Developing a multi-scale understanding of the B cell immune response

The immune system is composed of hundreds of highly-specialized cell types that collaboratively orchestrate an efficient response to pathogens and damage. Central to immune function, B lymphocytes participate in both the fast but non-specific innate, and persistent adaptive immune responses by sensing conserved pathogen-associated molecular patterns such as bacterial or viral CpG DNA as well as pathogen-specific patterns recognized by uniquely generated B-cell receptors. Upon activation, B cells undergo rapid expansion in number, deal with the threat by carrying out specific effector functions, and eventually die by programmed cell death or become long-lived memory cells. As a result, B-cell dynamics dictate vaccine efficiency, while aberrant proliferation and/or survival is the hallmark of autoimmune disorders, immune deficiency, and cancer. Decades of Nobel-worthy studies have characterized the key molecular players, cellular behaviors, and population dynamics of B cells, but the implicit heterogeneity and multi-scale nature of the B-cell response pose fundamental challenges to meaningful interpretation in specific contexts. A multi-scale understanding has only recently become possible with the advent of single-cell assays and the advancement of computational methods. To better-understand how individual cells orchestrate the population response, we developed CFSE flow cytometry deconvolution of cell populations, time-lapse cell tracking, and agent-based multi-scale computational modeling methods which we combined with single-cell and traditional biochemical assays and literature mining to develop a mechanistic understanding of the B cell immune response from the molecular pathways governing NFκB signaling, growth, cell-cycling, and apoptosis to cellular behavior and ultimately the population dynamics. We find that 1)the population behavior is best explained by individual B cells making decisions to either grow and divide, or die 2)that NFκB signaling serves as a central enforcer of B cell decision making by promoting division and survival and 3)that a multi-scale model can accurately predict population behavior with a lower dose of the stimulus, when NFκB cRel missing, and when pretreated with the drug rapamycin. The methods and models developed as part of this dissertation serve as predictive frameworks for future hypothesis-driven discovery and model-driven analysis, enabling meaningful interpretation of patient data, and drug target prediction across biological scales

FlowMax: A Computational Tool for Maximum Likelihood Deconvolution of CFSE Time Courses.

The immune response is a concerted dynamic multi-cellular process. Upon infection, the dynamics of lymphocyte populations are an aggregate of molecular processes that determine the activation, division, and longevity of individual cells. The timing of these single-cell processes is remarkably widely distributed with some cells undergoing their third division while others undergo their first. High cell-to-cell variability and technical noise pose challenges for interpreting popular dye-dilution experiments objectively. It remains an unresolved challenge to avoid under- or over-interpretation of such data when phenotyping gene-targeted mouse models or patient samples. Here we develop and characterize a computational methodology to parameterize a cell population model in the context of noisy dye-dilution data. To enable objective interpretation of model fits, our method estimates fit sensitivity and redundancy by stochastically sampling the solution landscape, calculating parameter sensitivities, and clustering to determine the maximum-likelihood solution ranges. Our methodology accounts for both technical and biological variability by using a cell fluorescence model as an adaptor during population model fitting, resulting in improved fit accuracy without the need for ad hoc objective functions. We have incorporated our methodology into an integrated phenotyping tool, FlowMax, and used it to analyze B cells from two NFκB knockout mice with distinct phenotypes; we not only confirm previously published findings at a fraction of the expended effort and cost, but reveal a novel phenotype of nfkb1/p105/50 in limiting the proliferative capacity of B cells following B-cell receptor stimulation. In addition to complementing experimental work, FlowMax is suitable for high throughput analysis of dye dilution studies within clinical and pharmacological screens with objective and quantitative conclusions

Effects of extrinsic mortality on the evolution of aging: a stochastic modeling approach.

