Order-of-Mutation Effects on Cancer Progression: Models for Myeloproliferative Neoplasm.

In some patients with myeloproliferative neoplasms (MPN), two genetic mutations are often found: JAK2 V617F and one in the TET2 gene. Whether one mutation is present influences how the other subsequent mutation will affect the regulation of gene expression. In other words, when a patient carries both mutations, the order of when they first arose has been shown to influence disease progression and prognosis. We propose a nonlinear ordinary differential equation, the Moran process, and Markov chain models to explain the non-additive and non-commutative mutation effects on recent clinical observations of gene expression patterns, proportions of cells with different mutations, and ages at diagnosis of MPN. Combined, these observations are used to shape our modeling framework. Our key proposal is that bistability in gene expression provides a natural explanation for many observed order-of-mutation effects. We also propose potential experimental measurements that can be used to confirm or refute predictions of our models.

The role of APOBEC3-induced mutations in the differential evolution of monkeypox virus.

Recent studies show that newly sampled monkeypox virus (MPXV) genomes exhibit mutations consistent with Apolipoprotein B mRNA Editing Catalytic Polypeptide-like3 (APOBEC3)-mediated editing compared to MPXV genomes collected earlier. It is unclear whether these single-nucleotide polymorphisms (SNPs) result from APOBEC3-induced editing or are a consequence of genetic drift within one or more MPXV animal reservoirs. We develop a simple method based on a generalization of the General-Time-Reversible model to show that the observed SNPs are likely the result of APOBEC3-induced editing. The statistical features allow us to extract lineage information and estimate evolutionary events.

Order-of-mutation effects on cancer progression: models for myeloproliferative neoplasm.

In some patients with myeloproliferative neoplasms (MPN), two genetic mutations are often found, JAK2 V617F and one in the TET2 gene. Whether or not one mutation is present will influence how the other subsequent mutation affects the regulation of gene expression. When both mutations are present, the order of their occurrence has been shown to influence disease progression and prognosis. We propose a nonlinear ordinary differential equation (ODE), Moran process, and Markov chain models to explain the non-additive and non-commutative mutation effects on recent clinical observations of gene expression patterns, proportions of cells with different mutations, and ages at diagnosis of MPN. These observations consistently shape our modeling framework. Our key proposal is that bistability in gene expression provides a natural explanation for many observed order-of-mutation effects. We also propose potential experimental measurements that can be used to confirm or refute predictions of our models.

Mathematical Characterization of Private and Public Immune Receptor Sequences.

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 and BCRs), respectively. Although receptor sequences are generated probabilistically by recombination processes, clinical studies found a high degree of sharing of TCRs and BCRs among different individuals. In this work, we use a general probabilistic model for T/B cell receptor clone abundances to define "publicness" or "privateness" and information-theoretic measures for comparing the frequency of sampled sequences observed across different individuals. We derive mathematical formulae to quantify the mean and the variances of clone richness and overlap. Our results can be used to evaluate the effect of different sampling protocols on abundances of clones within an individual as well as the commonality of clones across individuals. Using synthetic and empirical TCR amino acid sequence data, we perform simulations to study expected clonal commonalities across multiple individuals. Based on our formulae, we compare these simulated results with the analytically predicted mean and variances of the repertoire overlap. Complementing the results on simulated repertoires, we derive explicit expressions for the richness and its uncertainty for specific, single-parameter truncated power-law probability distributions. Finally, the information loss associated with grouping together certain receptor sequences, as is done in spectratyping, is also evaluated. Our approach can be, in principle, applied under more general and mechanistically realistic clone generation models.

Order-of-mutation effects on cancer progression: models for myeloproliferative neoplasm.

In some patients with myeloproliferative neoplasms (MPN), two genetic mutations are often found, JAK2 V617F and one in the TET2 gene. Whether or not one mutation is present will influence how the other subsequent mutation affects the regulation of gene expression. When both mutations are present, the order of their occurrence has been shown to influence disease progression and prognosis. We propose a nonlinear ordinary differential equation (ODE), Moran process, and Markov chain models to explain the non-additive and non-commutative mutation effects on recent clinical observations of gene expression patterns, proportions of cells with different mutations, and ages at diagnosis of MPN. These observations consistently shape our modeling framework. Our key proposal is that bistability in gene expression provides a natural explanation for many observed order-of-mutation effects. We also propose potential experimental measurements that can be used to confirm or refute predictions of our models.

