Modeling transcriptional regulation of the cell cycle using a novel cybernetic-inspired approach.

Quantitative understanding of cellular processes, such as cell cycle and differentiation, is impeded by various forms of complexity ranging from myriad molecular players and their multilevel regulatory interactions, cellular evolution with multiple intermediate stages, lack of elucidation of cause-effect relationships among the many system players, and the computational complexity associated with the profusion of variables and parameters. In this paper, we present a modeling framework based on the cybernetic concept that biological regulation is inspired by objectives embedding rational strategies for dimension reduction, process stage specification through the system dynamics, and innovative causal association of regulatory events with the ability to predict the evolution of the dynamical system. The elementary step of the modeling strategy involves stage-specific objective functions that are computationally determined from experiments, augmented with dynamical network computations involving endpoint objective functions, mutual information, change-point detection, and maximal clique centrality. We demonstrate the power of the method through application to the mammalian cell cycle, which involves thousands of biomolecules engaged in signaling, transcription, and regulation. Starting with a fine-grained transcriptional description obtained from RNA sequencing measurements, we develop an initial model, which is then dynamically modeled using the cybernetic-inspired method, based on the strategies described above. The cybernetic-inspired method is able to distill the most significant interactions from a multitude of possibilities. In addition to capturing the complexity of regulatory processes in a mechanistically causal and stage-specific manner, we identify the functional network modules, including novel cell cycle stages. Our model is able to predict future cell cycles consistent with experimental measurements. We posit that this innovative framework has the promise to extend to the dynamics of other biological processes, with a potential to provide novel mechanistic insights.

A comprehensive modeling approach for polymorph selection in Lennard-Jones crystallization.

Computational predictions of the polymorphic outcomes of a crystallization process, referred to as polymorph selection, can accelerate the process development for manufacturing solid products with targeted properties. Polymorph selection requires understanding the interplay between the thermodynamic and kinetic factors that drive nucleation. Moreover, post-nucleation events, such as crystal growth and polymorphic transformation, can affect the resulting crystal structures. Here, the nucleation kinetics of the Lennard-Jones (LJ) fluid from the melt is investigated with a focus on the competition between FCC and HCP crystal structures. Both molecular dynamics (MD) simulations and 2D free energy calculations reveal that polymorph selection occurs not during nucleation but when the cluster sizes exceed the critical cluster size. This result contrasts with the classical nucleation mechanism, where each polymorph is assumed to nucleate independently as an ideal bulk-like cluster, comprised only of its given structure. Using the 2D free energy surface and the MD simulation-derived diffusion coefficients, a structure-dependent nucleation rate is estimated, which agrees with the rate obtained from brute force MD simulations. Furthermore, a comprehensive population balance modeling (PBM) approach for polymorph selection is proposed. The PBM combines the calculated nucleation rate with post-nucleation kinetics while accounting for the structural changes of the clusters after nucleation. When applied to the LJ system, the PBM predicts with high accuracy the polymorphic distribution found in a population of crystals generated from MD simulations. Due to the non-classical nucleation mechanism of the LJ system, post-nucleation kinetic events are crucial in determining the structures of the grown crystals.

Brownian bridges for stochastic chemical processes-An approximation method based on the asymptotic behavior of the backward Fokker-Planck equation.

A Brownian bridge is a continuous random walk conditioned to end in a given region by adding an effective drift to guide paths toward the desired region of phase space. This idea has many applications in chemical science where one wants to control the endpoint of a stochastic process-e.g., polymer physics, chemical reaction pathways, heat/mass transfer, and Brownian dynamics simulations. Despite its broad applicability, the biggest limitation of the Brownian bridge technique is that it is often difficult to determine the effective drift as it comes from a solution of a Backward Fokker-Planck (BFP) equation that is infeasible to compute for complex or high-dimensional systems. This paper introduces a fast approximation method to generate a Brownian bridge process without solving the BFP equation explicitly. Specifically, this paper uses the asymptotic properties of the BFP equation to generate an approximate drift and determine ways to correct (i.e., re-weight) any errors incurred from this approximation. Because such a procedure avoids the solution of the BFP equation, we show that it drastically accelerates the generation of conditioned random walks. We also show that this approach offers reasonable improvement compared to other sampling approaches using simple bias potentials.

