Cell Birth Rate Research Articles

Understanding the origin and role of driver mutations in the case of Acute Myeloid Leukemia using a simulation study

Cancer is a leading cause of death worldwide, with millions of new cases diagnosed each year. Understanding how those cancers arise within individuals is a major challenge. Here we focus on Acute Myeloid Leukemia (AML) a type of blood cancer in the bone marrow that involves the formation of abnormal myeloid cells in an individual. Each year, 190,000 cases are diagnosed worldwide, of which 147,000 die. (Acute Myeloid Leukemia, n.d.)
 In this paper, we aim to better understand the origin of AML and the role of driver mutations at the individual level.
 We build a Birth-Death model to explore the role of mutation along with cell birth rate, cell death rate, and tissue size. Each simulation is individual-specific, which allows us to consider stochasticity across individuals.
 We show that initial cell birth rate and cell death rate only play a minor role in cancer progression, even if there is a large inter-individual variance. On the contrary, we show that driver mutation rates play a more critical role in causing Acute Myeloid Leukemia. All in all, our paper highlights large variability in cancer progression across individuals and the major role of driver mutations in causing AML. This simulation model could be used to study other types of cancers.

A stochastic analysis of the interplay between antibiotic dose, mode of action, and bacterial competition in the evolution of antibiotic resistance.

The use of an antibiotic may lead to the emergence and spread of bacterial strains resistant to this antibiotic. Experimental and theoretical studies have investigated the drug dose that minimizes the risk of resistance evolution over the course of treatment of an individual, showing that the optimal dose will either be the highest or the lowest drug concentration possible to administer; however, no analytical results exist that help decide between these two extremes. To address this gap, we develop a stochastic mathematical model of bacterial dynamics under antibiotic treatment. We explore various scenarios of density regulation (bacterial density affects cell birth or death rates), and antibiotic modes of action (biostatic or biocidal). We derive analytical results for the survival probability of the resistant subpopulation until the end of treatment, the size of the resistant subpopulation at the end of treatment, the carriage time of the resistant subpopulation until it is replaced by a sensitive one after treatment, and we verify these results with stochastic simulations. We find that the scenario of density regulation and the drug mode of action are important determinants of the survival of a resistant subpopulation. Resistant cells survive best when bacterial competition reduces cell birth and under biocidal antibiotics. Compared to an analogous deterministic model, the population size reached by the resistant type is larger and carriage time is slightly reduced by stochastic loss of resistant cells. Moreover, we obtain an analytical prediction of the antibiotic concentration that maximizes the survival of resistant cells, which may help to decide which drug dosage (not) to administer. Our results are amenable to experimental tests and help link the within and between host scales in epidemiological models.

Modelling evolution at the boundaries of solid tumours.

A mathematical model of eco-evolutionary dynamics estimates different birth rates of cells at the periphery of a tumour versus its centre, giving insight into locally stable evolutionary mechanisms that arise as a result of boundary-driven growth.

High Cell Death Rates at Start of Ibrutinib Therapy Predict for Deeper Remissions in Patients with Chronic Lymphocytic Leukemia (CLL)

