In vitro and in silico multidimensional modeling of oncolytic tumor virotherapy dynamics.

Tumor therapy with replication competent viruses is an exciting approach to cancer eradication where viruses are engineered to specifically infect, replicate, spread and kill tumor cells. The outcome of tumor virotherapy is complex due to the variable interactions between the cancer cell and virus populations as well as the immune response. Oncolytic viruses are highly efficient in killing tumor cells in vitro, especially in a 2D monolayer of tumor cells, their efficiency is significantly lower in a 3D environment, both in vitro and in vivo. This indicates that the spatial dimension may have a major influence on the dynamics of virus spread. We study the dynamic behavior of a spatially explicit computational model of tumor and virus interactions using a combination of in vitro 2D and 3D experimental studies to inform the models. We determine the number of nearest neighbor tumor cells in 2D (median = 6) and 3D tumor spheroids (median = 16) and how this influences virus spread and the outcome of therapy. The parameter range leading to tumor eradication is small and even harder to achieve in 3D. The lower efficiency in 3D exists despite the presence of many more adjacent cells in the 3D environment that results in a shorter time to reach equilibrium. The mean field mathematical models generally used to describe tumor virotherapy appear to provide an overoptimistic view of the outcomes of therapy. Three dimensional space provides a significant barrier to efficient and complete virus spread within tumors and needs to be explicitly taken into account for virus optimization to achieve the desired outcome of therapy.

Tumour and immune cell dynamics explain the PSA bounce after prostate cancer brachytherapy.

BACKGROUND: Interstitial brachytherapy for localised prostate cancer may be followed by transient increases in prostate-specific antigen (PSA) that resolve without therapy. Such PSA bounces may be associated with an improved outcome but often cause alarm in the patient and physician, and have defied explanation. METHODS: We developed a mathematical model to capture the interactions between the tumour, radiation and anti-tumour immune response. The model was fitted to data from a large cohort of patients treated exclusively with interstitial brachytherapy. Immunohistological analysis for T-cell infiltration within the same tumours was also performed. RESULTS: Our minimal model captures well the dynamics of the tumour after therapy, and suggests that a strong anti-tumour immune response coupled with the therapeutic effect of radiation on the tumour is responsible for the PSA bounce. Patients who experience a PSA bounce had a higher density of CD3 and CD8 cells within the tumour that likely contribute to the PSA bounce and the overall better outcomes observed. CONCLUSIONS: Our observations provide a novel and unifying explanation for the PSA bounce in patients with early prostate cancer and also have implications for the use of immune-based therapies in such patients to improve outcomes.

Controlled Delivery of Vancomycin via Charged Hydrogels.

Surgical site infection (SSI) remains a significant risk for any clean orthopedic surgical procedure. Complications resulting from an SSI often require a second surgery and lengthen patient recovery time. The efficacy of antimicrobial agents delivered to combat SSI is diminished by systemic toxicity, bacterial resistance, and patient compliance to dosing schedules. We submit that development of localized, controlled release formulations for antimicrobial compounds would improve the effectiveness of prophylactic surgical wound antibiotic treatment while decreasing systemic side effects. Our research group developed and characterized oligo(poly(ethylene glycol)fumarate)/sodium methacrylate (OPF/SMA) charged copolymers as biocompatible hydrogel matrices. Here, we report the engineering of this copolymer for use as an antibiotic delivery vehicle in surgical applications. We demonstrate that these hydrogels can be efficiently loaded with vancomycin (over 500 µg drug per mg hydrogel) and this loading mechanism is both time- and charge-dependent. Vancomycin release kinetics are shown to be dependent on copolymer negative charge. In the first 6 hours, we achieved as low as 33.7% release. In the first 24 hours, under 80% of total loaded drug was released. Further, vancomycin release from this system can be extended past four days. Finally, we show that the antimicrobial activity of released vancomycin is equivalent to stock vancomycin in inhibiting the growth of colonies of a clinically derived strain of methicillin-resistant Staphylococcus aureus. In summary, our work demonstrates that OPF/SMA hydrogels are appropriate candidates to deliver local antibiotic therapy for prophylaxis of surgical site infection.

