Medico-economic impact of thoracoscopy versus thoracotomy in lung cancer: multicentre randomised controlled trial (Lungsco01)

BACKGROUND

Lungsco01 is the first study assessing the real benefits and the medico-economic impact of video-thoracoscopy versus open thoracotomy for non-small cell lung cancer in the French context.

METHODS

Two hundred and fifty nine adult patients from 10 French centres were randomised in this prospective multicentre randomised controlled trial, between July 29, 2016, and November 24, 2020. Survival from surgical intervention to day 30 and later was compared with the log-rank test. Total quality-adjusted-life-years (QALYs) were calculated using the EQ-5D-3L®. For medico-economic analyses at 30 days and at 3 months after surgery, resources consumed were valorised (€ 2018) from a hospital perspective. First, since mortality was infrequent and not different between the two arms, cost-minimisation analyses were performed considering only the cost differential. Second, based on complete cases on QALYs, cost-utility analyses were performed taking into account cost and QALY differential. Acceptability curves and the 95% confidence intervals for the incremental ratios were then obtained using the non-parametric bootstrap method (10,000 replications). Sensitivity analyses were performed using multiple imputations with the chained equation method.

RESULTS

The average cumulative costs of thoracotomy were lower than those of video-thoracoscopy at 30 days (€9,730 (SD = 3,597) vs. €11,290 (SD = 4,729)) and at 3 months (€9,863 (SD = 3,508) vs. €11,912 (SD = 5,159)). In the cost-utility analyses, the incremental cost-utility ratio was €19,162 per additional QALY gained at 30 days (€36,733 at 3 months). The acceptability curve revealed a 64% probability of efficiency at 30 days for video-thoracoscopy, at a widely-accepted willingness-to-pay threshold of €25,000 (34% at 3 months). Ratios increased after multiple imputations, implying a higher cost for video-thoracoscopy for an additional QALY gain (ratios: €26,015 at 30 days, €42,779 at 3 months).

CONCLUSIONS

Given our results, the economic efficiency of video-thoracoscopy at 30 days remains fragile at a willingness-to-pay threshold of €25,000/QALY. The economic efficiency is not established beyond that time horizon. The acceptability curves given will allow decision-makers to judge the probability of efficiency of this technology at other willingness-to-pay thresholds.

TRIAL REGISTRATION

NCT02502318.

When to proceed to surgical rib fixation?-A single-institution clinical experience

Background

Surgical rib fixation for multiple rib fractures and flail chest has become more common in the 2000s with interesting results in selected patients. However, surgical rib fixation lacks a consensus on the delay to surgery and the benefits on postoperative clinical outcomes. Our goal was to determine if delay to surgery can affect postoperative outcomes.

Methods

We analyzed a retrospective database including all consecutive patients referred for surgical rib fixation. All outcomes were explored according to trauma mechanism, associated lesions, initial ventilatory status, delay to surgery, surgical technique and a specific focus was made towards post-operative care and pulmonary complications. Logistic regressions were performed to evaluate the association between delay to surgery [before 48 hours (early group), 48 hours to 7 days (mid group), more than 7 days (late group)] and pneumonia and failure of extubating.

Results

From 2010 to 2020, 159 patients underwent surgical rib fixation. The median hospital length of stay was 18 days (interquartile range, 13-30 days). Pulmonary infections were encountered in 67 patients (42.2%) with about two third of early pneumonia (<5 days). The one-month mortality rate was 1.9%. Delay to surgery was not associated with either pneumonia (P>0.05) or failure of extubating (P>0.05).

Conclusions

Surgical rib fixation can be delayed without increasing the risk of pulmonary complications. Stabilizing other clinical situations can be safely prioritized if needed. A global evaluation including characteristics of trauma and lung evaluation must be considered before surgical stabilization of rib fracture.

Subtotal Pleurectomy with Intrathoracic Chemo Hyperthermia (HITHOC) for IVa Thymomas: De Novo Versus Recurrent Pleural Disease

Simple Summary

Stage IVa thymomas are rare entities in thoracic oncology without a standard of care. Evidence-based guidelines for the management of located pleural carcinomatosis are lacking. Surgery when feasible has an excellent prognostic factor. However, the technical choice is vast, from extra pleural pneumonectomy with high rates of morbidity and/or mortality to debulking with high rates of relapse. We investigated parietal subtotal pleurectomy combined with HITHOC in highly selected patients. The goal was to determine overall survival (OS) and the disease-free interval (DFI). Our findings suggest a real impact of this surgical procedure in distant relapse (DR) or de novo tumors (DNT). In this orphan disease, prospective and randomized trials are needed to clarify the place of HITHOC in the multimodal modern care of these patients.