Introduction: The BTK inhibitor ibrutinib blocks B-cell receptor and other signaling pathways in CLL cells and has become a standard CLL therapy. Isotopic labeling with deuterated water (2H2O) to measure the effects of ibrutinib on CLL cell proliferation and death directly in patients revealed that ibrutinib profoundly inhibits proliferation and induces high rates of leukemia cell death (registered at clinicaltrials.gov as NCT01752426; Burger et al., JCI Insight, 2017). Here, we report a long-term follow-up of this trial in which we analyzed long-term outcomes and correlated CLL cell birth and death rates with depth of response over time. Methods: Thirty patients with previously untreated CLL/SLL enrolled in the study to receive continuous long-term ibrutinib monotherapy, after one month of labeling with deuterated water. For our analyses, we stratified patients in groups based on high or low CLL cell death rates in the peripheral blood (PB) or lymphatic tissues (lymph nodes, spleen), i.e. death rates above or below the median, assessed over the first months on therapy, as detailed in the original publication. Responses were assessed according to 2008 IWCLL guidelines, with the exception that lymphocytosis was not used as a sole criterion for progression. PB MRD was quantified by flow cytometry with a sensitivity 10-4. Results: The median age of the participants was 64 years (range, 48 - 78); 63.3% were male. Thirteen patients (43%) had advanced stage disease, 57% had unmutated IGHV genes, and 10% carried 17p deletion (del17p). Twenty-two patients (73%) completed 5 years of protocol treatment and subsequently continued treatment with commercial supply ibrutinib. The patients were followed for a median time of 107 months (range, 6 - 111). The reasons for eventual treatment discontinuation (n=21) were adverse events (n=8, 38%), progressive disease (n=4, 19%), change to another treatment (n=5, 24%), death (n=2, 7%) and other reasons (n=2, 7%). To date, nine patients are still receiving ibrutinib. Five patients (17%) achieved a complete remission, 24 (80%) achieved partial remission, and one patient (3%) had stable disease, resulting in an overall response rate of 97%. Median progression-free (PFS) and overall survival (OS) were not reached at a median follow-up of 107 months. Five-year PFS was 80.6%, and OS was 90%. PB MRD was measured in 18 patients after 5 years of ibrutinib (54 to 60 cycles); all patients had detectable MRD (median 11.8%, range, 0.06 - 47.30%). We found that CLL cell death rates in PB and tissues after treatment initiation inversely correlated with the level of PB MRD after 5 years (r=-0.5872, P=0.0104 and r=-0.4407, P=0.0672). MRD levels were significantly lower in patients with high CLL cell death rates in PB (7.03% ± 3.68% vs. 29.46% ± 5.53%, mean ± SEM, P=0.0056) and in tissues (9.73% ± 5.49% vs. 28.89% ± 4.42%, P=0.0155) as compared with patients with lower CLL cell death rates (Figure 1). Tissue CLL cell death rates were significantly higher in patients with IGHV-unmutated CLL compared to mutated (28.88% ± 2.75% vs. 13.16% ± 2.82%, P=0.0005), and MRD levels trended lower (IGHV-unmutated: 10.71% ± 5.39% vs. IGHV-mutated: 28.36% ± 6.02%, P=0.0878). No statistically significant correlation was found between CLL cell birth rate at baseline or after start of ibrutinib and MRD levels after 5 years of treatment. Conclusion: CLL cell death rates during early treatment correlated with achieving lower MRD levels. We found that CLL cell death rates are higher in IGHV-unmutated patients suggesting a higher dependency of IGHV-unmutated clones on BCR signaling and, therefore, resulting in deeper responses. Figure 1View largeDownload PPTFigure 1View largeDownload PPT Close modal

Quantifying the clonality and dynamics of the within-host HIV-1 latent reservoir.

Among people living with human immunodeficiency virus type 1 (HIV-1), the long-term persistence of a population of cells carrying transcriptionally silent integrated viral DNA (provirus) remains the primary barrier to developing an effective cure. Ongoing cell division via proliferation is generally considered to be the driving force behind the persistence of this latent HIV-1 reservoir. The contribution of this mechanism (clonal expansion) is supported by the observation that proviral sequences sampled from the reservoir are often identical. This outcome is quantified as the ‘clonality’ of the sample population, e.g. the fraction of provirus sequences observed more than once. However, clonality as a quantitative measure is inconsistently defined and its statistical properties are not well understood. In this Reflections article, we use mathematical and phylogenetic frameworks to formally examine the inherent problems of using clonality to characterize the dynamics and proviral composition of the reservoir. We describe how clonality is not adequate for this task due to the inherent complexity of how infected cells are ‘labeled’ by proviral sequences—the outcome of a sampling process from the evolutionary history of active viral replication before treatment—as well as variation in cell birth and death rates among lineages and over time. Lastly, we outline potential directions in statistical and phylogenetic research to address these issues.