A gamma variate model that includes stretched exponential is a better fit for gastric emptying data from mice.

Noninvasive breath tests for gastric emptying are important techniques for understanding the changes in gastric motility that occur in disease or in response to drugs. Mice are often used as an animal model; however, the gamma variate model currently used for data analysis does not always fit the data appropriately. The aim of this study was to determine appropriate mathematical models to better fit mouse gastric emptying data including when two peaks are present in the gastric emptying curve. We fitted 175 gastric emptying data sets with two standard models (gamma variate and power exponential), with a gamma variate model that includes stretched exponential and with a proposed two-component model. The appropriateness of the fit was assessed by the Akaike Information Criterion. We found that extension of the gamma variate model to include a stretched exponential improves the fit, which allows for a better estimation of T1/2 and Tlag. When two distinct peaks in gastric emptying are present, a two-component model is required for the most appropriate fit. We conclude that use of a stretched exponential gamma variate model and when appropriate a two-component model will result in a better estimate of physiologically relevant parameters when analyzing mouse gastric emptying data.

Plasma membrane Ca²âº-ATPases can shape the pattern of Ca²âº transients induced by store-operated Ca²âº entry.

Calcium (Ca(2+)) is a critical cofactor and signaling mediator in cells, and the concentration of cytosolic Ca(2+) is regulated by multiple proteins, including the plasma membrane Ca(2+)-ATPases (adenosine triphosphatases) (PMCAs), which use ATP to transport Ca(2+) out of cells. PMCA isoforms exhibit different kinetic and regulatory properties; thus, the presence and relative abundance of individual isoforms may help shape Ca(2+) transients and cellular responses. We studied the effects of three PMCA isoforms (PMCA4a, PMCA4b, and PMCA2b) on Ca(2+) transients elicited by conditions that trigger store-operated Ca(2+) entry (SOCE) and that blocked Ca(2+) 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 Ca(2+) 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 Ca(2+) transients, whereas PMCA4a reduced cytosolic Ca(2+), resulting in the establishment of a higher than baseline cytosolic Ca(2+) 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 Ca(2+) transients, which would thus affect the activation of downstream signaling pathways.

Regulatory T cell kinetics in the peripheral blood of patients with Crohn's disease.

Estimates of T regulatory cell populations in the periphery of patients with Crohn's disease are confounded by disease activity and concomitant immunotherapeutic agents known to affect T cell proliferation and survival. We performed deuterium pulse/chase experiments in patients with quiescent Crohn's disease on no immunotherapy and healthy control subjects to estimate T regulatory cell kinetics. Quantification of deuterated DNA isolated from T cell subsets over 10 days was determined by mass spectrophotometry. We demonstrate enhanced proliferation within the T regulatory cell population from patients with Crohn's disease when compared to non-T regulatory cells and T regulatory cells from healthy control subjects. We speculate that T regulatory cells isolated from the periphery of patients with Crohn's disease experience persistent antigen stimulation resulting in excess proliferative rates.

Controlled release of doxorubicin from pH-responsive microgels.

Stimuli-responsive hydrogels have enormous potential in drug delivery applications. They can be used for site-specific drug delivery due to environmental variables in the body such as pH and temperature. In this study, we have developed pH-responsive microgels for the delivery of doxorubicin (DOX) in order to optimize its anti-tumor activity while minimizing its systemic toxicity. We used a copolymer of oligo(polyethylene glycol) fumarate (OPF) and sodium methacrylate (SMA) to fabricate the pH-responsive microgels. We demonstrated that the microgels were negatively charged, and the amounts of charge on the microgels were correlated with the SMA concentration in their formulation. The resulting microgels exhibited sensitivity to the pH and ionic strength of the surrounding environment. We demonstrated that DOX was efficiently loaded into the microgels and released in a controlled fashion via an ion-exchange mechanism. Our data revealed that the DOX release was influenced by the pH and ionic strength of the solution. Moreover, we designed a phenomenological mathematical model, based on a stretched exponential function, to quantitatively analyze the cumulative release of DOX. We found a linear correlation between the maximum release of DOX calculated from the model and the SMA concentration in the microgel formulation. The anti-tumor activity of the released DOX was assessed using a human chordoma cell line. Our data revealed that OPF-SMA microgels prolonged the cell killing effect of DOX.

