A Local Auxin Gradient Regulates Root Cap Self-Renewal and Size Homeostasis.

Organ size homeostasis, compensatory growth to replace lost tissue, requires constant measurement of size and adjustment of growth rates. Morphogen gradients control organ and tissue sizes by regulating stem cell activity, cell differentiation, and removal in animals [1-3]. In plants, control of tissue size is of specific importance in root caps to protect the growing root tip from mechanical damage [4]. New root cap tissue is formed by the columella and lateral root-cap-epidermal stem cells, whose activity is regulated through non-dividing niche-like cells, the quiescent center (QC) [4, 5]. Columella daughter cells in contact with the QC retain the potency to divide, while derivatives oriented toward the mature cap undergo differentiation. The outermost columella layers are sequentially separated from the root body, involving remodeling of cell walls [6]. Factors regulating the balance between cell division, elongation, and separation to keep root cap size constant are currently unknown [4]. Here, we report that stem cell proliferation induced cell separation at the periphery of the root cap, resulting in tissue size homeostasis. An auxin response gradient with a maximum in the QC and a minimum in the detaching layer was established prior to the onset of cell separation. In agreement with a mathematical model, tissue size was positively regulated by the amount of auxin released from the source. Auxin transporters localized non-polarly to plasma membranes of the inner cap, partly isolating separating layers from the auxin source. Together, these results are in support of an auxin gradient measuring and regulating tissue size.

Establishment of Photosynthesis through Chloroplast Development Is Controlled by Two Distinct Regulatory Phases.

Chloroplasts develop from undifferentiated proplastids present in meristematic tissue. Thus, chloroplast biogenesis is closely connected to leaf development, which restricts our ability to study the process of chloroplast biogenesis per se. As a consequence, we know relatively little about the regulatory mechanisms behind the establishment of the photosynthetic reactions and how the activities of the two genomes involved are coordinated during chloroplast development. We developed a single cell-based experimental system from Arabidopsis (Arabidopsis thaliana) with high temporal resolution allowing for investigations of the transition from proplastids to functional chloroplasts. Using this unique cell line, we could show that the establishment of photosynthesis is dependent on a regulatory mechanism involving two distinct phases. The first phase is triggered by rapid light-induced changes in gene expression and the metabolome. The second phase is dependent on the activation of the chloroplast and generates massive changes in the nuclear gene expression required for the transition to photosynthetically functional chloroplasts. The second phase also is associated with a spatial transition of the chloroplasts from clusters around the nucleus to the final position at the cell cortex. Thus, the establishment of photosynthesis is a two-phase process with a clear checkpoint associated with the second regulatory phase allowing coordination of the activities of the nuclear and plastid genomes.

A quantitative model of the phytochrome-PIF light signalling initiating chloroplast development.

The components required for photosynthesis are encoded in two separate genomes, the nuclear and the plastid. To address how synchronization of the two genomes involved can be attained in early light-signalling during chloroplast development we have formulated and experimentally tested a mathematical model simulating light sensing and the following signalling response. The model includes phytochrome B (PhyB), the phytochrome interacting factor 3 (PIF3) and putative regulatory targets of PIF3. Closed expressions of the phyB and PIF3 concentrations after light exposure are derived, which capture the relevant timescales in the response of genes regulated by PIF3. Sequence analysis demonstrated that the promoters of the nuclear genes encoding sigma factors (SIGs) and polymerase-associated proteins (PAPs) required for expression of plastid encoded genes, contain the cis-elements for binding of PIF3. The model suggests a direct link between light inputs via PhyB-PIF3 to the plastid transcription machinery and control over the expression of photosynthesis components both in the nucleus and in the plastids. Using a pluripotent Arabidopsis cell culture in which chloroplasts develop from undifferentiated proplastids following exposure to light, we could experimentally verify that the expression of SIGs and PAPs in response to light follow the calculated expression of a PhyB-PIF3 regulated gene.

Intrinsic phenotypic stability of a bi-stable auto regulatory gene.

Even under homogenous conditions clonal cells can assume different distinct states for generations to follow, also known as epigenetic inheritance. Such long periods of different phenotypic states can be formed due to the existence of more than one stable state in the molecule concentration, where the different states are explored through molecular fluctuations. By formulating a single reaction variable representing the birth and death of molecules, including transcription, translation and decay, we calculate the escape time from the phenotypic states attained from autocatalytic synthesis through a Fokker- Planck formulation and integration of an effective pseudo-potential. We calculate the stability of the phenotypic states both for cooperative binding feedback and dimer binding feedback, resulting in non-linear decay.

Transcription factor binding kinetics constrain noise suppression via negative feedback.

Negative autoregulation, where a transcription factor regulates its own expression by preventing transcription, is commonly used to suppress fluctuations in gene expression. Recent single molecule in vivo imaging has shown that it takes significant time for a transcription factor molecule to bind its chromosomal binding site. Given the slow association kinetics, transcription factor mediated feedback cannot at the same time be fast and strong. Here we show that with a limited association rate follows an optimal transcription factor binding strength where noise is maximally suppressed. At the optimal binding strength the binding site is free a fixed fraction of the time independent of the transcription factor concentration. One consequence is that high-copy number transcription factors should bind weakly to their operators, which is observed for transcription factors in Escherichia coli. The results demonstrate that a binding site's strength may be uncorrelated to its functional importance.

Fractal profit landscape of the stock market.