EPCO-17. A SINGLE-CELL ATLAS OF GLIOBLASTOMA EVOLUTION UNDER THERAPY

Abstract Most clinical trials for glioblastoma (GBM) enroll patients at recurrence. However, most pre-clinical animal models are of primary disease. Most studies have used tissues from primary tumors. Knowledge of GBM cellular composition at recurrence is limited. We profiled 80 human IDH-wild-type GBM specimens via single-nucleus RNA sequencing, 40 primary tumors and 40 patient-matched recurrent tumors. Select cohorts were also profiled via single-cell assay for transposase-accessible chromatin, single-cell digital-spatial, and single-cell spatial-transcriptomic assays. All patients were treated only with standard-of-care therapy: temozolomide, radiation and surgical resection. The cohort had a 1.2 male/female ratio, ages 35–76. We found a significant increase at recurrence in cells with the Verhaak mesenchymal phenotype and fewer proneural cells. Although there was an increase in the percentage of cycling cells overall, the fraction of cycling proneural cells decreased while the fraction of cycling mesenchymal cells increased. These changes were concomitant with a significant increase in the percentage of tumor-infiltrating monocytic-lineage cells derived from the periphery. Taken together, these findings support a proneural-to-mesenchymal shift at recurrence due to an increase in the birth rate of mesenchymal cells, supported by an expansion of myeloid-derived cells from peripheral blood. Although the percentages of glioblastoma-infiltrating T-cells are generally low (~1% on average in our data), we found a statistically significant increase in T-cell abundance at recurrence. We identified a cohort of T-cell outliers that demonstrate 2-to-8-fold increases in T-cells over average levels. We validated that T-cells in these tumors have extravasated beyond the perivascular space and into the cellular tumor via immunohistochemistry and single-cell spatial profiling. We present our ongoing analysis of the paracrine signals, upstream transcription-factor expression, and cis-regulatory grammars utilized in immune-outlier GBMs. We describe how these programs change under therapy. These studies shed light on the effect of standard therapy in shaping GBM composition at recurrence.

CXCL13 plasma levels function as a biomarker for disease activity in patients with chronic lymphocytic leukemia.

The chemoattractant CXCL13 organizes the cellular architecture of B-cell follicles and germinal centers. During adaptive immune responses, CXCL13 plasma concentrations transiently increase and function as a biomarker for normal germinal center activity. Chronic lymphocytic leukemia (CLL) cells express high levels of CXCR5, the receptor for CXCL13, and proliferate in pseudofollicles within secondary lymphoid organs (SLO). Given the morphologic and functional similarities between normal and CLL B-cell expansion in SLO, we hypothesized that CXCL13 plasma concentrations would correlate with CLL disease activity and progression. We analyzed CXCL13 plasma concentrations in 400 CLL patients and correlated the findings with other prognostic markers, time to treatment (TTT), CCL3 and CCL4 plasma concentrations, and in vivo CLL cell proliferation. We found that CXCL13 plasma concentrations were higher in CLL patients with active and advanced stage disease, resulting in a significantly shorter TTT. Accordingly, high CXCL13 levels correlated with other markers of disease activity and CCL3 levels. Higher CLL cell birth rates in vivo also associated with higher CXCL13 plasma concentrations. Interestingly, elevated CXCL13 plasma levels normalized during ibrutinib therapy, and increased in ibrutinib resistance patients. Collectively, these studies emphasize the importance of CXCL13 in crosstalk between CLL cells and the SLO microenvironment.

Numerical Solution of a Two Dimensional Tumour Growth Model with Moving Boundary

We consider a biphasic continuum model for avascular tumour growth in two spatial dimensions, in which a cell phase and a fluid phase follow conservation of mass and momentum. A limiting nutrient that follows a diffusion process controls the birth and death rate of the tumour cells. The cell volume fraction, cell velocity--fluid pressure system, and nutrient concentration are the model variables. A coupled system of a hyperbolic conservation law, \cred{a viscous fluid model}, and a parabolic diffusion equation governs the dynamics of the model variables. The tumour boundary moves with the normal velocity of the outermost layer of cells, and this time--dependence is a challenge in designing and implementing a stable and fast numerical scheme. We recast the model into a form where the hyperbolic equation is defined on a fixed extended domain and retrieve the tumour boundary as the interface at which the cell volume fraction decreases below a threshold value. This procedure eliminates the need to track the tumour boundary explicitly and the computationally expensive re--meshing of the time--dependent domains. A numerical scheme based on finite volume methods for the hyperbolic conservation law, Lagrange $\mathbb{P}_2 - \mathbb{P}_1$ Taylor--Hood finite element method for the \cred{viscous} system, and mass--lumped finite element method for the parabolic equations is implemented in two spatial dimensions, and several cases are studied. We demonstrate the versatility of the numerical scheme in catering for irregular and asymmetric initial tumour geometries. We present numerical simulations for both cases and the results are consistent with theoretical and heuristic expectations such as early linear growth rate and preservation of radial symmetry when the boundary conditions are symmetric.

Contrasting the impact of cytotoxic and cytostatic drug therapies on tumour progression.

