A Two-Dimensional Simulation Model of the Bicoid Gradient in Drosophila

Background

Bicoid (Bcd) is a Drosophila morphogenetic protein responsible for patterning the anterior structures in embryos. Recent experimental studies have revealed important insights into the behavior of this morphogen gradient, making it necessary to develop a model that can recapitulate the biological features of the system, including its dynamic and scaling properties.

Methodology/Principal Findings

We present a biologically realistic 2-D model of the dynamics of the Bcd gradient in Drosophila embryos. This model is based on equilibrium binding of Bcd molecules to non-specific, low affinity DNA sites throughout the Drosophila genome. It considers both the diffusion media within which the Bcd gradient is formed and the dynamic and other relevant properties of bcd mRNA from which Bcd protein is produced. Our model recapitulates key features of the Bcd protein gradient observed experimentally, including its scaling properties and the stability of its nuclear concentrations during development. Our simulation model also allows us to evaluate the effects of other biological activities on Bcd gradient formation, including the dynamic redistribution of bcd mRNA in early embryos. Our simulation results suggest that, in our model, Bcd protein diffusion is important for the formation of an exponential gradient in embryos.

Conclusions/Significance

The 2-D model described in this report is a simple and versatile simulation procedure, providing a quantitative evaluation of the Bcd gradient system. Our results suggest an important role of Bcd binding to non-specific, low-affinity DNA sites in proper formation of the Bcd gradient in our model. They demonstrate that highly complex biological systems can be effectively modeled with relatively few parameters.     

Making space for criminalistics: Hans Gross and fin-de-siècle CSI

This article explores the articulation of a novel forensic object—the ‘crime scene’—and its corresponding expert—the investigating officer. Through a detailed engagement with the work of the late nineteenth-century Austrian jurist and criminalist Hans Gross, it analyses the dynamic and reflexive nature of this model of ‘CSI’, emphasising the material, physical, psychological and instrumental means through which the crime scene as a delineated space, and its investigator as a disciplined agent operating within it, jointly came into being. It has a further, historiographic, aim: to move away from the commonplace emphasis in histories of forensics on fin-de-siècle criminology and toward its comparatively under-explored contemporary, criminalistics. In so doing, it opens up new ways of thinking about the crime scene as a defining feature of our present-day forensic culture that recognise its historical contingency and the complex processes at work in its creation and development.     

Simple Quantitative PCR Approach to Reveal Naturally Occurring and Mutation-Induced Repetitive Sequence Variation on the Drosophila Y Chromosome

Heterochromatin is a significant component of the human genome and the genomes of most model organisms. Although heterochromatin is thought to be largely non-coding, it is clear that it plays an important role in chromosome structure and gene regulation. Despite a growing awareness of its functional significance, the repetitive sequences underlying some heterochromatin remain relatively uncharacterized. We have developed a real-time quantitative PCR-based method for quantifying simple repetitive satellite sequences and have used this technique to characterize the heterochromatic Y chromosome of Drosophila melanogaster. In this report, we validate the approach, identify previously unknown satellite sequence copy number polymorphisms in Y chromosomes from different geographic sources, and show that a defect in heterochromatin formation can induce similar copy number polymorphisms in a laboratory strain. These findings provide a simple method to investigate the dynamic nature of repetitive sequences and characterize conditions which might give rise to long-lasting alterations in DNA sequence.     