We investigate the structure of the profit landscape obtained from the most basic, fluctuation based, trading strategy applied for the daily stock price data. The strategy is parameterized by only two variables, p and q Stocks are sold and bought if the log return is bigger than p and less than -q, respectively. Repetition of this simple strategy for a long time gives the profit defined in the underlying two-dimensional parameter space of p and q. It is revealed that the local maxima in the profit landscape are spread in the form of a fractal structure. The fractal structure implies that successful strategies are not localized to any region of the profit landscape and are neither spaced evenly throughout the profit landscape, which makes the optimization notoriously hard and hypersensitive for partial or limited information. The concrete implication of this property is demonstrated by showing that optimization of one stock for future values or other stocks renders worse profit than a strategy that ignores fluctuations, i.e., a long-term buy-and-hold strategy.

Delay-induced anomalous fluctuations in intracellular regulation.

Direct negative feedback decreases fluctuations and is a ubiquitous mechanism for homoeostatic control. However, intracellular regulation frequently operates indirectly, resulting in delayed responses. Here we derive an analytical expression that quantifies the consequences from delayed negative feedback resulting from typical multistep synthesis pathways, for example, transcription or translation. We find that indirect feedback leads to more fluctuations than without feedback for intermediate delays, but surprisingly not for long delays. The anomalous fluctuations at intermediate delays emerge from positive correlations between the delayed regulatory events, and are shown to be equivalent to an increased stoichiometry in the synthesis of new molecules. The results primarily give us insight about the design principles of delayed stochastic control systems and why a fixed feedback delay gives more fluctuations than a broadly distributed feedback delay. It is also shown that the feedback delay of auto-repressed regulators can result in more sensitive regulation of downstream processes through stochastic focusing.

Costs and constraints from time-delayed feedback in small gene regulatory motifs.

The multistep character of transcription, translation, and protein modification inevitably leads to time delays between sensing gene regulatory signals and responding with changed concentrations of functional proteins. However, the interplay between the time-delayed and the stochastic nature of gene regulation has been poorly investigated. Here we present an extension of the linear noise approximation which makes it possible to estimate second moments--variances and covariances--of fluctuations around stationary states in time-delayed systems. The usefulness of the method is exemplified by analyzing two ubiquitous regulatory motifs. In the first system, we show that there is an optimal combination of transcriptional repression and direct product inhibition in determining the activity of an enzyme system. In particular, we demonstrate that direct product inhibition is necessary to avoid deleterious fluctuations in a system when the gene regulatory response is delayed. The second system is an anabolic motif where the substrate fluxes are balanced by time-delayed regulation responding to the substrate concentrations. The extended linear noise approximation makes it possible to show analytically that increased association rate between the substrates leads to a lower product flux because of increasing unbalance in substrate pools.

Modular gene expression in Poplar: a multilayer network approach.

By applying a multilayer network approach to an extensive set of Poplar microarray data, a genome-wide coexpression network has been detected and explored. Multilayer networks were generated from minimum spanning trees (MSTs) using Kruskal's algorithm from random jack-knife resamplings of half of the full data set. The final network is obtained from the union of all the generated MSTs. The gene expression correlations display a highly clustered topology, which is more pronounced when introducing links appearing in relatively few of the generated MSTs. The network also reveals a modular architecture, reflecting functional groups with relatively frequent gene-to-gene communication. Furthermore, the observed modular structure overlaps with different gene activities in different tissues, and closely related tissues show similar over- and/or under-expression patterns at the modular scale. It is shown that including links that appear in a few of the generated MSTs increases the information quality of the network. In other words, a link may be 'weak' because it reflects rare signaling events rather than merely a signal weakened by noise. The method allows, from comparisons of random 'null networks', tuning to maximize the information obtainable.

Integrated analysis of transcript, protein and metabolite data to study lignin biosynthesis in hybrid aspen.

Tree biotechnology will soon reach a mature state where it will influence the overall supply of fiber, energy and wood products. We are now ready to make the transition from identifying candidate genes, controlling important biological processes, to discovering the detailed molecular function of these genes on a broader, more holistic, systems biology level. In this paper, a strategy is outlined for informative data generation and integrated modeling of systematic changes in transcript, protein and metabolite profiles measured from hybrid aspen samples. The aim is to study characteristics of common changes in relation to genotype-specific perturbations affecting the lignin biosynthesis and growth. We show that a considerable part of the systematic effects in the system can be tracked across all platforms and that the approach has a high potential value in functional characterization of candidate genes.

Networking the seceder model: Group formation in social and economic systems.

The seceder model illustrates how the desire to be different from the average can lead to formation of groups in a population. We turn the original, agent based, seceder model into a model of network evolution. We find that the structural characteristics of our model closely match empirical social networks. Statistics for the dynamics of group formation are also given. Extensions of the model to networks of companies are also discussed.

Networking genetic regulation and neural computation: directed network topology and its effect on the dynamics.

Two different types of directed networks are investigated, transcriptional regulation networks and neural networks. The directed network structure is studied and is also shown to reflect the different processes taking place on the networks. The distribution of influence, identified as the the number of downstream vertices, are used as a tool for investigating random vertex removal. In the transcriptional regulation networks we observe that only a small number of vertices have a large influence. The small influences of most vertices limit the effect of a random removal to, in most cases, only a small fraction of vertices in the network. The neural network has a rather different topology with respect to the influence, which are large for most vertices. To further investigate the effect of vertex removal we simulate the biological processes taking place on the networks. Opposed to the presumed large effect of random vertex removal in the neural network, the high density of edges in conjunction with the dynamics used makes the change in the state of the system to be highly localized around the removed vertex.