Quantitative analysis of MBW complex formation in the context of trichome patterning.

Trichome patterning in Arabidopsis is regulated by R2R3MYB, bHLH and WDR (MBW) genes. These are considered to form a trimeric MBW protein complex that promotes trichome formation. The MBW proteins are engaged in a regulatory network to select trichome cells among epidermal cells through R3MYB proteins that can move between cells and repress the MBW complex by competitive binding with the R2R3MYB to the bHLHL protein. We use quantitative pull-down assays to determine the relative dissociation constants for the protein-protein interactions of the involved genes. We find similar binding strength between the trichome promoting genes and weaker binding of the R3MYB inhibitors. We used the dissociation constants to calculate the relative percentage of all possible complex combinations and found surprisingly low fractions of those complexes that are typically considered to be relevant for the regulation events. Finally, we predict an increased robustness in patterning as a consequence of higher ordered complexes mediated by GL3 dimerization.

Microparticles and multi-unit systems for advanced drug delivery.

Microparticles have unique benefits in the formulation of multiparticulate and multi-unit type pharmaceutical dosage forms allowing improved drug safety and efficacy with favorable pharmacokinetics and patient centricity. On the other hand, the above advantages are served by high and well reproducible quality attributes of the medicinal product where even flexible design and controlled processability offer success as well as possible longer product life-cycle for the manufacturers. Moreover, the specific demands of patients can be taken into account, including simplified dosing regimens, flexible dosage, drug combinations, palatability, and ease of swallowing. In the more than 70 years since the first modified-release formulation appeared on the market, many new formulations have been marketed and many publications have appeared in the literature. More unique and newer pharmaceutical technologies and excipients have become available for producing tailor-made particles with micrometer dimensions and beyond. All these have contributed to the fact that the sub-units (e.g. minitablets, pellets, microspheres) that make up a multiparticulate system can vary widely in composition and properties. Some units have mucoadhesive properties and others can float to contribute to a suitable release profile that can be designed for the multiparticulate formula as a whole. Nowadays, there are some available formulations on the market, which are able to release the active substance even for several months (3 or 6 months depending on the type of treatment). In this review, the latest developments in technologies that have been used for a long time are presented, as well as innovative solutions such as the applicability of 3D printing to produce subunits of multiparticulate systems. Furthermore, the diversity of multiparticulate systems, different routes of administration are also presented, touching the ones which are capable of carrying the active substance as well as the relevant, commercially available multiparticle-based medical devices. The versatility in size from 1 µm and multiplicity of formulation technologies promise a solid foundation for the future applications of dosage form design and development.

Hyaluronic Acid in Rheumatology.

Hyaluronic acid (HA), also known as hyaluronan, is an anionic glycosaminoglycan widely distributed throughout various tissues of the human body. It stands out from other glycosaminoglycans as it lacks sulfation and can attain considerable size: the average human synovial HA molecule weighs about 7 million Dalton (Da), equivalent to roughly 20,000 disaccharide monomers; although some sources report a lower range of 3-4 million Da. In recent years, HA has garnered significant attention in the field of rheumatology due to its involvement in joint lubrication, cartilage maintenance, and modulation of inflammatory and/or immune responses. This review aims to provide a comprehensive overview of HA's involvement in rheumatology, covering its physiology, pharmacology, therapeutic applications, and potential future directions for enhancing patient outcomes. Nevertheless, the use of HA therapy in rheumatology remains controversial with conflicting evidence regarding its efficacy and safety. In conclusion, HA represents a promising therapeutic option to improve joint function and alleviate inflammation and pain.

Review on Starter Pellets: Inert and Functional Cores.

A significant proportion of pharmaceuticals are now considered multiparticulate systems. Modified-release drug delivery formulations can be designed with engineering precision, and patient-centric dosing can be accomplished relatively easily using multi-unit systems. In many cases, Multiple-Unit Pellet Systems (MUPS) are formulated on the basis of a neutral excipient core which may carry the layered drug surrounded also by functional coating. In the present summary, commonly used starter pellets are presented. The manuscript describes the main properties of the various nuclei related to their micro- and macrostructure. In the case of layered pellets formed based on different inert pellet cores, the drug release mechanism can be expected in detail. Finally, the authors would like to prove the industrial significance of inert cores by presenting some of the commercially available formulations.