Computational analysis of a 9D model for a small DRG neuron.

Small dorsal root ganglion (DRG) neurons are primary nociceptors which are responsible for sensing pain. Elucidation of their dynamics is essential for understanding and controlling pain. To this end, we present a numerical bifurcation analysis of a small DRG neuron model in this paper. The model is of Hodgkin-Huxley type and has 9 state variables. It consists of a Nav1.7 and a Nav1.8 sodium channel, a leak channel, a delayed rectifier potassium, and an A-type transient potassium channel. The dynamics of this model strongly depend on the maximal conductances of the voltage-gated ion channels and the external current, which can be adjusted experimentally. We show that the neuron dynamics are most sensitive to the Nav1.8 channel maximal conductance ([Formula: see text]). Numerical bifurcation analysis shows that depending on [Formula: see text] and the external current, different parameter regions can be identified with stable steady states, periodic firing of action potentials, mixed-mode oscillations (MMOs), and bistability between stable steady states and stable periodic firing of action potentials. We illustrate and discuss the transitions between these different regimes. We further analyze the behavior of MMOs. As the external current is decreased, we find that MMOs appear after a cyclic limit point. Within this region, bifurcation analysis shows a sequence of isolated periodic solution branches with one large action potential and a number of small amplitude peaks per period. For decreasing external current, the number of small amplitude peaks is increasing and the distance between the large amplitude action potentials is growing, finally tending to infinity and thereby leading to a stable steady state. A closer inspection reveals more complex concatenated MMOs in between these periodic MMO branches, forming Farey sequences. Lastly, we also find small solution windows with aperiodic oscillations which seem to be chaotic. The dynamical patterns found here-as consequences of bifurcation points regulated by different parameters-have potential translational significance as repetitive firing of action potentials imply pain of some form and intensity; manipulating these patterns by regulating the different parameters could aid in investigating pain dynamics.

Exact sampling of polymer conformations using Brownian bridges.

The equilibrium conformation of a polymer molecule in an external field is often used in field theories to calculate macroscopic polymer properties of melts and solutions. We use a mathematical method called a Brownian bridge to exactly sample continuous polymer chains to end in a given state. We show that one can systematically develop such processes to sample specific polymer topologies, to confine polymers in a given geometry for its entire path, to efficiently generate high-probability conformations by excluding small Boltzmann weights, or to simulate rare events in a rugged energy landscape. This formalism can improve the polymer sampling efficiency significantly compared to traditional methods (e.g., Monte Carlo or Rosenbluth).

Sequential computation of elementary modes and minimal cut sets in genome-scale metabolic networks using alternate integer linear programming.

MOTIVATION: Elementary (flux) modes (EMs) have served as a valuable tool for investigating structural and functional properties of metabolic networks. Identification of the full set of EMs in genome-scale networks remains challenging due to combinatorial explosion of EMs in complex networks. It is often, however, that only a small subset of relevant EMs needs to be known, for which optimization-based sequential computation is a useful alternative. Most of the currently available methods along this line are based on the iterative use of mixed integer linear programming (MILP), the effectiveness of which significantly deteriorates as the number of iterations builds up. To alleviate the computational burden associated with the MILP implementation, we here present a novel optimization algorithm termed alternate integer linear programming (AILP). RESULTS: Our algorithm was designed to iteratively solve a pair of integer programming (IP) and linear programming (LP) to compute EMs in a sequential manner. In each step, the IP identifies a minimal subset of reactions, the deletion of which disables all previously identified EMs. Thus, a subsequent LP solution subject to this reaction deletion constraint becomes a distinct EM. In cases where no feasible LP solution is available, IP-derived reaction deletion sets represent minimal cut sets (MCSs). Despite the additional computation of MCSs, AILP achieved significant time reduction in computing EMs by orders of magnitude. The proposed AILP algorithm not only offers a computational advantage in the EM analysis of genome-scale networks, but also improves the understanding of the linkage between EMs and MCSs. AVAILABILITY AND IMPLEMENTATION: The software is implemented in Matlab, and is provided as supplementary information . CONTACT: hyunseob.song@pnnl.gov. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Nanocrystal Dissolution Kinetics and Solubility Increase Prediction from Molecular Dynamics: The Case of α-, ß-, and γ-Glycine.