The evolutionary theories of aging are useful for gaining insights into the complex mechanisms underlying senescence. Classical theories argue that high levels of extrinsic mortality should select for the evolution of shorter lifespans and earlier peak fertility. Non-classical theories, in contrast, posit that an increase in extrinsic mortality could select for the evolution of longer lifespans. Although numerous studies support the classical paradigm, recent data challenge classical predictions, finding that high extrinsic mortality can select for the evolution of longer lifespans. To further elucidate the role of extrinsic mortality in the evolution of aging, we implemented a stochastic, agent-based, computational model. We used a simulated annealing optimization approach to predict which model parameters predispose populations to evolve longer or shorter lifespans in response to increased levels of predation. We report that longer lifespans evolved in the presence of rising predation if the cost of mating is relatively high and if energy is available in excess. Conversely, we found that dramatically shorter lifespans evolved when mating costs were relatively low and food was relatively scarce. We also analyzed the effects of increased predation on various parameters related to density dependence and energy allocation. Longer and shorter lifespans were accompanied by increased and decreased investments of energy into somatic maintenance, respectively. Similarly, earlier and later maturation ages were accompanied by increased and decreased energetic investments into early fecundity, respectively. Higher predation significantly decreased the total population size, enlarged the shared resource pool, and redistributed energy reserves for mature individuals. These results both corroborate and refine classical predictions, demonstrating a population-level trade-off between longevity and fecundity and identifying conditions that produce both classical and non-classical lifespan effects

Comparison of FlowMax to the Cyton Calculator.

<p>The Cyton Calculator <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0067620#pone.0067620-Hawkins3" target="_blank">[9]</a> and a computational tool implementing our methodology, “FlowMax,” were used to train the cyton model with log-normally distributed division and death times on a CFSE time course of wildtype B cells stimulated with lipopolysaccharides (LPS). The best-fit generational cell counts were input to the Cyton Calculator. (A) Visual summary of solution quality estimation pipeline implemented as part of FlowMax. Candidate parameter sets are filtered by the normalized % area difference score, parameter sensitivity ranges are calculated, parameter sensitivity ranges are clustered to reveal non-redundant maximum-likelihood parameter ranges (red ranges). Jagged lines represent the sum of uniform parameter distributions in each cluster. (B) Best fit cyton model parameters determined using the Cyton Calculator (blue dots) and our phenotyping tool, FlowMax (square red individual fits with sensitivity ranges represented by error bars and square green weighted cluster averages with error bars representing the intersection of parameter sensitivity ranges for 41 solutions in the only identified cluster). (C) Plots of Fs (the fraction of cells dividing to the next generation), and log-normal distributions for the time to divide and die of undivided and dividing cells sampled uniformly from best-fit cluster ranges in (B). (D) Generational (colors) and total cell counts (black) are plotted as a function of time for 250 cyton parameter sets sampled uniformly from the intersection of best-fit cluster parameter ranges. Red dots show average experimental cell counts for each time point. Error bars show standard deviation for duplicate runs.</p

Proposed integrated phenotyping approach (FlowMax).

<p>CFSE flow-cytometry time series are preprocessed to create one-dimensional fluorescence histograms that are used to determine the cell proliferation parameters for each time point, using the parameters of the previous time points as added constraints (step 1). Fluorescence parameters are then used to extend a cell population model and allow for direct training of the cell population parameters on the fluorescence histograms (step 2). To estimate solution sensitivity and redundancy, step 2 is repeated many times, solutions are filtered by score, parameter sensitivities are determined for each solution, non-redundant maximum-likelihood parameter ranges are found after clustering, and a final filtering step eliminates clusters representing poor solutions (step 3).</p

FlowMax: A Computational Tool for Maximum Likelihood Deconvolution of CFSE Time Courses

