A mathematical model of combined CD8 T cell costimulation by 4-1BB (CD137) and OX40 (CD134) receptors.

Combined agonist stimulation of the TNFR costimulatory receptors 4-1BB (CD137) and OX40(CD134) has been shown to generate supereffector CD8 T cells that clonally expand to greater levels, survive longer, and produce a greater quantity of cytokines compared to T cells stimulated with an agonist of either costimulatory receptor individually. In order to understand the mechanisms for this effect, we have created a mathematical model for the activation of the CD8 T cell intracellular signaling network by mono- or dual-costimulation. We show that supereffector status is generated via downstream interacting pathways that are activated upon engagement of both receptors, and in silico simulations of the model are supported by published experimental results. The model can thus be used to identify critical molecular targets of T cell dual-costimulation in the context of cancer immunotherapy

Systems biology of ferroptosis: A modeling approach.

Ferroptosis is a recently discovered form of iron-dependent regulated cell death (RCD) that occurs via peroxidation of phospholipids containing polyunsaturated fatty acid (PUFA) moieties. Activating this form of cell death is an emerging strategy in cancer treatment. Because multiple pathways and molecular species contribute to the ferroptotic process, predicting which tumors will be sensitive to ferroptosis is a challenge. We thus develop a mathematical model of several critical pathways to ferroptosis in order to perform a systems-level analysis of the process. We show that sensitivity to ferroptosis depends on the activity of multiple upstream cascades, including PUFA incorporation into the phospholipid membrane, and the balance between levels of pro-oxidant factors (reactive oxygen species, lipoxogynases) and antioxidant factors (GPX4). We perform a systems-level analysis of ferroptosis sensitivity as an outcome of five input variables (ACSL4, SCD1, ferroportin, transferrin receptor, and p53) and organize the resulting simulations into \u27high\u27 and \u27low\u27 ferroptosis sensitivity groups. We make a novel prediction corresponding to the combinatorial requirements of ferroptosis sensitivity to SCD1 and ACSL4 activity. To validate our prediction, we model the ferroptotic response of an ovarian cancer stem cell line following single- and double-knockdown of SCD1 and ACSL4. We find that the experimental outcomes are consistent with our simulated predictions. This work suggests that a systems-level approach is beneficial for understanding the complex combined effects of ferroptotic input, and in predicting cancer susceptibility to ferroptosis

The role of Allee effect in modelling post resection recurrence of glioblastoma

Resection of the bulk of a tumour often cannot eliminate all cancer cells, due to their infiltration into the surrounding healthy tissue. This may lead to recurrence of the tumour at a later time. We use a reaction-diffusion equation based model of tumour growth to investigate how the invasion front is delayed by resection, and how this depends on the density and behaviour of the remaining cancer cells. We show that the delay time is highly sensitive to qualitative details of the proliferation dynamics of the cancer cell population. The typically assumed logistic type proliferation leads to unrealistic results, predicting immediate recurrence. We find that in glioblastoma cell cultures the cell proliferation rate is an increasing function of the density at small cell densities. Our analysis suggests that cooperative behaviour of cancer cells, analogous to the Allee effect in ecology, can play a critical role in determining the time until tumour recurrence

Determining the control networks regulating stem cell lineages in colonic crypts

The question of stem cell control is at the center of our understanding of tissue functioning, both in healthy and cancerous conditions. It is well accepted that cellular fate decisions (such as divisions, differentiation, apoptosis) are orchestrated by a network of regulatory signals emitted by different cell populations in the lineage and the surrounding tissue. The exact regulatory network that governs stem cell lineages in a given tissue is usually unknown. Here we propose an algorithm to identify a set of candidate control networks that are compatible with (a) measured means and variances of cell populations in different compartments, (b) qualitative information on cell population dynamics, such as the existence of local controls and oscillatory reaction of the system to population size perturbations, and (c) statistics of correlations between cell numbers in different compartments. Using the example of human colon crypts, where lineages are comprised of stem cells, transit amplifying cells, and differentiated cells, we start with a theoretically known set of 32 smallest control networks compatible with tissue stability. Utilizing near-equilibrium stochastic calculus of stem cells developed earlier, we apply a series of tests, where we compare the networks' expected behavior with the observations. This allows us to exclude most of the networks, until only three, very similar, candidate networks remain, which are most compatible with the measurements. This work demonstrates how theoretical analysis of control networks combined with only static biological data can shed light onto the inner workings of stem cell lineages, in the absence of direct experimental assessment of regulatory signaling mechanisms. The resulting candidate networks are dominated by negative control loops and possess the following properties: (1) stem cell division decisions are negatively controlled by the stem cell population, (2) stem cell differentiation decisions are negatively controlled by the transit amplifying cell population