Flux module decomposition for parameter estimation in a multiple-feedback loop model of biochemical networks

Computer simulation is an important technique to capture the dynamics of biochemical networks. Since few quantitative values are measured in vivo, the values for unmeasured parameters should be estimated so that the simulation agrees with the experimental data. Considering the sparsity and error rates of experimentally measured data, the first thing is not to find a numerically exact and global solution but to explore a variety of the plausible parameter solutions. To find many plausible parameter solutions without any biases, we developed the two-phase search (TPS) method. However, calculation complexity makes it hard for TPS to optimize a large-scale dynamic model. In this study divide-and-conquer methods are used to solve this problem. The flux module decomposition (FMD) is first proposed that separates a complex, large-scale dynamic model into multiple flux modules without deteriorating its basic control architectures. FMD is combined with TPS, named FMD-TPS, to find many plausible parameter solutions for a dynamic model. To demonstrate the feasibility of FMD-TPS, it is applied to the E. coli ammonia assimilation system that consists of multiple-feedback loops. The variability of the solutions is verified by measuring the space distribution of the parameter solution vectors and by defining the binary vectors checking the consistency with biological behaviors. Compared with non-decomposition methods, FMD-TPS efficiently explored a variety of plausible parameter solutions that reproduce the dynamic behaviors in vivo.     

Kinetic modeling of the assembly, dynamic steady state, and contraction of the FtsZ ring in prokaryotic cytokinesis

Cytokinesis in prokaryotes involves the assembly of a polymeric ring composed of FtsZ protein monomeric units. The Z ring forms at the division plane and is attached to the membrane. After assembly, it maintains a stable yet dynamic steady state. Once induced, the ring contracts and the membrane constricts. In this work, we present a computational deterministic biochemical model exhibiting this behavior. The model is based on biochemical features of FtsZ known from in vitro studies, and it quantitatively reproduces relevant in vitro data. An essential part of the model is a consideration of interfacial reactions involving the cytosol volume, where monomeric FtsZ is dispersed, and the membrane surface in the cell's mid-zone where the ring is assembled. This approach allows the same chemical model to simulate either in vitro or in vivo conditions by adjusting only two geometrical parameters. The model includes minimal reactions, components, and assumptions, yet is able to reproduce sought-after in vivo behavior, including the rapid assembly of the ring via FtsZ-polymerization, the formation of a dynamic steady state in which GTP hydrolysis leads to the exchange of monomeric subunits between cytoplasm and the ring, and finally the induced contraction of the ring. The model gives a quantitative estimate for coupling between the rate of GTP hydrolysis and of FtsZ subunit turnover between the assembled ring and the cytoplasmic pool as observed. Membrane constriction is chemically driven by the strong tendency of GTP-bound FtsZ to self-assembly. The model suggests a possible mechanism of membrane contraction without a motor protein. The portion of the free energy of GTP hydrolysis released in cyclization is indirectly used in this energetically unfavorable process. The model provides a limit to the mechanistic complexity required to mimic ring behavior, and it highlights the importance of parallel in vitro and in vivo modeling.     

On testing structural identifiability by a simple scaling method: Relying on scaling symmetries can be misleading

A recent paper published in PLOS Computational Biology [1] introduces the Scaling Invariance Method (SIM) for analysing structural local identifiability and observability. These two properties define mathematically the possibility of determining the values of the parameters (identifiability) and states (observability) of a dynamic model by observing its output. In this note we warn that SIM considers scaling symmetries as the only possible cause of non-identifiability and non-observability. We show that other types of symmetries can cause the same problems without being detected by SIM, and that in those cases the method may lead one to conclude that the model is identifiable and observable when it is actually not.     

Noise improves collective decision-making by ants in dynamic environments

Recruitment via pheromone trails by ants is arguably one of the best-studied examples of self-organization in animal societies. Yet it is still unclear if and how trail recruitment allows a colony to adapt to changes in its foraging environment. We study foraging decisions by colonies of the ant Pheidole megacephala under dynamic conditions. Our experiments show that P. megacephala, unlike many other mass recruiting species, can make a collective decision for the better of two food sources even when the environment changes dynamically. We developed a stochastic differential equation model that explains our data qualitatively and quantitatively. Analysing this model reveals that both deterministic and stochastic effects (noise) work together to allow colonies to efficiently track changes in the environment. Our study thus suggests that a certain level of noise is not a disturbance in self-organized decision-making but rather serves an important functional role.     

