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.
G-protein-coupled receptors (GPCRs) are key signaling proteins that mostly function as monomers, but for several receptors constitutive dimer formation has been described and in some cases is ...essential for function. Using single-molecule microscopy combined with super-resolution techniques on intact cells, we describe here a dynamic monomer-dimer equilibrium of µ-opioid receptors (µORs), where dimer formation is driven by specific agonists. The agonist DAMGO, but not morphine, induces dimer formation in a process that correlates both temporally and in its agonist- and phosphorylation-dependence with β-arrestin2 binding to the receptors. This dimerization is independent from, but may precede, µOR internalization. These data suggest a new level of GPCR regulation that links dimer formation to specific agonists and their downstream signals.
The joint analysis of two datasets Formula: see text and Formula: see text that describe the same phenomena (e.g. the cellular state), but measure disjoint sets of variables (e.g. mRNA vs. protein ...levels) is currently challenging. Traditional methods typically analyze single interaction patterns such as variance or covariance. However, problem-tailored external knowledge may contain multiple different information about the interaction between the measured variables. We introduce MIASA, a holistic framework for the joint analysis of multiple different variables. It consists of assembling multiple different information such as similarity vs. association, expressed in terms of interaction-scores or distances, for subsequent clustering/classification. In addition, our framework includes a novel qualitative Euclidean embedding method (qEE-Transition) which enables using Euclidean-distance/vector-based clustering/classification methods on datasets that have a non-Euclidean-based interaction structure. As an alternative to conventional optimization-based multidimensional scaling methods which are prone to uncertainties, our qEE-Transition generates a new vector representation for each element of the dataset union Formula: see text in a common Euclidean space while strictly preserving the original ordering of the assembled interaction-distances. To demonstrate our work, we applied the framework to three types of simulated datasets: samples from families of distributions, samples from correlated random variables, and time-courses of statistical moments for three different types of stochastic two-gene interaction models. We then compared different clustering methods with vs. without the qEE-Transition. For all examples, we found that the qEE-Transition followed by Ward clustering had superior performance compared to non-agglomerative clustering methods but had a varied performance against ultrametric-based agglomerative methods. We also tested the qEE-Transition followed by supervised and unsupervised machine learning methods and found promising results, however, more work is needed for optimal parametrization of these methods. As a future perspective, our framework points to the importance of more developments and validation of distance-distribution models aiming to capture multiple-complex interactions between different variables.
Despite recent advances in cellular cryo-electron tomography (CET), developing automated tools for macromolecule identification in submolecular resolution remains challenging due to the lack of ...annotated data and high structural complexities. To date, the extent of the deep learning methods constructed for this problem is limited to conventional Convolutional Neural Networks (CNNs). Identifying macromolecules of different types and sizes is a tedious and time-consuming task. In this paper, we employ a capsule-based architecture to automate the task of macromolecule identification, that we refer to as 3D-UCaps. In particular, the architecture is composed of three components: feature extractor, capsule encoder, and CNN decoder. The feature extractor converts voxel intensities of input sub-tomograms to activities of local features. The encoder is a 3D Capsule Network (CapsNet) that takes local features to generate a low-dimensional representation of the input. Then, a 3D CNN decoder reconstructs the sub-tomograms from the given representation by upsampling. We performed binary and multi-class localization and identification tasks on synthetic and experimental data. We observed that the 3D-UNet and the 3D-UCaps had an formula omittedscore mostly above 60% and 70%, respectively, on the test data. In both network architectures, we observed degradation of at least 40% in the formula omitted-score when identifying very small particles (PDB entry 3GL1) compared to a large particle (PDB entry 4D8Q). In the multi-class identification task of experimental data, 3D-UCaps had an formula omitted-score of 91% on the test data in contrast to 64% of the 3D-UNet. The better formula omitted-score of 3D-UCaps compared to 3D-UNet is obtained by a higher precision score. We speculate this to be due to the capsule network employed in the encoder. To study the effect of the CapsNet-based encoder architecture further, we performed an ablation study and perceived that the formula omitted-score is boosted as network depth is increased which is in contrast to the previously reported results for the 3D-UNet. To present a reproducible work, source code, trained models, data as well as visualization results are made publicly available. Quantitative and qualitative results show that 3D-UCaps successfully perform various downstream tasks including identification and localization of macromolecules and can at least compete with CNN architectures for this task. Given that the capsule layers extract both the existence probability and the orientation of the molecules, this architecture has the potential to lead to representations of the data that are better interpretable than those of 3D-UNet.
5q-spinal muscular atrophy (SMA) is a neuromuscular disorder (NMD) that has become one of the first 5% treatable rare diseases. The efficacy of new SMA therapies is creating a dynamic SMA patient ...landscape, where disease progression and scoliosis development play a central role, however, remain difficult to anticipate. New approaches to anticipate disease progression and associated sequelae will be needed to continuously provide these patients the best standard of care. Here we developed an interpretable machine learning (ML) model that can function as an assistive tool in the anticipation of SMA-associated scoliosis based on disease progression markers. We collected longitudinal data from 86 genetically confirmed SMA patients. We selected six features routinely assessed over time to train a random forest classifier. The model achieved a mean accuracy of 0.77 (SD 0.2) and an average ROC AUC of 0.85 (SD 0.17). For class 1 'scoliosis' the average precision was 0.84 (SD 0.11), recall 0.89 (SD 0.22), F1-score of 0.85 (SD 0.17), respectively. Our trained model could predict scoliosis using selected disease progression markers and was consistent with the radiological measurements. During post validation, the model could predict scoliosis in patients who were unseen during training. We also demonstrate that rare disease data sets can be wrangled to build predictive ML models. Interpretable ML models can function as assistive tools in a changing disease landscape and have the potential to democratize expertise that is otherwise clustered at specialized centers.