<div><p>The immune response is a concerted dynamic multi-cellular process. Upon infection, the dynamics of lymphocyte populations are an aggregate of molecular processes that determine the activation, division, and longevity of individual cells. The timing of these single-cell processes is remarkably widely distributed with some cells undergoing their third division while others undergo their first. High cell-to-cell variability and technical noise pose challenges for interpreting popular dye-dilution experiments objectively. It remains an unresolved challenge to avoid under- or over-interpretation of such data when phenotyping gene-targeted mouse models or patient samples. Here we develop and characterize a computational methodology to parameterize a cell population model in the context of noisy dye-dilution data. To enable objective interpretation of model fits, our method estimates fit sensitivity and redundancy by stochastically sampling the solution landscape, calculating parameter sensitivities, and clustering to determine the maximum-likelihood solution ranges. Our methodology accounts for both technical and biological variability by using a cell fluorescence model as an adaptor during population model fitting, resulting in improved fit accuracy without the need for <i>ad hoc</i> objective functions. We have incorporated our methodology into an integrated phenotyping tool, FlowMax, and used it to analyze B cells from two NFκB knockout mice with distinct phenotypes; we not only confirm previously published findings at a fraction of the expended effort and cost, but reveal a novel phenotype of nfkb1/p105/50 in limiting the proliferative capacity of B cells following B-cell receptor stimulation. In addition to complementing experimental work, FlowMax is suitable for high throughput analysis of dye dilution studies within clinical and pharmacological screens with objective and quantitative conclusions.</p></div

Classical and non-classical conditions identified by simulated annealing optimization.

<p>A simulated annealing optimization scheme was used to find values for six simulation-invariant parameters that would predispose populations toward either increased or decreased maintenance in response to increased extrinsic mortality. The fit score stochastically improved over the course of the optimization (<b>A and C</b>). The optimal starvation modifier (ε), growth efficiency (), initial energy of individuals (), mating energy (), mating energy threshold (<i>mateThreshold</i>), and death cost function type () for the classical (<b>B</b>), and non-classical (<b>D</b>) effect are shown as a function of optimization duration. D_type: 0 = Sigmoidal Low, 1 = Linear Low, 2 = Asymptotic Low, 3 = Sigmoidal High, 4 = Linear High, 5 = Asymptotic High. Colored dots indicate that the intrinsic death effect was monotonic.</p

The fcyton cell proliferation model.

<p>(A) A graphical representation summarizing the model parameters required to calculate the total number of cells in each generation as a function of time. Division and death times are assumed to be log-normally distributed and different between undivided and dividing cells. Progressor fractions (Fs) determine the fraction of responding cells in each generation committed to division and protected from death. (B,C) Analysis of the accuracy associated with fitting fcyton parameters for a set of 1,000 generated realistic datasets of generational cell counts assuming perfect cell counts and an optimized <i>ad hoc</i> objective function (see <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0067620#pone.0067620.s012" target="_blank">Text S1</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0067620#pone.0067620.s010" target="_blank">Tables S3</a> and <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0067620#pone.0067620.s011" target="_blank">S4</a>). (B) Average percent error in generational cell counts normalized to the maximum generational cell count for each time course. Numbers indicate an error ≥ 0.5%. (C) Analysis of the error associated with determining key fcyton parameters. Box plots represent 5, 25, 50, 75, and 95 percentile values. Outliers are not shown. For analysis of all fcyton parameter errors see also <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0067620#pone.0067620.s002" target="_blank">Figure S2</a> (green).</p

Deriving Quantitative Cell Biological Information from Dye-Dilution Lymphocyte Proliferation Experiments

The dye-dilution assay is a powerful tool to study lymphocyte expansion dynamics. By combining time course dye-dilution experiments with computational analysis, quantitative information about cell biological parameters, such as percentage of cells dividing, time of division, and time of death, can be produced. Here, we describe the method to generate quantitative cell biological insights from dye-dilution experiments. We describe experimental methods for generating dye-dilution data with murine lymphocytes and then describe the computational data analysis workflow using a recently developed software package called FlowMax. The aim is to interpret the dye-dilution data quantitatively and objectively, such that cell biological parameters can be reported with an appropriate measure of confidence, which in turn depends on the quality and quantity of available data