Quantifying the phosphorylation timescales of receptor-ligand complexes: a Markovian matrix-analytic approach.

Cells interact with the extracellular environment by means of receptor molecules on their surface. Receptors can bind different ligands, leading to the formation of receptor-ligand complexes. For a subset of receptors, called receptor tyrosine kinases, binding to ligand enables sequential phosphorylation of intra-cellular residues, which initiates a signalling cascade that regulates cellular function and fate. Most mathematical modelling approaches employed to analyse receptor signalling are deterministic, especially when studying scenarios of high ligand concentration or large receptor numbers. There exist, however, biological scenarios where low copy numbers of ligands and/or receptors need to be considered, or where signalling by a few bound receptor-ligand complexes is enough to initiate a cellular response. Under these conditions stochastic approaches are appropriate, and in fact, different attempts have been made in the literature to measure the timescales of receptor signalling initiation in receptor-ligand systems. However, these approaches have made use of numerical simulations or approximations, such as moment-closure techniques. In this paper, we study, from an analytical perspective, the stochastic times to reach a given signalling threshold for two receptor-ligand models. We identify this time as an extinction time for a conveniently defined auxiliary absorbing continuous time Markov process, since receptor-ligand association/dissociation events can be analysed in terms of quasi-birth-and-death processes. We implement algorithmic techniques to compute the different order moments of this time, as well as the steady-state probability distribution of the system. A novel feature of the approach introduced here is that it allows one to quantify the role played by each kinetic rate in the timescales of signal initiation, and in the steady-state probability distribution of the system. Finally, we illustrate our approach by carrying out numerical studies for the vascular endothelial growth factor and one of its receptors, the vascular endothelial growth factor receptor of human endothelial cells.

A window of opportunity for cooperativity in the T Cell Receptor.

The T-cell antigen receptor (TCR) is pre-organised in oligomers, known as nanoclusters. Nanoclusters could provide a framework for inter-TCR cooperativity upon peptide antigen-major histocompatibility complex (pMHC) binding. Here we have used soluble pMHC oligomers in search for cooperativity effects along the plasma membrane plane. We find that initial binding events favour subsequent pMHC binding to additional TCRs, during a narrow temporal window. This behaviour can be explained by a 3-state model of TCR transition from Resting to Active, to a final Inhibited state. By disrupting nanoclusters and hampering the Active conformation, we show that TCR cooperativity is consistent with TCR nanoclusters adopting the Active state in a coordinated manner. Preferential binding of pMHC to the Active TCR at the immunological synapse suggests that there is a transient time frame for signal amplification in the TCR, allowing the T cells to keep track of antigen quantity and binding time.

Stochastic descriptors to study the fate and potential of naive T cell clonotypes in the periphery.

The population of naive T cells in the periphery is best described by determining both its T cell receptor diversity, or number of clonotypes, and the sizes of its clonal subsets. In this paper, we make use of a previously introduced mathematical model of naive T cell homeostasis, to study the fate and potential of naive T cell clonotypes in the periphery. This is achieved by the introduction of several new stochastic descriptors for a given naive T cell clonotype, such as its maximum clonal size, the time to reach this maximum, the number of proliferation events required to reach this maximum, the rate of contraction of the clonotype during its way to extinction, as well as the time to a given number of proliferation events. Our results show that two fates can be identified for the dynamics of the clonotype: extinction in the short-term if the clonotype experiences too hostile a peripheral environment, or establishment in the periphery in the long-term. In this second case the probability mass function for the maximum clonal size is bimodal, with one mode near one and the other mode far away from it. Our model also indicates that the fate of a recent thymic emigrant (RTE) during its journey in the periphery has a clear stochastic component, where the probability of extinction cannot be neglected, even in a friendly but competitive environment. On the other hand, a greater deterministic behaviour can be expected in the potential size of the clonotype seeded by the RTE in the long-term, once it escapes extinction.

[Effectiveness of a recuperative primary care intervention in patients with chronic obstructive pulmonary disease]. / Efectividad de una intervención rehabilitadora, realizada en atención primaria, en la evolución de los pacientes con EPOC.

OBJECTIVES: The main objective is to assess the effect of a respiratory rehabilitation programme on the quality of life of patients with COPD. Secondary aims are to determine whether the intervention, as against the habitual monitoring, improves tolerance to exercise and pulmonary function, and reduces dyspnoea, the number of crises and hospital admissions due to COPD and the medication used to control the disease. DESIGN: Pragmatic cluster-randomised clinical trial. SETTING: Clinics of 16 PC teams in various health areas of the Community of Madrid. PARTICIPANTS: 476 patients with light-moderate COPD, who sign their informed consent. VARIABLES: Quality of life, number of crises, packages of medicines used to control the disease, unscheduled attendance, pulmonary function, dyspnoea and tolerance to exercise. METHOD: The consultations will be assigned to the control and intervention groups at random. At each clinic there will be a randomised selection from all patients with COPD and in a stable clinical condition. 238 patients are needed in each group, in order to detect a minimum difference of 4 points in quality of life, assuming a standard deviation of 16, 95% confidence level, 80% power and 20% losses. The effect between each factor and the variables evaluated through multivariate analysis will be calculated. DISCUSSION: This research project aims to show that a basic recuperative intervention, which is feasible and primary care-based, can achieve improvements in the quality of life of patients with COPD.

