An active poroelastic model for mechanochemical patterns in protoplasmic droplets of Physarum polycephalum

Motivated by recent experimental studies, we derive and analyze a twodimensional model for the contraction patterns observed in protoplasmic droplets of Physarum polycephalum. The model couples a model of an active poroelastic two-phase medium with equations describing the spatiotemporal dynamics of the intracellular free calcium concentration. The poroelastic medium is assumed to consist of an active viscoelastic solid representing the cytoskeleton and a viscous fluid describing the cytosol. The model equations for the poroelastic medium are obtained from continuum force-balance equations that include the relevant mechanical fields and an incompressibility relation for the two-phase medium. The reaction-diffusion equations for the calcium dynamics in the protoplasm of Physarum are extended by advective transport due to the flow of the cytosol generated by mechanical stresses. Moreover, we assume that the active tension in the solid cytoskeleton is regulated by the calcium concentration in the fluid phase at the same location, which introduces a chemomechanical feedback. A linear stability analysis of the homogeneous state without deformation and cytosolic flows exhibits an oscillatory Turing instability for a large enough mechanochemical coupling strength. Numerical simulations of the model equations reproduce a large variety of wave patterns, including traveling and standing waves, turbulent patterns, rotating spirals and antiphase oscillations in line with experimental observations of contraction patterns in the protoplasmic droplets.Comment: Additional supplemental material is supplie

Intracellular mechanochemical waves in an active poroelastic model

Many processes in living cells are controlled by biochemical substances regulating active stresses. The cytoplasm is an active material with both viscoelastic and liquid properties. We incorporate the active stress into a two-phase model of the cytoplasm which accounts for the spatiotemporal dynamics of the cytoskeleton and the cytosol. The cytoskeleton is described as a solid matrix that together with the cytosol as an interstitial fluid constitutes a poroelastic material. We find different forms of mechanochemical waves including traveling, standing, and rotating waves by employing linear stability analysis and numerical simulations in one and two spatial dimensions.Peer ReviewedPostprint (published version

Modeling and simulation of non-isothermal rate-dependent damage processes in inhomogeneous materials using the phase-field approach

We present a continuum model that incorporates rate-dependent damage and fracture, a material order parameter field and temperature. Different material characteristics throughout the medium yield a strong inhomogeneity and affect the way fracture propagates. The phasefield approach is employed to describe degradation. For the material order parameter we assume a Cahn Larché-type dynamics, which makes the model in particular applicable to binary alloys. We give thermodynamically consistent evolution equations resulting from a unified variational approach. Diverse coupling mechanisms can be covered within the model, such as heat dissipation during fracture, thermal-expansion-induced failure and elastic-inhomogeneity effects. We furthermore present an adaptive Finite Element code in two space dimensions that is capable of solving such a highly nonlinear and non-convex system of partial differential equations. With the help of this tool we conduct numerical experiments of different complexity in order to investigate the possibilities and limitations of the presented model. A main feature of our model is that we can describe the process of micro-crack nucleation in regions of partial damage to form macro-cracks in a unifying approach

Modeling and simulation of non-isothermal rate-dependent damage processes in inhomogeneous materials using the phase-field approach

We present a continuum model that incorporates rate-dependent damage and fracture, a material order parameter field and temperature. Different material characteristics throughout the medium yield a strong inhomogeneity and affect the way fracture propagates. The phasefield approach is employed to describe degradation. For the material order parameter we assume a Cahn Larch'e-type dynamics, which makes the model in particular applicable to binary alloys. We give thermodynamically consistent evolution equations resulting from a unified variational approach. Diverse coupling mechanisms can be covered within the model, such as heat dissipation during fracture, thermal-expansion-in- duced failure and elastic-inhomogeneity effects. We furthermore present an adaptive Finite Element code in two space dimensions, that is capable of solving such a highly nonlinear and non-convex system of partial differential equations. With the help of this tool we conduct numerical experiments of different complexity in order to investigate the possibilities and limitations of the presented model. A main feature of our model is that we can describe the process of micro-crack nucleation in regions of partial damage to form macro-cracks in a unifying approach

Cardiac contraction induces discordant alternans and localized block

In this paper we use a simplified model of cardiac excitation-contraction coupling to study the effect of tissue deformation on the dynamics of alternans, i.e. alternations in the duration of the cardiac action potential, that occur at fast pacing rates and are known to be pro-arrhythmic. We show that small stretch-activated currents can produce large effects and cause a transition from in-phase to off-phase alternations (i.e. from concordant to discordant alternans) and to conduction blocks. We demonstrate numerically and analytically that this effect is the result of a generic change in the slope of the conduction velocity restitution curve due to electromechanical coupling. Thus, excitation-contraction coupling can potentially play a relevant role in the transition to reentry and fibrillation

Cardiac contraction induces discordant alternans and localized block

In this paper we use a simplified model of cardiac excitation-contraction coupling to study the effect of tissue deformation on the dynamics of alternans, i.e. alternations in the duration of the cardiac action potential, that occur at fast pacing rates and are known to be pro-arrhythmic. We show that small stretch-activated currents can produce large effects and cause a transition from in-phase to off-phase alternations (i.e. from concordant to discordant alternans) and to conduction blocks. We demonstrate numerically and analytically that this effect is the result of a generic change in the slope of the conduction velocity restitution curve due to electromechanical coupling. Thus, excitation-contraction coupling can potentially play a relevant role in the transition to reentry and fibrillation