About and beyond the Henri-Michaelis-Menten rate equation for single-substrate enzyme kinetics.

For more than a century the simple single-substrate enzyme kinetics model and related Henri-Michaelis-Menten (HMM) rate equation have been thoroughly explored in various directions. In the present paper we are concerned with a possible generalization of this rate equation recently proposed by F. Kargi (BBRC 382 (2009) 157-159), which is assumed to be valid both in the case that the total substrate or enzyme is in excess and the quasi-steady-state is achieved. We demonstrate that this generalization is grossly inadequate and propose another generalization based on application of the quasi-steady-state condition and conservation equations for both enzyme and substrate. The standard HMM equation is derived by (a) assuming the quasi-steady-state condition, (b) applying the conservation equation only for the enzyme, and (c) assuming that the substrate concentration at quasi-steady-state can be approximated by the total substrate concentration [S](0). In our formula the rate is already expressed through [S](0), and we only assume that when quasi-steady-state is achieved the amount of product formed is negligible compared to [S](0). Numerical simulations show that our formula is generally more accurate than the HMM formula and also can provide a good approximation when the enzyme is in excess, which is not the case for the HMM formula. We show that the HMM formula can be derived from our expression by further assuming that the total enzyme concentration is negligible compared to [S](0).

Functional consequences and structural interpretation of mutations of human choline acetyltransferase.

Choline acetyltransferase (ChAT; EC 2.3.1.6) catalyzes synthesis of acetylcholine from acetyl-CoA (AcCoA) and choline in cholinergic neurons. Mutations in CHAT cause potentially lethal congenital myasthenic syndromes associated with episodic apnea (ChAT-CMS). Here, we analyze the functional consequences of 12 missense and one nonsense mutations of CHAT in 11 patients. Nine of the mutations are novel. We examine expression of the recombinant missense mutants in Bosc 23 cells, determine their kinetic properties and thermal stability, and interpret the functional effects of 11 mutations in the context of the atomic structural model of human ChAT. Five mutations (p.Trp421Ser, p.Ser498Pro, p.Thr553Asn, p.Ala557Thr, and p.Ser572Trp) reduce enzyme expression to less than 50% of wild-type. Mutations with severe kinetic effects are located in the active-site tunnel (p.Met202Arg, p.Thr553Asn, and p.Ala557Thr) or adjacent to the substrate binding site (p.Ser572Trp), or exert their effect allosterically (p.Trp421Ser and p.Ile689Ser). Two mutations with milder kinetic effects (p.Val136Met and p.Ala235Thr) are also predicted to act allosterically. One mutation (p.Thr608Asn) below the nucleotide binding site of CoA enhances dissociation of AcCoA from the enzyme-substrate complex. Two mutations introducing a proline residue into an α-helix (p.Ser498Pro and p.Ser704Pro) impair the thermal stability of ChAT.

Validation of fractal-like kinetic models by time-resolved binding kinetics of dansylamide and carbonic anhydrase in crowded media.

Kinetic studies of biochemical reactions are typically carried out in a dilute solution that rarely contains anything more than reactants, products, and buffers. In such studies, mass-action-based kinetic models are used to analyze the progress curves. However, intracellular compartments are crowded by macromolecules. Therefore, we investigated the adequacy of the proposed generalizations of the mass-action model, which are meant to describe reactions in crowded media. To validate these models, we measured time-resolved kinetics for dansylamide binding to carbonic anhydrase in solutions crowded with polyethylene glycol and Ficoll. The measured progress curves clearly show the effects of crowding. The fractal-like model proposed by Savageau was used to fit these curves. In this model, the association rate coefficient k(a) allometrically depends on concentrations of reactants. We also considered the fractal kinetic model proposed by Schnell and Turner, in which k(a) depends on time according to a Zipf-Mandelbrot distribution, and some generalizations of these models. We found that the generalization of the mass-action model, in which association and dissociation rate coefficients are concentration-dependent, represents the preferred model. Other models based on time-dependent rate coefficients were inadequate or not preferred by model selection criteria.

