PASCAR: a multiscale framework to explore the design space of constitutive and inducible CAR T cells.

CAR T cells are engineered to bind and destroy tumor cells by targeting overexpressed surface antigens. However, healthy cells expressing lower abundances of these antigens can also be lysed by CAR T cells. Various CAR T cell designs increase tumor cell elimination, whereas reducing damage to healthy cells. However, these efforts are costly and labor-intensive, constraining systematic exploration of potential hypotheses. We develop a protein abundance structured population dynamic model for CAR T cells (PASCAR), a framework that combines multiscale population dynamic models and multi-objective optimization approaches with data from cytometry and cytotoxicity assays to systematically explore the design space of constitutive and tunable CAR T cells. PASCAR can quantitatively describe in vitro and in vivo results for constitutive and inducible CAR T cells and can successfully predict experiments outside the training data. Our exploration of the CAR design space reveals that optimal CAR affinities in the intermediate range of dissociation constants effectively reduce healthy cell lysis, whereas maintaining high tumor cell-killing rates. Furthermore, our modeling offers guidance for optimizing CAR expressions in synthetic notch CAR T cells. PASCAR can be extended to other CAR immune cells.

Linear scaling between microbial predator and prey densities in the global ocean.

It has been proposed that microbial predator and prey densities are related through sublinear power laws. We revisited previously published biomass and abundance data and fitted Power-law Biomass Scaling Relationships (PBSRs) between marine microzooplankton predators (Z) and phytoplankton prey (P), and marine viral predators (V) and bacterial prey (B). We analysed them assuming an error structure given by Type II regression models which, in contrast to the conventional Type I regression model, accounts for errors in both the independent and the dependent variables. We found that the data support linear relationships, in contrast to the sublinear relationships reported by previous authors. The scaling exponent yields an expected value of 1 with some spread in different datasets that was well-described with a Gaussian distribution. Our results suggest that the ratios Z/P, and V/B are on average invariant, in contrast to the hypothesis that they systematically decrease with increasing P and B, respectively, as previously thought.

Mathematical Modeling to Guide Experimental Design: T Cell Clustering as a Case Study.

Mathematical modeling provides a rigorous way to quantify immunological processes and discriminate between alternative mechanisms driving specific biological phenomena. It is typical that mathematical models of immunological phenomena are developed by modelers to explain specific sets of experimental data after the data have been collected by experimental collaborators. Whether the available data are sufficient to accurately estimate model parameters or to discriminate between alternative models is not typically investigated. While previously collected data may be sufficient to guide development of alternative models and help estimating model parameters, such data often do not allow to discriminate between alternative models. As a case study, we develop a series of power analyses to determine optimal sample sizes that allow for accurate estimation of model parameters and for discrimination between alternative models describing clustering of CD8 T cells around Plasmodium liver stages. In our typical experiments, mice are infected intravenously with Plasmodium sporozoites that invade hepatocytes (liver cells), and then activated CD8 T cells are transferred into the infected mice. The number of T cells found in the vicinity of individual infected hepatocytes at different times after T cell transfer is counted using intravital microscopy. We previously developed a series of mathematical models aimed to explain highly variable number of T cells per parasite; one of such models, the density-dependent recruitment (DDR) model, fitted the data from preliminary experiments better than the alternative models, such as the density-independent exit (DIE) model. Here, we show that the ability to discriminate between these alternative models depends on the number of parasites imaged in the analysis; analysis of about [Formula: see text] parasites at 2, 4, and 8 h after T cell transfer will allow for over 95% probability to select the correct model. The type of data collected also has an impact; following T cell clustering around individual parasites over time (called as longitudinal (LT) data) allows for a more precise and less biased estimates of the parameters of the DDR model than that generated from a more traditional way of imaging individual parasites in different liver areas/mice (cross-sectional (CS) data). However, LT imaging comes at a cost of a need to keep the mice alive under the microscope for hours which may be ethically unacceptable. We finally show that the number of time points at which the measurements are taken also impacts the precision of estimation of DDR model parameters; in particular, measuring T cell clustering at one time point does not allow accurately estimating all parameters of the DDR model. Using our case study, we propose a general framework on how mathematical modeling can be used to guide experimental designs and power analyses of complex biological processes.

Dynamical regulations on mobility and vaccinations for controlling COVID-19 spread.