A tumour grows when the total division (birth) rate of its cells exceeds their total mortality (death) rate. The capability for uncontrolled growth within the host tissue is acquired via the accumulation of driver mutations which enable the tumour to progress through various hallmarks of cancer. We present a mathematical model of the penultimate stage in such a progression. We assume the tumour has reached the limit of its present growth potential due to cell competition that either results in total birth rate reduction or death rate increase. The tumour can then progress to the final stage by either seeding a metastasis or acquiring a driver mutation. We influence the ensuing evolutionary dynamics by cytotoxic (increasing death rate) or cytostatic (decreasing birth rate) therapy while keeping the effect of the therapy on net growth reduction constant. Comparing the treatments head to head we derive conditions for choosing optimal therapy. We quantify how the choice and the related gain of optimal therapy depends on driver mutation, metastasis, intrinsic cell birth and death rates, and the details of cell competition. We show that detailed understanding of the cell population dynamics could be exploited in choosing the right mode of treatment with substantial therapy gains.

Cancer cell population growth kinetics at low densities deviate from the exponential growth model and suggest an Allee effect.

Most models of cancer cell population expansion assume exponential growth kinetics at low cell densities, with deviations to account for observed slowing of growth rate only at higher densities due to limited resources such as space and nutrients. However, recent preclinical and clinical observations of tumor initiation or recurrence indicate the presence of tumor growth kinetics in which growth rates scale positively with cell numbers. These observations are analogous to the cooperative behavior of species in an ecosystem described by the ecological principle of the Allee effect. In preclinical and clinical models, however, tumor growth data are limited by the lower limit of detection (i.e., a measurable lesion) and confounding variables, such as tumor microenvironment, and immune responses may cause and mask deviations from exponential growth models. In this work, we present alternative growth models to investigate the presence of an Allee effect in cancer cells seeded at low cell densities in a controlled in vitro setting. We propose a stochastic modeling framework to disentangle expected deviations due to small population size stochastic effects from cooperative growth and use the moment approach for stochastic parameter estimation to calibrate the observed growth trajectories. We validate the framework on simulated data and apply this approach to longitudinal cell proliferation data of BT-474 luminal B breast cancer cells. We find that cell population growth kinetics are best described by a model structure that considers the Allee effect, in that the birth rate of tumor cells increases with cell number in the regime of small population size. This indicates a potentially critical role of cooperative behavior among tumor cells at low cell densities with relevance to early stage growth patterns of emerging and relapsed tumors.

Cell Growth Rate Dictates the Onset of Glass to Fluid-Like Transition and Long Time Super-Diffusion in an Evolving Cell Colony

Collective migration dominates many phenomena, from cell movement in living systems to abiotic self-propelling particles. Focusing on the early stages of tumor evolution, we enunciate the principles involved in cell dynamics and highlight their implications in understanding similar behavior in seemingly unrelated soft glassy materials and possibly chemokine-induced migration of CD8$^{+}$ T cells. We performed simulations of tumor invasion using a minimal three dimensional model, accounting for cell elasticity and adhesive cell-cell interactions as well as cell birth and death to establish that cell growth rate-dependent tumor expansion results in the emergence of distinct topological niches. Cells at the periphery move with higher velocity perpendicular to the tumor boundary, while motion of interior cells is slower and isotropic. The mean square displacement, $\Delta(t)$, of cells exhibits glassy behavior at times comparable to the cell cycle time, while exhibiting super-diffusive behavior, $\Delta (t) \approx t^{\alpha}$ ($\alpha > 1$), at longer times. We derive the value of $\alpha \approx 1.33$ using a field theoretic approach based on stochastic quantization. In the process we establish the universality of super-diffusion in a class of seemingly unrelated non-equilibrium systems. Super diffusion at long times arises only if there is an imbalance between cell birth and death rates. Our findings for the collective migration, which also suggests that tumor evolution occurs in a polarized manner, are in quantitative agreement with {\it in vitro} experiments. Although set in the context of tumor invasion the findings should also hold in describing collective motion in growing cells and in active systems where creation and annihilation of particles play a role.