Abstract

Introduction: Stage IVa thymoma is a rare disease without a standard of care. Subtotal pleurectomy and HITHOC introduced in highly selected patients may provide interesting oncologic results. The purpose of this study was to distinguish de novo stage IVa tumors (DNT) from distant relapse (DR) with respect to post-operative and long-term outcomes to provide the procedure efficacy. Methods: From July 1997–December 2021, 40 patients with IVa pleural involvement were retrospectively analyzed. The surgical procedure was subtotal pleurectomy and HITHOC (cisplatin 50 mg/m², mitomycin 25 mg/m², 42 °C, 90 min). The post-operative outcome, disease-free interval (DFI) and overall survival (OS) were analyzed. Results: Mean age was 52 ± 12 years. B2 and B3 thymomas were preponderant (27; 67.5%). The median number of pleural nodes were nine (4–81) vs. five (1–36); p = 0.004 * in DNT and DR, respectively. Hospital mortality rate was 2.5%. There were four specific HITHOC complications (10%). DFI were 49 and 85 months (p = 0.02 *), OS were 94 and 118 months (NS), in DNT and DR, respectively. Conclusions: Subtotal pleurectomy with HITHOC in IVa offers satisfying results in highly selected patients, for both DNT and DR. Due to the disease rarity, multicentric studies are needed to define HITHOC as a standard of care.

Impact of Lung Biopsy on Lung Function in Idiopathic Pulmonary Fibrosis

BACKGROUND

Video-assisted surgical lung biopsy (SLB) is performed in 10-30% of cases to establish the diagnosis of idiopathic pulmonary fibrosis (IPF).

OBJECTIVES

The aim of the study was to analyze the impact of SLB on lung function in patients eventually diagnosed with IPF.

METHODS

This is an observational, retrospective, monocentric study of all consecutive patients eventually diagnosed with IPF in multidisciplinary discussion who underwent SLB over 10 years in a specialized center. The primary end point was the variation in forced vital capacity (FVC) before and after the SLB. The secondary end points were the variations in forced expiratory volume in one second (FEV1), total lung capacity (TLC), carbon monoxide diffusion capacity (DLCO), and morbidity and mortality associated with the SLB.

RESULTS

In 118 patients who underwent SLB and were diagnosed with IPF, a relative decrease in FVC of 4.8% (p < 0.001) was found between measurements performed before and after the procedure. The mean FVC decrease was 156 ± 386 mL in an average period of 185 days, representing an annualized decline of 363 ± 764 mL/year. A significant decrease was also observed after SLB in FEV1, TLC, and DLCO. Complications within 30 days of SLB occurred in 14.4% of patients. Two patients (1.7%) died within 30 days, where one of them had poor lung function. Survival at 1 year was significantly poorer in patients with FVC <50% at baseline.

CONCLUSION

In this uncontrolled study in patients ultimately diagnosed with IPF, SLB was followed by a significant decline in FVC, which appears to be numerically greater than the average decline in the absence of treatment in the literature. Summary at a Glance: This study evaluated the change in lung function in 118 consecutive patients diagnosed with idiopathic pulmonary fibrosis by surgical lung biopsy. Forced vital capacity decreased by 156 ± 386 mL in a mean of 185 days between the last measurement before and first measurement after biopsy, representing an annualized decline of 363 ± 764 mL/year.

Airway complications after lung transplantation: benefit of a conservative bronchoscopy strategy

Background

After lung transplantation (LT), between 2% and 25% of bronchial anastomoses develop complications requiring therapeutic intervention. The status of healing of both bronchial anastomoses and downhill airways are well described by the French consensual MDS standardized grading system (Macroscopic, Diameter, Suture). We analyzed risks factors for airway complications (AC) after transplantation and the way we managed them. We report here our challenging method of early rigid bronchoscopic intervention with airway stenting on bronchial healing.

