Intra-tumor heterogeneity, turnover rate and karyotype space shape susceptibility to missegregation-induced extinction.

The phenotypic efficacy of somatic copy number alterations (SCNAs) stems from their incidence per base pair of the genome, which is orders of magnitudes greater than that of point mutations. One mitotic event stands out in its potential to significantly change a cell's SCNA burden-a chromosome missegregation. A stochastic model of chromosome mis-segregations has been previously developed to describe the evolution of SCNAs of a single chromosome type. Building upon this work, we derive a general deterministic framework for modeling missegregations of multiple chromosome types. The framework offers flexibility to model intra-tumor heterogeneity in the SCNAs of all chromosomes, as well as in missegregation- and turnover rates. The model can be used to test how selection acts upon coexisting karyotypes over hundreds of generations. We use the model to calculate missegregation-induced population extinction (MIE) curves, that separate viable from non-viable populations as a function of their turnover- and missegregation rates. Turnover- and missegregation rates estimated from scRNA-seq data are then compared to theoretical predictions. We find convergence of theoretical and empirical results in both the location of MIE curves and the necessary conditions for MIE. When a dependency of missegregation rate on karyotype is introduced, karyotypes associated with low missegregation rates act as a stabilizing refuge, rendering MIE impossible unless turnover rates are exceedingly high. Intra-tumor heterogeneity, including heterogeneity in missegregation rates, increases as tumors progress, rendering MIE unlikely.

spatialTIME and iTIME: R package and Shiny application for visualization and analysis of immunofluorescence data.

SUMMARY: Multiplex immunofluorescence (mIF) staining combined with quantitative digital image analysis is a novel and increasingly used technique that allows for the characterization of the tumor immune microenvironment (TIME). Generally, mIF data is used to examine the abundance of immune cells in the TIME; however, this does not capture spatial patterns of immune cells throughout the TIME, a metric increasingly recognized as important for prognosis. To address this gap, we developed an R package spatialTIME that enables spatial analysis of mIF data, as well as the iTIME web application that provides a robust but simplified user interface for describing both abundance and spatial architecture of the TIME. The spatialTIME package calculates univariate and bivariate spatial statistics (e.g. Ripley's K, Besag's L, Macron's M and G or nearest neighbor distance) and creates publication quality plots for spatial organization of the cells in each tissue sample. The iTIME web application allows users to statistically compare the abundance measures with patient clinical features along with visualization of the TIME for one tissue sample at a time. AVAILABILITY AND IMPLEMENTATION: spatialTIME is implemented in R and can be downloaded from GitHub (https://github.com/FridleyLab/spatialTIME) or CRAN. An extensive vignette for using spatialTIME can also be found at https://cran.r-project.org/web/packages/spatialTIME/index.html. iTIME is implemented within a R Shiny application and can be accessed online (http://itime.moffitt.org/), with code available on GitHub (https://github.com/FridleyLab/iTIME). SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

The roles of T cell competition and stochastic extinction events in chimeric antigen receptor T cell therapy.

Chimeric antigen receptor (CAR) T cell therapy is a remarkably effective immunotherapy that relies on in vivo expansion of engineered CAR T cells, after lymphodepletion (LD) by chemotherapy. The quantitative laws underlying this expansion and subsequent tumour eradication remain unknown. We develop a mathematical model of T cell-tumour cell interactions and demonstrate that expansion can be explained by immune reconstitution dynamics after LD and competition among T cells. CAR T cells rapidly grow and engage tumour cells but experience an emerging growth rate disadvantage compared to normal T cells. Since tumour eradication is deterministically unstable in our model, we define cure as a stochastic event, which, even when likely, can occur at variable times. However, we show that variability in timing is largely determined by patient variability. While cure events impacted by these fluctuations occur early and are narrowly distributed, progression events occur late and are more widely distributed in time. We parameterized our model using population-level CAR T cell and tumour data over time and compare our predictions with progression-free survival rates. We find that therapy could be improved by optimizing the tumour-killing rate and the CAR T cells' ability to adapt, as quantified by their carrying capacity. Our tumour extinction model can be leveraged to examine why therapy works in some patients but not others, and to better understand the interplay of deterministic and stochastic effects on outcomes. For example, our model implies that LD before a second CAR T injection is necessary.

