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Adjuvanted influenza vaccines constitute a key element towards inducing neutralizing antibody responses in populations with reduced responsiveness, such as infants and elderly subjects, as well as in devising antigen-sparing strategies. In particular, squalene-containing adjuvants have been observed to induce enhanced antibody responses, as well as having an influence on cross-reactive immunity. To explore the effects of adjuvanted vaccine formulations on antibody response and their relation to protein-specific immunity, we propose different mathematical models of antibody production dynamics in response to influenza vaccination. Data from ferrets immunized with commercial H1N1pdm09 vaccine antigen alone or formulated with different adjuvants was instrumental to adjust model parameters. While the affinity maturation process complexity is abridged, the proposed model is able to recapitulate the essential features of the observed dynamics. Our numerical results suggest that there exists a qualitative shift in protein-specific antibody response, with enhanced production of antibodies targeting the NA protein in adjuvanted versus non-adjuvanted formulations, in conjunction with a protein-independent boost that is over one order of magnitude larger for squalene-containing adjuvants. Furthermore, simulations predict that vaccines formulated with squalene-containing adjuvants are able to induce sustained antibody titers in a robust way, with little impact of the time interval between immunizations.
Ebola virus (EBOV) infection causes a high death toll, killing a high proportion of EBOV-infected patients within 7 days. Comprehensive data on EBOV infection are fragmented, hampering efforts in developing therapeutics and vaccines against EBOV. Under this circumstance, mathematical models become valuable resources to explore potential controlling strategies. In this paper, we employed experimental data of EBOV-infected nonhuman primates (NHPs) to construct a mathematical framework for determining windows of opportunity for treatment and vaccination. Considering a prophylactic vaccine based on recombinant vesicular stomatitis virus expressing the EBOV glycoprotein (rVSV-EBOV), vaccination could be protective if a subject is vaccinated during a period from one week to four months before infection. For the case of a therapeutic vaccine based on monoclonal antibodies (mAbs), a single dose might resolve the invasive EBOV replication even if it was administrated as late as four days after infection. Our mathematical models can be used as building blocks for evaluating therapeutic and vaccine modalities as well as for evaluating public health intervention strategies in outbreaks. Future laborator experiments will help to validate and refine the estimates of the windows of opportunity proposed here.
Motivation: Partial differential equations (PDEs) is a well-established and powerful tool to simulate multi-cellular biological systems. However, available free tools for validation against data are not established. The PDEparams module provides flexible functionality in Python for parameter estimation in PDE models.
Results: The PDEparams module provides a flexible interface and readily accommodates different parameter analysis tools in PDE models such as computation of likelihood profiles, and parametric boot-strapping, along with direct visualisation of the results. To our knowledge, it is the first open, freely available tool for parameter fitting of PDE models.
Availability and implementation: The PDEparams module is distributed under the MIT license. The source code, usage instructions and step-by-step examples are freely available on GitHub at github.com/systemsmedicine/PDE_params.
From August to November 2017, Madagascar endured an outbreak of plague. A total of 2417 cases of plague were confirmed, causing a death toll of 209. Public health intervention efforts were introduced and successfully stopped the epidemic at the end of November. The plague, however, is endemic in the region and occurs annually, posing the risk of future outbreaks. To understand the plague transmission, we collected real-time data from official reports, described the outbreak's characteristics, and estimated transmission parameters using statistical and mathematical models. The pneumonic plague epidemic curve exhibited multiple peaks, coinciding with sporadic introductions of new bubonic cases. Optimal climate conditions for rat flea to flourish were observed during the epidemic. Estimate of the plague basic reproduction number during the large wave of the epidemic was high, ranging from 5 to 7 depending on model assumptions. The incubation and infection periods for bubonic and pneumonic plague were 4.3 and 3.4 days and 3.8 and 2.9 days, respectively. Parameter estimation suggested that even with a small fraction of the population exposed to infected rat fleas (1/10,000) and a small probability of transition from a bubonic case to a secondary pneumonic case (3%), the high human-to-human transmission rate can still generate a large outbreak. Controlling rodent and fleas can prevent new index cases, but managing human-to-human transmission is key to prevent large-scale outbreaks.
Abstract
Co-infections by multiple pathogens have important implications in many aspects of health, epidemiology and evolution. However, how to disentangle the contributing factors of the immune response when two infections take place at the same time is largely unexplored. Using data sets of the immune response during influenza-pneumococcal co-infection in mice, we employ here topological data analysis to simplify and visualise high dimensional data sets.
