Tim Hohm

Phototropism: Translating light into directional growth

Phototropism allows plants to align their photosynthetic tissues with incoming light. The direction of incident light is sensed by the phototropin family of blue light photoreceptors (phot1 and phot2 in Arabidopsis), which are light-activated protein kinases. The kinase activity of phototropins and phosphorylation of residues in the activation loop of their kinase domains are essential for the phototropic response. These initial steps trigger the formation of the auxin gradient across the hypocotyl that leads to asymmetric growth. The molecular events between photoreceptor activation and the growth response are only starting to be elucidated. In this review, we discuss the major steps leading from light perception to directional growth concentrating on Arabidopsis. In addition, we highlight links that connect these different steps enabling the phototropic response.

A Dynamic Model for Stem Cell Homeostasis and Patterning in Arabidopsis Meristems

Plants maintain stem cells in their meristems as a source for new undifferentiated cells throughout their life. Meristems are small groups of cells that provide the microenvironment that allows stem cells to prosper. Homeostasis of a stem cell domain within a growing meristem is achieved by signalling between stem cells and surrounding cells. We have here simulated the origin and maintenance of a defined stem cell domain at the tip of Arabidopsis shoot meristems, based on the assumption that meristems are self-organizing systems. The model comprises two coupled feedback regulated genetic systems that control stem cell behaviour. Using a minimal set of spatial parameters, the mathematical model allows to predict the generation, shape and size of the stem cell domain, and the underlying organizing centre. We use the model to explore the parameter space that allows stem cell maintenance, and to simulate the consequences of mutations, gene misexpression and cell ablations.

Mirrored sampling and sequential selection for evolution strategies

This paper reveals the surprising result that a single-parent non-elitist evolution strategy (ES) can be locally faster than the (1+1)-ES. The result is brought about by mirrored sampling and sequential selection.With mirrored sampling, two offspring are generated symmetrically or mirrored with respect to their parent. In sequential selection, the offspring are evaluated sequentially and the iteration is concluded as soon as one offspring is better than the current parent. Both concepts complement each other well.We derive exact convergence rates of the (1, λ)-ES with mirrored sampling and/or sequential selection on the sphere model. The log-linear convergence of the ES is preserved. Both methods lead to an improvement and in combination the (1,4)-ES becomes about 10% faster than the (1+1)-ES. Naively implemented into the CMA-ES with recombination, mirrored sampling leads to a bias on the step-size. However, the (1,4)-CMA-ES with mirrored sampling and sequential selection is unbiased and appears to be faster, more robust, and as local as the (1+1)-CMA-ES.

Defining the Site of Light Perception and Initiation of Phototropism in Arabidopsis

Phototropism is an adaptive response allowing plants to optimize photosynthetic light capture. This is achieved by asymmetric growth between the shaded and lit sides of the stimulated organ. In grass seedlings, the site of phototropin-mediated light perception is distinct from the site of bending; however, in dicotyledonous plants (e.g., Arabidopsis), spatial aspects of perception remain debatable. We use morphological studies and genetics to show that phototropism can occur in the absence of the root, lower hypocotyl, hypocotyl apex, and cotyledons. Tissue-specific expression of the phototropin1 (phot1) photoreceptor demonstrates that light sensing occurs in the upper hypocotyl and that expression of phot1 in the hypocotyl elongation zone is sufficient to enable a normal phototropic response. Moreover, we show that efficient phototropism occurs when phot1 is expressed from endodermal, cortical, or epidermal cells and that its local activation rapidly leads to a global response throughout the seedling. We propose that spatial aspects in the steps leading from light perception to growth reorientation during phototropism differ between grasses and dicots. These results are important to properly interpret genetic experiments and establish a model connecting light perception to the growth response, including cellular and morphological aspects.

Plasma membrane H+-ATPase regulation is required for auxin gradient formation preceding phototropic growth

Phototropism is a growth response allowing plants to align their photosynthetic organs toward incoming light and thereby to optimize photosynthetic activity. Formation of a lateral gradient of the phytohormone auxin is a key step to trigger asymmetric growth of the shoot leading to phototropic reorientation. To identify important regulators of auxin gradient formation, we developed an auxin flux model that enabled us to test in silico the impact of different morphological and biophysical parameters on gradient formation, including the contribution of the extracellular space (cell wall) or apoplast. Our model indicates that cell size, cell distributions, and apoplast thickness are all important factors affecting gradient formation. Among all tested variables, regulation of apoplastic pH was the most important to enable the formation of a lateral auxin gradient. To test this prediction, we interfered with the activity of plasma membrane H+‐ATPases that are required to control apoplastic pH. Our results show that H+‐ATPases are indeed important for the establishment of a lateral auxin gradient and phototropism. Moreover, we show that during phototropism, H+‐ATPase activity is regulated by the phototropin photoreceptors, providing a mechanism by which light influences apoplastic pH.