Investigation into the mechanism and dynamics of DNA association and dissociation utilizing kinetic Monte Carlo simulations.

In this work, we present a kinetic Markov state Monte Carlo model designed to complement temperature-jump (T-jump) infrared spectroscopy experiments probing the kinetics and dynamics of short DNA oligonucleotides. The model is designed to be accessible to experimental researchers in terms of both computational simplicity and expense while providing detailed insights beyond those provided by experimental methods. The model is an extension of a thermodynamic lattice model for DNA hybridization utilizing the formalism of the nucleation-zipper mechanism. Association and dissociation trajectories were generated utilizing the Gillespie algorithm and parameters determined via fitting the association and dissociation timescales to previously published experimental data. Terminal end fraying, experimentally observed following a rapid T-jump, in the sequence 5'-ATATGCATAT-3' was replicated by the model that also demonstrated that experimentally observed fast dynamics in the sequences 5'-C(AT)nG-3', where n = 2-6, were also due to terminal end fraying. The dominant association pathways, isolated by transition pathway theory, showed two primary motifs: initiating at or next to a G:C base pair, which is enthalpically favorable and related to the increased strength of G:C base pairs, and initiating in the center of the sequence, which is entropically favorable and related to minimizing the penalty associated with the decrease in configurational entropy due to hybridization.

Time scales and wave formation in non-linear spatial public goods games.

The co-evolutionary dynamics of competing populations can be strongly affected by frequency-dependent selection and spatial population structure. As co-evolving populations grow into a spatial domain, their initial spatial arrangement and their growth rate differences are important factors that determine the long-term outcome. We here model producer and free-rider co-evolution in the context of a diffusive public good (PG) that is produced by the producers at a cost but evokes local concentration-dependent growth benefits to all. The benefit of the PG can be non-linearly dependent on public good concentration. We consider the spatial growth dynamics of producers and free-riders in one, two and three dimensions by modeling producer cell, free-rider cell and public good densities in space, driven by the processes of birth, death and diffusion (cell movement and public good distribution). Typically, one population goes extinct, but the time-scale of this process varies with initial conditions and the growth rate functions. We establish that spatial variation is transient regardless of dimensionality, and that structured initial conditions lead to increasing times to get close to an extinction state, called ε-extinction time. Further, we find that uncorrelated initial spatial structures do not influence this ε-extinction time in comparison to a corresponding well-mixed (non-spatial) system. In order to estimate the ε-extinction time of either free-riders or producers we derive a slow manifold solution. For invading populations, i.e. for populations that are initially highly segregated, we observe a traveling wave, whose speed can be calculated. Our results provide quantitative predictions for the transient spatial dynamics of cooperative traits under pressure of extinction.

Parallel magnetic field suppresses dissipation in superconducting nanostrips.

The motion of Abrikosov vortices in type-II superconductors results in a finite resistance in the presence of an applied electric current. Elimination or reduction of the resistance via immobilization of vortices is the "holy grail" of superconductivity research. Common wisdom dictates that an increase in the magnetic field escalates the loss of energy since the number of vortices increases. Here we show that this is no longer true if the magnetic field and the current are applied parallel to each other. Our experimental studies on the resistive behavior of a superconducting Mo0.79Ge0.21 nanostrip reveal the emergence of a dissipative state with increasing magnetic field, followed by a pronounced resistance drop, signifying a reentrance to the superconducting state. Large-scale simulations of the 3D time-dependent Ginzburg-Landau model indicate that the intermediate resistive state is due to an unwinding of twisted vortices. When the magnetic field increases, this instability is suppressed due to a better accommodation of the vortex lattice to the pinning configuration. Our findings show that magnetic field and geometrical confinement can suppress the dissipation induced by vortex motion and thus radically improve the performance of superconducting materials.

Circulating tumor DNA adds specificity to PET after axicabtagene ciloleucel in large B-cell lymphoma.

