Modelado matemático del efecto de las medidas de cuidado por COVID-19 sobre otras enfermedades respiratorias / Mathematical modelling of the impact of COVID-19 care measures on other respiratory diseases

RESUMEN INTRODUCCIÓN Los modelos matemáticos de la transmisión de enfermedades infecciosas permiten estudiar distintos mecanismos que afectan su comportamiento temporal. Este trabajo analizó el efecto sobre la dinámica de la influenza y el virus sincitial respiratorio (VSR) de la disminución de la transmisibilidad debida a las medidas de cuidado adoptadas para reducir la circulación de COVID-19. MÉTODOS Se empleó un modelo determinista tipo SIRS (susceptible-infectado-recuperado-susceptible) con modulación estacional para representar la influenza y el VSR, en ambos casos con inmunidad de corta duración y ciclo anual. Los cambios en la transmisibilidad de la enfermedad se modelaron reduciéndola durante dos años y planteando distintos escenarios. RESULTADOS En el modelo planteado, la reducción en la transmisibilidad genera cambios que se sostienen en los años siguientes: eventos epidémicos muy pronunciados con alargamiento del intervalo interbrote. Este efecto resulta dominante respecto del comportamiento estacional. El escenario de una reducción inicial de la transmisibilidad del 40% resulta compatible con el comportamiento de influenza y VSR reportados actualmente para Argentina. DISCUSIÓN El modelo general propuesto, en condiciones de disminución transitoria en la transmisibilidad, exhibe una epidemiología compatible con la observada recientemente en Argentina para ambas enfermedades e ilustra el modelado como herramienta útil en la comprensión de efectos no intuitivos.

ABSTRACT INTRODUCTION Mathematical models of infectious diseases transmission allow to study different mechanisms which affect their temporal behavior. This work analyzed the impact of the decrease in transmissibility, as a result of measures of personal care adopted to reduce circulation of COVID-19, on the dynamics of influenza and respiratory syncytial virus (RSV). METHODS A deterministic SIRS (susceptible-infected-recovered-susceptible) model with seasonal modulation was used to represent two diseases with short-term immunity and annual cycle: influenza and RSV. Changes in disease transmissibility were modeled by reducing it for two years and analyzing different scenarios. RESULTS In the proposed model, transmissibility reduction brings changes which sustain in the following years: very pronounced epidemic events with lengthening of the inter-outbreak interval. This effect prevails over the seasonal behavior. The scenario of 40% initial reduction in transmissibility is compatible with the behavior of influenza and RSV currently reported in Argentina. DISCUSSION The general model proposed here, under conditions of temporary reduced transmissibility, shows an epidemiology compatible with recently reported data of influenza and RSV in Argentina. This result illustrates modeling as a useful tool to understand non-intuitive effects.

Cell annotation using scRNA-seq data: A protein-protein interaction network approach.

Pathway analysis is an important step in the interpretation of single cell transcriptomic data, as it provides powerful information to detect which cellular processes are active in each individual cell. We have recently developed a protein-protein interaction network-based framework to quantify pluripotency associated pathways from scRNA-seq data. On this occasion, we extend this approach to quantify the activity of a pathway associated with any biological process, or even any list of genes. A systems-level characterization of pathway activities across multiple cell types provides a broadly applicable tool for the analysis of pathways in both healthy and disease conditions. Dysregulated cellular functions are a hallmark of a wide spectrum of human disorders, including cancer and autoimmune diseases. Here, we illustrate our method by analyzing various biological processes in healthy and cancer breast samples. Using this approach we found that tumor breast cells, even when they form a single group in the UMAP space, keep diverse biological programs active in a differentiated manner within the cluster.•We implement a protein-protein interaction network-based approach to quantify the activity of different biological processes.•The methodology can be used for cell annotation in scRNA-seq studies and is freely available as R package.

Mathematical modelling of the impact of COVID-19 care measures on other respiratory diseases / ¿Qué dicen los modelos matemáticos sobre el efecto de las medidas no farmacológicas de cuidado implementadas durante la pandemia por COVID-19 sobre otras enfermedades respiratorias?