Using a system of time-dynamical equations, we investigate how daily mobility indices, such as the homestay percentage above the pre-COVID normal ([Formula: see text]; or H-forcing), and the vaccinated percentage ([Formula: see text]; or V-forcing) impact the net reproductive rate (R0) of COVID-19 in ten island nations as a prototype, and then, extending it to 124 countries worldwide. Our H- and V-forcing model of R0 can explain the new trends in 106 countries. The disease transmission can be controlled by forcing down [Formula: see text] with an enforcement of continuous [Formula: see text] in [Formula: see text] of countries with [Formula: see text] vaccinated plus recovered, [Formula: see text]. The required critical [Formula: see text] decreases with increasing [Formula: see text], dropping it down to [Formula: see text] with [Formula: see text], and further down to [Formula: see text] with [Formula: see text]. However, the regulations on [Formula: see text] are context-dependent and country-specific. Our model gives insights into forecasting and controlling the disease's transmission behaviour when the effectiveness of the vaccines is a concern due to new variants, and/or there are delays in vaccination rollout programs.

Liver Environment-Imposed Constraints Diversify Movement Strategies of Liver-Localized CD8 T Cells.

Pathogen-specific CD8 T cells face the problem of finding rare cells that present their cognate Ag either in the lymph node or in infected tissue. Although quantitative details of T cell movement strategies in some tissues such as lymph nodes or skin have been relatively well characterized, we still lack quantitative understanding of T cell movement in many other important tissues, such as the spleen, lung, liver, and gut. We developed a protocol to generate stable numbers of liver-located CD8 T cells, used intravital microscopy to record movement patterns of CD8 T cells in livers of live mice, and analyzed these and previously published data using well-established statistical and computational methods. We show that, in most of our experiments, Plasmodium-specific liver-localized CD8 T cells perform correlated random walks characterized by transiently superdiffusive displacement with persistence times of 10-15 min that exceed those observed for T cells in lymph nodes. Liver-localized CD8 T cells typically crawl on the luminal side of liver sinusoids (i.e., are in the blood); simulating T cell movement in digital structures derived from the liver sinusoids illustrates that liver structure alone is sufficient to explain the relatively long superdiffusive displacement of T cells. In experiments when CD8 T cells in the liver poorly attach to the sinusoids (e.g., 1 wk after immunization with radiation-attenuated Plasmodium sporozoites), T cells also undergo Lévy flights: large displacements occurring due to cells detaching from the endothelium, floating with the blood flow, and reattaching at another location. Our analysis thus provides quantitative details of movement patterns of liver-localized CD8 T cells and illustrates how structural and physiological details of the tissue may impact T cell movement patterns.

Clustering of Activated CD8 T Cells Around Malaria-Infected Hepatocytes Is Rapid and Is Driven by Antigen-Specific Cells.

Malaria, a disease caused by parasites of the Plasmodium genus, begins when Plasmodium-infected mosquitoes inject malaria sporozoites while searching for blood. Sporozoites migrate from the skin via blood to the liver, infect hepatocytes, and form liver stages which in mice 48 h later escape into blood and cause clinical malaria. Vaccine-induced activated or memory CD8 T cells are capable of locating and eliminating all liver stages in 48 h, thus preventing the blood-stage disease. However, the rules of how CD8 T cells are able to locate all liver stages within a relatively short time period remains poorly understood. We recently reported formation of clusters consisting of variable numbers of activated CD8 T cells around Plasmodium yoelii (Py)-infected hepatocytes. Using a combination of experimental data and mathematical models we now provide additional insights into mechanisms of formation of these clusters. First, we show that a model in which cluster formation is driven exclusively by T-cell-extrinsic factors, such as variability in "attractiveness" of different liver stages, cannot explain distribution of cluster sizes in different experimental conditions. In contrast, the model in which cluster formation is driven by the positive feedback loop (i.e., larger clusters attract more CD8 T cells) can accurately explain the available data. Second, while both Py-specific CD8 T cells and T cells of irrelevant specificity (non-specific CD8 T cells) are attracted to the clusters, we found no evidence that non-specific CD8 T cells play a role in cluster formation. Third and finally, mathematical modeling suggested that formation of clusters occurs rapidly, within few hours after adoptive transfer of CD8 T cells, thus illustrating high efficiency of CD8 T cells in locating their targets in complex peripheral organs, such as the liver. Taken together, our analysis provides novel insights into and attempts to discriminate between alternative mechanisms driving the formation of clusters of antigen-specific CD8 T cells in the liver.