Evolutionary Pareto-optimization of stably folding peptides

BackgroundAs a rule, peptides are more flexible and unstructured than proteins with their substantial stabilizing hydrophobic cores. Nevertheless, a few stably folding peptides have been discovered. This raises the question whether there may be more such peptides that are unknown as yet. These molecules could be helpful in basic research and medicine.ResultsAs a method to explore the space of conformationally stable peptides, we have developed an evolutionary algorithm that allows optimization of sequences with respect to several criteria simultaneously, for instance stability, accessibility of arbitrary parts of the peptide, etc. In a proof-of-concept experiment we have perturbed the sequence of the peptide Villin Headpiece, known to be stable in vitro. Starting from the perturbed sequence we applied our algorithm to optimize peptide stability and accessibility of a loop. Unexpectedly, two clusters of sequences were generated in this way that, according to our criteria, should form structures with higher stability than the wild-type. The structures in one of the clusters possess a fold that markedly differs from the native fold of Villin Headpiece. One of the mutants predicted to be stable was selected for synthesis, its molecular 3D-structure was characterized by nuclear magnetic resonance spectroscopy, and its stability was measured by circular dichroism. Predicted structure and stability were in good agreement with experiment. Eight other sequences and structures, including five with a non-native fold are provided as bona fide predictions.ConclusionThe results suggest that much more conformationally stable peptides may exist than are known so far, and that small fold classes could comprise well-separated sub-folds.

A Multiobjective Evolutionary Method for the Design of Peptidic Mimotopes

Peptides that mimic protein epitopes are interesting drug candidates. However, the design of effective peptidic drugs is difficult for several reasons, such as the fast degradation of peptides, their high flexibility, and thus high entropy loss on binding to the target. We therefore propose an in silico method for the automated design of peptides that are optimal with respect to several objectives. We present a Pareto-based multiobjective evolutionary algorithm for in silico peptide design. Using a simple molecular model, we apply the method to the design of peptides that (a) mimic antibody epitopes of the proteins thrombin and blood coagulation factor VIII, respectively, that (b) are short, and (c) are conformationally stable.

Modeling the shoot apical meristem in A. thaliana: parameter estimation for spatial pattern formation

Understanding the self-regulatory mechanisms controlling the spatial and temporal structure of multicellular organisms represents one of the major challenges in molecular biology. In the context of plants, shoot apical meristems (SAMs), which are populations of dividing, undifferentiated cells that generate organs at the tips of stems and branches throughout the life of a plant, are of particular interest and currently studied intensively. Here, one key goal is to identify the genetic regulatory network organizing the structure of a SAM and generating the corresponding spatial gene expression patterns. This paper addresses one step in the design of SAM models based on ordinary differential equations (ODEs): parameter estimation for spatial pattern formation. We assume that the topology of the genetic regulatory network is given, while the parameters of an ODE system need to be determined such that a particular stable pattern over the SAM cell population emerges. To this end, we propose an evolutionary algorithm-based approach and investigate different ways to improve the efficiency of the search process. Preliminary results are presented for the Brusselator, a well-known reaction-diffusion system.

Investigating Coverage and Connectivity Trade-offs in Wireless Sensor Networks: The Benefits of MOEAs

How many wireless sensor nodes should be used and where should they be placed in order to form an optimal wireless sensor network (WSN) deployment? This is a difficult question to answer for a decision maker due to the conflicting objectives of deployment costs and wireless transmission reliability. Here, we address this problem using a multiobjective evolutionary algorithm (MOEA) which allows to identify the trade-offs between low-cost and highly reliable deployments–providing the decision maker with a set of good solutions to choose from. For the MOEA, we use an off-the-shelf selector and propose a problem-specific representation, an initialization scheme, and variation operators. The resulting algorithm is applied to a test deployment scenario to show the usefulness of the approach in terms of decision making.

Multicellular pattern formation

Understanding the self-regulatory mechanisms controlling the spatial and temporal structure of multicellular organisms represents one of the major challenges in molecular biology. Although high-throughput data have become available with the advances in experimental technologies at a large scale, measuring gene expression levels at a high spatial resolution remains extremely difficult. As a result, the study of genetic regulatory networks in the light of spatial expression patterns still relies mainly on qualitative data. This leads to the question of how to fit the parameters of a gene regulatory network model such that a purely qualitatively defined pattern can be reproduced. This article addresses this issue and presents a general approach to generate patterns reflecting basic geometric shapes. In combination with an appropriate ordinary differential equation (ODE)-based modeling and simulation framework, a formalism to quantify qualitative patterns and integrate this concept into an evolutionary algorithm for parameter estimation is presented and tested for stripe-like patterns on two test systems.