Computational Biology; Mathematical Biology; Stochastic Processes; Statistical Physics; Cell Biology; Computational Physics
Wald Sascha, Böttcher Lucas (2021), From classical to quantum walks with stochastic resetting on networks, in Physical Review E
, 103(1), 012122-012122.
BöttcherLucas, D'OrsognaMaria, ChouTom (2021), Using excess deaths and testing statistics to determine estimates of COVID-19 mortalities, in Eur. J. Epidemiol.
Böttcher Lucas, Gersbach Hans (2020), The great divide: drivers of polarization in the US public, in EPJ Data Science
, 9(1), 32-32.
Böttcher Lucas, Xia Mingtao, Chou Tom (2020), Why case fatality ratios can be misleading: individual- and population-based mortality estimates and factors influencing them, in Physical Biology
, 17(6), 065003-065003.
Richter Paul, Henkel Malte, Böttcher Lucas (2020), Aging and equilibration in bistable contagion dynamics, in Physical Review E
, 102(4), 042308-042308.
Böttcher Lucas (2020), A Random-Line-Graph Approach to Overlapping Line Segments, in Journal of Complex Networks
, 8(4), cnaa029.
Böttcher Lucas, Antulov-Fantulin Nino (2020), Unifying continuous, discrete, and hybrid susceptible-infected-recovered processes on networks, in Physical Review Research
, 2(3), 033121-033121.
D'Angelo Francesco, Böttcher Lucas (2020), Learning the Ising model with generative neural networks, in Physical Review Research
, 2(2), 023266-023266.
Böttcher Lucas, D'Orsogna Maria, Chou Tom, A statistical model of COVID-19 testing in populations: effects of sampling bias and testing errors, in Philos. Trans. Royal Soc. A
BöttcherLucas, PorterMason, Classical and quantum random-walk centrality measures in multilayer networks, in SIAM J. Appl. Math.
This research project seeks to formulate the fundamental high-dimensional mathematical structure shared by a number of related problems in cellular and developmental systems biology. Although the overall goal is to develop and analyze new mathematical and statistical approaches, we will focus on two specific biological systems studied at UCLA, for which significant data will be available:(i) Clonal tracking and stem cell dynamics: The overall process of hematopoiesis, the generation of blood and the adaptive immune system, involves a relatively small number of hematopoietic stem cells (HSCs) in the bone marrow, each occasionally differentiating to produce “transit-amplifying” or progenitor cells which expand in number while further differentiating into a diverse set of cell types (lineages). Recent experiments have used barcoded hematopoietic stem cells transplanted into rhesus macaques. Blood samples are then sequenced to determine the abundances of barcodes in samples of mature differentiated cells across different lineages. These data will, with appropriate theory and analysis, provide insight into the mechanisms of HSC differentiation, blood tissue aging, and clonal response to perturbations.(ii) Clonal distributions in Acute Myeloid Leukemia (AML): Another related system for which longitudinal clonal data will be available is the evolution of AML. Recent high-throughput sequencing studies have identified somatic mutations in individuals across a wide range of ages, including those who display significant mutational burden but who are completely asymptomatic to those with severe leukemia. Aging results in a gradual overall decline in hematopoiesis, a decrease in immunity, an accumulation in age-related mutations in most somatic cells. The clonal abundances of mutations in the hematopoietic system will also evolve, sharing processes that are expected in the HSC barcoding experiments. We will explore the hypothesis that aging of the immune system interacts with the mutational load to tip such stochastic differences in outcomes. We will model the above problems using a stochastic, heterogeneous, multispecies interacting birth-deathimmigration-mutation process. The different species or clones represent the different barcodes and cell lineages or mutational states. Immigration is mediated by differentiation of a relatively fixed pool of barcoded stem cells, while proliferation and mutation mediate differentiation and cancer progression. Interactions arise from global population regulation of myeloblast maintenance, HSC activation, or progenitor proliferation. Finally, in all of the above problems, clone abundances are determined through small (blood) samples randomly drawn from the organism. Thus, a statistical estimation framework (probably Bayesian) also needs to be developed in order to quantitatively incorporate the data being collected at UCLA.The expected results of this proposed project will include new data-motivated high-dimensional models of evolution of cell populations, providing mechanistic insight and parameter inference into hematopoiesis and leukemia progression. These new mathematical frameworks and statistical analyses will allow future testing and calibrating of models and inference of interaction terms amongst subpopulations. In particular, we expect the models and theoretical methods we develop will help guide experimentalists and clinicans in developing new experiments and measurements in the context of hematopoiesis and cancer progression.