Single cell variability of CRISPR-Cas interference and adaptation.

While CRISPR-Cas defence mechanisms have been studied on a population level, their temporal dynamics and variability in individual cells have remained unknown. Using a microfluidic device, time-lapse microscopy and mathematical modelling, we studied invader clearance in Escherichia coli across multiple generations. We observed that CRISPR interference is fast with a narrow distribution of clearance times. In contrast, for invaders with escaping PAM mutations we found large cell-to-cell variability, which originates from primed CRISPR adaptation. Faster growth and cell division and higher levels of Cascade increase the chance of clearance by interference, while slower growth is associated with increased chances of clearance by priming. Our findings suggest that Cascade binding to the mutated invader DNA, rather than spacer integration, is the main source of priming heterogeneity. The highly stochastic nature of primed CRISPR adaptation implies that only subpopulations of bacteria are able to respond quickly to invading threats. We conjecture that CRISPR-Cas dynamics and heterogeneity at the cellular level are crucial to understanding the strategy of bacteria in their competition with other species and phages.

Mathematical Modelling in Plant Synthetic Biology.

Mathematical modelling techniques are integral to current research in plant synthetic biology. Modelling approaches can provide mechanistic understanding of a system, allowing predictions of behaviour and thus providing a tool to help design and analyse biological circuits. In this chapter, we provide an overview of mathematical modelling methods and their significance for plant synthetic biology. Starting with the basics of dynamics, we describe the process of constructing a model over both temporal and spatial scales and highlight crucial approaches, such as stochastic modelling and model-based design. Next, we focus on the model parameters and the techniques required in parameter analysis. We then describe the process of selecting a model based on tests and criteria and proceed to methods that allow closer analysis of the system's behaviour. Finally, we highlight the importance of uncertainty in modelling approaches and how to deal with a lack of knowledge, noisy data, and biological variability; all aspects that play a crucial role in the cooperation between the experimental and modelling components. Overall, this chapter aims to illustrate the importance of mathematical modelling in plant synthetic biology, providing an introduction for those researchers who are working with or working on modelling techniques.

Comparative expression analysis in three Brassicaceae species revealed compensatory changes of the underlying gene regulatory network.

Trichomes are regularly distributed on the leaves of Arabidopsis thaliana. The gene regulatory network underlying trichome patterning involves more than 15 genes. However, it is possible to explain patterning with only five components. This raises the questions about the function of the additional components and the identification of the core network. In this study, we compare the relative expression of all patterning genes in A. thaliana, A. alpina and C. hirsuta by qPCR analysis and use mathematical modelling to determine the relative importance of patterning genes. As the involved proteins exhibit evolutionary conserved differential complex formation, we reasoned that the genes belonging to the core network should exhibit similar expression ratios in different species. However, we find several striking differences of the relative expression levels. Our analysis of how the network can cope with such differences revealed relevant parameters that we use to predict the relevant molecular adaptations in the three species.

What is quantitative plant biology?

Quantitative plant biology is an interdisciplinary field that builds on a long history of biomathematics and biophysics. Today, thanks to high spatiotemporal resolution tools and computational modelling, it sets a new standard in plant science. Acquired data, whether molecular, geometric or mechanical, are quantified, statistically assessed and integrated at multiple scales and across fields. They feed testable predictions that, in turn, guide further experimental tests. Quantitative features such as variability, noise, robustness, delays or feedback loops are included to account for the inner dynamics of plants and their interactions with the environment. Here, we present the main features of this ongoing revolution, through new questions around signalling networks, tissue topology, shape plasticity, biomechanics, bioenergetics, ecology and engineering. In the end, quantitative plant biology allows us to question and better understand our interactions with plants. In turn, this field opens the door to transdisciplinary projects with the society, notably through citizen science.

Identification of the Trichome Patterning Core Network Using Data from Weak ttg1 Alleles to Constrain the Model Space.

