A New Algorithm for Global Minimization Based on the Combination of Adaptive Random Search and Simplex Algorithm of Nelder and Mead

We propose a new general-purpose algorithm for locating global minima of differentiable and nondifferentiable multivariable functions. The algorithm is based on combination of the adaptive random search approach and the Nelder-Mead simplex minimization. We show that the new hybrid algorithm satisfies the conditions of the theorem for convergence (in probability) to global minimum. By using test functions we demonstrate that the proposed algorithm is far more efficient than the pure adaptive random search algorithm, Some of the considered test functions are related to membership set estimation method for model parameter determination which was successfully applied to kinetic problems in chemistry and biology

Plasma membrane Ca2+-ATPases can shape the pattern of Ca2+ transients induced by store-operated Ca2+ entry

Calcium (Ca2+) is a critical cofactor and signaling mediator in cells, and the concentration of cytosolic Ca2+ is regulated by multiple proteins, including the plasma membrane Ca2+-ATPases (adenosine triphosphatases) (PMCAs), which use ATP to transport Ca2+ out of cells. PMCA isoforms exhibit different kinetic and regulatory properties; thus, the presence and relative abundance of individual isoforms may help shape Ca2+ transients and cellular responses. We studied the effects of three PMCA isoforms (PMCA4a, PMCA4b, and PMCA2b) on Ca2+ transients elicited by conditions that trigger store-operated Ca2+ entry (SOCE) and that blocked Ca2+ uptake into the endoplasmic reticulum in HeLa cells, human embryonic kidney (HEK) 293 cells, or primary endothelial cell isolated from human umbilical cord veins (HUVECs). The slowly activating PMCA4b isoform produced long-lasting Ca2+ oscillations in response to SOCE. The fast-activating isoforms PMCA2b and PMCA4a produced different effects. PMCA2b resulted in rapid and highly PMCA abundance-sensitive clearance of SOCE-mediated Ca2+ transients, whereas PMCA4a reduced cytosolic Ca2+, resulting in the establishment of a higher than baseline cytosolic Ca2+ concentration. Mathematical modeling showed that slow activation was critical to the sustained oscillation induced by the "slow" PMCA4b pump. The modeling and experimental results indicated that the distinct properties of PMCA isoforms differentially regulate the pattern of SOCE-mediated Ca2+ transients, which would thus affect the activation of downstream signaling pathways

Mathematical model of heterogeneous cancer growth with an autocrine signalling pathway

[[abstract]]Objectives Cancer is a complex biological occurrence which is difficult to describe clearly and explain its growth development. As such, novel concepts, such as of heterogeneity and signalling pathways, grow exponentially and many mathematical models accommodating the latest knowledge have been proposed. Here, we present a simple mathematical model that exhibits many characteristics of experimental data, using prostate carcinoma cell spheroids under treatment. Materials and methods We have modelled cancer as a two-subpopulation system, with one subpopulation representing a cancer stem cell state, and the other a normal cancer cell state. As a first approximation, these follow a logistical growth model with self and competing capacities, but they can transform into each other by using an autocrine signalling pathway. Results and conclusion By analysing regulation behaviour of each of the system parameters, we show that the model exhibits many characteristics of actual cancer growth curves. Features reproduced in this model include delayed phase of evolving cancer under 17AAG treatment, and bi-stable behaviour under treatment by irradiation. In addition, our interpretation of the system parameters corresponds well with known facts involving 17AAG treatment. This model may thus provide insight into some of the mechanisms behind cancer.[[incitationindex]]SCI[[booktype]]電子版[[booktype]]紙

Empirical maximum lifespan of earthworms is twice that of mice

We considered a Gompertzian model for the population dynamics of Eisenia andrei case-cohorts in artificial OECD soil under strictly controlled conditions. The earthworm culture was kept between 18 and 22°C at a constant pH of 5.0. In all, 77 lumbricids were carefully followed for almost 9 years, until the oldest died. The Eisenia median longevity is 4.25 years and the oldest specimen was 8.73 years. Eisenia cocoons were hand-sorted every 3 weeks, washed in distilled water, placed in Petri dishes, and counted. Regular removal did not reduce breeding. Each fertile cocoon contained on average two or three embryos. The failure rates (mortality and infertility percentages) are smooth power functions where the rate at time (n + 1) captured most of the phenomenology of the previous rate at time n, as expected by the considered law, but not at both the beginning and the end of this long-term laboratory study

Interplay between distribution of live cells and growth dynamics of solid tumours