Nanocrystals are receiving increased attention for pharmaceutical applications due to their enhanced solubility relative to their micron-sized counterpart and, in turn, potentially increased bioavailability. In this work, a computational method is proposed to predict the following: (1) polymorph specific dissolution kinetics and (2) the multiplicative increase in the polymorph specific nanocrystal solubility relative to the bulk solubility. The method uses a combination of molecular dynamics and a parametric particle size dependent mass transfer model. The method is demonstrated using a case study of α-, ß-, and γ-glycine. It is shown that only the α-glycine form is predicted to have an increasing dissolution rate with decreasing particle size over the range of particle sizes simulated. On the contrary, γ-glycine shows a monotonically increasing dissolution rate with increasing particle size and dissolves at a rate 1.5 to 2 times larger than α- or ß-glycine. The accelerated dissolution rate of γ-glycine relative to the other two polymorphs correlates directly with the interfacial energy ranking of γ > ß > α obtained from the dissolution simulations, where γ- is predicted to have an interfacial energy roughly four times larger than either α- or ß-glycine. From the interfacial energies, α- and ß-glycine nanoparticles were predicted to experience modest solubility increases of up to 1.4 and 1.8 times the bulk solubility, where as γ-glycine showed upward of an 8 times amplification in the solubility. These MD simulations represent a first attempt at a computational (pre)screening method for the rational design of experiments for future engineering of nanocrystal API formulations.

Solubility curves and nucleation rates from molecular dynamics for polymorph prediction - moving beyond lattice energy minimization.

Current polymorph prediction methods, known as lattice energy minimization, seek to determine the crystal lattice with the lowest potential energy, rendering it unable to predict solvent dependent metastable form crystallization. Facilitated by embarrassingly parallel, multiple replica, large-scale molecular dynamics simulations, we report on a new method concerned with predicting crystal structures using the kinetics and solubility of the low energy polymorphs predicted by lattice energy minimization. The proposed molecular dynamics simulation methodology provides several new predictions to the field of crystallization. (1) The methodology is shown to correctly predict the kinetic preference for ß-glycine nucleation in water relative to α- and γ-glycine. (2) Analysis of nanocrystal melting temperatures show γ- nanocrystals have melting temperatures up to 20 K lower than either α- or ß-glycine. This provides a striking explanation of how an energetically unstable classical nucleation theory (CNT) transition state complex leads to kinetic inaccessibility of γ-glycine in water, despite being the thermodynamically preferred polymorph predicted by lattice energy minimization. (3) The methodology also predicts polymorph-specific solubility curves, where the α-glycine solubility curve is reproduced to within 19% error, over a 45 K temperature range, using nothing but atomistic-level information provided from nucleation simulations. (4) Finally, the methodology produces the correct solubility ranking of ß- > α-glycine. In this work, we demonstrate how the methodology supplements lattice energy minimization with molecular dynamics nucleation simulations to give the correct polymorph prediction, at different length scales, when lattice energy minimization alone would incorrectly predict the formation of γ-glycine in water from the ranking of lattice energies. Thus, lattice energy minimization optimization algorithms are supplemented with the necessary solvent/solute dependent solubility and nucleation kinetics of polymorphs to predict which structure will come out of solution, and not merely which structure has the most stable lattice energy.

Antagonistic self-sensing and mate-sensing signaling controls antibiotic-resistance transfer.

Conjugation is one of the most common ways bacteria acquire antibiotic resistance, contributing to the emergence of multidrug-resistant "superbugs." Bacteria of the genus Enterococcus faecalis are highly antibiotic-resistant nosocomial pathogens that use the mechanism of conjugation to spread antibiotic resistance between resistance-bearing donor cells and resistance-deficient recipient cells. Here, we report a unique quorum sensing-based communication system that uses two antagonistic signaling molecules to regulate conjugative transfer of tetracycline-resistance plasmid pCF10 in E. faecalis. A "mate-sensing" peptide sex pheromone produced by recipient cells is detected by donor cells to induce conjugative genetic transfer. Using mathematical modeling and experimentation, we show that a second antagonistic "self-sensing" signaling peptide, previously known to suppress self-induction of donor cells, also serves as a classic quorum-sensing signal for donors that functions to reduce antibiotic-resistance transfer at high donor density. This unique form of quorum sensing may provide a means of limiting the spread of the plasmid and present opportunities to control antibiotic-resistance transfer through manipulation of intercellular signaling, with implications in the clinical setting.