Human T-lymphotropic virus type-1 (HTLV-1) persists within hosts via infectious spread (de novo infection) and mitotic spread (infected cell proliferation), creating a population structure of ...multiple clones (infected cell populations with identical genomic proviral integration sites). The relative contributions of infectious and mitotic spread to HTLV-1 persistence are unknown, and will determine the efficacy of different approaches to treatment. The prevailing view is that infectious spread is negligible in HTLV-1 persistence beyond early infection. However, in light of recent high-throughput data on the abundance of HTLV-1 clones, and recent estimates of HTLV-1 clonal diversity that are substantially higher than previously thought (typically between 104 and 105 HTLV-1+ T cell clones in the body of an asymptomatic carrier or patient with HTLV-1-associated myelopathy/tropical spastic paraparesis), ongoing infectious spread during chronic infection remains possible. We estimate the ratio of infectious to mitotic spread using a hybrid model of deterministic and stochastic processes, fitted to previously published HTLV-1 clonal diversity estimates. We investigate the robustness of our estimates using three alternative estimators. We find that, contrary to previous belief, infectious spread persists during chronic infection, even after HTLV-1 proviral load has reached its set point, and we estimate that between 100 and 200 new HTLV-1 clones are created and killed every day. We find broad agreement between all estimators. The risk of HTLV-1-associated malignancy and inflammatory disease is strongly correlated with proviral load, which in turn is correlated with the number of HTLV-1-infected clones, which are created by de novo infection. Our results therefore imply that suppression of de novo infection may reduce the risk of malignant transformation.
We previously reported the successful design, synthesis and testing of the prototype opioid painkiller NFEPP that does not elicit adverse side effects. The design process of NFEPP was based on ...mathematical modelling of extracellular interactions between G-protein coupled receptors (GPCRs) and ligands, recognizing that GPCRs function differently under pathological versus healthy conditions. We now present an additional and novel stochastic model of GPCR function that includes intracellular dissociation of G-protein subunits and modulation of plasma membrane calcium channels and their dependence on parameters of inflamed and healthy tissue (pH, radicals). The model is validated against in vitro experimental data for the ligands NFEPP and fentanyl at different pH values and radical concentrations. We observe markedly reduced binding affinity and calcium channel inhibition for NFEPP at normal pH compared to lower pH, in contrast to the effect of fentanyl. For increasing radical concentrations, we find enhanced constitutive G-protein activation but reduced ligand binding affinity. Assessing the different effects, the results suggest that, compared to radicals, low pH is a more important determinant of overall GPCR function in an inflamed environment. Future drug design efforts should take this into account.
Osteoarthritis (OA) is the most common cause of disability in ageing societies, with no effective therapies available to date. Two preclinical models are widely used to validate novel OA ...interventions (MCL-MM and DMM). Our aim is to discern disease dynamics in these models to provide a clear timeline in which various pathological changes occur. OA was surgically induced in mice by destabilisation of the medial meniscus. Analysis of OA progression revealed that the intensity and duration of chondrocyte loss and cartilage lesion formation were significantly different in MCL-MM vs DMM. Firstly, apoptosis was seen prior to week two and was narrowly restricted to the weight bearing area. Four weeks post injury the magnitude of apoptosis led to a 40-60% reduction of chondrocytes in the non-calcified zone. Secondly, the progression of cell loss preceded the structural changes of the cartilage spatio-temporally. Lastly, while proteoglycan loss was similar in both models, collagen type II degradation only occurred more prominently in MCL-MM. Dynamics of chondrocyte loss and lesion formation in preclinical models has important implications for validating new therapeutic strategies. Our work could be helpful in assessing the feasibility and expected response of the DMM- and the MCL-MM models to chondrocyte mediated therapies.
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 (interactions 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.
Spreading processes are important drivers of change in social systems. To understand the mechanisms of spreading it is fundamental to have information about the underlying contact network and the ...dynamical parameters of the process. However, in many real-wold examples, this information is not known and needs to be inferred from data. State-of-the-art spreading inference methods have mostly been applied to modern social systems, as they rely on availability of very detailed data. In this paper we study the inference challenges for historical spreading processes, for which only very fragmented information is available. To cope with this problem, we extend existing network models by formulating a model on a mesoscale with temporal spreading rate. Furthermore, we formulate the respective parameter inference problem for the extended model. We apply our approach to the romanization process of Northern Tunisia, a scarce dataset, and study properties of the inferred time-evolving interregional networks. As a result, we show that (1) optimal solutions consist of very different network structures and spreading rate functions; and that (2) these diverse solutions produce very similar spreading patterns. Finally, we discuss how inferred dominant interregional connections are related to available archaeological traces. Historical networks resulting from our approach can help understanding complex processes of cultural change in ancient times.
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