We examined the meaning of metabolically active lesions on 1-month restaging nuclear imaging of patients with relapsed/refractory large B-cell lymphoma receiving axicabtagene ciloleucel (axi-cel) by assessing the relationship between total metabolic tumor volume (MTV) on positron emission tomography (PET) scans and circulating tumor DNA (ctDNA) in the plasma. In this prospective multicenter sample collection study, MTV was retrospectively calculated via commercial software at baseline, 1, and 3 months after chimeric antigen receptor (CAR) T-cell therapy; ctDNA was available before and after axi-cel administration. Spearman correlation coefficient (rs) was used to study the relationship between the variables, and a mathematical model was constructed to describe tumor dynamics 1 month after CAR T-cell therapy. The median time between baseline scan and axi-cel infusion was 33 days (range, 1-137 days) for all 57 patients. For 41 of the patients with imaging within 33 days of axi-cel or imaging before that time but no bridging therapy, the correlation at baseline became stronger (rs, 0.61; P < .0001) compared with all patients (rs, 0.38; P = .004). Excluding patients in complete remission with no measurable residual disease, ctDNA and MTV at 1 month did not correlate (rs, 0.28; P = .11) but correlated at 3 months (rs, 0.79; P = .0007). Modeling of tumor dynamics, which incorporated ctDNA and inflammation as part of MTV, recapitulated the outcomes of patients with positive radiologic 1-month scans. Our results suggested that nonprogressing hypermetabolic lesions on 1-month PET represent ongoing treatment responses, and their composition may be elucidated by concurrently examining the ctDNA.

Geospatial characterization of immune cell distributions and dynamics across the microenvironment in clear cell renal cell carcinoma.

INTRODUCTION: In clear cell renal cell carcinoma (ccRCC), tumor-associated macrophage (TAM) induction of CD8+T cells into a terminally exhausted state has been implicated as a major mechanism of immunotherapy resistance, but a deeper biological understanding is necessary. METHODS: Primary ccRCC tumor samples were obtained from 97 patients between 2004 and 2018. Multiplex immunofluorescence using lymphoid and myeloid markers was performed in seven regions of interest per patient across three predefined zones, and geospatial analysis was performed using Ripley's K analysis, a methodology adapted from ecology. RESULTS: Clustering of CD163+M2 like TAMs into the stromal compartment at the tumor-stroma interface was associated with worse clinical stage (tumor/CD163+nK(75): stage I/II: 4.4 (IQR -0.5 to 5.1); stage III: 1.4 (IQR -0.3 to 3.5); stage IV: 0.6 (IQR -2.1 to 2.1); p=0.04 between stage I/II and stage IV), and worse overall survival (OS) and cancer-specific survival (CSS) (tumor/CD163+nK(75): median OS-hi=149 months, lo=86 months, false-discovery rate (FDR)-adj. Cox p<0.001; median CSS-hi=174 months, lo=85 months; FDR-adj. Cox p<0.001). An RNA-seq differential gene expression score was developed using this geospatial metric, and was externally validated in multiple independent cohorts of patients with ccRCC including: TCGA KIRC, and the IMmotion151, IMmotion150, and JAVELIN Renal 101 clinical trials. In addition, this CD163+ geospatial pattern was found to be associated with a higher TIM-3+ proportion of CD8+T cells, indicative of terminal exhaustion (tumor-core: 0.07 (IQR 0.04-0.14) vs 0.40 (IQR 0.15-0.66), p=0.05). CONCLUSIONS: Geospatial clustering of CD163+M2 like TAMs into the stromal compartment at the tumor-stromal interface was associated with poor clinical outcomes and CD8+T cell terminal exhaustion.

Two-dimensional adaptive dynamics of evolutionary public goods games: finite-size effects on fixation probability and branching time.

