Molecular finite-size effects in stochastic models of equilibrium chemical systems.

The reaction-diffusion master equation (RDME) is a standard modelling approach for understanding stochastic and spatial chemical kinetics. An inherent assumption is that molecules are point-like. Here, we introduce the excluded volume reaction-diffusion master equation (vRDME) which takes into account volume exclusion effects on stochastic kinetics due to a finite molecular radius. We obtain an exact closed form solution of the RDME and of the vRDME for a general chemical system in equilibrium conditions. The difference between the two solutions increases with the ratio of molecular diameter to the compartment length scale. We show that an increase in the fraction of excluded space can (i) lead to deviations from the classical inverse square root law for the noise-strength, (ii) flip the skewness of the probability distribution from right to left-skewed, (iii) shift the equilibrium of bimolecular reactions so that more product molecules are formed, and (iv) strongly modulate the Fano factors and coefficients of variation. These volume exclusion effects are found to be particularly pronounced for chemical species not involved in chemical conservation laws. Finally, we show that statistics obtained using the vRDME are in good agreement with those obtained from Brownian dynamics with excluded volume interactions.

Radium 223 dichloride: a multidisciplinary approach to metastatic castration-resistant prostate cancer.

The role of nuclear medicine physicians in the multidisciplinary team for the management of patients with prostate cancer has been restricted because of a lack of available tools. The only drugs approved to relieve pain related to bone metastases were ß-emitting radiopharmaceuticals. These drugs did not prove to prolong survival when used as single agent and resulted associated with important adverse events. This situation has changed with the introduction of radium 223 because of evidence of improved survival in patients, the good safety profile and the opportunity to avoid clonal selection of tumor cells. Cooperation among physicians involved in cancer management will lead to improvements in the treatment of bone metastases due to prostate cancer and is thought to extend to other tumor types.

Model reduction for stochastic chemical systems with abundant species.

Biochemical processes typically involve many chemical species, some in abundance and some in low molecule numbers. We first identify the rate constant limits under which the concentrations of a given set of species will tend to infinity (the abundant species) while the concentrations of all other species remains constant (the non-abundant species). Subsequently, we prove that, in this limit, the fluctuations in the molecule numbers of non-abundant species are accurately described by a hybrid stochastic description consisting of a chemical master equation coupled to deterministic rate equations. This is a reduced description when compared to the conventional chemical master equation which describes the fluctuations in both abundant and non-abundant species. We show that the reduced master equation can be solved exactly for a number of biochemical networks involving gene expression and enzyme catalysis, whose conventional chemical master equation description is analytically impenetrable. We use the linear noise approximation to obtain approximate expressions for the difference between the variance of fluctuations in the non-abundant species as predicted by the hybrid approach and by the conventional chemical master equation. Furthermore, we show that surprisingly, irrespective of any separation in the mean molecule numbers of various species, the conventional and hybrid master equations exactly agree for a class of chemical systems.

Linear noise approximation for stochastic oscillations of intracellular calcium.

A stochastic model of intracellular calcium oscillations is analytically studied. The governing master equation is expanded under the linear noise approximation and a closed prediction for the power spectrum of fluctuations analytically derived. A peak in the obtained power spectrum profile signals the presence of stochastic, noise induced oscillations which extend also outside the region where a deterministic limit cycle is predicted to occur.

Stochastic amplification of spatial modes in a system with one diffusing species.

The problem of pattern formation in a generic two species reaction-diffusion model is studied, under the hypothesis that only one species can diffuse. For such a system, the classical Turing instability cannot take place. At variance, by working in the generalized setting of a stochastic formulation to the inspected problem, spatially organized patterns can develop, seeded by finite size corrections. General conditions are given for the stochastic patterns to occur. The predictions of the theory are tested for a specific case study.

Thermoplastic clear dental aligners under cyclic compression loading: A mechanical performance analysis using acoustic emission technique.

The objective of this work is to analyse the performance of clear aligners made of thermoplastic materials. Within this framework, the damage evolution stages and damage states of the aligners at different cycles of the compressive loading are evaluated using the Acoustic Emission (AE) technique. Three different clear aligner systems were prepared: thermoformed PET-g (polyethylene terephthalate glycol) and PU (polyurethane), and additively manufactured PU. Cyclic compression tests are performed to simulate 22500 swallows. The mechanical results show that the energy absorbed by the thermoformed PET-g aligner remains stable around 4 Nmm throughout the test. Although the PU-based aligners show a higher energy absorption of about 7 Nmm during the initial phase of the cyclic loading, this gradually decreases after 12500 cycles. The time-domain based, and frequency-based parameters of the stress wave acoustic signals generated by the aligners under compression loading are used to identify the damage evolution stages. The machine learning-based AE results reveal the initiation and termination of the different damage states in the aligners and the frequency-based results distinguish the different damage sources. Finally, the microscopy results validated the damage occurrences in the aligners identified by the AE results. The mechanical test results indicate that the thermoformed PET-g has the potential to match the performance and requirements of the dentistry of the popular Invisalign (additively manufactured PU). The AE results have the potential to identify at which cycles the aligners may start losing their functionality.