We identified persistent shapes of the simplicial complexes of the data in the three infection scenarios: single viral infection, single bacterial infection, and co-infection. The immune response was found to be distinct for each of the infection scenarios and we uncovered that the immune response during the co-infection has three phases and two transition points. During the first phase, its dynamics is inherited from its response to the primary (viral) infection. The immune response has an early (few hours post co-infection) and then modulates its response to finally react against the secondary (bacterial) infection. Between 18 to 26 hours post co-infection the nature of the immune response changes again and does no longer resembles either of the single infection scenarios.
Author summary
The mapper algorithm is a topological data analysis technique used for the qualitative analysis, simplification and visualisation of high dimensional data sets. It generates a low-dimensional image that captures topological and geometric information of the data set in high dimensional space, which can highlight groups of data points of interest and can guide further analysis and quantification.
To understand how the immune system evolves during the co-infection between viruses and bacteria, and the role of specific cytokines as contributing factors for these severe infections, we use Topological Data Analysis (TDA) along with an extensive semi-unsupervised parameter value grid search, and k-nearest neighbour analysis.
We find persistent shapes of the data in the three infection scenarios, single viral and bacterial infections and co-infection. The immune response is shown to be distinct for each of the infections scenarios and we uncover that the immune response during the co-infection has three phases and two transition points, a previously unknown property regarding the dynamics of the immune response during co-infection.
Stockpiling neuraminidase inhibitors (NAIs) such as oseltamivir and zanamivir is part of a global effort to be prepared for an influenza pandemic. However, the contribution of NAIs for treatment and prevention of influenza and its complications is largely debatable. Here, we developed a transparent mathematical modelling setting to analyse the impact of NAIs on influenza disease at within-host and population level. Analytical and simulation results indicate that even assuming unrealistically high efficacies for NAIs, drug intake starting on the onset of symptoms has a negligible effect on an individual's viral load and symptoms score. Increasing NAIs doses does not provide a better outcome as is generally believed. Considering Tamiflu's pandemic regimen for prophylaxis, different multiscale simulation scenarios reveal modest reductions in epidemic size despite high investments in stockpiling. Our results question the use of NAIs in general to treat influenza as well as the respective stockpiling by regulatory authorities.
The successful elimination of bacteria such as Streptococcus pneumoniae from a host involves the coordination between different parts of the immune system. Previous studies have explored the effects of the initial pneumococcal load (bacterial dose) on different representations of innate immunity, finding that pathogenic outcomes can vary with the size of the bacterial dose. However, others yield support to the notion of dose-independent factors contributing to bacterial clearance. In this paper, we seek to provide a deeper understanding of the immune responses associated to the pneumococcus. To this end, we formulate a model that realizes an abstraction of the innate-regulatory immune host response. Stability and bifurcation analyses of the model reveal the following trichotomy of pneumococcal outcomes determined by the bifurcation parameters: (i) dose-independent clearance; (ii) dose-independent persistence; and (iii) dose-limited clearance. Bistability, where the bacteria-free equilibrium co-stabilizes with the most substantial steady-state bacterial load is the specific result behind dose-limited clearance. The trichotomy of pneumococcal outcomes here described integrates all previously observed bacterial fates into a unified framework.
COVID-19 pandemic is a major public health threat with unanswered questions regarding the role of the immune system in the severity level of the disease. In this paper, based on antibody kinetic data of patients with different disease severity, topological data analysis highlights clear differences in the shape of antibody dynamics between three groups of patients, which were non-severe, severe, and one intermediate case of severity. Subsequently, different mathematical models were developed to quantify the dynamics between the different severity groups. The best model was the one with the lowest media value of Akaike Information Criterion for all groups of patients. Although it has been reported high IgG level in severe patients, our findings suggest that IgG antibodies in severe patients may be less effective than non-severe patients due to early B cell production and early activation of the seroconversion process from IgM to IgG antibody.
Untangling the cell immune response dynamic for severe and critical cases of SARS-CoV-2 infection
(2021)
COVID-19 is a global pandemic leading high death tolls worldwide day by day. Clinical evidence suggests that COVID-19 patients can be classified as non-severe, severe and critical cases. In particular, studies have highlighted the relationship between the lymphopenia and the severity of the illness, where CD8+ T cells have the lowest levels in critical cases. In this work, we aim to elucidate the key parameters that define the course of the disease deviating from severe to critical case. To this end, several mathematical models are proposed to represent the dynamic of the immune response in patients with SARS-CoV-2 infection. The best model had a good fit to reported experimental data, and in accordance with values found in the literature. Our results suggest that a rapid proliferation of CD8+ T cells is decisive in the severity of the disease.