Development of 41Ca-based pharmacokinetic model for the study of bone remodelling in humans.

BACKGROUND AND OBJECTIVE: Initial studies show that 41Ca may be employed as a useful diagnostic bioassay for monitoring metabolic bone disease and its treatment management. The 41Ca-based pharmacokinetic model is developed to assess its feasibility in monitoring bone disease and clinical responsiveness to therapeutic regimens. METHODS: A four-compartment calcium kinetic model is developed to interpret the results of clinically measured 41Ca tracer kinetics for oral and intravenous dose. This model is extended to simulate changes in bone turnover due to osteoporosis by using Gompertzian function with and without cellular accommodation. The rate constants obtained by fitting to the experimental data on drug intervention are used to simulate the impact of strategic treatment intervention. RESULTS: The present model fits well with the available experimental data on 41Ca tracer kinetics. In the simulated osteoporotic model, the negative bone balance (i.e. bone loss) reflected by 41Ca/Ca urine ratio is used to demonstrate slow/fast increase over time compared to the normal state. The cellular accommodation impact is reflected by a recovery from perturbed balance. The model's predictive ability on the impact of therapeutic intervention is verified using published experimental data. The effect of bisphosphonate intervention results in positive bone balance (i.e. bone gain). CONCLUSION: The four-compartment 41Ca tracer kinetic model can be flexibly used in the interpretation of results obtained from ongoing clinical studies.

Quantitative methods for measuring DNA flexibility in vitro and in vivo.

The double-helical DNA biopolymer is particularly resistant to bending and twisting deformations. This property has important implications for DNA folding in vitro and for the packaging and function of DNA in living cells. Among the outstanding questions in the field of DNA biophysics are the underlying origin of DNA stiffness and the mechanisms by which DNA stiffness is overcome within cells. Exploring these questions requires experimental methods to quantitatively measure DNA bending and twisting stiffness both in vitro and in vivo. Here, we discuss two classical approaches: T4 DNA ligase-mediated DNA cyclization kinetics and lac repressor-mediated DNA looping in Escherichia coli. We review the theoretical basis for these techniques and how each can be applied to quantitate biophysical parameters that describe the DNA polymer. We then show how we have modified these methods and applied them to quantitate how apparent DNA physical properties are altered in vitro and in vivo by sequence-nonspecific architectural DNA-binding proteins such as the E. coli HU protein and eukaryotic HMGB proteins.

Evolutionary dynamics of two related malignant plasma cell lines.

Cancer is the consequence of sequential acquisition of mutations within somatic cells. Mutations alter the relative reproductive fitness of cells, enabling the population to evolve in time as a consequence of selection. Cancer therapy itself can select for or against specific subclones. Given the large population of tumor cells, subclones inevitably emerge and their fate will depend on the evolutionary dynamics that define the interactions between such clones. Using a combination of in vitro studies and mathematical modeling, we describe the dynamic behavior of two cell lines isolated from the same patient at different time points of disease progression and show how the two clones relate to one another. We provide evidence that the two clones coexisted at the time of initial presentation. The dominant clone presented with biopsy proven cardiac AL amyloidosis. Initial therapy selected for the second clone that expanded leading to a change in the diagnosis to multiple myeloma. The evolutionary dynamics relating the two cell lines are discussed and a hypothesis is generated in regard to the mechanism of one of the phenotypic characteristics that is shared by these two cell lines.

Optimization of virotherapy for cancer.