Mechanochemical pattern formation in simple models of active viscoelastic fluids and solids

The cytoskeleton of the organism Physarum polycephalum is a prominent example of a complex active viscoelastic material wherein stresses induce flows along the organism as a result of the action of molecular motors and their regulation by calcium ions. Experiments in Physarum polycephalum have revealed a rich variety of mechanochemical patterns including standing, traveling and rotating waves that arise from instabilities of spatially homogeneous states without gradients in stresses and resulting flows. Herein, we investigate simple models where an active stress induced by molecular motors is coupled to a model describing the passive viscoelastic properties of the cellular material. Specifically, two models for viscoelastic fluids (Maxwell and Jeffrey model) and two models for viscoelastic solids (Kelvin–Voigt and Standard model) are investigated. Our focus is on the analysis of the conditions that cause destabilization of spatially homogeneous states and the related onset of mechano-chemical waves and patterns. We carry out linear stability analyses and numerical simulations in one spatial dimension for different models. In general, sufficiently strong activity leads to waves and patterns. The primary instability is stationary for all active fluids considered, whereas all active solids have an oscillatory primary instability. All instabilities found are of long-wavelength nature reflecting the conservation of the total calcium concentration in the models studied.Peer ReviewedPreprin

Uncovering NOTCH1 as a Promising Target in the Treatment of MLL-Rearranged Leukemia

MLL rearrangement (MLLr) is responsible for the development of acute leukemias with poor outcomes. Therefore, new therapeutic approaches are urgently needed. The NOTCH1 pathway plays a critical role in the pathogenesis of many cancers including acute leukemia. Using a CRISPR/Cas9 MLL-AF4/-AF9 translocation model, the newly developed NOTCH1 inhibitor CAD204520 with less toxic side effects allowed us to unravel the impact of NOTCH1 as a pathogenic driver and potential therapeutic target in MLLr leukemia. RNA sequencing (RNA-seq) and RT-qPCR of our MLLr model and MLLr cell lines showed the NOTCH1 pathway was overexpressed and activated. Strikingly, we confirmed this elevated expression level in leukemia patients. We also demonstrated that CAD204520 treatment of MLLr cells significantly reduces NOTCH1 and its target genes as well as NOTCH1 receptor expression. This was not observed with a comparable cytarabine treatment, indicating the specificity of the small molecule. Accordingly, treatment with CAD204520 resulted in dose-dependent reduced proliferation and viability, increased apoptosis, and the induction of cell cycle arrest via the downregulation of MLL and NOTCH1 target genes. In conclusion, our findings uncover the oncogenic relevance of the NOTCH1 pathway in MLLr leukemia. Its inhibition leads to specific anti-leukemic effects and paves the way for further evaluation in clinical settings

Treatment response of advanced HNSCC towards immune checkpoint inhibition is associated with an activated effector memory T cell phenotype

Locally advanced or metastatic head and neck squamous cell carcinoma (HNSCC) is associated with a poor prognosis. The introduction of PD-1 inhibitors has led to a significant improvement in survival, but only a subpopulation of patients responds to therapy. Current biomarkers cannot reliably identify these patients. The identification of biomarkers for the prediction and monitoring of immunotherapy is therefore of great importance. In this study, we characterized lymphocyte subsets in the peripheral blood of HNSCC patients under PD-1 inhibition. Patients with primary response (n=11) to PD-1 inhibition showed an increase of the CD3+ effector memory (CD3/EM) population and an elevated expression of the activation marker CD69 in CD3+ T cells, particularly in the CD3/EM subpopulation at 3 months when treatment response was assessed. In contrast, patients with primary treatment failure and progressive disease (n=9) despite PD-1 inhibition had lower absolute lymphocyte counts and an increased expression of CTLA-4 in CD3+ T cells at the time of treatment failure compared with baseline, particularly in CD4+ and CD8+ effector memory populations. Our results demonstrate that HNSCC patients’ response to immune checkpoint inhibition shows a distinct immune signature in peripheral blood, which could help identify refractory patients earlier. Furthermore, strategies to overcome primary therapy failure by inducing a beneficial T cell phenotype or adding alternative immune checkpoint inhibitors could improve response rates and survival of HNSCC patients

A review of mathematical models for the formation of vascular networks

Two major mechanisms are involved in the formation of blood vasculature: vasculogenesis and angiogenesis. The former term describes the formation of a capillary-like network from either a dispersed or a monolayered population of endothelial cells, reproducible also in vitro by specific experimental assays. The latter term describes the sprouting of new vessels from an existing capillary or post-capillary venule. Similar mechanisms are also involved in the formation of the lymphatic system through a process generally called lymphangiogenesis. A number of mathematical approaches have been used to analyse these phenomena. In this article, we review the different types of models, with special emphasis on their ability to reproduce different biological systems and to predict measurable quantities which describe the overall processes. Finally, we highlight the advantages specific to each of the different modelling approaches. The research that led to the present paper was partially supported by a grant of the group GNFM of INdA