Mathematical model for IL-2-based cancer immunotherapy.

A basic mathematical model for IL-2-based cancer immunotherapy is proposed and studied. Our analysis shows that the outcome of therapy is mainly determined by three parameters, the relative death rate of CD4+ T cells, the relative death rate of CD8+ T cells, and the dose of IL-2 treatment. Minimal equilibrium tumor size can be reached with a large dose of IL-2 in the case that CD4+ T cells die out. However, in cases where CD4+ and CD8+ T cells persist, the final tumor size is independent of the IL-2 dose and is given by the relative death rate of CD4+ T cells. Two groups of in silico clinical trials show some short-term behaviors of IL-2 treatment. IL-2 administration can slow the proliferation of CD4+ T cells, while high doses for a short period of time over several days transiently increase the population of CD8+ T cells during treatment before it recedes to its equilibrium. IL-2 administration for a short period of time over many days suppresses the tumor population for a longer time before approaching its steady-state levels. This implies that intermittent administration of IL-2 may be a good strategy for controlling tumor size.

A stochastic framework for evaluating CAR T cell therapy efficacy and variability.

Based on a deterministic and stochastic process hybrid model, we use white noises to account for patient variabilities in treatment outcomes, use a hyperparameter to represent patient heterogeneity in a cohort, and construct a stochastic model in terms of Ito stochastic differential equations for testing the efficacy of three different treatment protocols in CAR T cell therapy. The stochastic model has three ergodic invariant measures which correspond to three unstable equilibrium solutions of the deterministic system, while the ergodic invariant measures are attractors under some conditions for tumor growth. As the stable dynamics of the stochastic system reflects long-term outcomes of the therapy, the transient dynamics provide chances of cure in short-term. Two stopping times, the time to cure and time to progress, allow us to conduct numerical simulations with three different protocols of CAR T cell treatment through the transient dynamics of the stochastic model. The probability distributions of the time to cure and time to progress present outcome details of different protocols, which are significant for current clinical study of CAR T cell therapy.

Stabilization of Luminescent Mononuclear Three-Coordinate CuI Complexes by Two Distinct Cavity-Shaped Diphosphanes Obtained from a Single α-Cyclodextrin Precursor.

Slightly different reaction conditions afforded two distinct cavity-shaped cis-chelating diphosphanes from the same starting materials, namely diphenyl(2-phosphanylphenyl)phosphane and an α-cyclodextrin-derived dimesylate. Thanks to their metal-confining properties, the two diphosphanes form only mononuclear [CuX(PP)] complexes (X=Cl, Br, or I) with the tricoordinated metal ion located just above the center of the cavity. The two series of CuI complexes display markedly different luminescence properties that are both influenced by the electronic properties of the ligand and the unique steric environment provided by the cyclodextrin (CD) cavity. The excited state lifetimes of all complexes are significantly longer than those of the cavity-free analogues suggesting peculiar electronic effects that affect radiative deactivation constants. The overall picture stemming from absorption and emission data suggests close-lying charge-transfer (MLCT, XLCT) and triplet ligand-centered (LC) excited states.

Stochastic dynamics of human papillomavirus delineates cervical cancer progression.

Starting from a deterministic model, we propose and study a stochastic model for human papillomavirus infection and cervical cancer progression. Our analysis shows that the chronic infection state as random variables which have the ergodic invariant probability measure is necessary for progression from infected cell population to cervical cancer cells. It is shown that small progression rate from infected cells to precancerous cells and small microenvironmental noises associated with the progression rate and viral infection help to establish such chronic infection states. It implicates that large environmental noises associated with viral infection and the progression rate in vivo can reduce chronic infection. We further show that there will be a cervical cancer if the noise associated with precancerous cell growth is large enough. In addition, comparable numerical studies for the deterministic model and stochastic model, together with Hopf bifurcations in both deterministic and stochastic systems, highlight our analytical results.

High Levels of Extracellular Potassium Can Delay Myxoma Virus Replication by Preventing Release of Virions from the Endosomes.