The role of APOBEC3-induced mutations in the differential evolution of monkeypox virus.

Recent studies show that newly sampled monkeypox virus (MPXV) genomes exhibit mutations consistent with Apolipoprotein B mRNA Editing Catalytic Polypeptide-like3 (APOBEC3)-mediated editing, compared to MPXV genomes collected earlier. It is unclear whether these single nucleotide polymorphisms (SNPs) result from APOBEC3-induced editing or are a consequence of genetic drift within one or more MPXV animal reservoirs. We develop a simple method based on a generalization of the General-Time-Reversible (GTR) model to show that the observed SNPs are likely the result of APOBEC3-induced editing. The statistical features allow us to extract lineage information and estimate evolutionary events.

Machine learning and statistical prediction of patient quality-of-life after prostate radiation therapy.

Thanks to advancements in diagnosis and treatment, prostate cancer patients have high long-term survival rates. Currently, an important goal is to preserve quality of life during and after treatment. The relationship between the radiation a patient receives and the subsequent side effects he experiences is complex and difficult to model or predict. Here, we use machine learning algorithms and statistical models to explore the connection between radiation treatment and post-treatment gastro-urinary function. Since only a limited number of patient datasets are currently available, we used image flipping and curvature-based interpolation methods to generate more data to leverage transfer learning. Using interpolated and augmented data, we trained a convolutional autoencoder network to obtain near-optimal starting points for the weights. A convolutional neural network then analyzed the relationship between patient-reported quality-of-life and radiation doses to the bladder and rectum. We also used analysis of variance and logistic regression to explore organ sensitivity to radiation and to develop dosage thresholds for each organ region. Our findings show no statistically significant association between the bladder and quality-of-life scores. However, we found a statistically significant association between the radiation applied to posterior and anterior rectal regions and changes in quality of life. Finally, we estimated radiation therapy dose thresholds for each organ. Our analysis connects machine learning methods with organ sensitivity, thus providing a framework for informing cancer patient care using patient reported quality-of-life metrics.

A Mathematical Model of the Effects of Aging on Naive T Cell Populations and Diversity.

The human adaptive immune response is known to weaken in advanced age, resulting in increased severity of pathogen-born illness, poor vaccine efficacy, and a higher prevalence of cancer in the elderly. Age-related erosion of the T cell compartment has been implicated as a likely cause, but the underlying mechanisms driving this immunosenescence have not been quantitatively modeled and systematically analyzed. T cell receptor diversity, or the extent of pathogen-derived antigen responsiveness of the T cell pool, is known to diminish with age, but inherent experimental difficulties preclude accurate analysis on the full organismal level. In this paper, we formulate a mechanistic mathematical model of T cell population dynamics on the immunoclonal subpopulation level, which provides quantitative estimates of diversity. We define different estimates for diversity that depend on the individual number of cells in a specific immunoclone. We show that diversity decreases with age primarily due to diminished thymic output of new T cells and the resulting overall loss of small immunoclones.

Modeling large fluctuations of thousands of clones during hematopoiesis: The role of stem cell self-renewal and bursty progenitor dynamics in rhesus macaque.

In a recent clone-tracking experiment, millions of uniquely tagged hematopoietic stem cells (HSCs) and progenitor cells were autologously transplanted into rhesus macaques and peripheral blood containing thousands of tags were sampled and sequenced over 14 years to quantify the abundance of hundreds to thousands of tags or "clones." Two major puzzles of the data have been observed: consistent differences and massive temporal fluctuations of clone populations. The large sample-to-sample variability can lead clones to occasionally go "extinct" but "resurrect" themselves in subsequent samples. Although heterogeneity in HSC differentiation rates, potentially due to tagging, and random sampling of the animals' blood and cellular demographic stochasticity might be invoked to explain these features, we show that random sampling cannot explain the magnitude of the temporal fluctuations. Moreover, we show through simpler neutral mechanistic and statistical models of hematopoiesis of tagged cells that a broad distribution in clone sizes can arise from stochastic HSC self-renewal instead of tag-induced heterogeneity. The very large clone population fluctuations that often lead to extinctions and resurrections can be naturally explained by a generation-limited proliferation constraint on the progenitor cells. This constraint leads to bursty cell population dynamics underlying the large temporal fluctuations. We analyzed experimental clone abundance data using a new statistic that counts clonal disappearances and provided least-squares estimates of two key model parameters in our model, the total HSC differentiation rate and the maximum number of progenitor-cell divisions.