Methods

All single center consecutives LTs were retrospectively analyzed between 2010-2016. Patient-level data (demographic, peri-operative data) and anastomosis-level data (surgical parameters, bronchoscopy findings) were monitored. The incidence and contributive factors of ACs are reported. We also reported modalities of the conservative treatment and outcome.

Results

A total of 121 LTs were performed, 39 single-lung and 82 bilateral sequential LT. Main indication for LT were cystic fibrosis (45%) and emphysema (25%) and 58 were male patients (n=70). After a waiting period of healing, 28 patients presented AC on 41 anastomoses (prevalence: 23%). A multivariate analysis found as contributive factors of ACs, post-operative infection by Aspergillus [odds ratio (OR) 2.7, 95% confidence interval (CI): 1.08-6.75; P=0.033] at the patient level, and at the anastomosis level, emphysema (OR 2.4, 95% CI: 1.02-5.6; P=0.045), early dehiscence (OR 11.2, 95% CI: 1.7-76; P=0.01) and cold ischemia time >264 min (OR 2.45, 95% CI: 1.08-5.6; P=0.03). All the 41 ACs were managed conservatively with rigid bronchoscopy (range, 1-10), 41 stents (21 in silicone and 20 fully-covered Silicone Expandable Metallic Stents) without major complication. Two AC were still under regular bronchoscopic care and silicone stenting for long left bronchus reason. No surgical intervention was needed. The 2-years overall survival rate where not different between AC group and controls, respectively 85% and 81%.

Conclusions

Airway healing after transplantation remains a scalable process and the French consensual MDS classification helped us for therapeutic decisions. Rigid bronchoscopy and safety use of current stenting devices may have the pivotal role in the conservative management of ACs, avoiding perilous situation of surgery for AC. Despite a high rate of AC, their favorable evolution may be explained by the cautious care of airway healing and maybe by the use of the Celsior antioxidant solution.

Blood CD9+ B cell, a biomarker of bronchiolitis obliterans syndrome after lung transplantation

Bronchiolitis obliterans syndrome is the main limitation for long-term survival after lung transplantation. Some specific B cell populations are associated with long-term graft acceptance. We aimed to monitor the B cell profile during early development of bronchiolitis obliterans syndrome after lung transplantation. The B cell longitudinal profile was analyzed in peripheral blood mononuclear cells from patients with bronchiolitis obliterans syndrome and patients who remained stable over 3 years of follow-up. CD24^hi CD38^hi transitional B cells were increased in stable patients only, and reached a peak 24 months after transplantation, whereas they remained unchanged in patients who developed a bronchiolitis obliterans syndrome. These CD24^hi CD38^hi transitional B cells specifically secrete IL-10 and express CD9. Thus, patients with a total CD9⁺ B cell frequency below 6.6% displayed significantly higher incidence of bronchiolitis obliterans syndrome (AUC = 0.836, PPV = 0.75, NPV = 1). These data are the first to associate IL-10-secreting CD24^hi CD38^hi transitional B cells expressing CD9 with better allograft outcome in lung transplant recipients. CD9-expressing B cells appear as a contributor to a favorable environment essential for the maintenance of long-term stable graft function and as a new predictive biomarker of bronchiolitis obliterans syndrome-free survival.

Cytoreductive Pleurectomy and Intrathoracic Chemohyperthermia for Pleural Relapse of Thymomas

Several surgical procedures, from debulking to extrapleural pneumonectomy, may be applied for stage IVa Masaoka thymomas, but their efficiency is still controversial. Case studies have favored R₀ resection as the cornerstone of multimodal therapy for locoregional metastatic extension. This report describes a standardized procedure combining a cytoreductive surgical procedure and intrathoracic chemohyperthermia on a 46-year-old patient presenting with B2 thymoma and synchronous unilateral pleural metastasis.

Intra-Thoracic Chemo-Hyperthermia for pleural recurrence of thymoma

BACKGROUND

Pleural recurrences are a hallmark of thymomas, and represent a challenge for multidisciplinary management. The purpose of this study was to assess the feasibility and the results in terms of morbidity, mortality and survival rates, of Intra-Thoracic Chemo-Hyperthermia (ITCH) for the treatment of pleural recurrences of thymomas.

