Bistability and Stabilization of Human Visual Perception under Ambiguous Stimulation.

We discuss a computational model that describes stabilization of percept choices under intermittent viewing of an ambiguous visual stimulus at long stimulus intervals. Let T_off and T_on be the time that the stimulus is off and on, respectively. The behavior was studied by direct numerical simulation in a grid of (T_off, T_on) values in a 2007 paper of Noest, van Ee, Nijs, and van Wezel. They found that both alternating and repetitive sequences of percepts can appear stably, sometimes even for the same values of T_off and T_on. Longer T_off, however, always leads to a situation where, after transients, only repetitive sequences of percepts exist. We incorporate T_off and T_on explicitly as bifurcation parameters of an extended mathematical model of the perceptual choices. We elucidate the bifurcations of periodic orbits responsible for switching between alternating and repetitive sequences. We show that the stability borders of the alternating and repeating sequences in the (T_off, T_on) -parameter plane consist of curves of limit point and period-doubling bifurcations of periodic orbits. The stability regions overlap, resulting in a wedge with bistability of both sequences. We conclude by comparing our modeling results with the experimental results obtained by Noest, van Ee, Nijs, and van Wezel.

Recycling, clustering, and endocytosis jointly maintain PIN auxin carrier polarity at the plasma membrane.

Cell polarity reflected by asymmetric distribution of proteins at the plasma membrane is a fundamental feature of unicellular and multicellular organisms. It remains conceptually unclear how cell polarity is kept in cell wall-encapsulated plant cells. We have used super-resolution and semi-quantitative live-cell imaging in combination with pharmacological, genetic, and computational approaches to reveal insights into the mechanism of cell polarity maintenance in Arabidopsis thaliana. We show that polar-competent PIN transporters for the phytohormone auxin are delivered to the center of polar domains by super-polar recycling. Within the plasma membrane, PINs are recruited into non-mobile membrane clusters and their lateral diffusion is dramatically reduced, which ensures longer polar retention. At the circumventing edges of the polar domain, spatially defined internalization of escaped cargos occurs by clathrin-dependent endocytosis. Computer simulations confirm that the combination of these processes provides a robust mechanism for polarity maintenance in plant cells. Moreover, our study suggests that the regulation of lateral diffusion and spatially defined endocytosis, but not super-polar exocytosis have primary importance for PIN polarity maintenance.

Model-based analysis of Arabidopsis leaf epidermal cells reveals distinct division and expansion patterns for pavement and guard cells.

To efficiently capture sunlight for photosynthesis, leaves typically develop into a flat and thin structure. This development is driven by cell division and expansion, but the individual contribution of these processes is currently unknown, mainly because of the experimental difficulties to disentangle them in a developing organ, due to their tight interconnection. To circumvent this problem, we built a mathematic model that describes the possible division patterns and expansion rates for individual epidermal cells. This model was used to fit experimental data on cell numbers and sizes obtained over time intervals of 1 d throughout the development of the first leaf pair of Arabidopsis (Arabidopsis thaliana). The parameters were obtained by a derivative-free optimization method that minimizes the differences between the predicted and experimentally observed cell size distributions. The model allowed us to calculate probabilities for a cell to divide into guard or pavement cells, the maximum size at which it can divide, and its average cell division and expansion rates at each point during the leaf developmental process. Surprisingly, average cell cycle duration remained constant throughout leaf development, whereas no evidence for a maximum cell size threshold for cell division of pavement cells was found. Furthermore, the model predicted that neighboring cells of different sizes within the epidermis expand at distinctly different relative rates, which could be verified by direct observations. We conclude that cell division seems to occur independently from the status of cell expansion, whereas the cell cycle might act as a timer rather than as a size-regulated machinery.

Emergence of tissue polarization from synergy of intracellular and extracellular auxin signaling.

Plant development is exceptionally flexible as manifested by its potential for organogenesis and regeneration, which are processes involving rearrangements of tissue polarities. Fundamental questions concern how individual cells can polarize in a coordinated manner to integrate into the multicellular context. In canalization models, the signaling molecule auxin acts as a polarizing cue, and feedback on the intercellular auxin flow is key for synchronized polarity rearrangements. We provide a novel mechanistic framework for canalization, based on up-to-date experimental data and minimal, biologically plausible assumptions. Our model combines the intracellular auxin signaling for expression of PINFORMED (PIN) auxin transporters and the theoretical postulation of extracellular auxin signaling for modulation of PIN subcellular dynamics. Computer simulations faithfully and robustly recapitulated the experimentally observed patterns of tissue polarity and asymmetric auxin distribution during formation and regeneration of vascular systems and during the competitive regulation of shoot branching by apical dominance. Additionally, our model generated new predictions that could be experimentally validated, highlighting a mechanistically conceivable explanation for the PIN polarization and canalization of the auxin flow in plants.

Atypical E2F activity restrains APC/CCCS52A2 function obligatory for endocycle onset.