On speeding up stochastic simulations by parallelization of random number generation.

This paper adds to the tool kit of stochastic simulations based on a very simple idea. Applicable to both SSA and Tau-leap algorithms, it can notably reduce computational times. Stochastic simulations are based on computing sample paths based on the generation of random numbers with either exactly stipulated distribution functions as in SSA (Gillespie, 1977) or in the method of interval of quiescence (Shah et al., 1977) or distribution functions featuring approximations designed to promote efficiency (as in Tau-leap algorithms (Cao et al., 2006; Tian and Burrage, 2004; Peng et al., 2007; Gillespie, 2001; Ramkrishna et al., 2014) where a leap condition with the parameter epsilon is used). The usual strategy involves sequential computation of a large number of sample paths over a bounded time interval which is covered by a set of discrete time subintervals obtained by random number generation. The strategy here departs from the foregoing by parallelizing the generation of random subintervals for the set of sample paths until all sample paths have been computed for the stated time interval. The advantage of this procedure lies in the fact that the time for initiation of the random number generator has been notably reduced. Many examples are demonstrated from SSA as well as Tau-leap algorithms to establish that the advantage of the approach is much more than conceptual.

Lipase-catalyzed process for biodiesel production: protein engineering and lipase production.

Biodiesel is an environment-friendly and renewable fuel produced by transesterification of various feedstocks. Although the lipase-catalyzed biodiesel production has many advantages over the conventional alkali catalyzed process, its industrial applications have been limited by high-cost and low-stability of lipase enzymes. This review provides a general overview of the recent advances in lipase engineering, including both protein modification and production. Recent advances in biotechnology such as in protein engineering, recombinant methods and metabolic engineering have been employed but are yet to impact lipase engineering for cost-effective production of biodiesel. A summary of the current challenges and perspectives for potential solutions are also provided.

Convergent transcription confers a bistable switch in Enterococcus faecalis conjugation.

Convergent gene pairs with head-to-head configurations are widespread in both eukaryotic and prokaryotic genomes and are speculated to be involved in gene regulation. Here we present a unique mechanism of gene regulation due to convergent transcription from the antagonistic prgX/prgQ operon in Enterococcus faecalis controlling conjugative transfer of the antibiotic resistance plasmid pCF10 from donor cells to recipient cells. Using mathematical modeling and experimentation, we demonstrate that convergent transcription in the prgX/prgQ operon endows the system with the properties of a robust genetic switch through premature termination of elongating transcripts due to collisions between RNA polymerases (RNAPs) transcribing from opposite directions and antisense regulation between complementary counter-transcripts. Evidence is provided for the presence of truncated RNAs resulting from convergent transcription from both the promoters that are capable of sense-antisense interactions. A mathematical model predicts that both RNAP collision and antisense regulation are essential for a robust bistable switch behavior in the control of conjugation initiation by prgX/prgQ operons. Moreover, given that convergent transcription is conserved across species, the mechanism of coupling RNAP collision and antisense interaction is likely to have a significant regulatory role in gene expression.

Dynamic modeling of aerobic growth of Shewanella oneidensis. Predicting triauxic growth, flux distributions, and energy requirement for growth.

A model-based analysis is conducted to investigate metabolism of Shewanella oneidensis MR-1 strain in aerobic batch culture, which exhibits an intriguing growth pattern by sequentially consuming substrate (i.e., lactate) and by-products (i.e., pyruvate and acetate). A general protocol is presented for developing a detailed network-based dynamic model for S. oneidensis based on the Lumped Hybrid Cybernetic Model (L-HCM) framework. The L-HCM, although developed from only limited data, is shown to accurately reproduce exacting dynamic metabolic shifts, and provide reasonable estimates of energy requirement for growth. Flux distributions in S. oneidensis predicted by the L-HCM compare very favorably with (13)C-metabolic flux analysis results reported in the literature. Predictive accuracy is enhanced by incorporating measurements of only a few intracellular fluxes, in addition to extracellular metabolites. The L-HCM developed here for S. oneidensis is consequently a promising tool for the analysis of intracellular flux distribution and metabolic engineering.

Leveraging mathematical modeling to analyze nonadherence for hydroxyurea therapy in sickle cell disease.

