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  • 1
    Publication Date: 2021-03-16
    Description: Gene Regulatory Networks are powerful models for describing the mechanisms and dynamics inside a cell. These networks are generally large in dimension and seldom yield analytical formulations. It was shown that studying the conditional expectations between dimensions (vertices or species) of a network could lead to drastic dimension reduction. These conditional expectations were classically given by solving equations of motions derived from the Chemical Master Equation. In this paper we deviate from this convention and take an Algebraic approach instead. That is, we explore the consequences of conditional expectations being described by a polynomial function. There are two main results in this work. Firstly: if the conditional expectation can be described by a polynomial function, then coefficients of this polynomial function can be reconstructed using the classical moments. And secondly: there are dimensions in Gene Regulatory Networks which inherently have conditional expectations with algebraic forms. We demonstrate through examples, that the theory derived in this work can be used to develop new and effective numerical schemes for forward simulation and parameter inference. The algebraic line of investigation of conditional expectations has considerable scope to be applied to many different aspects of Gene Regulatory Networks; this paper serves as a preliminary commentary in this direction.
    Language: English
    Type: article , doc-type:article
    Format: application/pdf
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  • 2
    Publication Date: 2022-02-04
    Description: Standard correspondence analysis (CA) is a visualisation method to show the relationship between two categorical variables on a simplified figure (usually of two-dimensions). This method represents each variable separately, in different spaces, but combines the results on the same figure for interpretation. Consequently, the distance between two categories of different variables is not interpretable and this complicates the interpretation. Additionally, the plausibility of the interpretation depends on the amount of information traded for the simplifications. In this work, we present Tensor CA, a method that circumvents these issues. In our method, we represent the two variables in the same space and this enables us to accurately control the amount of information used to produce the results. We then provide a method to produce a two-dimensional figure in which the euclidean distances, both within and between the variables, are interpretable and indicate measures of independence, similarity, and association. We then use Tensor CA to extract new knowledge from historical linguistic data (ancient Egyptian).
    Language: English
    Type: article , doc-type:article
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  • 3
    Publication Date: 2020-11-24
    Description: Muscle fibre cross sectional area (CSA) is an important biomedical measure used to determine the structural composition of skeletal muscle, and it is relevant for tackling research questions in many different fields of research. To date, time consuming and tedious manual delineation of muscle fibres is often used to determine the CSA. Few methods are able to automatically detect muscle fibres in muscle fibre cross sections to quantify CSA due to challenges posed by variation of bright- ness and noise in the staining images. In this paper, we introduce SLCV, a robust semi-automatic pipeline for muscle fibre detection, which combines supervised learning (SL) with computer vision (CV). SLCV is adaptable to different staining methods and is quickly and intuitively tunable by the user. We are the first to perform an error analysis with respect to cell count and area, based on which we compare SLCV to the best purely CV-based pipeline in order to identify the contribution of SL and CV steps to muscle fibre detection. Our results obtained on 27 fluorescence-stained cross sectional images of varying staining quality suggest that combining SL and CV performs signifi- cantly better than both SL based and CV based methods with regards to both the cell separation- and the area reconstruction error. Furthermore, applying SLCV to our test set images yielded fibre detection results of very high quality, with average sensitivity values of 0.93 or higher on different cluster sizes and an average Dice Similarity Coefficient (DSC) of 0.9778.
    Language: English
    Type: article , doc-type:article
    Format: application/pdf
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  • 4
  • 5
    Publication Date: 2020-03-19
    Description: The reaction counts chemical master equation (CME) is a high-dimensional variant of the classical population counts CME. In the reaction counts CME setting, we count the reactions which have fired over time rather than monitoring the population state over time. Since a reaction either fires or not, the reaction counts CME transitions are only forward stepping. Typically there are more reactions in a system than species, this results in the reaction counts CME being higher in dimension, but simpler in dynamics. In this work, we revisit the reaction counts CME framework and its key theoretical results. Then we will extend the theory by exploiting the reactions counts’ forward stepping feature, by decomposing the state space into independent continuous-time Markov chains (CTMC). We extend the reaction counts CME theory to derive analytical forms and estimates for the CTMC decomposition of the CME. This new theory gives new insights into solving hitting times-, rare events-, and a priori domain construction problems.