Bidirectional Retroviral Integration Site PCR Methodology and Quantitative Data Analysis Workflow.

Integration Site (IS) assays are a critical component of the study of retroviral integration sites and their biological significance. In recent retroviral gene therapy studies, IS assays, in combination with next-generation sequencing, have been used as a cell-tracking tool to characterize clonal stem cell populations sharing the same IS. For the accurate comparison of repopulating stem cell clones within and across different samples, the detection sensitivity, data reproducibility, and high-throughput capacity of the assay are among the most important assay qualities. This work provides a detailed protocol and data analysis workflow for bidirectional IS analysis. The bidirectional assay can simultaneously sequence both upstream and downstream vector-host junctions. Compared to conventional unidirectional IS sequencing approaches, the bidirectional approach significantly improves IS detection rates and the characterization of integration events at both ends of the target DNA. The data analysis pipeline described here accurately identifies and enumerates identical IS sequences through multiple steps of comparison that map IS sequences onto the reference genome and determine sequencing errors. Using an optimized assay procedure, we have recently published the detailed repopulation patterns of thousands of Hematopoietic Stem Cell (HSC) clones following transplant in rhesus macaques, demonstrating for the first time the precise time point of HSC repopulation and the functional heterogeneity of HSCs in the primate system. The following protocol describes the step-by-step experimental procedure and data analysis workflow that accurately identifies and quantifies identical IS sequences.

Mechanisms of blood homeostasis: lineage tracking and a neutral model of cell populations in rhesus macaques.

BACKGROUND: How a potentially diverse population of hematopoietic stem cells (HSCs) differentiates and proliferates to supply more than 10(11) mature blood cells every day in humans remains a key biological question. We investigated this process by quantitatively analyzing the clonal structure of peripheral blood that is generated by a population of transplanted lentivirus-marked HSCs in myeloablated rhesus macaques. Each transplanted HSC generates a clonal lineage of cells in the peripheral blood that is then detected and quantified through deep sequencing of the viral vector integration sites (VIS) common within each lineage. This approach allowed us to observe, over a period of 4-12 years, hundreds of distinct clonal lineages. RESULTS: While the distinct clone sizes varied by three orders of magnitude, we found that collectively, they form a steady-state clone size-distribution with a distinctive shape. Steady-state solutions of our model show that the predicted clone size-distribution is sensitive to only two combinations of parameters. By fitting the measured clone size-distributions to our mechanistic model, we estimate both the effective HSC differentiation rate and the number of active HSCs. CONCLUSIONS: Our concise mathematical model shows how slow HSC differentiation followed by fast progenitor growth can be responsible for the observed broad clone size-distribution. Although all cells are assumed to be statistically identical, analogous to a neutral theory for the different clone lineages, our mathematical approach captures the intrinsic variability in the times to HSC differentiation after transplantation.

Fixation times in differentiation and evolution in the presence of bottlenecks, deserts, and oases.

Cellular differentiation and evolution are stochastic processes that can involve multiple types (or states) of particles moving on a complex, high-dimensional state-space or "fitness" landscape. Cells of each specific type can thus be quantified by their population at a corresponding node within a network of states. Their dynamics across the state-space network involve genotypic or phenotypic transitions that can occur upon cell division, such as during symmetric or asymmetric cell differentiation, or upon spontaneous mutation. Here, we use a general multi-type branching processes to study first passage time statistics for a single cell to appear in a specific state. Our approach readily allows for nonexponentially distributed waiting times between transitions, reflecting, e.g., the cell cycle. For simplicity, we restrict most of our detailed analysis to exponentially distributed waiting times (Poisson processes). We present results for a sequential evolutionary process in which L successive transitions propel a population from a "wild-type" state to a given "terminally differentiated," "resistant," or "cancerous" state. Analytic and numeric results are also found for first passage times across an evolutionary chain containing a node with increased death or proliferation rate, representing a desert/bottleneck or an oasis. Processes involving cell proliferation are shown to be "nonlinear" (even though mean-field equations for the expected particle numbers are linear) resulting in first passage time statistics that depend on the position of the bottleneck or oasis. Our results highlight the sensitivity of stochastic measures to cell division fate and quantify the limitations of using certain approximations (such as the fixed-population and mean-field assumptions) in evaluating fixation times.

Distinct HIV-1 entry phenotypes are associated with transmission, subtype specificity, and resistance to broadly neutralizing antibodies.

