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Examination of T-cell receptor (TCR) clonality has become a way of understanding immunologic response to cancer and its interventions in recent years. An aspect of these analyses is determining which receptors expand or contract…
Diverse T and B cell repertoires play an important role in mounting effective immune responses against a wide range of pathogens and malignant cells. The number of unique T and B cell clones is characterized by T and B cell receptors (TCRs…
We study the Langevin dynamics of the adaptive immune system, modelled by a lymphocyte network in which the B cells are interacting with the T cells and antigen. We assume that B clones and T clones are evolving in different thermal noise…
A key challenge in molecular biology is to decipher the mapping of protein sequence to function. To perform this mapping requires the identification of sequence features most informative about function. Here, we quantify the amount of…
In most of the recent immunological literature the differences across antigen receptor populations are examined via non-parametric statistical measures of species overlap and diversity borrowed from ecological studies. While this approach…
It is often of interest to perform clustering on longitudinal data, yet it is difficult to formulate an intuitive model for which estimation is computationally feasible. We propose a model-based clustering method for clustering objects that…
The clonal expansion of T cells during an infection is tightly regulated to ensure an appropriate immune response against invading pathogens. Although experiments have mapped the trajectory from expansion to contraction, the interplay…
This paper deals with a new model for clonal network dynamics. We describe in detail this model and derive special equations governing immune system dynamics based on the general gradient type principles that can be inherent to a wide class…
Differential abundance (DA) analysis in microbiome studies has recently been used to uncover a plethora of associations between microbial composition and various health conditions. While current approaches to DA typically apply only to…
Mixtures of linear mixed models are widely used for modelling longitudinal data for which observation times differ between subjects. In typical applications, temporal trends are described using a basis expansion, with basis coefficients…
T-cell receptor (TCR) repertoire data contain information about infections that could be used in disease diagnostics and vaccine development, but extracting that information remains a major challenge. Here we developed a statistical…
The diverse repertoire of T-cell receptors (TCR) plays a key role in the adaptive immune response to infections. Previous studies show that secondary responses to the yellow fever vaccine - the model for acute infection in humans - are…
Most statistical classifiers are designed to find patterns in data where numbers fit into rows and columns, like in a spreadsheet, but many kinds of data do not conform to this structure. To uncover patterns in non-conforming data, we…
Self-renewal is a constitutive property of stem cells. Testing the cancer stem cell hypothesis requires investigation of the impact of self-renewal on cancer expansion. To understand better this impact, we propose a mathematical model…
Mixed membership models are an extension of finite mixture models, where each observation can partially belong to more than one mixture component. A probabilistic framework for mixed membership models of high-dimensional continuous data is…
High-throughput sequencing of B- and T-cell receptors makes it possible to track immune repertoires across time, in different tissues, and in acute and chronic diseases or in healthy individuals. However, quantitative comparison between…
In a mathematical model of interacting biological organisms, where external interventions may alter behavior over time, traditional models that assume fixed parameters usually do not capture the evolving dynamics. In oncology, this is…
Despite initial success, cancer therapies often fail due to the emergence of drug-resistant cells. In this study, we use a mathematical model to investigate how cancer evolves over time, specifically focusing on the state of the tumor when…
Cluster analysis of biological samples using gene expression measurements is a common task which aids the discovery of heterogeneous biological sub-populations having distinct mRNA profiles. Several model-based clustering algorithms have…
Adaptive therapy (AT) is designed to postpone the emergence of drug resistance by exploiting evolutionary competition among tumor subclones. Most mathematical models of AT assume a binary population structure of drug-sensitive and…