We propose a generalized modeling framework for the kinetic mechanisms of transcriptional riboswitches. The formalism accommodates time-dependent transcription rates and changes of metabolite concentration and permits incorporation of variations in transcription rate depending on transcript length. We derive explicit analytical expressions for the fraction of transcripts that determine repression or activation of gene expression, pause site location and its slowing down of transcription for the case of the (2’dG)-sensing riboswitch from Mesoplasma florum. Our modeling challenges the current view on the exclusive importance of metabolite binding to transcripts containing only the aptamer domain. Numerical simulations of transcription proceeding in a continuous manner under time-dependent changes of metabolite concentration further suggest that rapid modulations in concentration result in a reduced dynamic range for riboswitch function regardless of transcription rate, while a combination of slow modulations and small transcription rates ensures a wide range of finely tuneable regulatory outcomes.
Bacteria of the genera Photorhabdus and Xenorhabdus produce a plethora of natural products to support their similar symbiotic lifecycles. For many of these compounds, the specific bioactivities are unknown. One common challenge in natural product research when trying to prioritize research efforts is the rediscovery of identical (or highly similar) compounds from different strains. Linking genome sequence to metabolite production can help in overcoming this problem. However, sequences are typically not available for entire collections of organisms. Here we perform a comprehensive metabolic screening using HPLC-MS data associated with a 114-strain collection (58 Photorhabdus and 56 Xenorhabdus) from across Thailand and explore the metabolic variation among the strains, matched with several abiotic factors. We utilize machine learning in order to rank the importance of individual metabolites in determining all given metadata. With this approach, we were able to prioritize metabolites in the context of natural product investigations, leading to the identification of previously unknown compounds. The top three highest-ranking features were associated with Xenorhabdus and attributed to the same chemical entity, cyclo(tetrahydroxybutyrate). This work addresses the need for prioritization in high-throughput metabolomic studies and demonstrates the viability of such an approach in future research.
COVID-19 pandemic has underlined the impact of emergent pathogens as a major threat for human health. The development of quantitative approaches to advance comprehension of the current outbreak is urgently needed to tackle this severe disease. In this work, several mathematical models are proposed to represent SARS-CoV-2 dynamics in infected patients. Considering different starting times of infection, parameters sets that represent infectivity of SARS-CoV-2 are computed and compared with other viral infections that can also cause pandemics.
Based on the target cell model, SARS-CoV-2 infecting time between susceptible cells (mean of 30 days approximately) is much slower than those reported for Ebola (about 3 times slower) and influenza (60 times slower). The within-host reproductive number for SARS-CoV-2 is consistent to the values of influenza infection (1.7-5.35). The best model to fit the data was including immune responses, which suggest a slow cell response peaking between 5 to 10 days post onset of symptoms. The model with eclipse phase, time in a latent phase before becoming productively infected cells, was not supported. Interestingly, both, the target cell model and the model with immune responses, predict that virus may replicate very slowly in the first days after infection, and it could be below detection levels during the first 4 days post infection. A quantitative comprehension of SARS-CoV-2 dynamics and the estimation of standard parameters of viral infections is the key contribution of this pioneering work.
Antimicrobial resistance is a major threat to global health and food security today. Scheduling cycling therapies by targeting phenotypic states associated to specific mutations can help us to eradicate pathogenic variants in chronic infections. In this paper, we introduce a logistic switching model in order to abstract mutation networks of collateral resistance. We found particular conditions for which unstable zero-equilibrium of the logistic maps can be stabilized through a switching signal. That is, persistent populations can be eradicated through tailored switching regimens.
Starting from an optimal-control formulation, the switching policies show their potential in the stabilization of the zero-equilibrium for dynamics governed by logistic maps. However, employing such switching strategies, deserve a specific characterization in terms of limit behaviour. Ultimately, we use evolutionary and control algorithms to find either optimal and sub-optimal switching policies. Simulations results show the applicability of Parrondo’s Paradox to design cycling therapies against drug resistance.
Tracking influenza a virus infection in the lung from hematological data with machine learning
(2022)
The tracking of pathogen burden and host responses with minimal-invasive methods during respiratory infections is central for monitoring disease development and guiding treatment decisions. Utilizing a standardized murine model of respiratory Influenza A virus (IAV) infection, we developed and tested different supervised machine learning models to predict viral burden and immune response markers, i.e. cytokines and leukocytes in the lung, from hematological data. We performed independently in vivo infection experiments to acquire extensive data for training and testing purposes of the models. We show here that lung viral load, neutrophil counts, cytokines like IFN-γ and IL-6, and other lung infection markers can be predicted from hematological data. Furthermore, feature analysis of the models shows that blood granulocytes and platelets play a crucial role in prediction and are highly involved in the immune response against IAV. The proposed in silico tools pave the path towards improved tracking and monitoring of influenza infections and possibly other respiratory infections based on minimal-invasively obtained hematological parameters.