The regular distribution of trichomes on leaves in Arabidopsis is a well-understood model system for two-dimensional pattern formation. It involves more than 10 genes and is governed by two patterning principles, the activator-inhibitor (AI) and the activator-depletion (AD) mechanisms, though their relative contributions are unknown. The complexity of gene interactions, protein interactions, and intra- and intercellular mobility of proteins makes it very challenging to understand which aspects are relevant for pattern formation. In this study, we use global mathematical methods combined with a constraining of data to identify the structure of the underlying network. To constrain the model, we perform a genetic, cell biological, and biochemical study of weak ttg1 alleles. We find that the core of trichome patterning is a combination of AI and AD mechanisms differentiating between two pathways activating the long-range inhibitor CPC and the short-range inhibitor TRY.

Live Cell Imaging of Male Meiosis in Arabidopsis by a Landmark-based System.

Live cell imaging has tremendously promoted our understanding of cellular and subcellular processes such as cell division. Here, we present a step-by-step protocol for a robust and easy-to-use live cell imaging approach to study male meiosis in the plant Arabidopsis thaliana as recently established. Our method relies on the concomitant analysis of two reporter genes that highlight chromosome configurations and microtubule dynamics. In combination, these reporter genes allowed the discrimination of five cellular parameters: cell shape, microtubule array, nucleus position, nucleolus position, and chromatin condensation. These parameters can adopt different states, e.g., the nucleus position can be central or lateral. Analyzing how tightly these states are associated gives rise to landmark stages that in turn allow a quantitative and qualitative dissection of meiotic progression. We envision that such an approach can also provide valuable criteria for the analysis of cell differentiation processes outside of meiosis.

Basic Phytochrome B Calculations.

Mathematical models are important tools in helping us to understand complex biological systems. Models of phytochrome-regulated systems in Arabidopsis thaliana have shown the importance of dimerization, nuclear transport, and thermal/dark reversion in mediating phytochrome activity and plant development. Here we go through the steps required to calculate the steady-state amounts of phytochrome subspecies relative to the total phytochrome molecule population. Starting from a simplified two-state system we expand and apply the technique to the extended phytochrome dimer model. Additionally, we provide a Python package that can automatically calculate the proportion of phytochrome B in a particular state given specific experimental conditions.

Extending the linear-noise approximation to biochemical systems influenced by intrinsic noise and slow lognormally distributed extrinsic noise.

It is well known that the kinetics of an intracellular biochemical network is stochastic. This is due to intrinsic noise arising from the random timing of biochemical reactions in the network as well as due to extrinsic noise stemming from the interaction of unknown molecular components with the network and from the cell's changing environment. While there are many methods to study the effect of intrinsic noise on the system dynamics, few exist to study the influence of both types of noise. Here we show how one can extend the conventional linear-noise approximation to allow for the rapid evaluation of the molecule numbers statistics of a biochemical network influenced by intrinsic noise and by slow lognormally distributed extrinsic noise. The theory is applied to simple models of gene regulatory networks and its validity confirmed by comparison with exact stochastic simulations. In particular, we consider three important biological examples. First, we investigate how extrinsic noise modifies the dependence of the variance of the molecule number fluctuations on the rate constants. Second, we show how the mutual information between input and output of a network motif is affected by extrinsic noise. And third, we study the robustness of the ubiquitously found feed-forward loop motifs when subjected to extrinsic noise.

Live cell imaging of meiosis in Arabidopsis thaliana.

To follow the dynamics of meiosis in the model plant Arabidopsis, we have established a live cell imaging setup to observe male meiocytes. Our method is based on the concomitant visualization of microtubules (MTs) and a meiotic cohesin subunit that allows following five cellular parameters: cell shape, MT array, nucleus position, nucleolus position, and chromatin condensation. We find that the states of these parameters are not randomly associated and identify 11 cellular states, referred to as landmarks, which occur much more frequently than closely related ones, indicating that they are convergence points during meiotic progression. As a first application of our system, we revisited a previously identified mutant in the meiotic A-type cyclin TARDY ASYNCHRONOUS MEIOSIS (TAM). Our imaging system enabled us to reveal both qualitatively and quantitatively altered landmarks in tam, foremost the formation of previously not recognized ectopic spindle- or phragmoplast-like structures that arise without attachment to chromosomes.

Genetic and molecular analysis of trichome development in Arabis alpina.