Being bullied reduces brain cell birth in harried weakly electric fish

South American knifefish are remarkably adaptable. While the loss of a tail would be a major concern for most fish, some knifefish can replace the lost appendage entirely in only 3 weeks – which is just as well in an environment where hungry catfish continually nibble at them. Despite the knifefish's extraordinary ability to recover from the most extreme injury, Kent Dunlap from Trinity College, USA, noticed that Brachyhypopomus occidentalis survivors that had lost their tails naturally to predators in the streams of Panama also had lower rates of cell birth in the part of the brain that controls responses to predators: the telencephalic region. Could this brain deficit be increasing the fish's vulnerability to a catfish attack, raising the number of wounded fish in the predator's vicinity? Or had living in the constant shadow of a predator affected cell birth in the region of the brain that could protect the fish from assault? And, if catfish attacks were the cause of the reduced brain growth, were the knifefish investing more of their resources in tail regrowth at the expense of their own brains?Intrigued by the possibility that living under the constant threat of predation was affecting the brains of knifefish, Dunlap and his colleagues decided to simulate the impact of the catfish's attentions in the laboratory. Dunlap admits, ‘Coming up with an experimental “chase” protocol for the lab that might mimic the experience of living among dense predators was hard’; it was not clear how closely tapping the fish lightly on the tail and amputating the rear portion of the body under anaesthetic reproduces the experience of a harried B. gauderio. However, when Vielka Salazar from Cape Breton University, Canada, measured the levels of the stress hormone cortisol in the blood of B. gauderio, it was apparent that losing the tail was stressful, although the fish didn't seem too bothered when they were harassed with a plastic rod as their cortisol levels did not rise.Next, Geoffrey Keane, Elise Lasky and Michael Ragazzi checked the amount of brain cell birth in the fish that had been disturbed with a rod but kept their tails, and found it was reduced to half of that of the undisturbed fish. Living under the constant threat of attack had altered cell birth in the agitated fish's brains. And when the team checked how losing a tail affected brain cell birth after 17 days, it was clear that the fish suffered a similar reduction. In addition, when they tested whether the fish had reduced brain cell birth in favour of regrowing their tails, it was clear that there was no trade-off. ‘The reduction of brain cell proliferation following tail amputation was… greatest even before the fish were adding a lot of tail cells and lower during the period of fastest tail generation’, says Dunlap, adding that brain cell birth plummeted by 80% within 24 h of the loss of the tail, which is before regrowth has began in earnest.So, B. gauderio fish reduce cell birth in the telencephalic region of the brain when they are bullied, and when Dunlap and his team tried to terrorise brown ghost knifefish (Apteronotus leptorhynchus), which are popular in the aquarium trade and more easily available, the fish suffered the same brain impairment. Speculating about possible reasons for the fish to scale back the region of the brain that might provide them with the best protection from lurking predators, Dunlap says, ‘We suspect that fish with a lower cell birth rate might be less exploratory and more timid. This could reduce their opportunity to forage and find mates, but might also reduce the probability of falling victim to a predator’.

An exactly solvable, spatial model of mutation accumulation in cancer.

One of the hallmarks of cancer is the accumulation of driver mutations which increase the net reproductive rate of cancer cells and allow them to spread. This process has been studied in mathematical models of well mixed populations, and in computer simulations of three-dimensional spatial models. But the computational complexity of these more realistic, spatial models makes it difficult to simulate realistically large and clinically detectable solid tumours. Here we describe an exactly solvable mathematical model of a tumour featuring replication, mutation and local migration of cancer cells. The model predicts a quasi-exponential growth of large tumours, even if different fragments of the tumour grow sub-exponentially due to nutrient and space limitations. The model reproduces clinically observed tumour growth times using biologically plausible rates for cell birth, death, and migration rates. We also show that the expected number of accumulated driver mutations increases exponentially in time if the average fitness gain per driver is constant, and that it reaches a plateau if the gains decrease over time. We discuss the realism of the underlying assumptions and possible extensions of the model.

In the linear quadratic model, the Poisson approximation and the Zaider-Minerbo formula agree on the ranking of tumor control probabilities, up to a critical cell birth rate

Purpose: To provide a rule for the agreement or disagreement of the Poisson approximation (PA) and the Zaider-Minerbo formula (ZM) on the ranking of treatment alternatives in terms of tumor control probability (TCP) in the linear quadratic model.Materials and methods: A general criterion involving a critical cell birth rate was formally derived. For demonstration, the criterion was applied to a distinct radiobiological model of fast growing head and neck tumors and a respective range of 22 conventional and nonconventional head and neck schedules.Results: There is a critical cell birth rate bcrit below which PA and ZM agree on which one out of two alternative treatment schemes with single-cell survival curves S′(t) and S′′(t) offers better TCP:For cell birth rates b above this critical cell birth rate, PA and ZM disagree if and only if b >bcrit > 0. In case of the exemplary head and neck schedules, out of 231 possible combinations, only 16 or 7% were found where PA and ZM disagreed. In all 231 cases the prediction of the criterion was numerically confirmed, and cell birth rates at crossovers between schedules matched the calculated critical cell birth rates.Conclusions: TCP estimated by PA and ZM almost never numerically coincide. Still, in many cases both formulas at least agree about which one out of two alternative fractionation schemes offers better TCP. In case of fast growing tumors featuring a high cell birth rate, however, ZM may suggest a re-evaluation of treatment options.