BACKGROUND: The efficiency of CD4/CCR5 mediated HIV-1 entry has important implications for pathogenesis and transmission. The HIV-1 receptor affinity profiling (Affinofile) system analyzes and quantifies the infectivity of HIV-1 envelopes (Envs) across a spectrum of CD4/CCR5 expression levels and distills these data into a set of Affinofile metrics. The Affinofile system has shed light on how differential CD4/CCR5 usage efficiencies contributes to an array of Env phenotypes associated with cellular tropism, viral pathogenesis, and CCR5 inhibitor resistance. To facilitate more rapid, convenient, and robust analysis of HIV-1 entry phenotypes, we engineered a reporter Affinofile system containing a Tat- and Rev-dependent Gaussia luciferase-eGFP-Reporter (GGR) that is compatible with the use of pseudotyped or replication competent viruses with or without a virally encoded reporter gene. This GGR Affinofile system enabled a higher throughput characterization of CD4/CCR5 usage efficiencies associated with differential Env phenotypes. RESULTS: We first validated our GGR Affinofile system on isogenic JR-CSF Env mutants that differ in their affinity for CD4 and/or CCR5. We established that their GGR Affinofile metrics reflected their differential entry phenotypes on primary PBMCs and CD4+ T-cell subsets. We then applied GGR Affinofile profiling to reveal distinct entry phenotypes associated with transmission, subtype specificity, and resistance to broadly neutralizing antibodies (BNAbs). First, we profiled a panel of reference subtype B transmitted/founder (T/F) and chronic Envs (n = 12) by analyzing the infectivity of each Env across 25 distinct combinations of CD4/CCR5 expression levels. Affinofile metrics revealed that at low CCR5 levels, our panel of subtype B T/F Envs was more dependent on high levels of CD4 for HIV-1 entry compared to chronic Envs. Next, we analyzed a reference panel of 28 acute/early subtype A-D Envs, and noted that subtype C Envs could be distinguished from the other subtypes based on their infectivity profiles and relevant Affinofile metrics. Lastly, mutations known to confer resistance to VRC01 or PG6/PG19 BNAbs, when engineered into subtypes A-D Envs, resulted in significantly decreased CD4/CCR5 usage efficiency. CONCLUSIONS: GGR Affinofile profiling reveals pathophysiological phenotypes associated with varying HIV-1 entry efficiencies, and highlight the fitness costs associated with resistance to some broadly neutralizing antibodies.

Tracking monotonically advancing boundaries in image sequences using graph cuts and recursive kernel shape priors.

We introduce a probabilistic computer vision technique to track monotonically advancing boundaries of objects within image sequences. Our method incorporates a novel technique for including statistical prior shape information into graph-cut based segmentation, with the aid of a majorization-minimization algorithm. Extension of segmentation from single images to image sequences then follows naturally using sequential Bayesian estimation. Our methodology is applied to two unrelated sets of real biomedical imaging data, and a set of synthetic images. Our results are shown to be superior to manual segmentation.

A mathematical model of intercellular signaling during epithelial wound healing.

Recent experiments monitoring the healing process of wounded epithelial monolayers have demonstrated the necessity of MAPK activation for coordinated cell movement after damage. This MAPK activity is characterized by two wave-like phenomena. One MAPK "wave" that originates immediately after injury, propagates deep into the cell sheet, away from the edge, and then rebounds back to the wound interface. After this initial MAPK activity has largely disappeared, a second MAPK front propagates slowly from the wound interface and also continues into the cell sheet, maintaining a sustained level of MAPK activity throughout the cell sheet. It has been suggested that the first wave is initiated by Reactive Oxygen Species (ROS) generated at the time of injury. In this work, we develop a minimal mathematical model that reproduces the observed behavior. The main ingredients of our model are a competition between ligand (e.g., Epithelial Growth Factor) and ROS for the activation of Epithelial Growth Factor Receptor, and a feedback loop between receptor occupancy and MAPK activation. We explore the mathematical properties of the model and look for traveling wave solutions consistent with the experimentally observed MAPK activity patterns.

Elite suppressor-derived HIV-1 envelope glycoproteins exhibit reduced entry efficiency and kinetics.

