Travelling waves for a fast reaction limit of a discrete coagulation-fragmentation model with diffusion and proliferation.

We study traveling wave solutions for a reaction-diffusion model, introduced in the article Calvez et al. (Regime switching on the propagation speed of travelling waves of some size-structured myxobacteriapopulation models, 2023), describing the spread of the social bacterium Myxococcus xanthus. This model describes the spatial dynamics of two different cluster sizes: isolated bacteria and paired bacteria. Two isolated bacteria can coagulate to form a cluster of two bacteria and conversely, a pair of bacteria can fragment into two isolated bacteria. Coagulation and fragmentation are assumed to occur at a certain rate denoted by k. In this article we study theoretically the limit of fast coagulation fragmentation corresponding mathematically to the limit when the value of the parameter k tends to + ∞ . For this regime, we demonstrate the existence and uniqueness of a transition between pulled and pushed fronts for a certain critical ratio θ ⋆ between the diffusion coefficient of isolated bacteria and the diffusion coefficient of paired bacteria. When the ratio is below θ ⋆ , the critical front speed is constant and corresponds to the linear speed. Conversely, when the ratio is above the critical threshold, the critical spreading speed becomes strictly greater than the linear speed.

Reduction of a stochastic model of gene expression: Lagrangian dynamics gives access to basins of attraction as cell types and metastabilty.

Differentiation is the process whereby a cell acquires a specific phenotype, by differential gene expression as a function of time. This is thought to result from the dynamical functioning of an underlying Gene Regulatory Network (GRN). The precise path from the stochastic GRN behavior to the resulting cell state is still an open question. In this work we propose to reduce a stochastic model of gene expression, where a cell is represented by a vector in a continuous space of gene expression, to a discrete coarse-grained model on a limited number of cell types. We develop analytical results and numerical tools to perform this reduction for a specific model characterizing the evolution of a cell by a system of piecewise deterministic Markov processes (PDMP). Solving a spectral problem, we find the explicit variational form of the rate function associated to a large deviations principle, for any number of genes. The resulting Lagrangian dynamics allows us to define a deterministic limit of which the basins of attraction can be identified to cellular types. In this context the quasipotential, describing the transitions between these basins in the weak noise limit, can be defined as the unique solution of an Hamilton-Jacobi equation under a particular constraint. We develop a numerical method for approximating the coarse-grained model parameters, and show its accuracy for a symmetric toggle-switch network. We deduce from the reduced model an approximation of the stationary distribution of the PDMP system, which appears as a Beta mixture. Altogether those results establish a rigorous frame for connecting GRN behavior to the resulting cellular behavior, including the calculation of the probability of jumps between cell types.

Stability Analysis of a Model of Interaction Between the Immune System and Cancer Cells in Chronic Myelogenous Leukemia.

We describe here a simple model for the interaction between leukemic cells and the autologous immune response in chronic phase chronic myelogenous leukemia (CML). This model is a simplified version of the model we proposed in Clapp et al. (Cancer Res 75:4053-4062, 2015). Our simplification is based on the observation that certain key characteristics of the dynamics of CML can be captured with a three-compartment model: two for the leukemic cells (stem cells and mature cells) and one for the immune response. We characterize the existence of steady states and their stability for generic forms of immunosuppressive effects of leukemic cells. We provide a complete co-dimension one bifurcation analysis. Our results show how clinical response to tyrosine kinase inhibitors treatment is compatible with the existence of a stable low disease, treatment-free steady state.

The Lacanian Concept of Paranoia: An Historical Perspective.

This article seeks to reopen a major question raised by the Lacanian nosology of the psychoses, by looking closely at Lacan's formulations of what he never ceased referring to as "paranoia". While almost all classification systems of modern psychiatry, such as the ICD-10 and the DSM-5, have abandoned the specific category of paranoia, Lacan always viewed paranoia as a major category of "functional psychosis". He held that paranoia was a qualitatively different disorder than schizophrenia, and considered it to be the principal or exemplary form of psychosis. Furthermore, in the middle period of his work, Lacan thought of paranoia in much broader terms than those of the definition proposed by Kraepelin, which he revisited, point by point, developing his theory of Freud's concept of "Verwerfung" or foreclosure; the latter became the focal diagnostic criterion in his nosographic construction. Lacan's privileging of and evolving theoretical views on paranoia provide a structural approach to what he called the "resistant nucleus" of psychosis; his work serves as a counterpoint to the more descriptive neo-Kraepelinian approach of contemporary psychiatric nosology.

Long-term treatment effects in chronic myeloid leukemia.

We propose and analyze a simplified version of a partial differential equation (PDE) model for chronic myeloid leukemia (CML) derived from an agent-based model proposed by Roeder et al. This model describes the proliferation and differentiation of leukemic stem cells in the bone marrow and the effect of the drug Imatinib on these cells. We first simplify the PDE model by noting that most of the dynamics occurs in a subspace of the original 2D state space. Then we determine the dominant eigenvalue of the corresponding linearized system that controls the long-term behavior of solutions. We mathematically show a non-monotonous dependence of the dominant eigenvalue with respect to treatment dose, with the existence of a unique minimal negative eigenvalue. In terms of CML treatment, this shows that there is a unique dose that maximizes the decay rate of the CML tumor load over long time scales. Moreover this unique dose is lower than the dose that maximizes the initial tumor load decay. Numerical simulations of the full model confirm that this phenomenon is not an artifact of the simplification. Therefore, while optimal asymptotic dosage might not be the best one at short time scales, our results raise interesting perspectives in terms of strategies for achieving and improving long-term deep response.