Dynamics of a Viral Infection Logistic Model with Delayed Nonlinear CTL Response and Periodic Immune Response

This paper investigates the global dynamics and bifurcation structure of a viral infection logistic model with delayed nonlinear CTL response and periodic immune response. It is proved that the basic reproduction numbers, $R_{0}$ and $R_{1}$, determine the outcome of viral infection. Besides changes in the amplititude of lytic component, we show, via numerical simulations, that , the birth rate of susceptible host cells and the maximum proliferation of target cells are crucial to the outcome of a viral infection. Time delay can alter the period of oscillation for the larger level of periodic forcing. Period doubling bifurcations of the system are observed via simulations. Our results can provide a possible explanation of the oscillation behaviors of virus population,which were observed in chronic HBV or HCV carriers.

Quantifying Clonal and Subclonal Passenger Mutations in Cancer Evolution.

The vast majority of mutations in the exome of cancer cells are passengers, which do not affect the reproductive rate of the cell. Passengers can provide important information about the evolutionary history of an individual cancer, and serve as a molecular clock. Passengers can also become targets for immunotherapy or confer resistance to treatment. We study the stochastic expansion of a population of cancer cells describing the growth of primary tumors or metastatic lesions. We first analyze the process by looking forward in time and calculate the fixation probabilities and frequencies of successive passenger mutations ordered by their time of appearance. We compute the likelihood of specific evolutionary trees, thereby informing the phylogenetic reconstruction of cancer evolution in individual patients. Next, we derive results looking backward in time: for a given subclonal mutation we estimate the number of cancer cells that were present at the time when that mutation arose. We derive exact formulas for the expected numbers of subclonal mutations of any frequency. Fitting this formula to cancer sequencing data leads to an estimate for the ratio of birth and death rates of cancer cells during the early stages of clonal expansion.

Kinetic Measurement of Leukemia-Cell Proliferation Rate By Deuterium Labeling Predicts Time to Initial Treatment of Patients with Chronic Lymphocytic Leukemia

Background: Chronic lymphocytic leukemia (CLL) patients exhibit variable times from diagnosis to the need to initiate therapy. Previous studies have demonstrated that the rates of CLL cell proliferation (birth) and elimination (death plus recirculation to solid tissues) could be estimated using the incorporation of deuterium (2H), taken in the form of heavy water (2H2O), into the DNA of dividing cells. In a cross-sectional study of patients with early and late stage CLL, birth rates above 0.35% per day were associated with more aggressive disease. The NIH-sponsored CLL Research Consortium (CRC) conducted a prospective study on patients with early stage disease to assess the relationship between CLL-cell birth rate and the length of time to initiation of initial therapy.Methods: Eligible patients had untreated early stage (Rai 0, 1 or 2) disease, and were no more than 3 years from diagnosis. Additional clinical parameters included age at diagnosis, gender, mutational status of the immunoglobulin heavy chain variable region (IGHV), 70-kD zeta-associated protein (ZAP-70) (binary split at 20%) and CD38 (binary split at 30%) expression, and FISH cytogenetics by the Dohner hierarchy. Heavy water was administered daily for 6 weeks, and peripheral blood was obtained for kinetic measurements at the end of weeks 3, 6, 9, 12, and 16. CLL birth rates for blood samples were measured at the same facility (KineMed, Inc, Emeryville, CA) by quantifying deuterium incorporation into the deoxyribose moiety of DNA of tumor cells, using isotope ratio mass spectrometry (IRMS). Subjects were followed for time to administration of therapy; subjects still without treatment at time of analysis were censored, as were subjects who exited the study to receive treatment outside of the established criteria. To assess the impact of birth rate and other factors on time to first therapy, Kaplan-Meier curves were compared using the logrank test for univariable analyses; stepwise Cox proportional hazards regression models were used to build multivariable models.Results: Between July 2005 and February 2009, 119 subjects were enrolled through the CRC. 107 subjects were eligible. For 10 eligible patients, exit from the study prior to completion of protocol-mandated heavy water consumption (n=5) or technical issues (n=5) made it impossible to obtain estimates of birth rate. The 97 eligible subjects for whom birth rates were available form the basis of this report. 60% of subjects were male; median age 57 years (range 40-85). Median birth rate was 0.32%/day (range 0.07-1.31%/day). 43 subjects (44%) had birth rates higher than the previously reported threshold of 0.35%/day. With a median follow up of 4 years, 33 eligible subjects (34%) required treatment. IGHV status (31 subjects unmutated), elevated ZAP-70 (31 subjects), elevated CD38 (21 subjects), and hierarchical categorization of FISH anomalies (4 del(17p), 5 del(11q), 8 tri(12), 50 del(13q)) were examined for association with differential time to first therapy in univariable analyses. All were associated with earlier need for therapy (p <0.001) except for genomic aberrations defined by FISH (p = 0.96). Birth rate > 0.35%/day was also significantly associated with shorter time to first therapy (p < 0.001). In multivariable modeling, only birth rate and IGHV status met the criteria for inclusion (Wald p-value < 0.05). Hazard ratios were 3.51 (p = 0.002) for birth rate above 0.35%/day and 5.0 for unmutated IGHV status (p < 0.001). The association between elevated birth rate and shorter time to first treatment was observed within subjects with both unmutated and mutated IGHV (see Figure 1).Conclusion: An increased birth rate of CLL cells early in the disease course is a strong predictor of an earlier need for treatment in univariable analysis, as are unmutated IGHV, elevated ZAP-70 expression and elevated CD38 expression. However, only unmutated IGHV and an increased birth rate contribute significantly to the multivariable model. This adds a direct measure of B-cell kinetics to the array of biomarkers available to subjects with CLL. [Display omitted] DisclosuresMurphy:KineMed, Inc: Equity Ownership. Emson:KineMed, Inc.: Employment, Equity Ownership. Li:KineMed, Inc.: Employment, Equity Ownership. McConnel:KineMed, Inc.: Equity Ownership. Turner:KineMed, Inc.: Employment, Equity Ownership. Busch:KineMed, Inc.: Equity Ownership. Hellerstein:KineMed Inc: Consultancy, Employment, Equity Ownership, Membership on an entity’s Board of Directors or advisory committees. Chiorazzi:KineMed, Inc.: Stock options Other.