METHODS

Retrospective analysis of 19 consecutives patients between 1997 and 2015 treated by surgical cytoreduction (pleurectomy) followed by ITCH with 25mg/m² of mitomycin, and 50mg/m² of Cisplatin.

RESULTS

There were 8 men and 11 women with a median age of 44 years. ITCH was combined with pleurectomy alone in 4 (22%) patients, pleurectomy and wedge resections in 14 (74%) patients; 1 (5%) patient had a pleuropneumonectomy. There were no perioperative deaths, and 5 patients (26%) presented with postoperative complication, including 3 (16%) cases related to chemotherapy (one case of reversible grade 2 bone marrow aplasia, and 2 cases of reversible, acute kidney failure). The median length of stay in intensive care unit and hospital were 1day and 10days, respectively. After a median follow-up period of 39 months (range 10-127 months), median disease-free survival was 42 months. Five patients (26%) died during follow-up.

CONCLUSIONS

Our data indicate that ITCH is a feasible option for selected patients with pleural recurrence of thymomas. ITCH clearly provides long local control, without major safety issues, and prolonged survival may be achieved in selected patients. This therapeutic option should be discussed at a multidisciplinary tumor board.

[Indications of lung transplantation: Patients selection, timing of listing, and choice of procedure]

Lung transplantation (LT) is now considered as an excellent treatment option for selected patients with end-stage pulmonary diseases, such as COPD, cystic fibrosis, idiopathic pulmonary fibrosis, and pulmonary arterial hypertension. The 2 goals of LT are to provide a survival benefit and to improve quality of life. The 3-step decision process leading to LT is discussed in this review. The first step is the selection of candidates, which requires a careful examination in order to check absolute and relative contraindications. The second step is the timing of listing for LT; it requires the knowledge of disease-specific prognostic factors available in international guidelines, and discussed in this paper. The third step is the choice of procedure: indications of heart-lung, single-lung, and bilateral-lung transplantation are described. In conclusion, this document provides guidelines to help pulmonologists in the referral and selection processes of candidates for transplantation in order to optimize the outcome of LT.

[Does antifungal therapy influence postoperative morbidity or long-term survival after surgical resection for pulmonary aspergilloma?]

BACKGROUND

Surgical resection of pulmonary aspergilloma is associated with symptoms control, complications prevention, and improved survival, given that the disease is localized and the patient fit enough to undergo surgery. In these operable forms, the impact of perioperative antifungal therapy remains controversial. The purpose of this study was to analyze the impact of antifungal therapy on postoperative morbidity and overall survival in patients with operable pulmonary aspergilloma.

METHODS

The clinical records of 113 patients who underwent thoracic surgery for aspergilloma in our institution from January 1989 to December 2010 were retrospectively reviewed. Of these, 64 patients received antifungal therapy in the perioperative period and were included in group 1, and 49 patients did not receive antifungal therapy and were included in group 2.

RESULTS

Postoperative complication rates were 31.2% in group 1 and 20.4% in group 2 (P = 0.30). Univariable analysis showed that immunocompromised status (P < 0.001), past history of cancer (P = 0.50), preoperative purulent sputum (P = 0.024), and pneumonectomy (P < 0.001) were significantly associated with postoperative complications, but that antifungal therapy was not. Five- and 10-year overall survival rates were respectively 78.3% and 57.8% in group 1 vs. 85.9% and 65.7% in group 2 (P = 0.23). Multivariate analysis revealed that age higher than 50, immunocompromised status and pneumonectomy were significantly associated with adverse long-term survival (χ(2) = 6.59, df = 5, P < 0.001), but that antifungal therapy was not.

CONCLUSION

Antifungal therapy has no significant impact on postoperative morbidity or long-term survival following surgical resection of pulmonary aspergilloma. Such procedure is associated with acceptable postoperative morbidity and long-term survival.