Efectividad de una intervención rehabilitadora, realizada en atención primaria, en la evolución / How much a recuperative primary care intervention affects the evolution of patients with chronic obstructive pulmonary disease

Objetivos. El objetivo principal es valorar la efectividad de un programa de rehabilitación respiratoria en la calidad de vida de pacientes con enfermedad pulmonar obstructiva crónica (EPOC). Los objetivos secundarios son: determinar si la intervención mejora la tolerancia al ejercicio y la función pulmonar, y disminuye la sensación de disnea, el número de exacerbaciones, los ingresos hospitalarios por EPOC y el consumo de medicación necesario para el adecuado control de la enfermedad frente al seguimiento habitual. Diseño. Ensayo clínico aleatorizado por grupos pragmático. Emplazamiento. Consultas de 16 equipos de atención primaria, repartidos por diferentes áreas sanitarias de la Comunidad de Madrid. Participantes. Se incluirá en el estudio a 476 pacientes con EPOC leve-moderada, que firmarán el consentimiento informado. Variables. Calidad de vida, número de agudizaciones, envases de medicación utilizados para el control, visitas no programadas, función pulmonar, disnea y tolerancia al ejercicio. Método. Se realizará asignación aleatoria de las consultas a cada grupo, control e intervención. En cada consulta se realizará una selección aleatoria del total de pacientes con EPOC, en situación clínica estable. Se precisan 238 pacientes en cada grupo para detectar una diferencia mínima de 4 puntos en la calidad de vida, asumiendo una desviación estándar de 16, un nivel de confianza del 95%, una potencia del 80% y unas pérdidas del 20%. Se estimará el efecto entre el factor de estudio y las variables evaluadas mediante análisis multivariante. Discusión. Este proyecto de investigación pretende demostrar que una intervención rehabilitadora básica, factible e implementada en atención primaria permite alcanzar mejoras en la calidad de vida de los pacientes con EPOC

Objectives. The main objective is to assess the effect of a respiratory rehabilitation programme on the quality of life of patients with COPD. Secondary aims are to determine whether the intervention, as against the habitual monitoring, improves tolerance to exercise and pulmonary function, and reduces dyspnoea, the number of crises and hospital admissions due to COPD and the medication used to control the disease. Design. Pragmatic cluster-randomised clinical trial. Setting. Clinics of 16 PC teams in various health areas of the Community of Madrid. Participants. 476 patients with light-moderate COPD, who sign their informed consent. Variables. Quality of life, number of crises, packages of medicines used to control the disease, unscheduled attendance, pulmonary function, dyspnoea and tolerance to exercise. Method. The consultations will be assigned to the control and intervention groups at random. At each clinic there will be a randomised selection from all patients with COPD and in a stable clinical condition. 238 patients are needed in each group, in order to detect a minimum difference of 4 points in quality of life, assuming a standard deviation of 16, 95% confidence level, 80% power and 20% losses. The effect between each factor and the variables evaluated through multivariate analysis will be calculated. Discussion. This research project aims to show that a basic recuperative intervention, which is feasible and primary care-based, can achieve improvements in the quality of life of patients with COPD

Heat kernel regularization of the effective action for stochastic reaction-diffusion equations.

The presence of fluctuations and nonlinear interactions can lead to scale dependence in the parameters appearing in stochastic differential equations. Stochastic dynamics can be formulated in terms of functional integrals. In this paper we apply the heat kernel method to study the short distance renormalizability of a stochastic (polynomial) reaction-diffusion equation with real additive noise. We calculate the one-loop effective action and its ultraviolet scale dependent divergences. We show that for white noise a polynomial reaction-diffusion equation is one-loop finite in d=0 and d=1, and is one-loop renormalizable in d=2 and d=3 space dimensions. We obtain the one-loop renormalization group equations and find they run with scale only in d=2.

Effective action for stochastic partial differential equations.

Stochastic partial differential equations (SPDEs) are the basic tool for modeling systems where noise is important. SPDEs are used for models of turbulence, pattern formation, and the structural development of the universe itself. It is reasonably well known that certain SPDEs can be manipulated to be equivalent to (nonquantum) field theories that nevertheless exhibit deep and important relationships with quantum field theory. In this paper we systematically extend these ideas: We set up a functional integral formalism and demonstrate how to extract all the one-loop physics for an arbitrary SPDE subject to arbitrary Gaussian noise. It is extremely important to realize that Gaussian noise does not imply that the field variables undergo Gaussian fluctuations, and that these nonquantum field theories are fully interacting. The limitation to one loop is not as serious as might be supposed: Experience with quantum field theories (QFTs) has taught us that one-loop physics is often quite adequate to give a good description of the salient issues. The limitation to one loop does, however, offer marked technical advantages: Because at one loop almost any field theory can be rendered finite using zeta function technology, we can sidestep the complications inherent in the Martin-Siggia-Rose formalism (the SPDE analog of the Becchi-Rouet-Stora-Tyutin formalism used in QFT) and instead focus attention on a minimalist approach that uses only the physical fields (this "direct approach" is the SPDE analog of canonical quantization using physical fields). After setting up the general formalism for the characteristic functional (partition function), we show how to define the effective action to all loops, and then focus on the one-loop effective action and its specialization to constant fields: the effective potential. The physical interpretation of the effective action and effective potential for SPDEs is addressed and we show that key features carry over from QFT to the case of SPDEs. An important result is that the amplitude of the two-point function governing the noise acts as the loop-counting parameter and is the analog of Planck's constant in this SPDE context. We derive a general expression for the one-loop effective potential of an arbitrary SPDE subject to translation-invariant Gaussian noise, and compare this with the one-loop potential for QFT.