Development of a structured dynamic model for the production of polyhydroxybutyrate (PHB) in Azohydromonas lata cultures

The development of an accurate model representation of the fermentative production of polyhydroxybutyrate (PHB) is a prerequisite for the optimal operation and control of the microbial process. In the present work, a macroscopic model is developed to quantify the intracellular production of PHB in Azohydromonas lata bacteria. The proposed two-compartment structured model provides an accurate prediction of the metabolic and macroscopic phenomena occurring in A. lata bacterial cultures. Precisely, the proposed dynamic model accounts for biomass growth, polymer accumulation, carbon and nitrogen sources utilization and oxygen mass transfer rates. It is shown that the model can closely describe the time evolution of the bacterial culture via its direct comparison with experiments performed in flasks or/and a bioreactor. Moreover, it is shown that the model can be used as a simulation tool for process optimization and scaling-up studies of the PHB fermentative production in A. lata cultures.     

Bacterial chemotaxis to saccharides is governed by a trade-off between sensing and uptake

To swim up gradients of nutrients, E. coli senses nutrient concentrations within its periplasm. For small nutrient molecules, periplasmic concentrations typically match extracellular concentrations. However, this is not necessarily the case for saccharides, such as maltose, which are transported into the periplasm via a specific porin. Previous observations have shown that, under various conditions, E. coli limits maltoporin abundance so that, for extracellular micromolar concentrations of maltose, there are predicted to be only nanomolar concentrations of free maltose in the periplasm. Thus, in the micromolar regime, the total uptake of maltose from the external environment into the cytoplasm is limited not by the abundance of cytoplasmic transport proteins but by the abundance of maltoporins. Here, we present results from experiments and modeling suggesting that this porin-limited transport enables E. coli to sense micromolar gradients of maltose despite having a high-affinity ABC transport system that is saturated at these micromolar levels. We used microfluidic assays to study chemotaxis of E. coli in various gradients of maltose and methyl-aspartate and leveraged our experimental observations to develop a mechanistic transport-and-sensing chemotaxis model. Incorporating this model into agent-based simulations, we discover a trade-off between uptake and sensing: although high-affinity transport enables higher uptake rates at low nutrient concentrations, it severely limits the range of dynamic sensing. We thus propose that E. coli may limit periplasmic uptake to increase its chemotactic sensitivity, enabling it to use maltose as an environmental cue.     

A Flexible Multidomain Structure Drives the Function of the Urokinase-type Plasminogen Activator Receptor (uPAR)

The urokinase-type plasminogen activator receptor (uPAR) provides a rendezvous between proteolytic degradation of the extracellular matrix and integrin-mediated adhesion to vitronectin. These processes are, however, tightly linked because the high affinity binding of urokinase regulates the binding of uPAR to matrix-embedded vitronectin. Although crystal structures exist to define the corresponding static bi- and trimolecular receptor complexes, it is evident that the dynamic property of uPAR plays a decisive role in its function. In the present study, we combine small angle x-ray scattering, hydrogen-deuterium exchange, and surface plasmon resonance to develop a structural model describing the allosteric regulation of uPAR. We show that the flexibility of its N-terminal domain provides the key for understanding this allosteric mechanism. Importantly, our model has direct implications for understanding uPAR-assisted cell adhesion and migration as well as for translational research, including targeted intervention therapy and non-invasive tumor imaging in vivo.     

Modeling the Growth of Listeria monocytogenes in Soft Blue-White Cheese

The aim of this study was to develop a predictive model simulating growth over time of the pathogenic bacterium Listeria monocytogenes in a soft blue-white cheese. The physicochemical properties in a matrix such as cheese are essential controlling factors influencing the growth of L. monocytogenes. We developed a predictive tertiary model of the bacterial growth of L. monocytogenes as a function of temperature, pH, NaCl, and lactic acid. We measured the variations over time of the physicochemical properties in the cheese. Our predictive model was developed based on broth data produced in previous studies. New growth data sets were produced to independently calibrate and validate the developed model. A characteristic of this tertiary model is that it handles dynamic growth conditions described in time series of temperature, pH, NaCl, and lactic acid. Supplying the model with realistic production and retail conditions showed that the number of L. monocytogenes cells increases 3 to 3.5 log within the shelf life of the cheese.     