The genetic and molecular analysis of trichome development in Arabidopsis thaliana has generated a detailed knowledge about the underlying regulatory genes and networks. However, how rapidly these mechanisms diverge during evolution is unknown. To address this problem, we used an unbiased forward genetic approach to identify most genes involved in trichome development in the related crucifer species Arabisalpina In general, we found most trichome mutant classes known in A. thaliana We identified orthologous genes of the relevant A. thaliana genes by sequence similarity and synteny and sequenced candidate genes in the A. alpina mutants. While in most cases we found a highly similar gene-phenotype relationship as known from Arabidopsis, there were also striking differences in the regulation of trichome patterning, differentiation, and morphogenesis. Our analysis of trichome patterning suggests that the formation of two classes of trichomes is regulated differentially by the homeodomain transcription factor AaGL2 Moreover, we show that overexpression of the GL3 basic helix-loop-helix transcription factor in A. alpina leads to the opposite phenotype as described in A. thaliana Mathematical modeling helps to explain how this nonintuitive behavior can be explained by different ratios of GL3 and GL1 in the two species.

Optogenetic control shows that kinetic proofreading regulates the activity of the T cell receptor.

The immune system distinguishes between self and foreign antigens. The kinetic proofreading (KPR) model proposes that T cells discriminate self from foreign ligands by the different ligand binding half-lives to the T cell receptor (TCR). It is challenging to test KPR as the available experimental systems fall short of only altering the binding half-lives and keeping other parameters of the interaction unchanged. We engineered an optogenetic system using the plant photoreceptor phytochrome B (PhyB) as a ligand to selectively control the dynamics of ligand binding to the TCR by light. This opto-ligand-TCR system was combined with the unique property of PhyB to continuously cycle between the binding and non-binding states under red light, with the light intensity determining the cycling rate and thus the binding duration. Mathematical modeling of our experimental datasets showed that indeed the ligand-TCR interaction half-life is the decisive factor for activating downstream TCR signaling, substantiating KPR.

Phytochrome B dynamics departs from photoequilibrium in the field.

Vegetation shade is characterized by marked decreases in the red/far-red ratio and photosynthetic irradiance. The activity of phytochrome in the field has typically been described by its photoequilibrium, defined by the photochemical properties of the pigment in combination with the spectral distribution of the light. This approach represents an oversimplification because phytochrome B (phyB) activity depends not only on its photochemical reactions but also on its rates of synthesis, degradation, translocation to the nucleus, and thermal reversion. To account for these complex cellular reactions, we used a model to simulate phyB activity under a range of field conditions. The model provided values of phyB activity that in turn predicted hypocotyl growth in the field with reasonable accuracy. On the basis of these observations, we define two scenarios, one is under shade, in cloudy weather, at the extremes of the photoperiod or in the presence of rapid fluctuations of the light environment caused by wind-induced movements of the foliage, where phyB activity departs from photoequilibrium and becomes affected by irradiance and temperature in addition to the spectral distribution. The other scenario is under full sunlight, where phyB activity responds mainly to the spectral distribution of the light.

DMPy: a Python package for automated mathematical model construction of large-scale metabolic systems.

BACKGROUND: Models of metabolism are often used in biotechnology and pharmaceutical research to identify drug targets or increase the direct production of valuable compounds. Due to the complexity of large metabolic systems, a number of conclusions have been drawn using mathematical methods with simplifying assumptions. For example, constraint-based models describe changes of internal concentrations that occur much quicker than alterations in cell physiology. Thus, metabolite concentrations and reaction fluxes are fixed to constant values. This greatly reduces the mathematical complexity, while providing a reasonably good description of the system in steady state. However, without a large number of constraints, many different flux sets can describe the optimal model and we obtain no information on how metabolite levels dynamically change. Thus, to accurately determine what is taking place within the cell, finer quality data and more detailed models need to be constructed. RESULTS: In this paper we present a computational framework, DMPy, that uses a network scheme as input to automatically search for kinetic rates and produce a mathematical model that describes temporal changes of metabolite fluxes. The parameter search utilises several online databases to find measured reaction parameters. From this, we take advantage of previous modelling efforts, such as Parameter Balancing, to produce an initial mathematical model of a metabolic pathway. We analyse the effect of parameter uncertainty on model dynamics and test how recent flux-based model reduction techniques alter system properties. To our knowledge this is the first time such analysis has been performed on large models of metabolism. Our results highlight that good estimates of at least 80% of the reaction rates are required to accurately model metabolic systems. Furthermore, reducing the size of the model by grouping reactions together based on fluxes alters the resulting system dynamics. CONCLUSION: The presented pipeline automates the modelling process for large metabolic networks. From this, users can simulate their pathway of interest and obtain a better understanding of how altering conditions influences cellular dynamics. By testing the effects of different parameterisations we are also able to provide suggestions to help construct more accurate models of complete metabolic systems in the future.

