Fundamental bound on epidemic overshoot in the SIR model.

We derive an exact upper bound on the epidemic overshoot for the Kermack-McKendrick SIR model. This maximal overshoot value of 0.2984 · · · occurs at [Formula: see text]. In considering the utility of the notion of overshoot, a rudimentary analysis of data from the first wave of the COVID-19 pandemic in Manaus, Brazil highlights the public health hazard posed by overshoot for epidemics with R0 near 2. Using the general analysis framework presented within, we then consider more complex SIR models that incorporate vaccination.

Parameterizing network graph heterogeneity using a modified Weibull distribution.

We present a simple method to quantitatively capture the heterogeneity in the degree distribution of a network graph using a single parameter σ . Using an exponential transformation of the shape parameter of the Weibull distribution, this control parameter allows the degree distribution to be easily interpolated between highly symmetric and highly heterogeneous distributions on the unit interval. This parameterization of heterogeneity also recovers several other canonical distributions as intermediate special cases, including the Gaussian, Rayleigh, and exponential distributions. We then outline a general graph generation algorithm to produce graphs with a desired amount of heterogeneity. The utility of this formulation of a heterogeneity parameter is demonstrated with examples relating to epidemiological modeling and spectral analysis.

Transcriptional differences between JAK2-V617F and wild-type bone marrow cells in patients with myeloproliferative neoplasms.

The JAK2-V617F mutation is the most common cause of myeloproliferative neoplasms. Although experiments have revealed that this gain-of-function mutation is associated with myeloid blood cell expansion and increased production of white cells, red cells, and platelets, the transcriptional consequences of the JAK2-V617F mutation in different cellular compartments of the bone marrow have not yet been fully elucidated. To study the direct effects of JAK2-V617F on bone marrow cells in patients with myeloproliferative neoplasms, we performed joint single-cell RNA sequencing and JAK2 genotyping on CD34+-enriched cells from eight patients with newly diagnosed essential thrombocythemia or polycythemia vera. We found that the JAK2-V617F mutation increases the expression of interferon-response genes (e.g., HLAs) and the leptin receptor in hematopoietic progenitor cells. Furthermore, we sequenced a population of CD34- bone marrow monocytes and found that the JAK2 mutation increased expression of intermediate monocyte genes and the fibrocyte-associated surface protein SLAMF7 in these cells.

Integrating readout of somatic mutations in individual cells with single-cell transcriptional profiling.

In many biological applications, the readout of somatic mutations in individual cells is essential. For example, it can be used to mark individual cancer cells or identify progenies of a stem cell. Here, we present a protocol to perform single-cell RNA-seq and single-cell amplicon-seq using 10X Chromium technology. Our protocol demonstrates how to (1) isolate CD34+ progenitor cells from human bone marrow aspirate, (2) prepare single-cell amplicon libraries, and (3) analyze the libraries to assign somatic mutations to individual cells. For complete details on the use and execution of this protocol, please refer to Van Egeren et al. (2021).

Reconstructing the Lineage Histories and Differentiation Trajectories of Individual Cancer Cells in Myeloproliferative Neoplasms.

Some cancers originate from a single mutation event in a single cell. Blood cancers known as myeloproliferative neoplasms (MPNs) are thought to originate when a driver mutation is acquired by a hematopoietic stem cell (HSC). However, when the mutation first occurs in individuals and how it affects the behavior of HSCs in their native context is not known. Here we quantified the effect of the JAK2-V617F mutation on the self-renewal and differentiation dynamics of HSCs in treatment-naive individuals with MPNs and reconstructed lineage histories of individual HSCs using somatic mutation patterns. We found that JAK2-V617F mutations occurred in a single HSC several decades before MPN diagnosis-at age 9 ± 2 years in a 34-year-old individual and at age 19 ± 3 years in a 63-year-old individual-and found that mutant HSCs have a selective advantage in both individuals. These results highlight the potential of harnessing somatic mutations to reconstruct cancer lineages.