INTRODUCTION: Mathematical models of infectious disease transmission allow to study different mechanisms which affect the temporal behavior. This work analyzed the impact of the decrease in transmissibility, as a result of measures of personal care adopted to reduce circulation of COVID-19, on the dynamics of influenza and respiratory syncytial virus (RSV). METHODS: A deterministic SIRS (susceptible-infected-recovered-susceptible) model with seasonal modulation was used to represent two diseases with short-term immunity and annual cycle: influenza and RSV. Changes in disease transmissibility were modeled by reducing it for two years and analyzing different scenarios. RESULTS: In this model, transmissibility reduction brings changes which sustain in the following years: very pronounced epidemic events with lengthening of the inter-outbreak interval. This effect prevails over the seasonal behavior. The scenario of 40% initial reduction in transmissibility is compatible with the behavior of influenza and RSV currently reported in Argentina. DISCUSSION: The general model proposed here, under conditions of temporary reduced transmissibility, shows an epidemiology compatible with recently reported data of influenza and RSV in Argentina. This result illustrates modeling as a useful tool to understand non-intuitive effects.

Introducción: Uno de los usos de los modelos matemáticos de la transmisión de enfermedades es el estudio del efecto de diferentes cambios en las condiciones que determinan el comportamiento de las mismas, como la vacunación, las restricciones en la movilidad de las personas o las medidas de cuidado personal. Se sabe que frente a cambios abruptos en los parámetros que representan estas condiciones, los modelos exhiben cambios en la epidemiología, tanto en la magnitud y periodicidad de los brotes como en el perfil etario de la población afectada.  En este trabajo analizamos mediante herramientas de modelado matemático posibles efectos de la pandemia sobre la transmisión de otras enfermedades infecciosas debido a la disminución de la transmisibilidad, como resultado de las medidas de cuidado personal, ventilación y reducción en los contactos sociales adoptados para reducir la circulación de COVID-19. Método: Empleamos un modelo matemático determinista SIRS (susceptible-infectado-recuperado-susceptible) con modulación estacional para representar enfermedades con inmunidad conferida de corta duración y que presentan un ciclo anual. Se utilizaron dos escenarios de parámetros, uno de ellos más apropiado para una enfermedad tipo influenza, con tasa de contagio relativamente baja y con vacuna, y otro más apropiado para una enfermedad tipo virus sincitial respiratorio (VSR), con mayor contagiosidad y sin vacunación. Los cambios en la transmisibilidad de la enfermedad se modelaron reduciéndola durante dos años, planteando distintos escenarios respecto de la reducción de la transmisibilidad. Resultados: La reducción en la transmisibilidad de la enfermedad durante dos años genera cambios en el comportamiento de la enfermedad que se sostienen en los años siguientes: eventos epidémicos pronunciados (que pueden superar los máximos previos) con alargamiento del intervalo interbrote e incluso pérdida del comportamiento estacional típico. Aún en casos en que el inicio de la reducción de la transmisibilidad ocurre en momentos diferentes de un brote (cerca del máximo o cerca del mínimo), su efecto resulta dominante respecto del comportamiento estacional. El escenario de una reducción inicial de la transmisibilidad del 40% resulta compatible con el comportamiento de influenza y VSR reportados actualmente para nuestro país. Discusión: El modelo general propuesto, en determinadas condiciones de baja transitoria en la transmisibilidad, exhibe una epidemiología compatible con la observada recientemente en nuestra región para la influenza y el VSR. Este resultado ilustra el valor del modelado como herramienta útil en la compresión de la transmisión de enfermedades, alertando sobre posibles efectos no intuitivos.

ORIGINS: A protein network-based approach to quantify cell pluripotency from scRNA-seq data.

Trajectory inference is a common application of scRNA-seq data. However, it is often necessary to previously determine the origin of the trajectories, the stem or progenitor cells. In this work, we propose a computational tool to quantify pluripotency from single cell transcriptomics data. This approach uses the protein-protein interaction (PPI) network associated with the differentiation process as a scaffold and the gene expression matrix to calculate a score that we call differentiation activity. This score reflects how active the differentiation network is in each cell. We benchmark the performance of our algorithm with two previously published tools, LandSCENT (Chen et al., 2019) and CytoTRACE (Gulati et al., 2020), for four healthy human data sets: breast, colon, hematopoietic and lung. We show that our algorithm is more efficient than LandSCENT and requires less RAM memory than the other programs. We also illustrate a complete workflow from the count matrix to trajectory inference using the breast data set.•ORIGINS is a methodology to quantify pluripotency from scRNA-seq data implemented as a freely available R package.•ORIGINS uses the protein-protein interaction network associated with differentiation and the data set expression matrix to calculate a score (differentiation activity) that quantifies pluripotency for each cell.