Nonadherence is common in individuals with sickle cell disease (SCD) on hydroxyurea therapy and can be observed with waning improvements in hematologic parameters or biomarkers like mean cell volume and fetal hemoglobin level over time. We modeled the impact of hydroxyurea nonadherence on longitudinal biomarker profiles. We estimated the potential nonadherent days in individuals exhibiting a drop in biomarker levels by modifying the dosing profile using a probabilistic approach. Incorporating additional nonadherence using our approach besides existing ones in the dosing profile improves the model fits. We also studied how different patterns in adherence give rise to various physiological profiles of biomarkers. The key finding is consecutive days of nonadherence are less favorable than when nonadherence is interspersed. These findings improve our understanding of nonadherence and how appropriate intervention strategies can be applied for individuals with SCD susceptible to the severe impacts of nonadherence.

Modeling transcriptional regulation of the cell cycle using a novel cybernetic-inspired approach.

Quantitative understanding of cellular processes, such as cell cycle and differentiation, is impeded by various forms of complexity ranging from myriad molecular players and their multilevel regulatory interactions, cellular evolution with multiple intermediate stages, lack of elucidation of cause-effect relationships among the many system players, and the computational complexity associated with the profusion of variables and parameters. In this paper, we present an elegant modeling framework based on the cybernetic concept that biological regulation is inspired by objectives embedding entirely novel strategies for dimension reduction, process stage specification through the system dynamics, and innovative causal association of regulatory events with the ability to predict the evolution of the dynamical system. The elementary step of the modeling strategy involves stage-specific objective functions that are computationally-determined from experiments, augmented with dynamical network computations involving end point objective functions, mutual information, change point detection, and maximal clique centrality. We demonstrate the power of the method through application to the mammalian cell cycle, which involves thousands of biomolecules engaged in signaling, transcription, and regulation. Starting with a fine-grained transcriptional description obtained from RNA sequencing measurements, we develop an initial model, which is then dynamically modeled using the cybernetic-inspired method (CIM), utilizing the strategies described above. The CIM is able to distill the most significant interactions from a multitude of possibilities. In addition to capturing the complexity of regulatory processes in a mechanistically causal and stage-specific manner, we identify the functional network modules, including novel cell cycle stages. Our model is able to predict future cell cycles consistent with experimental measurements. We posit that this state-of-the-art framework has the promise to extend to the dynamics of other biological processes, with a potential to provide novel mechanistic insights. STATEMENT OF SIGNIFICANCE: Cellular processes like cell cycle are overly complex, involving multiple players interacting at multiple levels, and explicit modeling of such systems is challenging. The availability of longitudinal RNA measurements provides an opportunity to "reverse-engineer" for novel regulatory models. We develop a novel framework, inspired using goal-oriented cybernetic model, to implicitly model transcriptional regulation by constraining the system using inferred temporal goals. A preliminary causal network based on information-theory is used as a starting point, and our framework is used to distill the network to temporally-based networks containing essential molecular players. The strength of this approach is its ability to dynamically model the RNA temporal measurements. The approach developed paves the way for inferring regulatory processes in many complex cellular processes.

Prediction of dynamic behavior of mutant strains from limited wild-type data.

Metabolic engineering is the field of introducing genetic changes in organisms so as to modify their function towards synthesizing new products of high impact to society. However, engineered cells frequently have impaired growth rates thus seriously limiting the rate at which such products are made. The problem is attributable to inadequate understanding of how a metabolic network functions in a dynamic sense. Predictions of mutant strain behavior in the past have been based on steady state theories such as flux balance analysis (FBA), minimization of metabolic adjustment (MOMA), and regulatory on/off minimization (ROOM). Such predictions are restricted to product yields and cannot address productivity, which is of focal interest to applications. We demonstrate that our framework ( [Song and Ramkrishna, 2010] and [Song and Ramkrishna, 2011]), based on a "cybernetic" view of metabolic systems, makes predictions of the dynamic behavior of mutant strains of Escherichia coli from a limited amount of data obtained from the wild-type. Dynamic frameworks must necessarily address the issue of metabolic regulation, which the cybernetic approach does by postulating that metabolism is an optimal dynamic response of the organism to the environment in driving reactions towards ensuring survival. The predictions made in this paper are without parallel in the literature and lay the foundation for rational metabolic engineering.