Steady-state fluctuations of a genetic feedback loop: an exact solution

Genetic feedback loops in cells break detailed balance and involve bimolecular reactions; hence, exact solutions revealing the nature of the stochastic fluctuations in these loops are lacking. We here consider the master equation for a gene regulatory feedback loop: a gene produces protein which then binds to the promoter of the same gene and regulates its expression. The protein degrades in its free and bound forms. This network breaks detailed balance and involves a single bimolecular reaction step. We provide an exact solution of the steady-state master equation for arbitrary values of the parameters, and present simplified solutions for a number of special cases. The full parametric dependence of the analytical non-equilibrium steady-state probability distribution is verified by direct numerical solution of the master equations. For the case where the degradation rate of bound and free protein is the same, our solution is at variance with a previous claim of an exact solution [J. E. M. Hornos, D. Schultz, G. C. P. Innocentini, J. Wang, A. M. Walczak, J. N. Onuchic, and P. G. Wolynes, Phys. Rev. E 72, 051907 (2005), and subsequent studies]. We show explicitly that this is due to an unphysical formulation of the underlying master equation in those studies.

[Lung volume reduction surgery for emphysema and bullous pulmonary emphysema]

The improvement of respiratory symptoms for emphysematous patients by surgery is a concept that has evolved over time. Initially used for giant bullae, this surgery was then applied to patients with diffuse microbullous emphysema. The physiological and pathological concepts underlying these surgical procedures are the same in both cases: improve respiratory performance by reducing the high intrapleural pressure. The functional benefit of lung volume reduction surgery (LVRS) in the severe diffuse emphysema has been validated by the National Emphysema Treatment Trial (NETT) and the later studies which allowed to identify prognostic factors. The quality of the clinical, morphological and functional data made it possible to develop recommendations now widely used in current practice. Surgery for giant bullae occurring on little or moderately emphysematous lung is often a simpler approach but also requires specialised support to optimize its results.

An effective rate equation approach to reaction kinetics in small volumes: theory and application to biochemical reactions in nonequilibrium steady-state conditions

Chemical master equations provide a mathematical description of stochastic reaction kinetics in well-mixed conditions. They are a valid description over length scales that are larger than the reactive mean free path and thus describe kinetics in compartments of mesoscopic and macroscopic dimensions. The trajectories of the stochastic chemical processes described by the master equation can be ensemble-averaged to obtain the average number density of chemical species, i.e., the true concentration, at any spatial scale of interest. For macroscopic volumes, the true concentration is very well approximated by the solution of the corresponding deterministic and macroscopic rate equations, i.e., the macroscopic concentration. However, this equivalence breaks down for mesoscopic volumes. These deviations are particularly significant for open systems and cannot be calculated via the Fokker-Planck or linear-noise approximations of the master equation. We utilize the system-size expansion including terms of the order of Omega(-1/2) to derive a set of differential equations whose solution approximates the true concentration as given by the master equation. These equations are valid in any open or closed chemical reaction network and at both the mesoscopic and macroscopic scales. In the limit of large volumes, the effective mesoscopic rate equations become precisely equal to the conventional macroscopic rate equations. We compare the three formalisms of effective mesoscopic rate equations, conventional rate equations, and chemical master equations by applying them to several biochemical reaction systems (homodimeric and heterodimeric protein-protein interactions, series of sequential enzyme reactions, and positive feedback loops) in nonequilibrium steady-state conditions. In all cases, we find that the effective mesoscopic rate equations can predict very well the true concentration of a chemical species. This provides a useful method by which one can quickly determine the regions of parameter space in which there are maximum differences between the solutions of the master equation and the corresponding rate equations. We show that these differences depend sensitively on the Fano factors and on the inherent structure and topology of the chemical network. The theory of effective mesoscopic rate equations generalizes the conventional rate equations of physical chemistry to describe kinetics in systems of mesoscopic size such as biological cells.

Crowding-induced anisotropic transport modulates reaction kinetics in nanoscale porous media

We quantify the emergence of persistent anisotropy in the diffusion of spherical tracer particles through a nanoscale porous medium composed of a uniform distribution of purely symmetric crowding particles. We focus on the interior of a biological cell as an example of such a medium and find that diffusion is highly directional for distances comparable to the size of some organelles. We use a geometrical procedure that avoids the standard orientational averaging to quantify the anisotropy of diffusive paths and show that the point source distributions are predominantly of prolate ellipsoidal shape as a result of local volume exclusion. This geometrical symmetry breaking strongly skews the distribution of kinetic rates of diffusion-limited reactions toward small values, leading to the result that, for short to intermediate times, almost 80% of the rates measured in an ensemble of heterogeneous media are smaller than the expected rate in an ideal homogeneous medium of similar excluded volume fraction. This crowding-induced modulation may have implications for our understanding and measurement of diffusion-controlled intracellular reaction kinetics and for experimental nanotechnology applications, such as nanoparticle-based bioimaging and drug delivery, where diffusion plays an important role.