Following the footprints of variability during filopodial growth.

Filopodia are actin-built finger-like dynamic structures that protrude from the cell cortex. These structures can sense the environment and play key roles in migration and cell-cell interactions. The growth-retraction cycle of filopodia is a complex process exquisitely regulated by intra- and extra-cellular cues, whose nature remains elusive. Filopodia present wide variation in length, lifetime and growth rate. Here, we investigate the features of filopodia patterns in fixed prostate tumor cells by confocal microscopy. Analysis of almost a thousand filopodia suggests the presence of two different populations: one characterized by a narrow distribution of lengths and the other with a much more variable pattern with very long filopodia. We explore a stochastic model of filopodial growth which takes into account diffusion and reactions involving actin and the regulatory proteins formin and capping, and retrograde flow. Interestingly, we found an inverse dependence between the filopodial length and the retrograde velocity. This result led us to propose that variations in the retrograde velocity could explain the experimental lengths observed for these tumor cells. In this sense, one population involves a wider range of retrograde velocities than the other population, and also includes low values of this velocity. It has been hypothesized that cells would be able to regulate retrograde flow as a mechanism to control filopodial length. Thus, we propound that the experimental filopodia pattern is the result of differential retrograde velocities originated from heterogeneous signaling due to cell-substrate interactions or prior cell-cell contacts.

Alternating regimes of motion in a model with cell-cell interactions.

Cellular movement is a complex dynamic process, resulting from the interaction of multiple elements at the intra- and extracellular levels. This epiphenomenon presents a variety of behaviors, which can include normal and anomalous diffusion or collective migration. In some cases, cells can get neighborhood information through chemical or mechanical cues. A unified understanding about how such information can influence the dynamics of cell movement is still lacking. In order to improve our comprehension of cell migration we have considered a cellular Potts model where cells move actively in the direction of a driving field. The intensity of this driving field is constant, while its orientation can evolve according to two alternative dynamics based on the Ornstein-Uhlenbeck process. In one case, the next orientation of the driving field depends on the previous direction of the field. In the other case, the direction update considers the mean orientation performed by the cell in previous steps. Thus, the latter update rule mimics the ability of cells to perceive the environment, avoiding obstacles and thus increasing the cellular displacement. Different cell densities are considered to reveal the effect of cell-cell interactions. Our results indicate that both dynamics introduce temporal and spatial correlations in cell velocity in a friction-coefficient and cell-density-dependent manner. Furthermore, we observe alternating regimes in the mean-square displacement, with normal and anomalous diffusion. The crossovers between diffusive and directed motion regimes are strongly affected by both the driving field dynamics and cell-cell interactions. In this sense, when cell polarization update grants information about the previous cellular displacement, the duration of the diffusive regime decreases, particularly in high-density cultures.

Diversity of fate outcomes in cell pairs under lateral inhibition.

Cell fate determination by lateral inhibition via Notch/Delta signalling has been extensively studied. Most formalised models consider Notch/Delta interactions in fields of cells, with parameters that typically lead to symmetry breaking of signalling states between neighbouring cells, commonly resulting in salt-and-pepper fate patterns. Here, we consider the case of signalling between isolated cell pairs, and find that the bifurcation properties of a standard mathematical model of lateral inhibition can lead to stable symmetric signalling states. We apply this model to the adult intestinal stem cell (ISC) of Drosophila, the fate of which is stochastic but dependent on the Notch/Delta pathway. We observe a correlation between signalling state in cell pairs and their contact area. We interpret this behaviour in terms of the properties of our model in the presence of population variability in contact areas, which affects the effective signalling threshold of individual cells. Our results suggest that the dynamics of Notch/Delta signalling can contribute to explain stochasticity in stem cell fate decisions, and that the standard model for lateral inhibition can account for a wider range of developmental outcomes than previously considered.