Elite suppressors (ES) are a rare subset of HIV-1-infected individuals who are able to maintain HIV-1 viral loads below the limit of detection by ultra-sensitive clinical assays in the absence of antiretroviral therapy. Mechanism(s) responsible for this elite control are poorly understood but likely involve both host and viral factors. This study assesses ES plasma-derived envelope glycoprotein (env) fitness as a function of entry efficiency as a possible contributor to viral suppression. Fitness of virus entry was first evaluated using a novel inducible cell line with controlled surface expression levels of CD4 (receptor) and CCR5 (co-receptor). In the context of physiologic CCR5 and CD4 surface densities, ES envs exhibited significantly decreased entry efficiency relative to chronically infected viremic progressors. ES envs also demonstrated slow entry kinetics indicating the presence of virus with reduced entry fitness. Overall, ES env clones were less efficient at mediating entry than chronic progressor envs. Interestingly, acute infection envs exhibited an intermediate phenotypic pattern not distinctly different from ES or chronic progressor envs. These results imply that lower env fitness may be established early and may directly contribute to viral suppression in ES individuals.

Mechanisms of receptor/coreceptor-mediated entry of enveloped viruses.

Enveloped viruses enter host cells either through endocytosis, or by direct fusion of the viral envelope and the membrane of the host cell. However, some viruses, such as HIV-1, HSV-1, and Epstein-Barr can enter a cell through either mechanism, with the choice of pathway often a function of the ambient physical chemical conditions, such as temperature and pH. We develop a stochastic model that describes the entry process at the level of binding of viral glycoprotein spikes to cell membrane receptors and coreceptors. In our model, receptors attach the cell membrane to the viral membrane, while subsequent binding of coreceptors enables fusion. The model quantifies the competition between fusion and endocytotic entry pathways. Relative probabilities for each pathway are computed numerically, as well as analytically in the high viral spike density limit. We delineate parameter regimes in which fusion or endocytosis is dominant. These parameters are related to measurable and potentially controllable quantities such as membrane bending rigidity and receptor, coreceptor, and viral spike densities. Experimental implications of our mechanistic hypotheses are proposed and discussed.

Brownian ratchets driven by asymmetric nucleation of hydrolysis waves.

We propose a stochastic process wherein molecular transport is mediated by asymmetric nucleation of domains on a one-dimensional substrate, in contrast with molecular motors that hydrolyze nucleotide triphosphates and undergo conformational change. We show that asymmetric nucleation of hydrolysis waves on a track can also result in directed motion of an attached particle. Asymmetrically cooperative kinetics between hydrolyzed and unhydrolyzed states on each lattice site generate moving domain walls that push a particle sitting on the track. We use a novel fluctuating-frame, finite-segment mean field theory to accurately compute steady-state velocities of the driven particle and to discover parameter regimes yielding maximal domain wall flux, leading to optimal particle drift.

Physics of RecA-mediated homologous recognition.

To accomplish its DNA strand exchange activities, the Escherichia coli protein RecA polymerizes onto DNA to form a stiff helical nucleoprotein filament within which the DNA is extended by 50%. Homology search and recognition occurs between ssDNA within the filament and an external dsDNA molecule. We show that stretching the internal DNA greatly enhances homology recognition by increasing the probability that the homologous regions of a stretched DNA molecule and a parallel, unstretched DNA molecule will be "in register" at some position. We also show that the stretching and stiffness of the filament act together to ensure that initiation of homologous exchange between the substrate DNA molecules at one position precludes initiation of homologous exchange at any other position. This prevents formation of multiple exchange site "topological traps" which would prevent completion of the exchange reaction and resolution of the products.

Physical mechanisms of gas and perfluoron retinopexy and sub-retinal fluid displacement.

Injection of gas into the eye, followed by face-down positioning, is a common protocol for the reseating of the retina in posterior and superior retinal tears and breaks. The physical mechanism by which injected gas helps reattach retinal flaps is often ascribed to the 'buoyancy' force of the injected gas bubble. The various forces at play in this system (surface tension and buoyancy) were calculated and compared. The results are extended to the case in which the retina is intact (pneumatic displacement of blood) and to the use of intraocular perfluoron (n-perfluorooctane). We show that buoyancy forces are applicable only for gas or n-perfluorooctane bubbles that are smaller than the detached retina and that do not invade underneath the retina. For larger bubbles, as is normally used in reattachment protocols, we show that it is the interfacial tension that reattaches the retina. The range of angles within which patients can position, and still maintain a gas-vitreous interface along a tear is calculated as a function of the volume of injected gas and size of the tear. The maximum retinal flap size that can be reattached using surface tension forces is also estimated.