Experiments show that simple diffusion of nutrients and waste molecules is not sufficient to explain the typical multilayered structure of solid tumours, where an outer rim of proliferating cells surrounds a layer of quiescent but viable cells and a central necrotic region. These experiments challenge models of tumour growth based exclusively on diffusion. Here we propose a model of tumour growth that incorporates the volume dynamics and the distribution of cells within the viable cell rim. The model is suggested by in silico experiments and is validated using in vitro data. The results correlate with in vivo data as well, and the model can be used to support experimental and clinical oncology

Reaction Kinetics in Intracellular Environments: The Two Proposed Models Yield Qualitatively Different Predictions

A recently proposed model by Schnell and Turner for reaction kinetics in environments crowded by macromolecules is applied to elementary bimolecular binding. It is found that it leads to an unusual equilibrium constant equal to zero. The progress curves are qualitatively different from the prediction of a model based on a non-integer (fractal) power law proposed earlier by Savageau. In the case of the Michaelis-Menten reaction, the two models predict qualitatively similar progress curves and identical equilibrium concentrations. The two models are investigated analytically and numerically, and their differences are discussed in regard to possible validation of the models by use of experimental data

Effective carrying capacity and analytical solution of a particular case of the Richards-like two-species population dynamics model

We consider a generalized two-species population dynamic model and analytically solve it for the amensalism and commensalism ecological interactions. These two-species models can be simplified to a one-species model with a time dependent extrinsic growth factor. With a one-species model with an effective carrying capacity one is able to retrieve the steady state solutions of the previous one-species model. The equivalence obtained between the effective carrying capacity and the extrinsic growth factor is complete only for a particular case, the Gompertz model. Here we unveil important aspects of sigmoid growth curves, which are relevant to growth processes and population dynamics.Comment: To appear in Physica A (6 pages, 5 figures

Predicting Outcomes of Prostate Cancer Immunotherapy by Personalized Mathematical Models

Therapeutic vaccination against disseminated prostate cancer (PCa) is partially effective in some PCa patients. We hypothesized that the efficacy of treatment will be enhanced by individualized vaccination regimens tailored by simple mathematical models.We developed a general mathematical model encompassing the basic interactions of a vaccine, immune system and PCa cells, and validated it by the results of a clinical trial testing an allogeneic PCa whole-cell vaccine. For model validation in the absence of any other pertinent marker, we used the clinically measured changes in prostate-specific antigen (PSA) levels as a correlate of tumor burden. Up to 26 PSA levels measured per patient were divided into each patient's training set and his validation set. The training set, used for model personalization, contained the patient's initial sequence of PSA levels; the validation set contained his subsequent PSA data points. Personalized models were simulated to predict changes in tumor burden and PSA levels and predictions were compared to the validation set. The model accurately predicted PSA levels over the entire measured period in 12 of the 15 vaccination-responsive patients (the coefficient of determination between the predicted and observed PSA values was R(2) = 0.972). The model could not account for the inconsistent changes in PSA levels in 3 of the 15 responsive patients at the end of treatment. Each validated personalized model was simulated under many hypothetical immunotherapy protocols to suggest alternative vaccination regimens. Personalized regimens predicted to enhance the effects of therapy differed among the patients.Using a few initial measurements, we constructed robust patient-specific models of PCa immunotherapy, which were retrospectively validated by clinical trial results. Our results emphasize the potential value and feasibility of individualized model-suggested immunotherapy protocols

Computational Modeling of PI3K/AKT and MAPK Signaling Pathways in Melanoma Cancer

Background Malignant melanoma is an aggressive tumor of the skin and seems to be resistant to current therapeutic approaches. Melanocytic transformation is thought to occur by sequential accumulation of genetic and molecular alterations able to activate the Ras/Raf/MEK/ERK (MAPK) and/or the PI3K/AKT (AKT) signalling pathways. Specifically, mutations of B-RAF activate MAPK pathway resulting in cell cycle progression and apoptosis prevention. According to these findings, MAPK and AKT pathways may represent promising therapeutic targets for an otherwise devastating disease. Result Here we show a computational model able to simulate the main biochemical and metabolic interactions in the PI3K/AKT and MAPK pathways potentially involved in melanoma development. Overall, this computational approach may accelerate the drug discovery process and encourages the identification of novel pathway activators with consequent development of novel antioncogenic compounds to overcome tumor cell resistance to conventional therapeutic agents. The source code of the various versions of the model are available as S1 Archive