Potassium (K+) is one of the most abundant cations in the human body. Under normal conditions, the vast majority of K+ is found within cells, and the extracellular [K+] is tightly regulated to within 3.0 to 5.0 mM. However, it has recently been shown that high levels of localized necrosis can increase the extracellular concentration of K+ to above 50 mM. This raises the possibility that elevated extracellular K+ might influence a variety of biological processes that occur within regions of necrotic tissue. For example, K+ has been shown to play a central role in the replication cycles of numerous viral families, and in cases of lytic infection, localized regions containing large numbers of necrotic cells can be formed. Here, we show that the replication of the model poxvirus myxoma virus (MYXV) is delayed by elevated levels of extracellular K+. These increased K+ concentrations alter the cellular endocytic pathway, leading to increased phagocytosis but a loss of endosomal/lysosomal segregation. This slows the release of myxoma virus particles from the endosomes, resulting in delays in genome synthesis and infectious particle formation as well as reduced viral spread. Additionally, mathematical modeling predicts that the extracellular K+ concentrations required to impact myxoma virus replication can be reached in viral lesions under a variety of conditions. Taken together, these data suggest that the extracellular [K+] plays a role in determining the outcomes of myxoma infection and that this effect could be physiologically relevant during pathogenic infection. IMPORTANCE Intracellular K+ homeostasis has been shown to play a major role in the replication of numerous viral families. However, the potential impact of altered extracellular K+ concentrations is less well understood. Our work demonstrates that increased concentrations of extracellular K+ can delay the replication cycle of the model poxvirus MYXV by inhibiting virion release from the endosomes. Additionally, mathematical modeling predicts that the levels of extracellular K+ required to impact MYXV replication can likely be reached during pathogenic infection. These results suggest that localized viral infection can alter K+ homeostasis and that these alterations might directly affect viral pathogenesis.

Stable Luminescent [Cu(NN)(PP)]+ Complexes Incorporating a ß-Cyclodextrin-Based Diphosphane Ligand with Metal-Confining Properties.

A ß-cyclodextrin-based diphosphane with metal-confining properties was efficiently synthesized thanks to an unprecedented Smiles-like rearrangement of diphenyl-(2-phosphanylphenyl)phosphane in the presence of excess n-BuLi. The cis-chelating bidentate ligand is capable of forming very stable heteroleptic [Cu(NN)(PP)]+ complexes in which a metal-bound diimine ligand (bpy, phen, or mmp) is located within the cyclodextrin cavity. As a result of ligand encapsulation, flattening of the metal tetrahedral geometry in the excited state is disfavored, thereby resulting in enhanced luminescent properties.

Photoactive Copper Complexes: Properties and Applications.

Photocatalyzed and photosensitized chemical processes have seen growing interest recently and have become among the most active areas of chemical research, notably due to their applications in fields such as medicine, chemical synthesis, material science or environmental chemistry. Among all homogeneous catalytic systems reported to date, photoactive copper(I) complexes have been shown to be especially attractive, not only as alternative to noble metal complexes, and have been extensively studied and utilized recently. They are at the core of this review article which is divided into two main sections. The first one focuses on an exhaustive and comprehensive overview of the structural, photophysical and electrochemical properties of mononuclear copper(I) complexes, typical examples highlighting the most critical structural parameters and their impact on the properties being presented to enlighten future design of photoactive copper(I) complexes. The second section is devoted to their main areas of application (photoredox catalysis of organic reactions and polymerization, hydrogen production, photoreduction of carbon dioxide and dye-sensitized solar cells), illustrating their progression from early systems to the current state-of-the-art and showcasing how some limitations of photoactive copper(I) complexes can be overcome with their high versatility.

Hopf bifurcation without parameters in deterministic and stochastic modeling of cancer virotherapy, part II.

In part II, we analyze our stochastic model which incorporates microenvironmental noises and uncertainties related to immune responses. Outcomes of the therapy in our model are largely determined by the infectivity constant, the infection value, and stochastic relative immune clearance rates. The infection value is a universal critical value for immune-free ergodic invariant probability measures and persistence in all cases. Asymptotic behaviors of the stochastic model are similar to those of its deterministic counterpart. Our stochastic model displays an interesting dynamical behavior, stochastic Hopf bifurcation without parameters, which is a new phenomenon. We perform numerical study to demonstrate how stochastic Hopf bifurcation without parameters occurs. In addition, we give biological implications about our analytical results in stochastic setting versus deterministic setting.

Deterministic and stochastic modeling for PDGF-driven gliomas reveals a classification of gliomas.