In Vitro Effects of Low-energy Ultrasound Treatment on Healthy CD3/CD8+ Lymphocytes, Red blood cells, Acute Myeloid leukemia cells, and Jurkat cell line.

The study of the biological effects of low-energy ultrasound and its applications is a rapidly expanding research area. Low-energy ultrasound could be used as anti-tumoral therapy with or without the pharmacological combination even if the second situation has been scarcely investigated up to now. Very little information is available about the ultrasound effects on healthy red blood cells, CD3, and mainly CD8 subset lymphocytes which is the main subset cell having cytotoxic function towards cancer cells. In this study, we investigated in vitro the bioeffects of low energy ultrasound on red blood cells and PBMCs isolated from healthy donors as well as on two myeloid leukemia cell lines (OCI- AML-3 MOLM-13) and lymphoblastic Jurkat cell line. Using low-energy ultrasound (US), a study was conducted to determine how it affects CD3/CD8 lymphocytes and leukemia cells, as well as its potential role in treating blood cancers, by analyzing changes in mitochondrial membrane potential, phosphatidylserine asymmetry, morphological changes for myeloid AML cell lines, proliferation and cytotoxic activation of healthy lymphocytes, and apoptosis for RBCs after US exposure. Overall, we demonstrated that CD3/CD8 lymphocytes proliferation/activation and cytotoxic functions are fully preserved after ultrasound treatments, whereas leukemia cell lines undergo apoptosis and stop proliferating suggesting a potential method of treating blood cancer.

Cytochrome 450 1B1 (CYP1B1) polymorphisms associated with response to docetaxel in Castration-Resistant Prostate Cancer (CRPC) patients.

BACKGROUND: The selection of patients according to key genetic characteristics may help to tailor chemotherapy and optimize the treatment in Castration-Resistant Prostate Cancer (CRPC) patients. Functional polymorphisms within the cytochrome P450 1B1 (CYP1B1) gene have been associated with alterations in enzymatic expression and activity and may change sensitivity to the widely used docetaxel regimen. METHODS: CYP1B1 genotyping was performed on blood samples of 60 CRPC patients treated with docetaxel, using TaqMan probes-based assays. Association between CYP1B1-142C>G (leading to the 48ArgGly transition), 4326C>G (432LeuVal), and 4390A>G (453AsnSer) polymorphisms and treatment response, progression-free-survival (PFS) and overall-survival (OS) was estimated using Pearson χ2 test, Kaplan-Meier curves and Log-rank test. RESULTS: Patients carrying the CYP1B1-432ValVal genotype experienced a significantly lower response-rate (P = 0.014), shorter progression-free-survival (P = 0.032) and overall-survival (P < 0.001). Multivariate analyses and correction for multiple comparisons confirmed its prognostic significance for OS. No significant associations were found among other polymorphisms and both response and clinical outcome. CONCLUSIONS: CYP1B1-4326C>G (432LeuVal) polymorphism emerged as possible predictive marker of response and clinical outcome to docetaxel in CRPC patients and may represent a potential new tool for treatment optimization. Larger prospective trials are warranted to validate these findings, which might be applied to the future practice of CRPC treatment.

Experimental Study of the Pressures and Points of Application of the Forces Exerted between Aligner and Tooth.

The analysis of forces, moments and pressure points has long been of great interest in orthodontics. Hence, we set out to define a method for measuring the pressure exerted by aligners on the teeth, and specifically to identify the precise points of pressure exertion. Intraoral scans were performed on a patient with optimal alignment and levelling before and after 2º vestibularisation of the upper central incisor. Pressure sensor film was placed in a dedicated housing between the aligner and teeth in order to record the pressure exerted after 15 s of aligner application. The images captured by the film were scanned, digitised, and subsequently analysed. Areas and amounts of pressure generated by the aligners were evaluated, and the net force of each was calculated, adjusted to take into consideration passive values. The method revealed the areas of contact by which the aligner transmits force on the teeth, and the pressures at which it does so. The pressure exerted by an aligner is not evenly distributed across the entire surface of the tooth during lingual tipping of an upper incisor. The areas of force concentration were not identical, as these are influenced by factors resulting from the manufacturing and casting processes.

223Ra-chloride therapy in men with hormone-refractory prostate cancer and skeletal metastases: Real-world experience.