Functional Evidence from Deuterated Water Labeling That the Bruton Tyrosine Kinase Inhibitor Ibrutinib Blocks Leukemia Cell Proliferation and Trafficking and Promotes Leukemia Cell Death in Patients with Chronic Lymphocytic Leukemia and small Lymphocytic Lymphoma

BACKGROUND: In patients with chronic lymphocytic leukemia (CLL), the Bruton tyrosine kinase(BTK) inhibitor ibrutinib induces a rapid reduction in lymphadenopathy, accompanied by a transient lymphocytosis. Continuation of therapy leads to a reduction in peripheral blood disease burden with achievement of objective responses in a majority of patients over time. Inhibition of B cell receptor (BCR) and chemokine receptor signaling are considered the mechanisms for redistribution lymphocytosis and CLL cell death. However, these mechanisms of action have not been formally documented directly in patients. To address this, before initiating therapy with ibrutinib, we labeled the DNA of proliferating CLL cells with deuterium (2H) by asking patients to drink deuterated water (2H2O) and then determined the effects of ibrutinib on leukemia cell kinetics (proliferation and death rates) and mobilization of cells from lymphoid tissues (trafficking) after ibrutinib administration.METHODS: 30 previously untreated CLL/SLL patients were enrolled between December 2012 and June 2013 at MD Anderson Cancer Center. Patients required treatment per iwCLL guidelines, had adequate hematopoietic (platelets > 50,000/μL, ANC > 750/μL) and organ functions. Patients drank 50 mL of 70% 2H2O 3 times a day for 5 days, followed by 60 mL daily for a total of 4 weeks (“labeling phase”). After a 6-12 week “washout phase”, patients started once-daily ibrutinib 420 mg continuously on 28 day cycles. Study objectives were to determine the impact on CLL cell proliferation and death rates, before and after ibrutinib, and on CLL cell trafficking after ibrutinib.PATIENT CHARACTERISTICS: Median age of the 30 patients was 64 years (range 48–78) with 19 males. 16 patients exhibited early stage (Rai stage 0-2), and 14 advanced stage (Rai stage 3-4) disease. 17 patients expressed unmutated IGHVs, 11 patients had mutated IGHVs, and 2 had inconclusive IGHV results. 8 were CD38+ and 15 ZAP-70+ by immunohistochemistry. FISH cytogenetics revealed 11 patients with del13q, 6 with trisomy 12, 3 with del17p or TP53 mutation, 4 with del11q, and 6 without abnormalities. Median β2 microglobulin level was 2.8 mg/L (1.6 - 7.4).RESPONSE TO THERAPY: At a median follow up of 13 months, 28 of 30 patients continued on therapy without disease progression. All patients were evaluable for response assessment per 2008 IWCLL guidelines: 28 (93%) achieved partial remission, 1 (3%) complete remission, and 1 (3%) had stable disease, yielding an ORR of 97%. Two patients came off study at 184 and 480 days, respectively.CLL CELL KINETICS AND TRAFFICKING: The average CLL cell birth rate determined before ibrutinib therapy was 0.42% per day (range 0.32 – 1.42%). After initiating ibrutinib, there was a rapid increase in absolute lymphocyte count in the blood in 26 of 30 patients; this contained previously labeled CLL cells rather than newly-divided unlabeled cells. Over time, the proportion of circulating CLL cells that were labeled did not decrease appreciably despite a concomitant fall in circulating lymphocytes, indicating that newly divided cells were not entering the circulation and strongly suggesting that ibrutinib had a major inhibitory effect on leukemia cell proliferation. In 3 of the 4 patients in whom there was a rapid influx of unlabeled cells with the onset of ibrutinib treatment, maintenance of circulating labeled cells concomitant with a significant fall in circulating lymphocytes