The endocycle represents an alternative cell cycle that is activated in various developmental processes, including placental formation, Drosophila oogenesis, and leaf development. In endocycling cells, mitotic cell cycle exit is followed by successive doublings of the DNA content, resulting in polyploidy. The timing of endocycle onset is crucial for correct development, because polyploidization is linked with cessation of cell division and initiation of terminal differentiation. The anaphase-promoting complex/cyclosome (APC/C) activator genes CDH1, FZR, and CCS52 are known to promote endocycle onset in human, Drosophila, and Medicago species cells, respectively; however, the genetic pathways governing development-dependent APC/C(CDH1/FZR/CCS52) activity remain unknown. We report that the atypical E2F transcription factor E2Fe/DEL1 controls the expression of the CDH1/FZR orthologous CCS52A2 gene from Arabidopsis thaliana. E2Fe/DEL1 misregulation resulted in untimely CCS52A2 transcription, affecting the timing of endocycle onset. Correspondingly, ectopic CCS52A2 expression drove cells into the endocycle prematurely. Dynamic simulation illustrated that E2Fe/DEL1 accounted for the onset of the endocycle by regulating the temporal expression of CCS52A2 during the cell cycle in a development-dependent manner. Analogously, the atypical mammalian E2F7 protein was associated with the promoter of the APC/C-activating CDH1 gene, indicating that the transcriptional control of APC/C activator genes by atypical E2Fs might be evolutionarily conserved.

Bifurcation software in Matlab with applications in neuronal modeling.

Many biological phenomena, notably in neuroscience, can be modeled by dynamical systems. We describe a recent improvement of a Matlab software package for dynamical systems with applications to modeling single neurons and all-to-all connected networks of neurons. The new software features consist of an object-oriented approach to bifurcation computations and the partial inclusion of C-code to speed up the computation. As an application, we study the origin of the spiking behaviour of neurons when the equilibrium state is destabilized by an incoming current. We show that Class II behaviour, i.e. firing with a finite frequency, is possible even if the destabilization occurs through a saddle-node bifurcation. Furthermore, we show that synchronization of an all-to-all connected network of such neurons with only excitatory connections is also possible in this case.

WOX5-IAA17 feedback circuit-mediated cellular auxin response is crucial for the patterning of root stem cell niches in Arabidopsis.

In plants, the patterning of stem cell-enriched meristems requires a graded auxin response maximum that emerges from the concerted action of polar auxin transport, auxin biosynthesis, auxin metabolism, and cellular auxin response machinery. However, mechanisms underlying this auxin response maximum-mediated root stem cell maintenance are not fully understood. Here, we present unexpected evidence that WUSCHEL-RELATED HOMEOBOX 5 (WOX5) transcription factor modulates expression of auxin biosynthetic genes in the quiescent center (QC) of the root and thus provides a robust mechanism for the maintenance of auxin response maximum in the root tip. This WOX5 action is balanced through the activity of indole-3-acetic acid 17 (IAA17) auxin response repressor. Our combined genetic, cell biology, and computational modeling studies revealed a previously uncharacterized feedback loop linking WOX5-mediated auxin production to IAA17-dependent repression of auxin responses. This WOX5-IAA17 feedback circuit further assures the maintenance of auxin response maximum in the root tip and thereby contributes to the maintenance of distal stem cell (DSC) populations. Our experimental studies and in silico computer simulations both demonstrate that the WOX5-IAA17 feedback circuit is essential for the maintenance of auxin gradient in the root tip and the auxin-mediated root DSC differentiation.

Feedback models for polarized auxin transport: an emerging trend.

The phytohormone auxin is vital to plant growth and development. A unique property of auxin among all other plant hormones is its cell-to-cell polar transport that requires activity of polarly localized PIN-FORMED (PIN) auxin efflux transporters. Despite the substantial molecular insight into the cellular PIN polarization, the mechanistic understanding for developmentally and environmentally regulated PIN polarization is scarce. The long-standing belief that auxin modulates its own transport by means of a positive feedback mechanism has inspired both experimentalists and theoreticians for more than two decades. Recently, theoretical models for auxin-dependent patterning in plants include the feedback between auxin transport and the PIN protein localization. These computer models aid to assess the complexity of plant development by testing and predicting plausible scenarios for various developmental processes that occur in planta. Although the majority of these models rely on purely heuristic principles, the most recent mechanistic models tentatively integrate biologically testable components into known cellular processes that underlie the PIN polarity regulation. The existing and emerging computational approaches to describe PIN polarization are presented and discussed in the light of recent experimental data on the PIN polar targeting.

Prototype cell-to-cell auxin transport mechanism by intracellular auxin compartmentalization.

Carrier-dependent, intercellular auxin transport is central to the developmental patterning of higher plants (tracheophytes). The evolution of this polar auxin transport might be linked to the translocation of some PIN auxin efflux carriers from their presumably ancestral localization at the endoplasmic reticulum (ER) to the polar domains at the plasma membrane. Here we propose an eventually ancient mechanism of intercellular auxin distribution by ER-localized auxin transporters involving intracellular auxin retention and switch-like release from the ER. The proposed model integrates feedback circuits utilizing the conserved nuclear auxin signaling for the regulation of PIN transcription and a hypothetical ER-based signaling for the regulation of PIN-dependent transport activity at the ER. Computer simulations of the model revealed its plausibility for generating auxin channels and localized auxin maxima highlighting the possibility of this alternative mechanism for polar auxin transport.