arabidopsis root cell types (Ma et al., 2020). Whereas BRI1 and BIR3 transcripts accumulated in all cell types of the root more or less equally and did not alter much in their amount during cell development along the root axis, AHA2 and to lesser extent also AHA1 transcripts were found predominantly in the epidermal cells and the root cortex (Figure 3A). During root development, the AHA2 transcript amount but not those of BRI1 and BIR3 started to increase strongly in the cortex and epidermis cells of the TZ and EZ (Figure 3B). This transcript pattern was less for AHA1 (Figure in with that the AHA1 is not very active in root epidermis This indicates that AHA1 not a in the control of cell et al., its transcript accumulation was already by the data not be used for BAK1 with to the expression along the root axis (Ma et al., 2020). Figure 3 Download asset Open asset The constituents of the BRI1 complex are in the epidermal cells along the Arabidopsis root tip (A) BIR3 and BRI1 transcript levels in the different cell types of the Arabidopsis root tip derived from data (Ma et al., 2020). The and together the epidermal (B) of and BRI1 transcript accumulation along the root tip (Ma et al., 2020). The transition from the MZ to the EZ is at a of of the indicated proteins in the plasma membrane of epidermal cells along the root tip The for and were from the literature (Wilma van Esse et al., 2011). The but here the of and molecules in the plasma membrane are the basis of the data we our further studies on the in protein of the of BRI1, BAK1, BIR3 and AHA2 in epidermal cells along the root tip For the PM of cells of the the amount of was already to receptor molecules and for to 5 by van Esse et al., To this data we quantitative for the of and in the epidermal root cells of Arabidopsis that the protein the et al., et al., 2017). these proteins carry the identical their can be set in to the to the receptor amount in the PM. The of was in μm at the epidermis along the root tip set of root tip is in Appendix 1—figure 2). The amount of and did not alter much in the epidermal cells in the MZ and early as it was reported before (Figure van Esse et al., 2011). A distribution was also for that to about inhibitor molecules PM in the MZ and in the early EZ (Figure In there was a gradient of along the root axis, low in the MZ AHA2 molecules PM but in the late EZ zone about 10 AHA2 molecules PM (Figure A of the amount was detected for the TZ (Figure the amount of and molecules was set in to the number molecules in the PM along the root tip axis, there was with to BIR3 about but a increase regarding AHA2 from in the MZ to up to 5 in the late EZ. Our refinement of previous data (Pacifici et al., by and quantitative demonstrate a of AHA2 protein accumulation with the onset of growth in the EZ. These results that there be a regulatory link between AHA2 protein accumulation and activity pattern and and BR-regulated root growth along the root tip This is plausible that AHA2 with BRI1 and BAK1 and is within 5 min upon BR treatment in (Caesar et al., 2011; Ladwig et al., 2015; et al., 2015; et al., 2018). Modeling predicts the H+-ATPases crucial regulators of the pH in the response To the we decided to the functional of AHA in the of BR-regulated signaling activity both experimentally and Here, we first to quantify and analyze the response in the EZ. the key components of the and nano-organized BRI1 complex (see Figure we were able to the model to a single epidermis cell in the EZ. By further using a combination of data and to the remaining unknown model parameters, we be able to analyze both the response and the dynamics of the BR signaling module. To the behavior and the response to BR stimulation experimentally, we on the a that into the plant cell wall and the of the pH at cellular et al., 2017; Appendix 1—figure To determine the apoplastic pH min after brassinolide application in the we a A of the apoplastic pH was already at a BL of that up to a of 10 (Figure of BL did not further increase the cellular response in the EZ. This behavior is by the model ensemble (Figure Figure Download asset Open asset The computational model quantitatively and captures the and of apoplastic acidification in Arabidopsis epidermal cells of the root EZ in response to (A) and behavior of apoplastic or BL incubation was for for the experimental data and the of different model parameterizations to the effect of BL on experimental data, were by an followed by a not by letter are The can be found in the data (B) and of apoplastic pH change in response to 10 a for the experimental data the data and for the of different model parameterizations on experimental data were as described in time course of wall swelling in response to 10 The of BL at time is indicated by the Figure data 1 data the of the experimental results of Figure Download To not only the response to BL stimulation in the EZ but also its we further of the apoplastic pH in response to 10 BL using Here, we a rapid acidification within 10 min after hormone application that is for the of the (Figure This was by the model ensemble (Figure the we also the cell wall swelling in the model that has been in response to BL application (Elgass et al., 2009; Caesar et al., 2011; Figure this model ensemble that describes the behavior of a single epidermis cell in the we analyzed the of the individual model components and parameters for the cell physiological response by the In this means that we calculated the change of the cell wall acidification in response to in model parameters the BR response stimulated with 10 BL for 5 min and The results of the for all model parameterizations (n=10) are in Figure a positive on the BR response is in is in and a is by with the the of the at the of the BR response the initial of the receptor BRI1 and the proton a large In parameters proton such as the of inhibition and the activity of the ATPases strongly controlled the early BR response across all model parameterizations (Figure The of the acidification min after BL application in a control of elements such as the inhibitory phosphorylation of the receptor (Appendix 1—figure the amount of proton as well as their activity our previous protein data a level of the receptor the AHA2 levels change this strongly the that the proton are the key elements that determine the competence of cells to to BR stimulation and with elongation Figure 5 Download asset Open asset calculation of of the cell wall acidification predicts AHA2 activity and molecules in the PM as well as BRI1 expression and molecules in the PM to be the factors for the competence of Arabidopsis epidermal root cells to in response to 5 min BL application for all parameterizations of the A positive is in a in and a in with the the of the Figure data 1 data the of the Download In the cells in the MZ a pH and less strongly to BR stimulation to the expression levels of To the behavior of an epidermis cell in the we the model ensemble to a single epidermis cell in the MZ in terms of protein and compartment