Insight into nuclear body formation of phytochromes through stochastic modelling and experiment.

Spatial relocalization of proteins is crucial for the correct functioning of living cells. An interesting example of spatial ordering is the light-induced clustering of plant photoreceptor proteins. Upon irradiation by white or red light, the red light-active phytochrome, phytochrome B, enters the nucleus and accumulates in large nuclear bodies (NBs). The underlying physical process of nuclear body formation remains unclear, but phytochrome B is thought to coagulate via a simple protein-protein binding process. We measure, for the first time, the distribution of the number of phytochrome B-containing NBs as well as their volume distribution. We show that the experimental data cannot be explained by a stochastic model of nuclear body formation via simple protein-protein binding processes using physically meaningful parameter values. Rather modelling suggests that the data is consistent with a two step process: a fast nucleation step leading to macroparticles followed by a subsequent slow step in which the macroparticles bind to form the nuclear body. An alternative explanation for the observed nuclear body distribution is that the phytochromes bind to a so far unknown molecular structure. We believe it is likely this result holds more generally for other nuclear body-forming plant photoreceptors and proteins.

Data-Driven Modeling of Intracellular Auxin Fluxes Indicates a Dominant Role of the ER in Controlling Nuclear Auxin Uptake.

In plants, the phytohormone auxin acts as a master regulator of developmental processes and environmental responses. The best characterized process in the auxin regulatory network occurs at the subcellular scale, wherein auxin mediates signal transduction into transcriptional programs by triggering the degradation of Aux/IAA transcriptional repressor proteins in the nucleus. However, whether and how auxin movement between the nucleus and the surrounding compartments is regulated remain elusive. Using a fluorescent auxin analog, we show that its diffusion into the nucleus is restricted. By combining mathematical modeling with time course assays on auxin-mediated nuclear signaling and quantitative phenotyping in single plant cell systems, we show that ER-to-nucleus auxin flux represents a major subcellular pathway to directly control nuclear auxin levels. Our findings propose that the homeostatically regulated auxin pool in the ER and ER-to-nucleus auxin fluxes underpin auxin-mediated downstream responses in plant cells.

Designing synthetic networks in silico: a generalised evolutionary algorithm approach.

BACKGROUND: Evolution has led to the development of biological networks that are shaped by environmental signals. Elucidating, understanding and then reconstructing important network motifs is one of the principal aims of Systems & Synthetic Biology. Consequently, previous research has focused on finding optimal network structures and reaction rates that respond to pulses or produce stable oscillations. In this work we present a generalised in silico evolutionary algorithm that simultaneously finds network structures and reaction rates (genotypes) that can satisfy multiple defined objectives (phenotypes). RESULTS: The key step to our approach is to translate a schema/binary-based description of biological networks into systems of ordinary differential equations (ODEs). The ODEs can then be solved numerically to provide dynamic information about an evolved networks functionality. Initially we benchmark algorithm performance by finding optimal networks that can recapitulate concentration time-series data and perform parameter optimisation on oscillatory dynamics of the Repressilator. We go on to show the utility of our algorithm by finding new designs for robust synthetic oscillators, and by performing multi-objective optimisation to find a set of oscillators and feed-forward loops that are optimal at balancing different system properties. In sum, our results not only confirm and build on previous observations but we also provide new designs of synthetic oscillators for experimental construction. CONCLUSIONS: In this work we have presented and tested an evolutionary algorithm that can design a biological network to produce desired output. Given that previous designs of synthetic networks have been limited to subregions of network- and parameter-space, the use of our evolutionary optimisation algorithm will enable Synthetic Biologists to construct new systems with the potential to display a wider range of complex responses.