    Language: English
    Type: article , doc-type:article
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  • 6
    Publication Date: 2021-12-23
    Description: Molecular simulations of ligand-receptor interactions are a computational challenge, especially when their association- (``on''-rate) and dissociation- (``off''-rate) mechanisms are working on vastly differing timescales. In addition, the timescale of the simulations themselves is, in practice, orders of magnitudes smaller than that of the mechanisms; which further adds to the complexity of observing these mechanisms, and of drawing meaningful and significant biological insights from the simulation. One way of tackling this multiscale problem is to compute the free-energy landscapes, where molecular dynamics (MD) trajectories are used to only produce certain statistical ensembles. The approach allows for deriving the transition rates between energy states as a function of the height of the activation-energy barriers. In this article, we derive the association rates of the opioids fentanyl and N-(3-fluoro-1-phenethylpiperidin-4-yl)- N-phenyl propionamide (NFEPP) in a $\mu$-opioid receptor by combining the free-energy landscape approach with the square-root-approximation method (SQRA), which is a particularly robust version of Markov modelling. The novelty of this work is that we derive the association rates as a function of the pH level using only an ensemble of MD simulations. We also verify our MD-derived insights by reproducing the in vitro study performed by the Stein Lab, who investigated the influence of pH on the inhibitory constant of fentanyl and NFEPP (Spahn et al. 2017). MD simulations are far more accessible and cost-effective than in vitro and in vivo studies. Especially in the context of the current opioid crisis, MD simulations can aid in unravelling molecular functionality and assist in clinical decision-making; the approaches presented in this paper are a pertinent step forward in this direction.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 7
    Publication Date: 2021-12-23
    Description: Molecular simulations of ligand–receptor interactions are a computational challenge, especially when their association- (‘on’-rate) and dissociation- (‘off’-rate) mechanisms are working on vastly differing timescales. One way of tackling this multiscale problem is to compute the free-energy landscapes, where molecular dynamics (MD) trajectories are used to only produce certain statistical ensembles. The approach allows for deriving the transition rates between energy states as a function of the height of the activation-energy barriers. In this article, we derive the association rates of the opioids fentanyl and N-(3-fluoro-1-phenethylpiperidin-4-yl)-N-phenyl propionamide (NFEPP) in a μ-opioid receptor by combining the free-energy landscape approach with the square-root-approximation method (SQRA), which is a particularly robust version of Markov modelling. The novelty of this work is that we derive the association rates as a function of the pH level using only an ensemble of MD simulations. We also verify our MD-derived insights by reproducing the in vitro study performed by the Stein Lab.
    Language: English
    Type: article , doc-type:article
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  • 8
    Publication Date: 2021-04-14
    Description: Due to the increase in accessibility and robustness of sequencing technology, single cell RNA-seq (scRNA-seq) data has become abundant. The technology has made significant contributions to discovering novel phenotypes and heterogeneities of cells. Recently, there has been a push for using single-- or multiple scRNA-seq snapshots to infer the underlying gene regulatory networks (GRNs) steering the cells' biological functions. To date, this aspiration remains unrealised. In this paper, we took a bottom-up approach and curated a stochastic two gene interaction model capturing the dynamics of a complete system of genes, mRNAs, and proteins. In the model, the regulation was placed upstream from the mRNA on the gene level. We then inferred the underlying regulatory interactions from only the observation of the mRNA population through~time. We could detect signatures of the regulation by combining information of the mean, covariance, and the skewness of the mRNA counts through time. We also saw that reordering the observations using pseudo-time did not conserve the covariance and skewness of the true time course. The underlying GRN could be captured consistently when we fitted the moments up to degree three; however, this required a computationally expensive non-linear least squares minimisation solver. There are still major numerical challenges to overcome for inference of GRNs from scRNA-seq data. These challenges entail finding informative summary statistics of the data which capture the critical regulatory information. Furthermore, the statistics have to evolve linearly or piece-wise linearly through time to achieve computational feasibility and scalability.
    Language: English
    Type: reportzib , doc-type:preprint
    Format: application/pdf
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  • 9
    Publication Date: 2021-04-13
    Language: English
    Type: article , doc-type:article
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  • 10
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