Several viruses preferentially infect and replicate in cancer cells by usurping pathways that are defective in the tumor cell population. Such viruses have a potential as oncolytic agents. The aim of tumor virotherapy is that after injection of the replicating virus, it propagates in the tumor cell population with amplification. As a result, the oncolytic virus spreads to eradicate the tumor. The outcome of tumor virotherapy is determined by population dynamics and different from standard cancer therapy. Several models have been developed that provided considerable insights on the potential therapeutic scenarios. However, virotherapy is potentially risky since large amounts of a replicating virus are injected in the host with a risk of adverse effects. Therefore, the optimal dose, number of doses, and timing are expected to play an important role on the outcome both for the tumor and the host. In the current work, we combine a model of the dynamics of tumor virotherapy that was validated with experimental data with optimization theory to illustrate how we can improve the outcome of tumor therapy. In this first report, we demonstrate that (i) in most circumstances, anything more than two administrations of a vector is not helpful, (ii) correctly timed delivery of the virus provides superior results compared to regularly scheduled therapy or continuous infusion, (iii) a second dose of virus that is not properly timed leads to a worse outcome compared to a single dose of virus, and (iv) it is less costly to treat larger tumors.

Distinct role of PLCbeta3 in VEGF-mediated directional migration and vascular sprouting.

Endothelial cell proliferation and migration is essential to angiogenesis. Typically, proliferation and chemotaxis of endothelial cells is driven by growth factors such as vascular endothelial growth factor (VEGF) and basic fibroblast growth factor (bFGF). VEGF activates phospholipases (PLCs) - specifically PLCgamma1 - that are important for tubulogenesis, differentiation and DNA synthesis. However, we show here that VEGF, specifically through VEGFR2, induces phosphorylation of two serine residues on PLCbeta3, and this was confirmed in an ex vivo embryoid body model. Knockdown of PLCbeta3 in HUVEC cells affects IP3 production, actin reorganization, migration and proliferation; whereas migration is inhibited, proliferation is enhanced. Our data suggest that enhanced proliferation is precipitated by an accelerated cell cycle, and decreased migration by an inability to activate CDC42. Given that PLCbeta3 is typically known as an effector of heterotrimeric G-proteins, our data demonstrate a unique crosstalk between the G-protein and receptor tyrosine kinase (RTK) axes and reveal a novel molecular mechanism of VEGF signaling and, thus, angiogenesis.

Alveolar recruitment and arterial desflurane concentration during bariatric surgery.

BACKGROUND: We investigated whether reversal of intraoperative atelectasis with the lung recruitment maneuver (RM) affects desflurane arterial concentrations during bariatric surgery. METHODS: After anesthetic induction and maintenance with propofol, patients were randomized to receive alveolar RM at intervals (RM group) or not (controls). Desflurane 6% was initiated, and rate of increase of alveolar desflurane concentration (ratio of end-expiratory to inspiratory concentrations, F(A)/F(I)) and desflurane blood concentrations were measured in both groups. Blood and end-tidal desflurane concentrations were also measured after the discontinuation of anesthesia. RESULTS: The RM group had higher intraoperative Pao(2)/Fio(2) compared with the control group (both, P < 0.001). During induction, the rate of increase in blood desflurane concentrations was rapid in both groups. At comparable mechanical ventilation settings, median times to achieve 0.5 mM (approximately 3%) were 2.1 and 1.59 min (P = 0.09) in the control and RM group, respectively. The times to achieve 0.7 mM (approximately 4.2%) desflurane were 15.9 and 9.3 min in the control and RM group, respectively (P = 0.08). Desflurane blood concentrations tended to be higher during the first 30 min after induction in the RM group (P = 0.066). During maintenance or emergence, the blood desflurane concentrations were not different between control and RM groups. Consequently, the time to eye opening did not differ between groups. CONCLUSION: Although the RM during bariatric surgery represents an effective method for improving intraoperative oxygenation, it does not significantly affect the desflurane blood concentrations during anesthesia or its elimination during emergence.

Kinetic analysis of interaction of BRCA1 tandem breast cancer c-terminal domains with phosphorylated peptides reveals two binding conformations.