Mathematical modeling of tumor-microenvironment dynamics

In this thesis we explore tumor-microenvironment dynamics using three models of decreasing complexity. The first is a multispecies, spatiotemporal model of tumor development in tumor-derived growth factor responsive stroma that is activated to secrete the tumor growth and dispersal activator HGF. We show that HGF-induced invasive tumor morphology is promoted by increased heterogeneity at the tumor-host boundary. The second model is a system of ODEs that explores hypotheses based on experimental observations that tumor growth inhibition can occur at high levels of HGF. The model allows for the prediction of the molecular mechanism of HGF action via dose-response curve analysis. The final model is a system of two ODEs for stem cell and chemical activator of stem cell self-renewal concentrations, and allows for the approximation of the separatrix of the phase space that divides the space into basins of attraction for tumor eradication and tumor maintenance. The multiple models allow us to consider tumor-host interactions at various levels of abstraction and thus to infer both qualitative and quantitative results regarding tumor response to host and tumor-derived growth activators

Mathematical modeling of tumor-microenvironment dynamics

In this thesis we explore tumor-microenvironment dynamics using three models of decreasing complexity. The first is a multispecies, spatiotemporal model of tumor development in tumor-derived growth factor responsive stroma that is activated to secrete the tumor growth and dispersal activator HGF. We show that HGF-induced invasive tumor morphology is promoted by increased heterogeneity at the tumor-host boundary. The second model is a system of ODEs that explores hypotheses based on experimental observations that tumor growth inhibition can occur at high levels of HGF. The model allows for the prediction of the molecular mechanism of HGF action via dose-response curve analysis. The final model is a system of two ODEs for stem cell and chemical activator of stem cell self-renewal concentrations, and allows for the approximation of the separatrix of the phase space that divides the space into basins of attraction for tumor eradication and tumor maintenance. The multiple models allow us to consider tumor-host interactions at various levels of abstraction and thus to infer both qualitative and quantitative results regarding tumor response to host and tumor-derived growth activators

Systems biology of ferroptosis: a modeling approach (source code)

Source code to reproduce figures in A. Konstorum, L. Tesfay and B.T. Paul et al., Systems biology of ferroptosis: a modeling approach, Journal of Theoretical Biology, https://doi.org/10.1016/j.jtbi.2020.110222 Software necessary for the code: Matlab Contact: Anna Konstorum ([email protected]) Instructions to reproduce select figures (code below can be modified to reproduce the remaining simulation figures): Figure 2: Panel (a) >>Ferroptosis_model(40,2,0,0); Panel (b) + Erastin: >>Ferroptosis_model(40,2,2,0); + RSL3: >>Ferroptosis_model(40,2,0,2); Figure 3: Panel (a) >>Ferroptosis_model(40,0,0,0); Panel (b) >>Ferroptosis_model(40,0,0,2); Figure 6: Require: Ferroptosis_model_index.m to run Ferop_index_full.m >>[Ferrop_Index_Base,Ferrop_Index_Erastin] = Ferrop_index_full(40); Test varying initial conditions (see Supplementary Information, S1) If base_var=erastin_var=0, then 1000 different runs of the simulations with varying initial conditions result in the same steady state Require: Ferroptosis_model_IC.m to run Ferrop_IC.m >>[base_var,erastin_var] = Ferrop_IC(1000