Interrogating the substrate specificity landscape of UvrC reveals novel insights into its non-canonical function

Although it is relatively unexplored, accumulating data highlight the importance of tripartite crosstalk between nucleotide excision repair (NER), DNA replication, and recombination in the maintenance of genome stability; however, elucidating the underlying mechanisms remains challenging. While Escherichia coli uvrA and uvrB can fully complement polAΔ cells in DNA replication, uvrC attenuates this alternative DNA replication pathway, but the exact mechanism by which uvrC suppresses DNA replication is unknown. Furthermore, the identity of bona fide canonical and non-canonical substrates for UvrCs are undefined. Here, we reveal that Mycobacterium tuberculosis UvrC (MtUvrC) strongly binds to, and robustly cleaves, key intermediates of DNA replication/recombination as compared with the model NER substrates. Notably, inactivation of MtUvrC ATPase activity significantly attenuated its endonuclease activity, thus suggesting a causal link between these two functions. We built an in silico model of the interaction of MtUvrC with the Holliday junction (HJ), using a combination of homology modeling, molecular docking, and molecular dynamic simulations. The model predicted residues that were potentially involved in HJ binding. Six of these residues were mutated either singly or in pairs, and the resulting MtUvrC variants were purified and characterized. Among them, residues Glu595 and Arg597 in the helix-hairpin-helix motif were found to be crucial for the interaction between MtUvrC and HJ; consequently, mutations in these residues, or inhibition of ATP hydrolysis, strongly abrogated its DNA-binding and endonuclease activities. Viewed together, these findings expand the substrate specificity landscape of UvrCs and provide crucial mechanistic insights into the interplay between NER and DNA replication/recombination.     

Membrane Binding of MinE Allows for a Comprehensive Description of Min-Protein Pattern Formation

The rod-shaped bacterium Escherichia coli selects the cell center as site of division with the help of the proteins MinC, MinD, and MinE. This protein system collectively oscillates between the two cell poles by alternately binding to the membrane in one of the two cell halves. This dynamic behavior, which emerges from the interaction of the ATPase MinD and its activator MinE on the cell membrane, has become a paradigm for protein self-organization. Recently, it has been found that not only the binding of MinD to the membrane, but also interactions of MinE with the membrane contribute to Min-protein self-organization. Here, we show that by accounting for this finding in a computational model, we can comprehensively describe all observed Min-protein patterns in vivo and in vitro. Furthermore, by varying the system''s geometry, our computations predict patterns that have not yet been reported. We confirm these predictions experimentally.     

Mathematical modelling and assessment of the pH homeostasis mechanisms in Aspergillus niger while in citric acid producing conditions

In this work we introduce an extended model of the Aspergillus niger metabolism while in citrate production conditions. The model includes many recent findings related to various transport processes. It now considers a new information about the fructose uptake system and the proton and amino acids carriers between cytoplasm and the external medium. It also accounts for recent information about both the malate-citrate antiport between mitochondria and cytoplasm and the dihydrogen citrate ion excretion symport with protons. Finally, the model also accounts for new information about the glycerol-3-phosphate shuttle and pH buffering systems. Provided with this updated representation and after having assessed its quality and dynamic behaviour, we were able to explain the observed pH homoeostasis found in A. niger while in citrate producing conditions. The model also serves to enhance our comprehension of the molecular mechanisms operating in order to keep homoeostasis of pH in A. niger and other fungi, bacteria and yeast of biotechnological relevance.     