Tandem breast cancer C-terminal (BRCT) domains, present in many DNA repair and cell cycle checkpoint signaling proteins, are phosphoprotein binding modules. The best-characterized tandem BRCT domains to date are from the protein BRCA1 (BRCA1-BRCT), an E3 ubiquitin ligase that has been linked to breast and ovarian cancer. While X-ray crystallography and NMR spectroscopy studies have uncovered the structural determinants of specificity of BRCA1-BRCT for phosphorylated peptides, a detailed kinetic and thermodynamic characterization of the interaction is also required to understand how structure and dynamics are connected and therefore better probe the mechanism of phosphopeptide recognition by BRCT domains. Through a global analysis of binding kinetics data obtained from surface plasmon resonance (SPR) and stopped-flow fluorescence spectroscopy, we show that the recognition mechanism is complex and best modeled by two equilibrium conformations of BRCA1-BRCT in the free state that both interact with a phosphopeptide, with dissociation constants ( K d) in the micromolar range. We show that the apparent global dissociation constant derived from this kinetic analysis is similar to the K d values measured using steady-state SPR, isothermal titration calorimetry, and fluorescence anisotropy. The dynamic nature of BRCA1-BRCT may facilitate the binding of BRCA1 to different phosphorylated protein targets.

Mathematical analysis of models for reaction kinetics in intracellular environments.

Two models that have been proposed in the literature for description of kinetics in intracellular environments characterized by macromolecular crowding and inhomogeneities, are mathematically analyzed and discussed. The models are first derived by using phenomenological arguments that lead to generalizations of the law of mass action. The prediction of these models in the case of bimolecular binding reaction is then analyzed. It is mathematically proved that the models may predict qualitatively different behavior of progress curves. In particular, they also predict asymptotic steady state concentrations that cannot be reconciled. In this paper we propose and discuss generalizations of these models which under specified conditions lead to qualitatively similar behavior of reaction progress curves. We believe that these generalized models are better suited for data analysis.

Modeling of cancer virotherapy with recombinant measles viruses.

The Edmonston vaccine strain of measles virus has potent and selective activity against a wide range of tumors. Tumor cells infected by this virus or genetically modified strains express viral proteins that allow them to fuse with neighboring cells to form syncytia that ultimately die. Moreover, infected cells may produce new virus particles that proceed to infect additional tumor cells. We present a model of tumor and virus interactions based on established biology and with proper accounting of the free virus population. The range of model parameters is estimated by fitting to available experimental data. The stability of equilibrium states corresponding to complete tumor eradication, therapy failure and partial tumor reduction is discussed. We use numerical simulations to explore conditions for which the model predicts successful therapy and tumor eradication. The model exhibits damped, as well as stable oscillations in a range of parameter values. These oscillatory states are organized by a Hopf bifurcation.

A microenvironment based model of antimitotic therapy of Gompertzian tumor growth.

A model of tumor growth, based on two-compartment cell population dynamics, and an overall Gompertzian growth has been previously developed. The main feature of the model is an inter-compartmental transfer function that describes the net exchange between proliferating (P) and quiescent (Q) cells and yields Gompertzian growth for tumor cell population N = P + Q. Model parameters provide for cell reproduction and cell death. This model is further developed here and modified to simulate antimitotic therapy. Therapy decreases the reproduction-rate constant and increases the death-rate constant of proliferating cells with no direct effect on quiescent cells. The model results in a system of two ODE equations (in N and P/N) that has an analytical solution. Net tumor growth depends on support from the microenvironment. Indirectly, this is manifested in the transfer function, which depends on the proliferation ratio, P/N. Antimitotic therapy will change P/N, and the tumor responds by slowing the transfer rate from P to Q. While the cellular effects of therapy are modeled as dependent only on antimitotic activity of the drug, the tumor response also depends on the tumor age and any previous therapies--after therapy, it is not the same tumor. The strength of therapy is simulated by the parameter lambda, which is the ratio of therapy induced net proliferation rate constant versus the original. A pharmacodynamic factor inversely proportional to tumor size is implemented. Various chemotherapy regimens are simulated and the outcomes of therapy administered at different time points in the life history of the tumor are explored. Our analysis shows: (1) for a constant total dose administered, a decreasing dose schedule is marginally superior to an increasing or constant scheme, with more pronounced benefit for faster growing tumors, (2) the minimum dose to stop tumor growth is age dependent, and (3) a dose-dense schedule is favored. Faster growing tumors respond better to dose density.