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TIR1 AFB Aux IAA auxin perception mediates rapid cell wall acidification and growth of Arabidopsis hypocotyls
Despite being composed of immobile cells, plants reorient along directional stimuli. The hormone auxin is redistributed in stimulated organs leading to differential growth and bending. Auxin application triggers rapid cell wall acidification and elongation of aerial organs of plants, but the molecular players mediating these effects are still controversial. Here we use genetically-encoded pH and auxin signaling sensors, pharmacological and genetic manipulations available for Arabidopsis etiolated hypocotyls to clarify how auxin is perceived and the downstream growth executed. We show that auxin-induced acidification occurs by local activation of H+-ATPases, which in the context of gravity response is restricted to the lower organ side. This auxin-stimulated acidification and growth require TIR1/AFB-Aux/IAA nuclear auxin perception. In addition, auxin-induced gene transcription and specifically SAUR proteins are crucial downstream mediators of this growth. Our study provides strong experimental support for the acid growth theory and clarified the contribution of the upstream auxin perception mechanisms
Towards a runtime comparison of natural and artificial evolution
Evolutionary algorithms (EAs) form a popular optimisation paradigm inspired by natural evolution. In recent years the field of evolutionary computation has developed a rigorous analytical theory to analyse the runtimes of EAs on many illustrative problems. Here we apply this theory to a simple model of natural evolution. In the Strong Selection Weak Mutation (SSWM) evolutionary regime the time between occurrences of new mutations is much longer than the time it takes for a mutated genotype to take over the population. In this situation, the population only contains copies of one genotype and evolution can be modelled as a stochastic process evolving one genotype by means of mutation and selection between the resident and the mutated genotype. The probability of accepting the mutated genotype then depends on the change in fitness. We study this process, SSWM, from an algorithmic perspective, quantifying its expected optimisation time for various parameters and investigating differences to a similar evolutionary algorithm, the well-known (1+1) EA. We show that SSWM can have a moderate advantage over the (1+1) EA at crossing fitness valleys and study an example where SSWM outperforms the (1+1) EA by taking advantage of information on the fitness gradient
Vascular cambium regeneration and vessel formation in wounded inflorescence stems of Arabidopsis
Synchronized tissue polarization during regeneration or de novo vascular tissue formation is a plant-specific example of intercellular communication and coordinated development. According to the canalization hypothesis, the plant hormone auxin serves as polarizing signal that mediates directional channel formation underlying the spatio-temporal vasculature patterning. A necessary part of canalization is a positive feedback between auxin signaling and polarity of the intercellular auxin flow. The cellular and molecular mechanisms of this process are still poorly understood, not the least, because of a lack of a suitable model system. We show that the main genetic model plant, Arabidopsis (Arabidopsis thaliana) can be used to study the canalization during vascular cambium regeneration and new vasculature formation. We monitored localized auxin responses, directional auxin-transport channels formation, and establishment of new vascular cambium polarity during regenerative processes after stem wounding. The increased auxin response above and around the wound preceded the formation of PIN1 auxin transporter-marked channels from the primarily homogenous tissue and the transient, gradual changes in PIN1 localization preceded the polarity of newly formed vascular tissue. Thus, Arabidopsis is a useful model for studies of coordinated tissue polarization and vasculature formation after wounding allowing for genetic and mechanistic dissection of the canalization hypothesis
Beyond the French flag model: Exploiting spatial and gene regulatory interactions for positional information
A crucial step in the early development of multicellular organisms involves the establishment of spatial patterns of gene expression which later direct proliferating cells to take on different cell fates. These patterns enable the cells to infer their global position within a tissue or an organism by reading out local gene expression levels. The patterning system is thus said to encode positional information, a concept that was formalized recently in the framework of information theory. Here we introduce a toy model of patterning in one spatial dimension, which can be seen as an extension of Wolpert's paradigmatic "French Flag" model, to patterning by several interacting, spatially coupled genes subject to intrinsic and extrinsic noise. Our model, a variant of an Ising spin system, allows us to systematically explore expression patterns that optimally encode positional information. We find that optimal patterning systems use positional cues, as in the French Flag model, together with gene-gene interactions to generate combinatorial codes for position which we call "Counter" patterns. Counter patterns can also be stabilized against noise and variations in system size or morphogen dosage by longer-range spatial interactions of the type invoked in the Turing model. The simple setup proposed here qualitatively captures many of the experimentally observed properties of biological patterning systems and allows them to be studied in a single, theoretically consistent framework
A central limit theorem for products of random matrices and GOE statistics for the Anderson model on long boxes
