Mass concentration in a nonlocal model of clonal selection

Self-renewal is a constitutive property of stem cells. Testing the cancer stem cell hypothesis requires investigation of the impact of self-renewal on cancer expansion. To understand better this impact, we propose a mathematical model describing dynamics of a continuum of cell clones structured by the self-renewal potential. The model is an extension of the finite multi-compartment models of interactions between normal and cancer cells in acute leukemias. It takes a form of a system of integro-differential equations with a nonlinear and nonlocal coupling, which describes regulatory feedback loops in cell proliferation and differentiation process. We show that such coupling leads to mass concentration in points corresponding to maximum of the self-renewal potential and the model solutions tend asymptotically to a linear combination of Dirac measures. Furthermore, using a Lyapunov function constructed for a finite dimensional counterpart of the model, we prove that the total mass of the solution converges to a globally stable equilibrium. Additionally, we show stability of the model in space of positive Radon measures equipped with flat metric. The analytical results are illustrated by numerical simulations

Classification results of coronary heart disease database by using the clonal selection method with receptor editing

The clonal selection principle is used to explain the basic features of an adaptive immune response to a antigenic stimulus. It established the idea that only those cells that recognize the antigens are selected to proliferate and differentiate. This paper explains a computational implementation of the clonal selection principle that explicitly takes into account the affinity maturation of the immune response. The clonal selection algorithm by incorporating receptor editing method, RECSA, has been proposed by Gao. This paper tries to classify the medical database of Coronary Heart Disease databases and reports the computational results for 4 kinds of training datasets

A structured population model of clonal selection in acute leukemias with multiple maturation stages

Funding: TS and AM-C were supported by research funding from the German Research Foundation DFG (SFB 873; subproject B08). TL gratefully acknowledges support from the Heidelberg Graduate School (HGS).Recent progress in genetic techniques has shed light on the complex co-evolution of malignant cell clones in leukemias. However, several aspects of clonal selection still remain unclear. In this paper, we present a multi-compartmental continuously structured population model of selection dynamics in acute leukemias, which consists of a system of coupled integro-differential equations. Our model can be analysed in a more efficient way than classical models formulated in terms of ordinary differential equations. Exploiting the analytical tractability of this model, we investigate how clonal selection is shaped by the self-renewal fraction and the proliferation rate of leukemic cells at different maturation stages. We integrate analytical results with numerical solutions of a calibrated version of the model based on real patient data. In summary, our mathematical results formalise the biological notion that clonal selection is driven by the self-renewal fraction of leukemic stem cells and the clones that possess the highest value of this parameter are ultimately selected. Moreover, we demonstrate that the self-renewal fraction and the proliferation rate of non-stem cells do not have a substantial impact on clonal selection. Taken together, our results indicate that interclonal variability in the self-renewal fraction of leukemic stem cells provides the necessary substrate for clonal selection to act upon.PostprintPeer reviewe

Optimal Control of Class of Non-Linear Plants using Artificial Immune Systems: Application of the Clonal Selection Algorithm

The function of natural immune system is to protect the living organisms against invaders/pathogens. Artificial Immune System (AIS) is a computational intelligence paradigm inspired by the natural immune system. Diverse engineering problems have been solved in the recent past using AIS. Clonal selection is one of the few algorithms that belong to the family of AIS techniques. Clonal selection algorithm is the computational implementation of the clonal selection principle. The process of affinity maturation of the immune system is explicitly incorporated in this algorithm. This paper presents the application of AIS for the optimal control of a class of non-linear plants which are affine in control. The clonal selection algorithm is adapted for optimal control. A new mutation operator that operates on real values and one that aids in fast convergence is developed in this paper. AIS is used to obtain constant coefficient Kalman gain matrices. The validation and evaluation of the results thus obtained are carried out by comparing with standard and the widely used State Dependent Algebraic Riccati Equation (SDARE) method for the non-linear plants. In case of non-linear systems with hard state constraints, the SDARE formulation requires the use of mathematically involved expressions to incorporate these state constraints. However, the modified clonal selection algorithm developed in this paper has been used with hardly any changes to incorporate the hard state constraints and obtain the Kalman gain matrix