A model of insect—pathogen dynamics in which a pathogenic bacterium can also reproduce saprophytically

We developed a model of the population dynamic interaction between an insect and a pathogenic bacterium motivated by study of Serratia entomophila, a commercially exploited pathogen of the New Zealand grass grub (Costelytra zealandica). The bacterium is able to reproduce saprophytically, though it competes for saprophytic substrates with non-pathogenic strains, which appear to be superior competitors, probably because they lack a plasmid that carries genes required for pathogenicity. The effect of saprophytism and competition on the invasion criterion (R₀), short-term dynamics and long-term dynamics are described. Saprophytism can reduce (possibly to zero) the host threshold at which the pathogen can invade, though this reduction is less when there is competition with non-pathogenic strains. In a model of short-term population dynamics designed to mimic the application of bacteria to a host epizootic, saprophytism enhances the reduction in host density, though again this is tempered by competition with non-pathogens. In the long term, a pathogen that can develop saprophytically can drive its host to extinction in the absence of competition with non-pathogens. When the latter are present, host extinction is prevented. The addition of saprophytic reproduction can stabilize an otherwise unstable host–pathogen model, but we were unable to find a stable equilibrium given the further addition of a wholly saprophytic bacterial strain. The model suggests that enhancing or selecting for saprophytic ability could be a way of improving biological control.     

Inhibition of hyaluronan degradation by dextran sulphate facilitates characterisation of hyaluronan synthesis: An in vitro and in vivo study

The concentration and molecular weight of hyaluronan often dictates its physiological function. Consequently full characterisation of the anabolic products and turnover rates of HA could facilitate understanding of the role that HA metabolism plays in disease processes. In order to achieve this it is necessary to interrupt the dynamic balance between concurrent HA synthesis and degradation, achievable through the inhibition of the hyaluronidases, a group of enzymes which degrade HA. The sulphated polysaccharide, dextran sulphate has been demonstrated to competitively inhibit testicular hyaluronidase in a non-biological system, but its application to in vitro biological systems had yet to be developed and evaluated. This study determined the inhibitory concentrations of dextran sulphate against both testicular and Streptomyces hyaluronidase in a cell-free and breast cancer model followed by characterisation of the effect that hyaluronidase inhibition exerted on HA synthesis and degradation. The IC₁₀₀ of dextran sulphate for both hyaluronidases in a cell-free and biological system was determined to be ≥400 μg/ml. At concentrations up to 10 mg/ml the dextran sulphate did not effect breast cancer cell proliferation or morphology, while at 400 μg/ml HA degradation was totally inhibited, enabling an accurate quantitation of HA production as well as characterisation of the cell-associated and liberated HA. FACS quantitation of the HA receptor CD44, HA synthase and the hyaluronidases HYAL 1 and HYAL 2 demonstrated that dextran sulphate down-regulated CD44 and HA synthase while upregulating the hyaluronidases. These results suggest dynamic feedback signalling and complex mechanisms occur in the net deposition of HA in vivo. Published in 2004.     

Photoheterotrophic growth of Physcomitrella patens

Physcomitrella patens is a model bryophyte representing an early land plant in the green plant lineage. This organism possesses many advantages as a model organism. Its genome has been sequenced, its predominant life cycle stage is the haploid gametophyte, it is readily transformable and it can integrate transformed DNA into its genome by homologous recombination. One limitation for the use of P. patens in photosynthesis research is its reported inability to grow photoheterotrophically, in the presence of sucrose and the Photosystem II inhibitor 3-(3,4-dichlorophenyl)-1,1-dimethylurea, which prevents linear photosynthetic electron transport. In this communication we describe the facile isolation of a P. patens strain which can grow photoheterotrophically. Additionally, we have examined a number of photosynthetic parameters for this strain grown under photoautotrophic, mixotrophic (in the presence of sucrose) and photoheterotrophic conditions, as well as the 3-(3,4-dichlorophenyl)-1,1-dimethylurea-inhibited state. The ability to grow P. patens photoheterotrophically should significantly facilitate its use in photosynthetic studies.