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

Effect of macromolecular crowding on the rate of diffusion-limited enzymatic reaction

The cytoplasm of a living cell is crowded with several macromolecules of different shapes and sizes. Molecular diffusion in such a medium becomes anomalous due to the presence of macromolecules and diffusivity is expected to decrease with increase in macromolecular crowding. Moreover, many cellular processes are dependent on molecular diffusion in the cell cytosol. The enzymatic reaction rate has been shown to be affected by the presence of such macromolecules. A simple numerical model is proposed here based on percolation and diffusion in disordered systems to study the effect of macromolecular crowding on the enzymatic reaction rates. The model explains qualitatively some of the experimental observations.Comment: 6 pages, 4 figure

Identification of Key Processes that Control Tumor Necrosis Factor Availability in a Tuberculosis Granuloma

Tuberculosis (TB) granulomas are organized collections of immune cells comprised of macrophages, lymphocytes and other cells that form in the lung as a result of immune response to Mycobacterium tuberculosis (Mtb) infection. Formation and maintenance of granulomas are essential for control of Mtb infection and are regulated in part by a pro-inflammatory cytokine, tumor necrosis factor-α (TNF). To characterize mechanisms that control TNF availability within a TB granuloma, we developed a multi-scale two compartment partial differential equation model that describes a granuloma as a collection of immune cells forming concentric layers and includes TNF/TNF receptor binding and trafficking processes. We used the results of sensitivity analysis as a tool to identify experiments to measure critical model parameters in an artificial experimental model of a TB granuloma induced in the lungs of mice following injection of mycobacterial antigen-coated beads. Using our model, we then demonstrated that the organization of immune cells within a TB granuloma as well as TNF/TNF receptor binding and intracellular trafficking are two important factors that control TNF availability and may spatially coordinate TNF-induced immunological functions within a granuloma. Further, we showed that the neutralization power of TNF-neutralizing drugs depends on their TNF binding characteristics, including TNF binding kinetics, ability to bind to membrane-bound TNF and TNF binding stoichiometry. To further elucidate the role of TNF in the process of granuloma development, our modeling and experimental findings on TNF-associated molecular scale aspects of the granuloma can be incorporated into larger scale models describing the immune response to TB infection. Ultimately, these modeling and experimental results can help identify new strategies for TB disease control/therapy

A model for multiexponential tryptophan fluorescence intensity decay in proteins.

Tryptophan fluorescence intensity decay in proteins is modeled by multiexponential functions characterized by lifetimes and preexponential factors. Commonly, multiple conformations of the protein are invoked to explain the recovery of two or more lifetimes from the experimental data. However, in many proteins the structure seems to preclude the possibility of multiple conformers sufficiently different from one another to justify such an inference. We present here another plausible multiexponential model based on the assumption that an energetically excited donor surrounded by N acceptor molecules decays by specific radiative and radiationless relaxation processes, and by transferring its energy to acceptors present in or close to the protein matrix. If interactions between the acceptors themselves and back energy transfer are neglected, we show that the intensity decay function contain 2N exponential components characterized by the unperturbed donor lifetime, by energy transfer rates and a probability of occurrence for the corresponding process. We applied this model to the fluorescence decay of holo- and apoazurin, ribonuclease T1, and the reduced single tryptophan mutant (W28F) of thioredoxin. Use of a multiexponential model for the analysis of the fluorescence intensity decay can therefore be justified, without invoking multiple protein conformations

Analytical approach to the recovery of short fluorescence lifetimes from fluorescence decay curves.

Considerable effort in instrument development has made possible detection of picosecond fluorescence lifetimes by time-correlated single-photon counting. In particular, efforts have been made to narrow markedly the instrument response function (IRF). Less attention has been paid to analytical methods, especially to problem of discretization of the convolution integral, on which the detection and quantification of short lifetimes critically depends. We show that better discretization methods can yield acceptable results for short lifetimes even with an IRF several times wider than necessary for the standard discretization based on linear approximation (LA). A general approach to discretization, also suitable for nonexponential models, is developed. The zero-time shift is explicitly included. Using simulations, we compared LA, quadratic, and cubic approximations. The latter two proved much better for detection of short lifetimes and, in that respect, they do not differ except when the zero-time shift exceeds two channels, when one can benefit from using the cubic approximation. We showed that for LA in some cases narrowing the IRF beyond FWHM = 150 ps is actually counterproductive. This is not so for quadratic and cubic approximations, which we recommend for general use

Complex homogeneous and heterogeneous fluorescence anisotropy decays: enhancing analysis accuracy.

In biological macromolecules, fluorophores often exhibit multiple depolarizing motions that require multiple lifetimes and rotational relaxation times to define fluorescence intensity and anisotropy decays. The related analysis of time-correlated single-photon counting data becomes uncertain due to the multitude of decay parameters and numerical sensitivity to deconvolution of the instrument response function (IRF) via discretization of integrals. By using simulations we show that improved discretizations based on quadratic and cubic local approximations of the IRF yield more accurate estimation of short rotational relaxation times and lifetimes than the commonly used Grinvald-Steinberg discretization, which in turn appears more reliable than two discretizations based on linear local approximations of the IRF. In addition, our simulation suggests that cubic approximation is the most advantageous in discriminating complex heterogeneous and homogeneous anisotropy decay. We show that among three different information criteria, the Akaike information criterion is best suited for detection of heterogeneity in rotational relaxation times. It is capable of detecting heterogeneity even when anisotropy decay appears homogeneous within statistical errors of estimation