We consider products of random matrices that are small, independent identically distributed perturbations of a fixed matrix (Formula presented.). Focusing on the eigenvalues of (Formula presented.) of a particular size we obtain a limit to a SDE in a critical scaling. Previous results required (Formula presented.) to be a (conjugated) unitary matrix so it could not have eigenvalues of different modulus. From the result we can also obtain a limit SDE for the Markov process given by the action of the random products on the flag manifold. Applying the result to random Schrödinger operators we can improve some results by Valko and Virag showing GOE statistics for the rescaled eigenvalue process of a sequence of Anderson models on long boxes. In particular, we solve a problem posed in their work
Optogenetic control of nodal signaling reveals a temporal pattern of nodal signaling regulating cell fate specification during gastrulation
During metazoan development, the temporal pattern of morphogen signaling is critical for organizing cell fates in space and time. Yet, tools for temporally controlling morphogen signaling within the embryo are still scarce. Here, we developed a photoactivatable Nodal receptor to determine how the temporal pattern of Nodal signaling affects cell fate specification during zebrafish gastrulation. By using this receptor to manipulate the duration of Nodal signaling in vivo by light, we show that extended Nodal signaling within the organizer promotes prechordal plate specification and suppresses endoderm differentiation. Endoderm differentiation is suppressed by extended Nodal signaling inducing expression of the transcriptional repressor goosecoid (gsc) in prechordal plate progenitors, which in turn restrains Nodal signaling from upregulating the endoderm differentiation gene sox17 within these cells. Thus, optogenetic manipulation of Nodal signaling identifies a critical role of Nodal signaling duration for organizer cell fate specification during gastrulation
FlexMolds: Automatic design of flexible shells for molding
We present FlexMolds, a novel computational approach to automatically design flexible, reusable molds that, once 3D printed, allow us to physically fabricate, by means of liquid casting, multiple copies of complex shapes with rich surface details and complex topology. The approach to design such flexible molds is based on a greedy bottom-up search of possible cuts over an object, evaluating for each possible cut the feasibility of the resulting mold. We use a dynamic simulation approach to evaluate candidate molds, providing a heuristic to generate forces that are able to open, detach, and remove a complex mold from the object it surrounds. We have tested the approach with a number of objects with nontrivial shapes and topologies
Scale-invariant systems realize nonlinear differential operators
In recent years, several biomolecular systems have been shown to be scale-invariant (SI), i.e. to show the same output dynamics when exposed to geometrically scaled input signals (u -> pu, p > 0) after pre-adaptation to accordingly scaled constant inputs. In this article, we show that SI systems-as well as systems invariant with respect to other input transformations-can realize nonlinear differential operators: when excited by inputs obeying functional forms characteristic for a given class of invariant systems, the systems' outputs converge to constant values directly quantifying the speed of the input
Centering the organizing center in the Arabidopsis thaliana shoot apical meristem by a combination of cytokinin signaling and self-organization
Plants have the ability to continously generate new organs by maintaining populations of stem cells throught their lives. The shoot apical meristem (SAM) provides a stable environment for the maintenance of stem cells. All cells inside the SAM divide, yet boundaries and patterns are maintained. Experimental evidence indicates that patterning is independent of cell lineage, thus a dynamic self-regulatory mechanism is required. A pivotal role in the organization of the SAM is played by the WUSCHEL gene (WUS). An important question in this regard is that how WUS expression is positioned in the SAM via a cell-lineage independent signaling mechanism. In this study we demonstrate via mathematical modeling that a combination of an inhibitor of the Cytokinin (CK) receptor, Arabidopsis histidine kinase 4 (AHK4) and two morphogens originating from the top cell layer, can plausibly account for the cell lineage-independent centering of WUS expression within SAM. Furthermore, our laser ablation and microsurgical experiments support the hypothesis that patterning in SAM occurs at the level of CK reception and signaling. The model suggests that the interplay between CK signaling, WUS/CLV feedback loop and boundary signals can account for positioning of the WUS expression, and provides directions for further experimental investigation
Comparing reactive and memory-one strategies of direct reciprocity
Direct reciprocity is a mechanism for the evolution of cooperation based on repeated interactions. When individuals meet repeatedly, they can use conditional strategies to enforce cooperative outcomes that would not be feasible in one-shot social dilemmas. Direct reciprocity requires that individuals keep track of their past interactions and find the right response. However, there are natural bounds on strategic complexity: Humans find it difficult to remember past interactions accurately, especially over long timespans. Given these limitations, it is natural to ask how complex strategies need to be for cooperation to evolve. Here, we study stochastic evolutionary game dynamics in finite populations to systematically compare the evolutionary performance of reactive strategies, which only respond to the co-player's previous move, and memory-one strategies, which take into account the own and the co-player's previous move. In both cases, we compare deterministic strategy and stochastic strategy spaces. For reactive strategies and small costs, we find that stochasticity benefits cooperation, because it allows for generous-tit-for-tat. For memory one strategies and small costs, we find that stochasticity does not increase the propensity for cooperation, because the deterministic rule of win-stay, lose-shift works best. For memory one strategies and large costs, however, stochasticity can augment cooperation