BACKGROUND: Radium-223 (223Ra) chloride, an alpha emitter, has been shown to improve overall survival (OS) and pain control, and to delay skeletal-related events, in patients with castration-resistant prostate cancer (CRPC) and bone metastases. Our retrospective observational study presents the first Italian experience on the efficacy and safety of 223Ra therapy in routine clinical practice. METHODS: A total of 83 patients with metastatic CRPC were treated with 223Ra at 3 Italian centers between August 2013 and August 2016. 223Ra-chloride (55 kBq/kg) was administered every 4 weeks for a total of 6 cycles. Primary endpoints were OS and progression-free survival (PFS). Secondary endpoints included toxicity, pain evaluation using numeric rating scale (NRS), symptomatic skeletal-related events and biomarkers response. RESULTS: Patients had a median age of 75 (range 53-89) years. The majority of men showed a Gleason score of 7, 8, or 9. Forty-one patients completed 6 treatment cycles; 33 stopped treatment before completing 6 cycles. Nine were still receiving therapy at the time of data collection. At the end of therapy, NRS pain scores significantly improved ( p < .000001). OS was a mean of 10.1 months, while median OS had not been attained. According to Kaplan-Meier estimation, OS and PFS were 17.5 and 7.7 months, respectively. There was a significant correlation between OS and PFS with the number of 223Ra cycles; patients receiving all 6 cycles experienced the major benefit from the therapy. 223Ra was well-tolerated. CONCLUSIONS: 223Ra alpha therapy is an important therapeutic option for men with CRPC and symptomatic skeletal metastases.

Capturing Brownian dynamics with an on-lattice model of hard-sphere diffusion.

Conventional master equation approaches approximate the diffusion of molecules in continuum space by the process of particles hopping on a spatial lattice. The hopping probability from one voxel (spatial lattice point) to its neighbor is usually considered to be constant throughout space. Such an assumption is only consistent with pointlike molecules and thus neglects volume-exclusion effects due to finite particle size. A few studies have attempted to introduce volume-exclusion effects by choosing the hopping probability from one voxel to a neighboring one to be a linear function of the number density. Here, we formulate an alternative master equation in which the hopping probability is equal to the fraction of available space in the neighboring voxel as estimated using scaled particle theory. This leads to the hopping probability being a nonlinear function of the number density. A mean-field approximation (mfa) leads to a partial differential equation of the advection-diffusion type. We show that the time evolution of the particle number density sampled using the stochastic simulation algorithm associated with the new master equation and the number density obtained by numerical integration of the mfa are in good agreement with each other. They are also distinctly different than the time evolution predicted by the conventional master equation and those with hopping probabilities which are linear functions of the number density. The results from the new lattice description are also shown to be in very good agreement with the lattice-free method of Brownian dynamics, even for highly crowded scenarios.

Macromolecular crowding directs the motion of small molecules inside cells.

It is now well established that cell interiors are significantly crowded by macromolecules, which impede diffusion and enhance binding rates. However, it is not fully appreciated that levels of crowding are heterogeneous, and can vary substantially between subcellular regions. In this article, starting from a microscopic model, we derive coupled nonlinear partial differential equations for the concentrations of two populations of large and small spherical particles with steric volume exclusion. By performing an expansion in the ratio of the particle sizes, we find that the diffusion of a small particle in the presence of large particles obeys an advection-diffusion equation, with a reduced diffusion coefficient and a velocity directed towards less crowded regions. The interplay between advection and diffusion leads to behaviour that differs significantly from Brownian diffusion. We show that biologically plausible distributions of macromolecules can lead to highly non-Gaussian probability densities for the small particle position, including asymmetrical and multimodal densities. We confirm all our results using hard-sphere Brownian dynamics simulations.

Analytical approximations for spatial stochastic gene expression in single cells and tissues.

Gene expression occurs in an environment in which both stochastic and diffusive effects are significant. Spatial stochastic simulations are computationally expensive compared with their deterministic counterparts, and hence little is currently known of the significance of intrinsic noise in a spatial setting. Starting from the reaction-diffusion master equation (RDME) describing stochastic reaction-diffusion processes, we here derive expressions for the approximate steady-state mean concentrations which are explicit functions of the dimensionality of space, rate constants and diffusion coefficients. The expressions have a simple closed form when the system consists of one effective species. These formulae show that, even for spatially homogeneous systems, mean concentrations can depend on diffusion coefficients: this contradicts the predictions of deterministic reaction-diffusion processes, thus highlighting the importance of intrinsic noise. We confirm our theory by comparison with stochastic simulations, using the RDME and Brownian dynamics, of two models of stochastic and spatial gene expression in single cells and tissues.