Public goods games (PGGs) describe situations in which individuals contribute to a good at a private cost, but others can free-ride by receiving a share of the public benefit at no cost. The game occurs within local neighbourhoods, which are subsets of the whole population. Free-riding and maximal production are two extremes of a continuous spectrum of traits. We study the adaptive dynamics of production and neighbourhood size. We allow the public good production and the neighbourhood size to coevolve and observe evolutionary branching. We explain how an initially monomorphic population undergoes evolutionary branching in two dimensions to become a dimorphic population characterized by extremes of the spectrum of trait values. We find that population size plays a crucial role in determining the final state of the population. Small populations may not branch or may be subject to extinction of a subpopulation after branching. In small populations, stochastic effects become important and we calculate the probability of subpopulation extinction. Our work elucidates the evolutionary origins of heterogeneity in local PGGs among individuals of two traits (production and neighbourhood size), and the effects of stochasticity in two-dimensional trait space, where novel effects emerge.

Geospatial Cellular Distribution of Cancer-Associated Fibroblasts Significantly Impacts Clinical Outcomes in Metastatic Clear Cell Renal Cell Carcinoma.

Cancer-associated fibroblasts (CAF) are highly prevalent cells in the tumor microenvironment in clear cell renal cell carcinoma (ccRCC). CAFs exhibit a pro-tumor effect in vitro and have been implicated in tumor cell proliferation, metastasis, and treatment resistance. Our objective is to analyze the geospatial distribution of CAFs with proliferating and apoptotic tumor cells in the ccRCC tumor microenvironment and determine associations with survival and systemic treatment. Pre-treatment primary tumor samples were collected from 96 patients with metastatic ccRCC. Three adjacent slices were obtained from 2 tumor-core regions of interest (ROI) per patient, and immunohistochemistry (IHC) staining was performed for αSMA, Ki-67, and caspase-3 to detect CAFs, proliferating cells, and apoptotic cells, respectively. H-scores and cellular density were generated for each marker. ROIs were aligned, and spatial point patterns were generated, which were then used to perform spatial analyses using a normalized Ripley's K function at a radius of 25 µm (nK(25)). The survival analyses used an optimal cut-point method, maximizing the log-rank statistic, to stratify the IHC-derived metrics into high and low groups. Multivariable Cox regression analyses were performed accounting for age and International Metastatic RCC Database Consortium (IMDC) risk category. Survival outcomes included overall survival (OS) from the date of diagnosis, OS from the date of immunotherapy initiation (OS-IT), and OS from the date of targeted therapy initiation (OS-TT). Therapy resistance was defined as progression-free survival (PFS) <6 months, and therapy response was defined as PFS >9 months. CAFs exhibited higher cellular clustering with Ki-67+ cells than with caspase-3+ cells (nK(25): Ki-67 1.19; caspase-3 1.05; p = 0.04). The median nearest neighbor (NN) distance from CAFs to Ki-67+ cells was shorter compared to caspase-3+ cells (15 µm vs. 37 µm, respectively; p < 0.001). Multivariable Cox regression analyses demonstrated that both high Ki-67+ density and H-score were associated with worse OS, OS-IT, and OS-TT. Regarding αSMA+CAFs, only a high H-score was associated with worse OS, OS-IT, and OS-TT. For caspase-3+, high H-score and density were associated with worse OS and OS-TT. Patients whose tumors were resistant to targeted therapy (TT) had higher Ki-67 density and H-scores than those who had TT responses. Overall, this ex vivo geospatial analysis of CAF distribution suggests that close proximity clustering of tumor cells and CAFs potentiates tumor cell proliferation, resulting in worse OS and resistance to TT in metastatic ccRCC.

Spatial clustering of CD68+ tumor associated macrophages with tumor cells is associated with worse overall survival in metastatic clear cell renal cell carcinoma.

Immune infiltration is typically quantified using cellular density, not accounting for cellular clustering. Tumor-associated macrophages (TAM) activate oncogenic signaling through paracrine interactions with tumor cells, which may be better reflected by local cellular clustering than global density metrics. Using multiplex immunohistochemistry and digital pathologic analysis we quantified cellular density and cellular clustering for myeloid cell markers in 129 regions of interest from 55 samples from 35 patients with metastatic ccRCC. CD68+ cells were found to be clustered with tumor cells and dispersed from stromal cells, while CD163+ and CD206+ cells were found to be clustered with stromal cells and dispersed from tumor cells. CD68+ density was not associated with OS, while high tumor/CD68+ cell clustering was associated with significantly worse OS. These novel findings would not have been identified if immune infiltrate was assessed using cellular density alone, highlighting the importance of including spatial analysis in studies of immune cell infiltration of tumors. Significance: Increased clustering of CD68+ TAMs and tumor cells was associated with worse overall survival for patients with metastatic ccRCC. This effect would not have been identified if immune infiltrate was assessed using cell density alone, highlighting the importance of including spatial analysis in studies of immune cell infiltration of tumors.

