Construction And Prediction Of Cancer Evolution Landscape Based On Multiscale Modeling

Cancer is a systemic disease with continuous dynamic evolution.Its complex intraand inter-patient heterogeneity has brought great difficulties and challenges to cancer treatment.With the maturity of high-throughput sequencing technology,especially the single-cell biotechnology,scientists have dived into the details of cancer progression at an unprecedented resolution.Mathematical oncology method combining multiscale modeling and multiomics data analysis,plays a key role in understanding cancer mechanisms and predicting cancer progression.This dissertation mainly focuses on exploring the relationship between cancer development and cellular composition,establishes a multiscale framework among cell,subclone,and tumor and constructs the evolutionary trajectories of cancer.Furthermore,the long-term growth patterns and evolutionary trajectories are predicted based on short-term measurements.The main innovative work of this dissertation includes the following three aspects.1.In order to reveal cancer evolution and intra-tumor heterogeneity,a multiscale mathematical framework is proposed to quantitatively delineating the evolution landscape of cancer.Considering the heterogeneity of cancer spans multiple scales,three ordinary differential equation models for describing three different patterns at the population level and a cellular probabilistic model at the cellular level are constructed to describe the inter-and intra-patient heterogeneity of cancer,respectively.In addition,due to the natural fact that cancer cells belonging to distinct subclones collectively constitute tumor,we bridge the gap between cellular scale and population scale.Firstly,due to the non-negativity of the number of cells,the connection between different scales is transformed into a non-negative LASSO problem in this dissertation.The coordinate descent method is used to seek the solutions under different growth patterns.Furthermore,through reconstructing and deducing the solutions,we obtain the composition of subclones at any time.Therefore,evolution landscapes can be displayed at the subclonal level.In order to verify the rationality of the proposed framework,the real data for white blood cell counts of 21 chronic lymphocytic leukemia patients is used to construct their evolutionary trajectories.Quantitative indices such as intra-tumor heterogeneity and probability of cell division are calculated based on the obtained evolution landscape of each patient.It is found that the average heterogeneity level of patients with exponential pattern is higher while the probability of cell division of patients with SF3B1 mutation is lower,which is in line with the conclusion of biological experiments,proving the effectiveness of the landscapes constructed by our multiscale framework.2.According to the significant differences between heterogeneous growth patterns,the prediction of long-term growth patterns based on short-term subclonal compositions is achieved.For the three typical growth patterns,we calculate several quantitative indices,including number of subclone,intra-tumor heterogeneity,frequency of evolution,probability of cell division,etc..The results indicate that there are significant differences in subclonal compositions between different growth patterns,especially at the initial time,which further inspires us to explore the prediction of long-term growth patterns from short-term subclonal information.Firstly,we build a training dataset composed of subclonal information obtained from multiple simulations.Taking the number of subclones or the proportion of subclones as the input,it shows good performances to predict the three growth patterns in different machine learning models,especially the distinction between indolent and nonindolent patterns.Furthermore,we identify several types of subclones that have the greatest impact on the growth pattern and construct a more concise prediction model.In addition,the prediction model demonstrates that the subclones at the initial time have contained the evolutionary information for a long time.In a study of six patients with triple-negative breast cancer,a personalized model is constructed for each patient.The prediction of growth pattern is realized by calculating each patient’s subclonal composition based on gene signature scoring analysis of single cell RNA sequencing data,which is further supported through clinical data.3.For a given growth pattern,a Darwinian index is proposed to quantify and predict the evolutionary trajectory of cancer.There are various evolutionary trajectories under the same growth pattern,and determining the exact one in advance is of great significance for the development of adaptive therapy and personalized medicine.Based on the new-Darwinian evolution hypothesis of cancer,we propose the Darwinian index to describe the degree of evolution,which enables quantitative distinction and accurate prediction of different evolutionary trajectories under a given growth pattern.Firstly,given the mathematical definition of the Darwinian index,subclone pools with different evolution steps are designed accordingly.Based on the multiscale framework,the solutions and corresponding evolution landscape under different Darwinian indices could be calculated and depicted,respectively.By deconstructing these landscapes,the evolution details,including evolution type,evolution direction,and evolution speed,could be described under different Darwinian indices.Furthermore,the subclonal compositions at the initial moment successfully predicts the Darwinian index and the corresponding evolutionary trajectory.In the case of melanoma patient with known longitudinal tumor sizes,its evolutionary trajectory is successfully inferred from singlecell RNA sequencing data and supported by relevant researches.Finally,two types of subclones are identified to have ability to predict the malignant degree of cancer recurrence,which has an important significance for guiding cancer prognosis.