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Register a new userA hybrid algorithm for coupling PDE and compartment-based dynamics
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Stochastic simulation methods can be applied successfully to model exact spatio-temporally resolved reaction-diffusion systems. However, in many cases, these methods can quickly become extremely computationally intensive with increasing particle numbers. An alternative description of many of these systems can be derived in the diffusive limit as a deterministic, continuum system of partial differential equations. Although the numerical solution of such partial differential equations is, in general, much more efficient than the full stochastic simulation, the deterministic continuum description is generally not valid when copy numbers are low and stochastic effects dominate. Therefore, to take advantage of the benefits of both of these types of models, each of which may be appropriate in different parts of a spatial domain, we have developed an algorithm that can be used to couple these two types of model together. This hybrid coupling algorithm uses an overlap region between the two modelling regimes. By coupling fluxes at one end of the interface and using a concentration-matching condition at the other end, we ensure that mass is appropriately transferred between PDE- and compartment-based regimes. Our methodology gives notable reductions in simulation time in comparison with using a fully stochastic model, whilst maintaining the important stochastic features of the system and providing detail in appropriate areas of the domain. We test our hybrid methodology robustly by applying it to several biologically motivated problems including diffusion and morphogen gradient formation. Our analysis shows that the resulting error is small, unbiased and does not grow over time.
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COVID-19 pandemic is severely impacting the lives of billions across the globe. Even after taking massive protective measures like nation-wide lockdowns, discontinuation of international flight services, rigorous testing etc., the infection spreading is still growing steadily, causing thousands of deaths and serious socio-economic crisis. Thus, the identification of the major factors of this infection spreading dynamics is becoming crucial to minimize impact and lifetime of COVID-19 and any future pandemic. In this work, a probabilistic cellular automata based method has been employed to model the infection dynamics for a significant number of different countries. This study proposes that for an accurate data-driven modeling of this infection spread, cellular automata provides an excellent platform, with a sequential genetic algorithm for efficiently estimating the parameters of the dynamics. To the best of our knowledge, this is the first attempt to understand and interpret COVID-19 data using optimized cellular automata, through genetic algorithm. It has been demonstrated that the proposed methodology can be flexible and robust at the same time, and can be used to model the daily active cases, total number of infected people and total death cases through systematic parameter estimation. Elaborate analyses for COVID-19 statistics of forty countries from different continents have been performed, with markedly divergent time evolution of the infection spreading because of demographic and socioeconomic factors. The substantial predictive power of this model has been established with conclusions on the key players in this pandemic dynamics.
Persistent Homology is a fairly new branch of Computational Topology which combines geometry and topology for an effective shape description of use in Pattern Recognition. In particular it registers through Betti Numbers the presence of holes and their persistence while a parameter (filtering function) is varied. In this paper, some recent developments in this field are integrated in a k-Nearest Neighbor search algorithm suited for an automatic retrieval of melanocytic lesions. Since long, dermatologists use five morphological parameters (A = Asymmetry, B = Boundary, C = Color, D = Diameter, E = Elevation or Evolution) for assessing the malignancy of a lesion. The algorithm is based on a qualitative assessment of the segmented images by computing both 1 and 2-dimensional Persistent Betti Numbers functions related to the ABCDE parameters and to the internal texture of the lesion. The results of a feasibility test on a set of 107 melanocytic lesions are reported in the section dedicated to the numerical experiments.
In the past few decades, the development of fluorescent technologies and microscopic techniques has greatly improved scientists ability to observe real-time single-cell activities. In this paper, we consider the filtering problem associate with these advanced technologies, i.e., how to estimate latent dynamic states of an intracellular multiscale stochastic reaction network from time-course measurements of fluorescent reporters. A good solution to this problem can further improve scientists ability to extract information about intracellular systems from time-course experiments. A straightforward approach to this filtering problem is to use a particle filter where particles are generated by simulation of the full model and weighted according to observations. However, the exact simulation of the full dynamic model usually takes an impractical amount of computational time and prevents this type of particle filters from being used for real-time applications, such as transcription regulation networks. Inspired by the recent development of hybrid approximations to multiscale chemical reaction networks, we approach the filtering problem in an alternative way. We first prove that accurate solutions to the filtering problem can be constructed by solving the filtering problem for a reduced model that represents the dynamics as a hybrid process. The model reduction is based on exploiting the time-scale separations in the original network and, therefore, can greatly reduce the computational effort required to simulate the dynamics. As a result, we are able to develop efficient particle filters to solve the filtering problem for the original model by applying particle filters to the reduced model. We illustrate the accuracy and the computational efficiency of our approach using several numerical examples.
The ongoing COVID-19 pandemic highlights the essential role of mathematical models in understanding the spread of the virus along with a quantifiable and science-based prediction of the impact of various mitigation measures. Numerous types of models have been employed with various levels of success. This leads to the question of what kind of a mathematical model is most appropriate for a given situation. We consider two widely used types of models: equation-based models (such as standard compartmental epidemiological models) and agent-based models. We assess their performance by modeling the spread of COVID-19 on the Hawaiian island of Oahu under different scenarios. We show that when it comes to information crucial to decision making, both models produce very similar results. At the same time, the two types of models exhibit very different characteristics when considering their computational and conceptual complexity. Consequently, we conclude that choosing the model should be mostly guided by available computational and human resources.
An unsolved challenge in the development of antigen specific immunotherapies is determining the optimal antigens to target. Comprehension of antigen-MHC binding is paramount towards achieving this goal. Here, we present CASTELO, a combined machine learning-molecular dynamics (ML-MD) approach to design novel antigens of increased MHC binding affinity for a Type 1 diabetes (T1D)-implicated system. We build upon a small molecule lead optimization algorithm by training a convolutional variational autoencoder (CVAE) on MD trajectories of 48 different systems across 4 antigens and 4 HLA serotypes. We develop several new machine learning metrics including a structure-based anchor residue classification model as well as cluster comparison scores. ML-MD predictions agree well with experimental binding results and free energy perturbation-predicted binding affinities. Moreover, ML-MD metrics are independent of traditional MD stability metrics such as contact area and RMSF, which do not reflect binding affinity data. Our work supports the role of structure-based deep learning techniques in antigen specific immunotherapy design.
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