Optimizing methods to estimate zooplankton concentration based on generalized patterns of patchiness inside ballast tanks and ballast water discharges.

Zooplankton populations are spatially heterogeneous in nature and inside ship ballast tanks. Sampling methods should take heterogeneity into account, particularly when estimating quantitative variables such as abundance or concentration. It is particularly important to generate unbiased estimates of zooplankton concentration in ballast water when assessing compliance with new international ballast water discharge standards. We measured spatial heterogeneity of zooplankton within ballast water using three sampling methodologies. In-tank pump samples were collected at fixed depths within the vertical part of the ballast tank (side tank). Vertical net-haul samples were collected from the upper portion of the tank as a depth-integrated and historically relevant method. In-line, time-integrated samples were collected during ballast discharge by an isokinetic sample probe, likely representing the double bottom part of the ballast tank. The bias and precision associated with each sampling method were evaluated in reference to the estimated average abundance of the entire ballast tank, which was modeled from the data collected by all methods. In-tank pump samples provided robust evidence for vertical stratification of zooplankton concentration in the side tank. A consistent trend was also observed for in-line discharge samples, with zooplankton concentration decreasing through time as the ballast tank is being discharged. Sample representativeness, as compared to the tank average, varied depending on the depth or tank volume discharged. In-line discharge samples provided the least biased and most precise estimate of average tank abundance (having lowest mean squared error) when collected during the time frame of 20%-60% of the tank volume being discharged. Results were consistent across five trips despite differences in ballast water source, season, and age.

Temperature cycles affect colonization potential of calanoid copepods.

Marine calanoid copepods colonize new habitats, and some become invasive. Their fitness, measured by intrinsic growth rate and net reproductive rate, is partially driven by biochemical processes. Thus, it is a function of ambient temperature. Biochemical processes may not be approximated well by yearly mean temperature alone when temperature cycles yearly, largely. Higher order moments may also be important. The amplitude of yearly fluctuations of monthly and seasonal sea temperatures varies dramatically across the northern temperate regions. Thus, they can impact the fitness, thereby the colonization potential of copepods migrating across such region. To investigate this, we derive approximate metrics of periodic (yearly) fitness: the yearly intrinsic growth rate, and a weighted net reproductive rate. We use them to measure the persistence and the growth of an Allee-effect free, stage-structured, fast-maturing, small population of invasive copepods that reproduces year-round in habitats with yearly temperature cycles. We show that the yearly fitness increases substantially when a population is introduced from a habitat with large amplitude to that with small amplitude yearly fluctuating temperatures, given that their mean temperatures and other environmental and ecological factors are constant. The detected range-expansion of the modeled species matches the potential fitness gradient predicted by the metrics. The study leads to the question whether the gradient of the amplitudes of temperature between habitats with similar yearly mean temperatures impacts a class of fast-maturating calanoid copepods, colonizing new habitats, and becoming invasive.

Optimizing performance of nonparametric species richness estimators under constrained sampling.

Understanding the functional relationship between the sample size and the performance of species richness estimators is necessary to optimize limited sampling resources against estimation error. Nonparametric estimators such as Chao and Jackknife demonstrate strong performances, but consensus is lacking as to which estimator performs better under constrained sampling. We explore a method to improve the estimators under such scenario. The method we propose involves randomly splitting species-abundance data from a single sample into two equally sized samples, and using an appropriate incidence-based estimator to estimate richness. To test this method, we assume a lognormal species-abundance distribution (SAD) with varying coefficients of variation (CV), generate samples using MCMC simulations, and use the expected mean-squared error as the performance criterion of the estimators. We test this method for Chao, Jackknife, ICE, and ACE estimators. Between abundance-based estimators with the single sample, and incidence-based estimators with the split-in-two samples, Chao2 performed the best when CV < 0.65, and incidence-based Jackknife performed the best when CV > 0.65, given that the ratio of sample size to observed species richness is greater than a critical value given by a power function of CV with respect to abundance of the sampled population. The proposed method increases the performance of the estimators substantially and is more effective when more rare species are in an assemblage. We also show that the splitting method works qualitatively similarly well when the SADs are log series, geometric series, and negative binomial. We demonstrate an application of the proposed method by estimating richness of zooplankton communities in samples of ballast water. The proposed splitting method is an alternative to sampling a large number of individuals to increase the accuracy of richness estimations; therefore, it is appropriate for a wide range of resource-limited sampling scenarios in ecology.