On enhancing productivity of bioethanol with multiple species.

The present work is initiated to investigate whether a defined culture comprising a mixture of three yeast species, Kluyveromyces marxianus, Saccharomyces cerevisiae, and Pichia stipitis can ferment a mixture of sugars to produce bioethanol at rates higher than those achieved by pure cultures of the same. For this purpose, we develop models of single species based on the hybrid cybernetic model framework, and simulate fermentations in the mixed culture by combining individual models. An underlying assumption is that the behavior of each species is determined only by the common environment independently of the presence and metabolism of other species. Model performance is thoroughly assessed using the experimental data available in the literature. The dynamic behavior of mixed cultures in mixed culture experiments are accurately predicted by the model reflecting faithfully the simultaneous/sequential uptake patterns of mixed substrates. This model is then used to investigate performance of various possible reactor configurations. With the foregoing species of organisms, mixed culture itself does not lead to a significant increase of bioethanol productivity. Rather, the model shows that substantial improvement is acquired by sequential use of different, properly chosen organisms during fermentation. Thus, the successive use of K. marxianus and P. stipitis is shown to increase bioethanol productivity up to about 58% in comparison to fermentation by single species alone.

Bistability versus bimodal distributions in gene regulatory processes from population balance.

In recent times, stochastic treatments of gene regulatory processes have appeared in the literature in which a cell exposed to a signaling molecule in its environment triggers the synthesis of a specific protein through a network of intracellular reactions. The stochastic nature of this process leads to a distribution of protein levels in a population of cells as determined by a Fokker-Planck equation. Often instability occurs as a consequence of two (stable) steady state protein levels, one at the low end representing the "off" state, and the other at the high end representing the "on" state for a given concentration of the signaling molecule within a suitable range. A consequence of such bistability has been the appearance of bimodal distributions indicating two different populations, one in the "off" state and the other in the "on" state. The bimodal distribution can come about from stochastic analysis of a single cell. However, the concerted action of the population altering the extracellular concentration in the environment of individual cells and hence their behavior can only be accomplished by an appropriate population balance model which accounts for the reciprocal effects of interaction between the population and its environment. In this study, we show how to formulate a population balance model in which stochastic gene expression in individual cells is incorporated. Interestingly, the simulation of the model shows that bistability is neither sufficient nor necessary for bimodal distributions in a population. The original notion of linking bistability with bimodal distribution from single cell stochastic model is therefore only a special consequence of a population balance model.

MODELING OF GENE REGULATORY PROCESSES BY POPULATION MEDIATED SIGNALING. NEW APPLICATIONS OF POPULATION BALANCES.

Population balance modeling is considered for cell populations in gene regulatory processes in which one or more intracellular variables undergo stochastic dynamics as determined by Ito stochastic differential equations. This paper addresses formulation and computational issues with sample applications to the spread of drug resistance among bacterial cells. It is shown that predictions from population balances can display qualitative differences from those made with single cell models which are usually encountered in the literature. Such differences are deemed to be important.

Modeling COVID-19 transmission between age groups in the United States considering virus mutations, vaccinations, and reinfection.

The in-depth understanding of the dynamics of COVID-19 transmission among different age groups is of great interest for governments and health authorities so that strategies can be devised to reduce the pandemic's detrimental effects. We developed the SIRDV-Virulence (Susceptible-Infected-Recovered-Dead-Vaccinated-Virulence) epidemiological model based on a population balance equation to study the effects virus mutants, vaccination strategies, 'Anti/Non Vaxxer' proportions, and reinfection rates to provide methods to mitigate COVID-19 transmission among the United States population. Based on publicly available data, we obtain the key parameters governing the spread of the pandemic. The results show that a large fraction of infected cases comes from the adult and children populations in the presence of a highly infectious COVID-19 mutant. Given the situation at the end of July 2021, the results show that prioritizing children and adult vaccinations over that of seniors can contain the spread of the active cases, thereby preventing the healthcare system from being overwhelmed and minimizing subsequent deaths. The model suggests that the only option to curb the effects of this pandemic is to reduce the population of unvaccinated individuals. A higher fraction of 'Anti/Non-vaxxers' and a higher reinfection rate can both independently lead to the resurgence of the pandemic.