Motivated by our study of infiltrating dynamics of immune cells into tumors, we propose a stochastic model in terms of Ito stochastic differential equations to study how two parameters, the chemoattractant production rate and the chemotactic coefficient, influence immune cell migration and how these parameters distinguish two types of gliomas. We conduct a detailed analysis of the stochastic model and its deterministic counterpart. The deterministic model can differentiate two types of gliomas according to the range of the chemoattractant production rate as two equilibrium solutions, while the stochastic model also can differentiate two types of gliomas according to the ranges of the chemoattractant production rate and chemotactic coefficient with thresholds as one non-zero ergodic invariant measure and one weak persistent state when the noise intensities are small. When the noise intensities are large comparing with the chemotactic coefficient, there is only one type of glioma that corresponds to a non-zero ergodic invariant measure. Using our experimental data, numerical simulations are carried out to demonstrate properties of our models, and we give medical interpretations and implications for our analytical results and numerical simulations. This study also confirms some of our results about IDH gliomas.

DYNAMICS OF CHOLERA EPIDEMIC MODELS IN FLUCTUATING ENVIRONMENTS.

Based on our deterministic models for cholera epidemics, we propose a stochastic model for cholera epidemics to incorporate environmental fluctuations which is a nonlinear system of Itô stochastic differential equations. We conduct an asymptotical analysis of dynamical behaviors for the model. The basic stochastic reproduction value R s is defined in terms of the basic reproduction number R 0 for the corresponding deterministic model and noise intensities. The basic stochastic reproduction value determines the dynamical patterns of the stochastic model. When R s < 1 , the cholera infection will extinct within finite periods of time almost surely. When R s > 1 , the cholera infection will persist most of time, and there exists a unique stationary ergodic distribution to which all solutions of the stochastic model will approach almost surely as noise intensities are bounded. When the basic reproduction number R 0 for the corresponding deterministic model is greater than 1, and the noise intensities are large enough such that R s < 1 , the cholera infection is suppressed by environmental noises. We carry out numerical simulations to illustrate our analysis, and to compare with the corresponding deterministic model. Biological implications are pointed out.

Basic stochastic model for tumor virotherapy.

The complexity of oncolytic virotherapy arises from many factors. In this study, we incorporate environmental noise and stochastic effects to our basic deterministic model and propose a stochastic model for viral therapy in terms of Ito stochastic differential equations. We conduct a detailed analysis of the model using boundary methods. We find two combined parameters, one describes possibilities of eradicating tumors and one is an increasing function of the viral burst size, which serve as thresholds to classify asymptotical dynamics of the model solution paths. We show there are three ergodic invariant probability measures which correspond to equilibrium states of the deterministic model, and extra possibility to eradicate tumor due to strong variance of tumor growth rate and medium viral burst size. Numerical analysis demonstrates several typical solution paths with biological explanations. In addition, we provide some medical interpretations and implications.

Mathematical modeling of PDGF-driven glioma reveals the dynamics of immune cells infiltrating into tumors.

BACKGROUND: Tumor-infiltrated immune cells compose a significant component of many cancers. They have been observed to have contradictory impacts on tumors. Although the primary reasons for these observations remain elusive, it is important to understand how immune cells infiltrating into tumors is regulated. Recently our group conducted a series of experimental studies, which showed that muIDH1 gliomas have a significant global reduction of immune cells and suggested that the longer survival time of mice with CIMP gliomas may be due to the IDH mutation and its effect on reducing of the tumor-infiltrated immune cells. However, to comprehend how IDH1 mutants regulate infiltration of immune cells into gliomas and how they affect the aggressiveness of gliomas, it is necessary to integrate our experimental data into a dynamical system to acquire a much deeper understanding of subtle regulation of immune cell infiltration. METHODS: The method is integration of mathematical modeling and experiments. According to mass conservation laws and assumption that immune cells migrate into the tumor site along a chemotactic gradient field, a mathematical model is formulated. Parameters are estimated from our experiments. Numerical methods are developed to solve the problem. Numerical predictions are compared with experimental results. RESULTS: Our analysis shows that the net rate of increase of immune cells infiltrated into the tumor is approximately proportional to the 4/5 power of the chemoattractant production rate, and it is an increasing function of time while the percentage of immune cells infiltrated into the tumor is a decreasing function of time. Our model predicts that wtIDH1 mice will survive longer if the immune cells are blocked by reducing chemotactic coefficient. For more aggressive gliomas, our model shows that there is little difference in their survivals between wtIDH1 and muIDH1 tumors, and the percentage of immune cells infiltrated into the tumor is much lower. These predictions are verified by our experimental results. In addition, wtIDH1 and muIDH1 can be quantitatively distinguished by their chemoattractant production rates, and the chemotactic coefficient determines possibilities of immune cells migration along chemoattractant gradient fields. CONCLUSIONS: The chemoattractant gradient field produced by tumor cells may facilitate immune cells migration to the tumor cite. The chemoattractant production rate may be utilized to classify wtIDH1 and muIDH1 tumors. The dynamics of immune cells infiltrating into tumors is largely determined by tumor cell chemoattractant production rate and chemotactic coefficient.