Combining Ballast Water Exchange and Treatment To Maximize Prevention of Species Introductions to Freshwater Ecosystems.

The most effective way to manage species transfers is to prevent their introduction via vector regulation. Soon, international ships will be required to meet numeric ballast discharge standards using ballast water treatment (BWT) systems, and ballast water exchange (BWE), currently required by several countries, will be phased out. However, there are concerns that BWT systems may not function reliably in fresh and/or turbid water. A land-based evaluation of simulated "BWE plus BWT" versus "BWT alone" demonstrated potential benefits of combining BWE with BWT for protection of freshwater ecosystems. We conducted ship-based testing to compare the efficacy of "BWE plus BWT" versus "BWT alone" on voyages starting with freshwater ballast. We tested the hypotheses that there is an additional effect of "BWE plus BWT" compared to "BWT alone" on the reduction of plankton, and that taxa remaining after "BWE plus BWT" will be marine (low risk for establishment at freshwater recipient ports). Our study found that BWE has significant additional effect on the reduction of plankton, and this effect increases with initial abundance. As per expectations, "BWT alone" tanks contained higher risk freshwater or euryhaline taxa at discharge, while "BWE plus BWT" tanks contained mostly lower risk marine taxa unlikely to survive in recipient freshwater ecosystems.

Allee threshold and stochasticity in biological invasions: colonization time at low propagule pressure.

We consider the problem of estimating the time needed for species colonization. The analysis is based upon the known population dynamic models by Dennis with minor modification to the Allee effect description, which allows us to obtain an analytical expression for the colonization time. For the stochastic counterpart of the models in diffusion approximation, we (1) propose the description of immigration stochasticity, (2) provide the estimates of time required for the population to overcome strong demographic Allee effect, and (3) consider the numerical results for mean colonization time and its uncertainty. Strong Allee effect strictly disallows populations at small immigration rates to colonize new habitats, unless the stochasticity in immigration, environment, or demography is present, or incorporated into the model. Immigration stochasticity, complementing with environmental and demographic stochasticity, enables the populations to overcome the Allee threshold even at low values of propagule pressure.

Impact of stochasticity in immigration and reintroduction on colonizing and extirpating populations.

A thorough quantitative understanding of populations at the edge of extinction is needed to manage both invasive and extirpating populations. Immigration can govern the population dynamics when the population levels are low. It increases the probability of a population establishing (or reestablishing) before going extinct (EBE). However, the rate of immigration can be highly fluctuating. Here, we investigate how the stochasticity in immigration impacts the EBE probability for small populations in variable environments. We use a population model with an Allee effect described by a stochastic differential equation (SDE) and employ the Fokker-Planck diffusion approximation to quantify the EBE probability. We find that, the effect of the stochasticity in immigration on the EBE probability depends on both the intrinsic growth rate (r) and the mean rate of immigration (p). In general, if r is large and positive (e.g. invasive species introduced to favorable habitats), or if p is greater than the rate of population decline due to the demographic Allee effect (e.g., effective stocking of declining populations), then the stochasticity in immigration decreases the EBE probability. If r is large and negative (e.g. endangered populations in unfavorable habitats), or if the rate of decline due to the demographic Allee effect is much greater than p (e.g., weak stocking of declining populations), then the stochasticity in immigration increases the EBE probability. However, the mean time for EBE decreases with the increasing stochasticity in immigration with both positive and negative large r. Thus, results suggest that ecological management of populations involves a tradeoff as to whether to increase or decrease the stochasticity in immigration in order to optimize the desired outcome. Moreover, the control of invasive species spread through stochastic means, for example, by stochastic monitoring and treatment of vectors such as ship-ballast water, may be suitable strategies given the environmental and demographic uncertainties at introductions. Similarly, the recovery of declining and extirpated populations through stochastic stocking, translocation, and reintroduction, may also be suitable strategies.