Early life imprints the hierarchy of T cell clone sizes.

The adaptive immune system responds to pathogens by selecting clones of cells with specific receptors. While clonal selection in response to particular antigens has been studied in detail, it is unknown how a lifetime of exposures to many antigens collectively shape the immune repertoire. Here, using mathematical modeling and statistical analyses of T cell receptor sequencing data, we develop a quantitative theory of human T cell dynamics compatible with the statistical laws of repertoire organization. We find that clonal expansions during a perinatal time window leave a long-lasting imprint on the human T cell repertoire, which is only slowly reshaped by fluctuating clonal selection during adult life. Our work provides a mechanism for how early clonal dynamics imprint the hierarchy of T cell clone sizes with implications for pathogen defense and autoimmunity.

The human immune system develops a memory of pathogens that it encounters over its lifetime, allowing it to respond quickly to future infections. It does this partly through T cells, white blood cells that can recognize different pathogens. During an infection, the T cells that recognize the specific pathogen attacking the body will divide until a large number of clones of these T cells is available to help in the fight. After the infection clears, the immune system 'keeps' some of these cells so it can recognize the pathogen in the future, and respond quicker to an infection. Over the course of their lives, people will be infected by many different pathogens, leading to a wide variety of T cells that each respond to one of these pathogens. However, it is not well understood how various infections throughout the human lifespan shape the overall population of different T cells. Gaimann et al. used mathematical modelling to study how the composition of the immune system changes in people of different ages. Different populations of T cells ­ each specialized against a specific antigen ­ had been previously identified through genetic sequencing. Gaimann et al. analyzed their dynamics to show that many of the largest populations originate around birth, during the formation of the immune system. These findings suggest a potential mechanism for how exposure to pathogens in infancy can influence the immune system much later in life. The results may also explain variations in how people respond to infections and in their risk of developing autoimmune conditions. This understanding could help develop new treatments or interventions to guide the immune system as it develops.

An Engineered CRISPR-Cas9 Mouse Line for Simultaneous Readout of Lineage Histories and Gene Expression Profiles in Single Cells.

Tracing the lineage history of cells is key to answering diverse and fundamental questions in biology. Coupling of cell ancestry information with other molecular readouts represents an important goal in the field. Here, we describe the CRISPR array repair lineage tracing (CARLIN) mouse line and corresponding analysis tools that can be used to simultaneously interrogate the lineage and transcriptomic information of single cells in vivo. This model exploits CRISPR technology to generate up to 44,000 transcribed barcodes in an inducible fashion at any point during development or adulthood, is compatible with sequential barcoding, and is fully genetically defined. We have used CARLIN to identify intrinsic biases in the activity of fetal liver hematopoietic stem cell (HSC) clones and to uncover a previously unappreciated clonal bottleneck in the response of HSCs to injury. CARLIN also allows the unbiased identification of transcriptional signatures associated with HSC activity without cell sorting.

Negative reciprocity, not ordered assembly, underlies the interaction of Sox2 and Oct4 on DNA.

The mode of interaction of transcription factors (TFs) on eukaryotic genomes remains a matter of debate. Single-molecule data in living cells for the TFs Sox2 and Oct4 were previously interpreted as evidence of ordered assembly on DNA. However, the quantity that was calculated does not determine binding order but, rather, energy expenditure away from thermodynamic equilibrium. Here, we undertake a rigorous biophysical analysis which leads to the concept of reciprocity. The single-molecule data imply that Sox2 and Oct4 exhibit negative reciprocity, with expression of Sox2 increasing Oct4's genomic binding but expression of Oct4 decreasing Sox2's binding. Models show that negative reciprocity can arise either from energy expenditure or from a mixture of positive and negative cooperativity at distinct genomic loci. Both possibilities imply unexpected complexity in how TFs interact on DNA, for which single-molecule methods provide novel detection capabilities.