Current indications and results for thoracoplasty and intrathoracic muscle transposition

OBJECTIVES

Thoracoplasty has lost much of its popularity and is being supplanted by space-reduction operations using muscle flaps. Our purpose is to retrospectively study the remaining indications and the evolving modifications of this ancient technique in our current surgical practice.

PATIENTS AND METHODS

From 1994 to 2008, 35 patients underwent a thoracoplasty procedure in a single thoracic surgery centre for treatment of infectious complications of previous thoracic surgery. The number and length of ribs excised were dictated by the size and location of the thoracic cavity to obliterate. Muscle flaps were used to buttress bronchial fistulas and to fill out residual spaces. We reviewed the immediate and long-term results concerning infection control and procedure tolerance.

RESULTS

The infectious complications of previous thoracic surgery were related to cancer in 25, tuberculosis in six, oesophageo-pleural fistula in two, ruptured lung abscess and pleural thickening in one each. The thoracoplasty procedure was performed for: (1) post-pneumonectomy empyema, n=20 (bronchial fistula, n=11; open window thoracostomy, n=14; mean number of resected ribs, n=7.5; associated intrathoracic muscle transposition, n=12; postoperative death, n=3); (2) post-lobectomy empyema, n=8 (bronchial fistula n=8; open window thoracostomy n=1; mean number of resected ribs n=3.6; associated intrathoracic muscle transposition n=7; no death); (3) other indications, n=7 (mean number of resected ribs n=4.8; associated intrathoracic muscle transposition n=3; no death). All patients discharged from the hospital except one were cured and did not complain of symptoms of secondary lung function and shoulder impairment.

CONCLUSION

Although thoracoplasty is rarely indicated nowadays, this does not imply that the procedure should be avoided. Thoracoplasty may be associated with myoplasty, which permits achieving complete space obliteration by combining resection of a few rib segments and limited intrathoracic muscle transposition.

Noise-induced breakdown of the Michaelis-Menten equation in steady-state conditions

The Michaelis-Menten (MM) equation is the basic equation of enzyme kinetics; it is also a basic building block of many models of biological systems. We build a stochastic and microscopic model of enzyme kinetics inside a small subcellular compartment. Using both theory and simulations, we show that intrinsic noise induces a breakdown of the MM equation even if steady-state metabolic conditions are enforced. In particular, we show that (i) given a reaction velocity, deterministic rate equations can severely underestimate steady-state intracellular substrate concentrations and (ii) different reaction schemes which on a macroscopic level are indistinguishable because they are described by the same MM equation obey distinctly different equations in subcellular compartments.

Brownian motion of an asymmetrical particle in a potential field

It is well known that a free ellipsoidal Brownian particle exhibits anisotropic diffusion for short times which changes to isotropic at long times, and, that the long-time diffusion coefficient is an average of the translational diffusion coefficients along the different semiaxes of the particle. We show analytically that in the presence of external forces, the long-time diffusion coefficient is different from that of a free particle. The magnitude of the difference in the two diffusion coefficients is found to increase proportionately with the particle's asymmetry, being zero only for a perfectly spherical Brownian particle. It is also found that, for asymmetrical particles, the application of external forces can amplify the non-Gaussian character of the spatial probability distributions which consequently delays the transition to the classical behavior. We illustrate these phenomena by considering the quasi-two-dimensional Brownian motion of an ellipsoidal rigid particle in linear and harmonic potential fields. These two examples provide insight into the role played by particle asymmetry in electrophoresis and microconfinement due to a laser trap or due to intracellular macromolecular crowding.