Pinning-depinning transition in a stochastic growth model for the evolution of cell colony fronts in a disordered medium.

We study a stochastic lattice model for cell colony growth, which takes into account proliferation, diffusion, and rotation of cells, in a culture medium with quenched disorder. The medium is composed of sites that inhibit any possible change in the internal state of the cells, representing the disorder, as well as by active medium sites that do not interfere with the cell dynamics. By means of Monte Carlo simulations we find that the velocity of the growing interface, which is taken as the order parameter of the model, strongly depends on the density of active medium sites (ρ_{A}). In fact, the model presents a (continuous) second-order pinning-depinning transition at a certain critical value of ρ_{A}^{crit}, such as, for ρ_{A}>ρ_{A}^{crit}, the interface moves freely across the disordered medium, but for ρ_{A}<ρ_{A}^{crit} the interface becomes irreversible pinned by the disorder. By determining the relevant critical exponents, our study reveals that within the depinned phase the interface can be rationalized in terms of the Kardar-Parisi-Zhang universality class, but when approaching the critical threshold, the nonlinear term of the Kardar-Parisi-Zhang equation tends to vanish and then the pinned interface belongs to the quenched Edwards-Wilkinson universality class.

Abortive and propagating intracellular calcium waves: analysis from a hybrid model.

The functional properties of inositol(1,4,5)-triphosphate (IP3) receptors allow a variety of intracellular Ca(2+) phenomena. In this way, global phenomena, such as propagating and abortive Ca(2+) waves, as well as local events such as puffs, have been observed. Several experimental studies suggest that many features of global phenomena (e.g., frequency, amplitude, speed wave) depend on the interplay of biophysical processes such as diffusion, buffering, efflux and influx rates, which in turn depend on parameters such as buffer concentration, Ca(2+) pump density, cytosolic IP3 level, and intercluster distance. Besides, it is known that cells are able to modify some of these parameters in order to regulate the Ca(2+) signaling. By using a hybrid model, we analyzed different features of the hierarchy of calcium events as a function of two relevant parameters for the calcium signaling, the intercluster distance and the pump strength or intensity. In the space spanned by these two parameters, we found two modes of calcium dynamics, one dominated by abortive calcium waves and the other by propagating waves. Smaller distances between the release sites promote propagating calcium waves, while the increase of the efflux rate makes the transition from propagating to abortive waves occur at lower values of intercluster distance. We determined the frontier between these two modes, in the parameter space defined by the intercluster distance and the pump strength. Furthermore, we found that the velocity of simulated calcium waves accomplishes Luther's law, and that an effective rate constant for autocatalytic calcium production decays linearly with both the intercluster distance and the pump strength.

Phase diagram of a cyclic predator-prey model with neutral-pair exchange.

In this paper we obtain the phase diagram of a four-species predator-prey lattice model by using the proposed gradient method. We consider cyclic transitions between consecutive states, representing invasion or predation, and allowed the exchange between neighboring neutral pairs. By applying a gradient in the invasion rate parameter one can see, in the same simulation, the presence of two symmetric absorbing phases, composed by neutral pairs, and an active phase that includes all four species. In this sense, the study of a single-valued interface and its fluctuations give the critical point of the irreversible phase transition and the corresponding universality classes. Also, the consideration of a multivalued interface and its fluctuations bring the percolation threshold. We show that the model presents two lines of irreversible first-order phase transition between the two absorbing phases and the active phase. Depending on the value of the system parameters, these lines can converge into a triple point, which is the beginning of a first-order irreversible line between the two absorbing phases, or end in two critical points belonging to the directed percolation universality class. Standard simulations for some characteristic values of the parameters confirm the order of the transitions as determined by the gradient method. Besides, below the triple point the model presents two standard percolation lines in the active phase and above a first-order percolation transition as already found in other similar models.

Phase diagram and critical behavior of a forest-fire model in a gradient of immunity.