Early and prolonged response to pazopanib in a patient with multiple metastases from renal cell carcinoma: a case report.

AIMS AND BACKGROUND: In recent years, targeted agents have replaced cytokine therapy as the standard of care for patients with metastatic renal cell carcinoma. METHODS AND STUDY DESIGN: We report a patient with multiple metastases from renal cell carcinoma treated with cytoreductive surgery and pazopanib. RESULTS AND CONCLUSIONS: The treatment resulted in an early and prolonged response, without toxicity.

Safety and antitumor efficacy of (153)Sm-EDTMP and docetaxel administered sequentially to patients with metastatic castration-resistant prostate cancer.

BACKGROUND: Bone metastases are responsible for most of the morbidity associated with metastatic castration-resistant prostate cancer (mCRPC). Bone-seeking radiopharmaceuticals have been approved for palliation of painful skeletal metastases, but their clinical use is limited by concerns of toxicities both when administered alone and especially when combined with chemotherapy agents. OBJECTIVE: We investigated whether docetaxel administered to mCRPC patients after treatment with samarium-153-labeled ethylene-diamine-tetra-methylene-phosphonic acid (Sm-EDTMP) has increased toxicity and/or reduced antitumor efficacy. MATERIALS AND METHODS: Thirty mCRPC patients with skeletal metastases were enrolled. Patients received standard therapy with docetaxel (75 mg/m intravenously every 21 days for at least six cycles) on average 6 weeks after Sm-EDTMP (37 MBq/kg). Patients were monitored for the presence of toxicities, and antitumor efficacy was assessed by changes in serum prostate-specific antigen levels. Besides standard descriptive statistical analysis, progression-free survival and overall survival were defined using the Kaplan-Meier method. RESULTS: Over 80% of the patients showed favorable biochemical responses. Median time to progression was 9.1 months (mean 9.8, 95% confidence interval 7.8-9.9), and median overall survival was 19.9 months (mean 24.5, 95% confidence interval 16.9-22.8); five patients were still alive over 5 years after enrollment. No additional hematological toxicities were observed when docetaxel was administered after Sm-EDTMP other than those expected when administering the agent alone. CONCLUSION: Prior administration of Sm-EDTMP does not cause additional toxicities for subsequent treatment with docetaxel and does not reduce the antitumor efficacy of the latter. This work justifies further investigations on the possible synergistic effects of combined strategies with the two agents.

Clinical benefit of bone-targeted radiometabolic therapy with 153Sm-EDTMP combined with chemotherapy in patients with metastatic hormone-refractory prostate cancer.

BACKGROUND: Bone metastases are responsible for most of the morbidity associated with hormone-refractory prostate cancer (HRPC). 153Sm-ethylenediaminetetramethylene phosphonate (153Sm-EDTMP) has been approved for palliation of painful skeletal metastases. We retrospectively investigated the possible synergistic effect on survival of 153Sm-EDTMP (given to HRPC patients for bone pain palliation) and chemotherapy. METHODS: Forty-five HRPC patients were evaluated, with a median age of 71 years. The number of metastatic bone sites was 10 in 20 patients. Median serum PSA was 224 ng/ml. Bone pain was mild in 6 patients, moderate in 16, severe in 22 and intolerable in 1. Fifteen patients were only treated with 153Sm-EDTMP (group A), while 30 patients also received chemotherapy (estramustine phosphate or mitoxantrone plus prednisone) at variable times: between 3 and 5 months after 153Sm-EDTMP (14 patients, group B) or within 1 month after 153Sm-EDTMP (16 patients, group C). RESULTS: Haematological toxicities observed after either regimen were in general mild, consistent with common observations after either 153Sm-EDTMP or chemotherapy, and without any additive adverse effects in the patients receiving both 153Sm-EDTMP and chemotherapy. Bone pain palliation to some degree was induced by 153Sm-EDTMP in 32/45 patients (71.1%), the proportion of patients with a favourable clinical response being significantly higher in group C than in group A (87.5% vs 53.3%, p = 0.0388). Also in terms of biochemical response (serum PSA levels), patients of group C performed significantly better than patients of group A (p = 0.0235). Overall median survival from the time of administration of 153Sm-EDTMP was 15 months in the total cohort of 45 patients, and was significantly longer in group C than in either group B (30 months vs 11 months, p = 0.023) or group A (30 months vs 10 months, p = 0.008). CONCLUSION: The results of this study confirm that 153Sm-EDTMP is effective in terms of pain relief and PSA response, with minimal toxicity. When it was administered in combination with chemotherapy, prolonged survival indicated actual clinical benefit, while there were no additive toxicities. These results provide the rationale for future prospective evaluation of combined therapeutic strategies.