A systematic investigation of the rate laws valid in intracellular environments

Recently there has been significant interest in deducing the form of the rate laws for chemical reactions occurring in the intracellular environment. This environment is typically characterized by low-dimensionality and a high macromolecular content; this leads to a spatial heterogeneity not typical of the well stirred in vitro environments. For this reason, the classical law of mass action has been presumed to be invalid for modeling intracellular reactions. Using lattice-gas automata models, it has recently been postulated [H. Berry, Monte Carlo simulations of enzyme reactions in two dimensions: Fractal kinetics and spatial segregation, Biophys. J. 83 (2002) 1891-1901; S. Schnell, T.E. Turner, Reaction kinetics in intracellular environments with macromolecular crowding: simulations and rate laws, Prog. Biophys. Mol. Biol. 85 (2004) 235-260] that the reaction kinetics is fractal-like. In this article we systematically investigate for the first time how the rate laws describing intracellular reactions vary as a function of: the geometry and size of the intracellular surface on which the reactions occur, the mobility of the macromolecules responsible for the crowding effects, the initial reactant concentrations and the probability of reaction between two reactant molecules. We also compare the rate laws valid in heterogeneous environments in which there is an underlying spatial lattice, for example crystalline alloys, with the rate laws valid in heterogeneous environments where there is no such natural lattice, for example in intracellular environments. Our simulations indicate that: (i) in intracellular environments both fractal kinetics and mass action can be valid, the major determinant being the probability of reaction, (ii) the geometry and size of the intracellular surface on which reactions are occurring does not significantly affect the rate law, (iii) there are considerable differences between the rate laws valid in heterogeneous non-living structures such as crystals and those valid in intracellular environments. Deviations from mass action are less pronounced in intracellular environments than in a crystalline material of similar heterogeneity.

Phase transitions and superuniversality in the dynamics of a self-driven particle

We study an active random walker model in which a particle's motion is determined by a self-generated field. The field encodes information about the particle's path history. This leads to either self-attractive or self-repelling behavior. For self-repelling behavior, we find a phase transition in the dynamics: when the coupling between the field and the walker exceeds a critical value, the particle's behavior changes from renormalized diffusion to one characterized by a diverging diffusion coefficient. The dynamical behavior for all cases is surprisingly independent of dimension and of the noise amplitude.

Strong-coupling dynamics of a multicellular chemotactic system

Chemical signaling is one of the ubiquitous mechanisms by which intercellular communication takes place at the microscopic level, particularly via chemotaxis. Such multicellular systems are popularly studied using continuum, mean-field equations. In this Letter we study a stochastic model of chemotactic signaling. The Langevin formalism of the model makes it amenable to calculation via nonperturbative analysis, which enables a quantification of the effect of fluctuations on both the weak and the strongly coupled biological dynamics. In particular, we show that the (i) self-localization due to autochemotaxis is impossible. (ii) When aggregation occurs, the aggregate performs a random walk with a renormalized diffusion coefficient D(R) proportiuonal to epsilon-2N-3. (iii) The stochastic model exhibits sharp transitions in cell motile behavior for negative chemotaxis, behavior that has no parallel in the mean-field Keller-Segel equations.

Many-body theory of chemotactic cell-cell interactions

We consider an individual-based stochastic model of cell movement mediated by chemical signaling fields. This model is formulated using Langevin dynamics, which allows an analytic study using methods from statistical and many-body physics. In particular we construct a diagrammatic framework within which to study cell-cell interactions. In the mean-field limit, where statistical correlations between cells are neglected, we recover the deterministic Keller-Segel equations. Within exact perturbation theory in the chemotactic coupling epsilon , statistical correlations are non-negligible at large times and lead to a renormalization of the cell diffusion coefficient D(R)--an effect that is absent at mean-field level. An alternative closure scheme, based on the necklace approximation, probes the strong coupling behavior of the system and predicts that D(R) is renormalized to zero at a critical value of epsilon, indicating self-localization of the cell. Stochastic simulations of the model give very satisfactory agreement with the perturbative result. At higher values of the coupling simulations indicate that D(R) approximately epsilon(-2) , a result at odds with the necklace approximation. We briefly discuss an extension of our model, which incorporates the effects of short-range interactions such as cell-cell adhesion.

Accurate discretization of advection-diffusion equations

We present an exact mathematical transformation which converts a wide class of advection-diffusion equations into a form allowing simple and direct spatial discretization in all dimensions, and thus the construction of accurate and more efficient numerical algorithms. These discretized forms can also be viewed as master equations which provide an alternative mesoscopic interpretation of advection-diffusion processes in terms of diffusion with spatially varying hopping rates.