Stochastic growth pattern of untreated human glioblastomas predicts the survival time for patients.

Glioblastomas are highly malignant brain tumors. Knowledge of growth rates and growth patterns is useful for understanding tumor biology and planning treatment logistics. Based on untreated human glioblastoma data collected in Trondheim, Norway, we first fit the average growth to a Gompertz curve, then find a best fitted white noise term for the growth rate variance. Combining these two fits, we obtain a new type of Gompertz diffusion dynamics, which is a stochastic differential equation (SDE). Newly collected untreated human glioblastoma data in Seattle, US, re-verify our model. Instead of growth curves predicted by deterministic models, our SDE model predicts a band with a center curve as the tumor size average and its width as the tumor size variance over time. Given the glioblastoma size in a patient, our model can predict the patient survival time with a prescribed probability. The survival time is approximately a normal random variable with simple formulas for its mean and variance in terms of tumor sizes. Our model can be applied to studies of tumor treatments. As a demonstration, we numerically investigate different protocols of surgical resection using our model and provide possible theoretical strategies.

Photomodulation of DNA-Templated Supramolecular Assemblies.

A new type of DNA ligand that contains a phosphate-binding group and a photoresponsive azobenzene moiety is reported. When the azobenzene is in trans configuration, the ligand binds to the minor groove of a double-stranded DNA, whereas it partially desorbs upon trans-cis isomerisation with light. The ability to photoswitch the ligand upon interaction with DNA is evidenced by (chir)optical signatures, and deciphered by the differences of binding geometry, stability, and dynamics of the DNA/ligand complexes for the two isomers. We exploit these properties to photomodulate DNA-templated self-assembly, through the incorporation of another π-stacking DNA ligand, which together with the photoresponsive ligand form mixed supramolecular complexes along DNA. Our study demonstrates that well-designed photoresponsive DNA binders can be used to modulate multicomponent supramolecular DNA assemblies.

The Role of the Innate Immune System in Oncolytic Virotherapy.

The complexity of the immune responses is a major challenge in current virotherapy. This study incorporates the innate immune response into our basic model for virotherapy and investigates how the innate immunity affects the outcome of virotherapy. The viral therapeutic dynamics is largely determined by the viral burst size, relative innate immune killing rate, and relative innate immunity decay rate. The innate immunity may complicate virotherapy in the way of creating more equilibria when the viral burst size is not too big, while the dynamics is similar to the system without innate immunity when the viral burst size is big.

Transcriptional and metabolic response in yeast Saccharomyces cerevisiae cells during polyethylene glycol-dependent transformation.

Intact cells of the yeast Saccharomyces cerevisiae were transformed with exogenous DNA by incubating the cells with plasmid in the presence of polyethylene glycol (PEG), which has been shown to be required, although the underlying has not been elucidated. In this study, we found that incubation of the S. cerevisiae cells with PEG was not only required for the PEG-dependent transformation but also enhanced transformation, suggesting that PEG might cause an intracellular response. To understand the response, microarray and metabolome analyses were conducted. We found that incubation of the cells without PEG caused up-regulation of several genes, including those which are involved in carbon source metabolisms, e.g. fatty acid metabolism, yielding acetyl-CoA and those involved in stress-response. Contrary to this, incubation of the cells with PEG gave no transcriptional change. These microarray data were supported by the results of metabolome analysis for anionic metabolites, implying that the physical effect of PEG on cell membrane, rather than the effect of PEG itself on the intracellular response, could cause high transformation in the PEG-dependent transformation.