BCR-ABL transcript variations in chronic phase chronic myelogenous leukemia patients on imatinib first-line: Possible role of the autologous immune system.

Many chronic myelogenous leukemia (CML) patients in chronic phase who respond well to imatinib therapy show fluctuations in their leukemic loads in the long-term. We developed a mathematical model of CML that incorporates the intervention of an autologous immune response. Our results suggest that the patient's immune system plays a crucial role in imatinib therapy in maintaining disease control over time. The observed BCR-ABL/ABL oscillations in such patients provide a signature of the autologous immune response.

Implication of the Autologous Immune System in BCR-ABL Transcript Variations in Chronic Myelogenous Leukemia Patients Treated with Imatinib.

Imatinib and other tyrosine kinase inhibitors (TKI) have improved treatment of chronic myelogenous leukemia (CML); however, most patients are not cured. Deeper mechanistic understanding may improve TKI combination therapies to better control the residual leukemic cell population. In analyzing our patients' data, we found that many patients who otherwise responded well to imatinib therapy still showed variations in their BCR-ABL transcripts. To investigate this phenomenon, we applied a mathematical model that integrates CML and an autologous immune response to the patients' data. We define an immune window or a range of leukemic loads for which the autologous immune system induces an improved response. Our modeling results suggest that, at diagnosis, a patient's leukemic load is able to partially or fully suppress the autologous immune response developed in a majority of patients, toward the CML clone(s). Imatinib therapy drives the leukemic population into the "immune window," allowing the patient's autologous immune cells to expand and eventually mount an efficient recognition of the residual leukemic burden. This response drives the leukemic load below this immune window, allowing the leukemic population to partially recover until another weaker immune response is initiated. Thus, the autologous immune response may explain the oscillations in BCR-ABL transcripts regularly observed in patients on imatinib.

Discrete limit and monotonicity properties of the Floquet eigenvalue in an age structured cell division cycle model.

We consider a cell population described by an age-structured partial differential equation with time periodic coefficients. We assume that division only occurs within certain time intervals at a rate [Formula: see text] for cells who have reached minimal positive age (maturation). We study the asymptotic behavior of the dominant Floquet eigenvalue, or Perron-Frobenius eigenvalue, representing the growth rate, as a function of the maturation age, when the division rate [Formula: see text] tends to infinity (divisions become instantaneous). We show that the dominant Floquet eigenvalue converges to a staircase function with an infinite number of steps, determined by a discrete dynamical system. This indicates that, in the limit, the growth rate is governed by synchronization phenomena between the maturation age and the length of the time intervals in which division may occur. As an intermediate result, we give a sufficient condition which guarantees that the dominant Floquet eigenvalue is a nondecreasing function of the division rate. We also give a counter example showing that the latter monotonicity property does not hold in general.

Freud with Charcot: Freud's discovery and the question of diagnosis.

Although Charcot's seminal role in influencing Freud is widely stated, although Freud's trip to Paris to study with Charcot is well recognized as pivotal in his shift from neurological to psychopathological work, a key fact of the Freudian heuristic remains largely underestimated: namely, that Freud's psychopathological breakthrough, which gave birth to psychoanalysis, cannot be separated from his 'diagnostic preoccupation', which is a crucial and at times the first organizing principle of his earliest writings. The purpose of this article is therefore to reopen the question of diagnosis by following its development along the path leading from Charcot to Freud. The authors demonstrate that Freud's careful attention to diagnostic distinctions follows strictly in the direction of Charcot's 'nosological method'. More importantly, the article intends to identify the precise way in which his ideas operate in Freud's own work, in order to understand how Freud reinvests them to forge his own nosological system. If the authors trace the destiny of Charcot's lessons as they reach Freud's hands, it is the importance granted to mixed neuroses in Freud's psychopathology that allows them to pinpoint the role played by the diagnostic process in the rationality of psychoanalysis.

Applying ecological and evolutionary theory to cancer: a long and winding road.

Since the mid 1970s, cancer has been described as a process of Darwinian evolution, with somatic cellular selection and evolution being the fundamental processes leading to malignancy and its many manifestations (neoangiogenesis, evasion of the immune system, metastasis, and resistance to therapies). Historically, little attention has been placed on applications of evolutionary biology to understanding and controlling neoplastic progression and to prevent therapeutic failures. This is now beginning to change, and there is a growing international interest in the interface between cancer and evolutionary biology. The objective of this introduction is first to describe the basic ideas and concepts linking evolutionary biology to cancer. We then present four major fronts where the evolutionary perspective is most developed, namely laboratory and clinical models, mathematical models, databases, and techniques and assays. Finally, we discuss several of the most promising challenges and future prospects in this interdisciplinary research direction in the war against cancer.