Integrating Mathematical Modeling with High-Throughput Imaging Explains How Polyploid Populations Behave in Nutrient-Sparse Environments.

Breast cancer progresses in a multistep process from primary tumor growth and stroma invasion to metastasis. Nutrient-limiting environments promote chemotaxis with aggressive morphologies characteristic of invasion. It is unknown how coexisting cells differ in their response to nutrient limitations and how this impacts invasion of the metapopulation as a whole. In this study, we integrate mathematical modeling with microenvironmental perturbation data to investigate invasion in nutrient-limiting environments inhabited by one or two cancer cell subpopulations. Subpopulations were defined by their energy efficiency and chemotactic ability. Invasion distance traveled by a homogeneous population was estimated. For heterogeneous populations, results suggest that an imbalance between nutrient efficacy and chemotactic superiority accelerates invasion. Such imbalance will spatially segregate the two populations and only one type will dominate at the invasion front. Only if these two phenotypes are balanced, the two subpopulations compete for the same space, which decelerates invasion. We investigate ploidy as a candidate biomarker of this phenotypic heterogeneity and discuss its potential to inform the dose of mTOR inhibitors (mTOR-I) that can inhibit chemotaxis just enough to facilitate such competition. SIGNIFICANCE: This study identifies the double-edged sword of high ploidy as a prerequisite to personalize combination therapies with cytotoxic drugs and inhibitors of signal transduction pathways such as mTOR-Is. GRAPHICAL ABSTRACT: http://cancerres.aacrjournals.org/content/canres/80/22/5109/F1.large.jpg.

Neighborhood size-effects shape growing population dynamics in evolutionary public goods games.

An evolutionary game emerges when a subset of individuals incur costs to provide benefits to all individuals. Public goods games (PGG) cover the essence of such dilemmas in which cooperators are prone to exploitation by defectors. We model the population dynamics of a non-linear PGG and consider density-dependence on the global level, while the game occurs within local neighborhoods. At low cooperation, increases in the public good provide increasing returns. At high cooperation, increases provide diminishing returns. This mechanism leads to diverse evolutionarily stable strategies, including monomorphic and polymorphic populations, and neighborhood-size-driven state changes, resulting in hysteresis between equilibria. Stochastic or strategy-dependent variations in neighborhood sizes favor coexistence by destabilizing monomorphic states. We integrate our model with experiments of cancer cell growth and confirm that our framework describes PGG dynamics observed in cellular populations. Our findings advance the understanding of how neighborhood-size effects in PGG shape the dynamics of growing populations.

Edge effect pinning in mesoscopic superconducting strips with non-uniform distribution of defects.

Transport characteristics of nano-sized superconducting strips and bridges are determined by an intricate interplay of surface and bulk pinning. In the limiting case of a very narrow bridge, the critical current is mostly defined by its surface barrier, while in the opposite case of very wide strips it is dominated by its bulk pinning properties. Here we present a detailed study of the intermediate regime, where the critical current is determined, both, by randomly placed pinning centres and by the Bean-Livingston barrier at the edge of the superconducting strip in an external magnetic field. We use the time-dependent Ginzburg-Landau equations to describe the vortex dynamics and current distribution in the critical regime. Our studies reveal that while the bulk defects arrest vortex motion away from the edges, defects in their close vicinity promote vortex penetration, thus suppressing the critical current. We determine the spatial distribution of the defects optimizing the critical current and find that it is in general non-uniform and asymmetric: the barrier at the vortex-exit edge influence the critical current much stronger than the vortex-entrance edge. Furthermore, this optimized defect distribution has a more than 30% higher critical current density than a homogeneously disorder superconducting film.