Chimeric antigen receptor (CAR) T-cell therapy has shown promise in the treatment of haematological cancers and is currently being investigated for solid tumours, including high-grade glioma brain tumours. There is a desperate need to quantitatively study the factors that contribute to the efficacy of CAR T-cell therapy in solid tumours. In this work, we use a mathematical model of predator–prey dynamics to explore the kinetics of CAR T-cell killing in glioma: the Chimeric Antigen Receptor T-cell treatment Response in GliOma (CARRGO) model. The model includes rates of cancer cell proliferation, CAR T-cell killing, proliferation, exhaustion, and persistence. We use patient-derived and engineered cancer cell lines with an in vitro real-time cell analyser to parametrize the CARRGO model. We observe that CAR T-cell dose correlates inversely with the killing rate and correlates directly with the net rate of proliferation and exhaustion. This suggests that at a lower dose of CAR T-cells, individual T-cells kill more cancer cells but become more exhausted when compared with higher doses. Furthermore, the exhaustion rate was observed to increase significantly with tumour growth rate and was dependent on level of antigen expression. The CARRGO model highlights nonlinear dynamics involved in CAR T-cell therapy and provides novel insights into the kinetics of CAR T-cell killing. The model suggests that CAR T-cell treatment may be tailored to individual tumour characteristics including tumour growth rate and antigen level to maximize therapeutic benefit.

Temporal dynamics of gene expression inform cellular and molecular perturbations associated with disease development and evolution. Given the complexity of high-dimensional temporal genomic data, an analytic framework guided by a robust theory is needed to interpret time-sequential changes and to predict system dynamics. Here we model temporal dynamics of the transcriptome of peripheral blood mononuclear cells in a two-dimensional state-space representing states of health and leukemia using time-sequential bulk RNA-seq data from a murine model of acute myeloid leukemia (AML). The state-transition model identified critical points that accurately predict AML development and identifies stepwise transcriptomic perturbations that drive leukemia progression. The geometry of the transcriptome state-space provided a biological interpretation of gene dynamics, aligned gene signals that are not synchronized in time across mice, and allowed quantification of gene and pathway contributions to leukemia development. Our state-transition model synthesizes information from multiple cell types in the peripheral blood and identifies critical points in the transition from health to leukemia to guide interpretation of changes in the transcriptome as a whole to predict disease progression. Significance: These findings apply the theory of state transitions to model the initiation and development of acute myeloid leukemia, identifying transcriptomic perturbations that accurately predict time to disease development. See related commentary by Kuijjer, p. 3072

We study the relaxation of a two-dimensional (2D) ultracold Bose gas from a nonequilibrium initial state containing vortex excitations in experimentally realizable square and rectangular traps. We show that the subsystem of vortex gas excitations results in the spontaneous emergence of a coherent superfluid flow with a nonzero coarse-grained vorticity field. The stream function of this emergent quasiclassical 2D flow is governed by a Poisson-Boltzmann equation. This equation reveals that maximum entropy states of a neutral vortex gas that describe the spectral condensation of energy can be classified into types of flow depending on whether or not the flow spontaneously acquires angular momentum. Numerical simulations of a neutral point vortex model and a Bose gas governed by the 2D Gross-Pitaevskii equation in a square reveal that a large-scale monopole flow field with net angular momentum emerges that is consistent with predictions of the Poisson-Boltzmann equation. The results allow us to characterize the spectral energy condensate in a 2D quantum fluid that bears striking similarity to similar flows observed in experiments of 2D classical turbulence. By deforming the square into a rectangular region, the resulting maximum entropy state switches to a dipolar flow field with zero net angular momentum.

We study the dynamics and statistical mechanical equilibria of a neutral two-dimensional point vortex gas with Coulomb-like interactions confined in a squared and a rectangular domain. Using a punctuated Hamiltonian model in which we model the process of vortex–antivortex annihilation in superfluids by removing vortex dipoles, we show that this leads to evaporative heating of the system. Consequently, the vortex gas enters the negative temperature regime and subsequently relaxes to a maximum entropy configuration. We demonstrate that the large scale flows that emerge in this regime can be explained by using an equilibrium statistical mechanical mean field theory of point vortices based on a Poisson–Boltzmann equation. In particular, we observe that the emergent large scale flows in our point vortex simulations in the squared domain give rise to a spontaneous acquisition of angular momentum whereas the flows in the rectangular domain prefers a state with zero angular momentum. In addition to the observed qualitative agreement between the dynamical simulations and the theory that we demonstrate for the two geometries, we also present an approach that allows us to accurately compute a coarse-grained vorticity field, and henceforth recover the entropy from our dynamical runs. This allows us to perform a quantitative comparison between the dynamical point vortex simulations and the statistical mechanical predictions of the mean field theory thereby allowing us to clearly assert the validity of the assumptions of the statistical approaches as applied to this system with long-range interactions.

The wave kinetic equation has become an important tool in different fields of physics. In particular, for surface gravity waves, it is the backbone of wave forecasting models. Its derivation is based on the Hamiltonian dynamics of surface gravity waves. Only at the end of the derivation are the non-conservative effects, such as forcing and dissipation, included as additional terms to the collision integral. In this paper, we present a first attempt to derive the wave kinetic equation when the dissipation/forcing is included in the deterministic dynamics. If, in the dynamical equations, the dissipation/forcing is one order of magnitude smaller than the nonlinear effect, then the classical wave action balance equation is obtained and the kinetic time scale corresponds to the dissipation/forcing time scale. However, if we assume that the nonlinearity and the dissipation/forcing act on the same dynamical time scale, we find that the dissipation/forcing dominates the dynamics and the resulting collision integral appears in a modified form, at a higher order.

Here we present a theoretical and mathematical perspective on the process of aging. We extend the concepts of physical space and time to an abstract, mathematically-defined space, which we associate with a concept of “biological space-time” in which biological dynamics may be represented. We hypothesize that biological dynamics, represented as trajectories in biological space-time, may be used to model and study different rates of biological aging. As a consequence of this hypothesis, we show how dilation or contraction of time analogous to relativistic corrections of physical time resulting from accelerated or decelerated biological dynamics may be used to study precipitous or protracted aging. We show specific examples of how these principles may be used to model different rates of aging, with an emphasis on cancer in aging. We discuss how this theory may be tested or falsified, as well as novel concepts and implications of this theory that may improve our interpretation of biological aging.