The forest-fire model with immune trees (FFMIT) is a cellular automaton early proposed by Drossel and Schwabl [Physica A 199, 183 (1993)], in which each site of a lattice can be in three possible states: occupied by a tree, empty, or occupied by a burning tree (fire). The trees grow at empty sites with probability p, healthy trees catch fire from adjacent burning trees with probability (1-g), where g is the immunity, and a burning tree becomes an empty site spontaneously. In this paper we study the FFMIT by means of the recently proposed gradient method (GM), considering the immunity as a uniform gradient along the horizontal axis of the lattice. The GM allows the simultaneous treatment of both the active and the inactive phases of the model in the same simulation. In this way, the study of a single-valued interface gives the critical point of the active-absorbing transition, whereas the study of a multivalued interface brings the percolation threshold into the active phase. Therefore we present a complete phase diagram for the FFMIT, for all range of p, where, besides the usual active-absorbing transition of the model, we locate a transition between the active percolating and the active nonpercolating phases. The average location and the width of both interfaces, as well as the absorbing and percolating cluster densities, obey a scaling behavior that is governed by the exponent α=1/(1+ν), where ν is the suitable correlation length exponent (ν(⊥) for the directed percolation transition and ν for the standard percolation transition). We also show that the GM allows us to calculate the critical exponents associated with both the order parameter of the absorbing transition and the number of particles in the multivalued interface. Besides, we show that by using the gradient method, the collapse in a single curve of cluster densities obtained for samples of different side is a very sensitive method in order to obtain the critical points and the percolation thresholds.

Proposal and applications of a method for the study of irreversible phase transitions.

The gradient method for the study of irreversible phase transitions in far-from-equilibrium lattice systems is proposed and successfully applied to both the archetypical case of the Ziff-Gulari-Barshad model [R. M. Ziff, Phys. Rev. Lett. 56, 2553 (1986)] and a forest-fire cellular automaton. By setting a gradient of the control parameter along one axis of the lattice, one can simultaneously treat both the active and the inactive phases of the system. In this way different interfaces are defined whose study allows us to find the active-inactive phase transition (both of first and second order), as well as the description of the active phase as composed of two further phases: the percolating and the nonpercolating ones. The average location and the width of the interfaces obey standard scaling behavior that is essentially governed by the roughness exponent alpha=1/(1+nu) , where nu is the suitable correlation length exponent.

Hydrophobic hydration in an orientational lattice model.

To shed light on the microscopic mechanism of hydrophobic hydration, we study a simplified lattice model for water solutions in which the orientational nature of hydrogen bonding as well as the degeneracy related to proton distribution are taken into account. Miscibility properties of the model are looked at for both polar (hydrogen bonding) and nonpolar (non-hydrogen bonding) solutes. A quasichemical solution for the pure system is reviewed and extended to include the different kinds of solute. A Monte Carlo study of our model yields a novel feature for the local structure of the hydration layer: energy correlation relaxation times for solvation water are larger than the corresponding relaxation times for bulk water. This result suggests the presence of ordering of water particles in the first hydration shell. A nonassociating model solvent, represented by a lattice gas, presents opposite behavior, indicating that this effect is a result of the directionality of the interaction. In presence of polar solutes, we find an ordered mixed pseudophase at low temperatures, indicating the possibility of closed loops of immiscibility.

Calcium dynamics on a stochastic reaction-diffusion lattice model.

We study a stochastic reaction-diffusion lattice model for describing the calcium dynamics in the endoplasmic reticulum (ER) membrane. Calcium channels and calcium ions are placed in two interpenetrating square lattices which are connected by calcium release and diffusion. Calcium ions are released from the ER through the channels and they can both remain in the membrane or spontaneously leave the membrane into the cytosol. The state of the channel is modulated by calcium ions: a channel can be open, closed, or inactive. The model is studied by numerical simulations and mean field theory and exhibits a phase transition from an active state to an absorbing state which is the result of the catalytic calcium release. The critical behavior of the model is in the directed percolation universality class.

Lattice model for calcium dynamics.

We present a simplified lattice model to study calcium dynamics in the endoplasmic reticulum membrane. Calcium channels and calcium ions are placed in two interpenetrating square lattices which are connected in two ways: (i) via calcium release and (ii) because transitions between channel states are calcium dependent. The opening or closing of a channel is a stochastic process controlled by two functions which depend on the calcium density on the channel neighborhood. The model is studied through mean field calculations and simulations. We show that the critical behavior of the model changes drastically depending on the opening/closing functions. For certain choices of these functions, all channels are closed at very low and high calcium densities and the model presents one absorbing state.