suggested proliferation of CLL cells was inhibited with extended treatment. Prior to ibrutinib therapy, the measured proliferation rate of CLL cells was 0.42 % per day. Because after ibrutinib therapy both cell proliferation and exiting from the blood were markedly reduced, the elimination rate should equal the death rate. Notably, with treatment the elimination rate of CLL cells was much faster than before ibrutinib, revealing a “true” death rate of 1.48 % of the clone per day.CONCLUSIONS: Using 2H-labelling of dividing leukemic cells, we have shown for the first time directly in CLL patients that ibrutinib significantly inhibits leukemia cell proliferation, leads to an efflux of CLL cells from tissues into the blood, and promotes a remarkably high death rate of CLL cells in an apparently indirect manner, likely due to the interruption of survival signals from the BCR and other receptors that are engaged in lymphoid tissues. DisclosuresBurger:Pharmacyclics, Inc.: Research Funding; Janssen: Membership on an entity’s Board of Directors or advisory committees. Li:KineMed, Inc.: Employment, Equity Ownership. O’Brien:Pharmacyclics, Inc.: Membership on an entity’s Board of Directors or advisory committees, Research Funding. Hellerstein:KineMed Inc: Consultancy, Employment, Equity Ownership, Membership on an entity’s Board of Directors or advisory committees. Turner:KineMed, Inc.: Employment, Equity Ownership. Emson:KineMed, Inc.: Employment, Equity Ownership. Chiorazzi:Pharmacyclics, Inc.: Research Funding; KineMed: Equity Ownership.

Immune Response to Combination Therapy for Non-Hodgkin Lymphomas

A parametric model of tumor response to combination therapy in the presence of an immune system is described. Synergistic mechanisms which induce tumor regression are simulated with a coupled set of equations. The simulations are first compared to tumor history data obtained with a SCID mouse model to determine key parameters; predictions are then made for an immune-competent animal. The minimum immune cell birth rate relative to malignant B-cell birth rate necessary to induce tumor regression is determined, and optimization of drug combinations in the presence of an immune response is explored. The delayed effect of an immune response relative to drug scheduling is examined, and a mechanism for disease transformation in heterogeneous tumors is proposed.

Physiologic Parameter Estimation Using Inverse Problems

The estimation of in vivo physiologic parameters is an important, but difficult, issue in bio-medicine. Therefore the development of mathematical techniques predicting these parameter values is very relevant. In a previous work we have proposed a convection-diffusion-shape model, which correlates colonic crypt patterns with the cellular kinetics occurring inside the crypts (this correlation is significant in the context of colorectal cancer). This model involves several physiologic parameters, for which only qualitative information is available in the literature, such as the birth rate of proliferative cells. In this paper we present a framework for estimating this birth rate parameter, in a colonic crypt, assuming that the distribution of proliferative cells is known in that crypt. More precisely, we resolve an inverse problem, where the unknown coefficient field, the birth rate, is connected to the observed measurements, the proliferative cell density, through a partial differential equation. This inverse problem is a PDE-constrained optimization problem, highly nonlinear and time-dependent, which is solved by an inexact Newton method. Some test simulations illustrate the efficacy of the proposed parameter inversion and forecast its application with real patient data.