Modeling the CD8＋ T cell immune response to influenza infection in adult and aged mice.

The CD8＋ T cell response is the main determinant of viral clearance during influenza infection. However, influenza viral dynamics and the respective immune responses are affected by the host's age. To investigate age-related differences in the CD8＋ T cell immune response dynamics, we propose 16 ordinary differential equation models of existing experimental data. These data consist of viral titer and CD8＋ T cell counts collected periodically over a period of 19 days from adult and aged mice infected with influenza A/Puerto Rico/8/34 (H1N1). We use the corrected Akaike Information Criterion to identify the models which best represent the considered data. Our model selection process indicates differences in mechanisms which reduce the CD8＋ T cell response: linear downregulation is favored for adult mice, while baseline exponential decay is favored for aged mice. Parameter fitting of the top ranked models suggests that the aged population has reduced CD8＋ T cell proliferation compared to the adult population. More experimental work is needed to determine the specific immunological features through which age might cause these differences. A better understanding of the immunological mechanisms by which aging leads to discrepant CD8＋ T cell dynamics may inform future treatment strategies.

Confinement tonicity on epidemic spreading.

Emerging and re-emerging pathogens are latent threats in our society with the risk of killing millions of people worldwide, without forgetting the severe economic and educational backlogs. From COVID-19, we learned that self isolation and quarantine restrictions (confinement) were the main way of protection till availability of vaccines. However, abrupt lifting of social confinement would result in new waves of new infection cases and high death tolls. Here, inspired by how an extracellular solution can make water move into or out of a cell through osmosis, we define confinement tonicity. This can serve as a standalone measurement for the net direction and magnitude of flows between the confined and deconfined susceptible compartments. Numerical results offer insights on the effects of easing quarantine restrictions.

A new computational approach, based on images trajectories, to identify the subjacent heterogeneity of sperm to the effects of ketanserin.

The identification of kinematic subpopulations is of paramount importance to understanding the biological nature of the sperm heterogeneity. Nowadays, the data of motility parameters obtained by a computer-assisted sperm analysis (CASA) system has been used as input to distinct algorithms to identify kinematic subpopulations. In contrast, the images of the trajectories were depicted only as examples of the patterns of motility in each subpopulation. Here, python code was written to reconstruct the images of trajectories, from their coordinates, then the images of trajectories were used as input to a machine learning clustering algorithm of classification, and the subpopulations were described statistically by the motility parameters. Finally, the images of trajectories in each subpopulation were displayed in a way we called Pollock plots. Semen samples of boar sperm were treated with distinct concentrations of ketanserin (an antagonist of the 5-HT2 receptor of serotonin) and untreated samples were used as a control. The motility of sperm in each sample was analyzed at 0 and 30 min of incubation. Six subpopulations were found. The subpopulation 2 presented the highest values of velocities at 0 or 30 min. After 30 min of incubation, the ketanserin increased the values of the curvilinear velocity at high concentrations, whereas the linearity and the straight velocity decreased. Our computational model permits better identification of the kinematic subpopulations than the traditional approach and provides insights onto the heterogeneity of the response to ketanserin; thus, it could significantly impact the research on the relationship between sperm heterogeneity-fertility.

Uncovering antibody cross-reaction dynamics in influenza A infections.

MOTIVATION: Influenza viruses are a cause of large outbreaks and pandemics with high death tolls. A key obstacle is that flu vaccines have inconsistent performance, in the best cases up to 60% effectiveness, but it can be as low as 10%. Uncovering the hidden pathways of how antibodies (Abs) induced by one influenza strain are effective against another, cross-reaction, is a central vexation for the design of universal flu vaccines. RESULTS: We conceive a stochastic model that successfully represents the antibody cross-reactive data from mice infected with H3N2 influenza strains and further validation with cross-reaction data of H1N1 strains. Using a High-Performance Computing cluster, several aspects and parameters in the model were tested. Computational simulations highlight that changes in time of infection and the B-cells population are relevant, however, the affinity threshold of B-cells between consecutive infections is a necessary condition for the successful Abs cross-reaction. Our results suggest a 3-D reformulation of the current influenza antibody landscape for the representation and modeling of cross-reactive data. AVAILABILITY AND IMPLEMENTATION: The full code as a testing/simulation platform is freely available here: https://github.com/systemsmedicine/Antibody_cross-reaction_dynamics. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Minimizing the epidemic final size while containing the infected peak prevalence in SIR systems.

Mathematical models are critical to understand the spread of pathogens in a population and evaluate the effectiveness of non-pharmaceutical interventions (NPIs). A plethora of optimal strategies has been recently developed to minimize either the infected peak prevalence ( I P P ) or the epidemic final size ( E F S ). While most of them optimize a simple cost function along a fixed finite-time horizon, no consensus has been reached about how to simultaneously handle the I P P and the E F S , while minimizing the intervention's side effects. In this work, based on a new characterization of the dynamical behaviour of SIR-type models under control actions (including the stability of equilibrium sets in terms of herd immunity), we study how to minimize the E F S while keeping the I P P controlled at any time. A procedure is proposed to tailor NPIs by separating transient from stationary control objectives: the potential benefits of the strategy are illustrated by a detailed analysis and simulation results related to the COVID-19 pandemic.

PDEparams: parameter fitting toolbox for partial differential equations in python.

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 on development. 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 bootstrapping, along with direct visualization of the results. To our knowledge, it is the first open, freely available tool for parameter fitting of PDE models. AVAILABILITY AND IMPLEMENTATION: PDEparams is distributed under the MIT license. The source code, usage instructions and examples are freely available on GitHub at github.com/systemsmedicine/PDE_params. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Network models to evaluate vaccine strategies towards herd immunity in COVID-19.

Vaccination remains a critical element in the eventual solution to the COVID-19 public health crisis. Many vaccines are already being mass produced and supplied in many countries. However, the COVID-19 vaccination programme will be the biggest in history. Reaching herd immunity will require an unprecedented mass immunisation campaign that will take several months and millions of dollars. Using different network models, COVID-19 pandemic dynamics of different countries can be recapitulated such as in Italy. Stochastic computational simulations highlight that peak epidemic sizes in a population strongly depend on the network structure. Assuming a vaccine efficacy of at least 80% in a mass vaccination program, at least 70% of a given population should be vaccinated to obtain herd immunity, independently of the network structure. If the vaccine efficacy reports lower levels of efficacy in practice, then the coverage of vaccination would be needed to be even higher. Simulations suggest that the "Ring of Vaccination" strategy, vaccinating susceptible contact and contact of contacts, would prevent new waves of COVID -19 meanwhile a high percent of the population is vaccinated.

Stability analysis in COVID-19 within-host model with immune response.

The 2019 coronavirus disease (COVID-19) is now a global pandemic. Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2) is the causative pathogen of COVID-19. Here, we study an in-host model that highlights the effector T cell response to SARS-CoV-2. The stability of a unique positive equilibrium point, with viral load V * , suggests that the virus may replicate fast enough to overcome T cell response and cause infection. This overcoming is the bifurcation point, near which the orders of magnitude for V * can be sensitive to numerical changes in the parameter values. Our work offers a mathematical insight into how SARS-CoV-2 causes the disease.

Dynamical characterization of antiviral effects in COVID-19.

Mathematical models describing SARS-CoV-2 dynamics and the corresponding immune responses in patients with COVID-19 can be critical to evaluate possible clinical outcomes of antiviral treatments. In this work, based on the concept of virus spreadability in the host, antiviral effectiveness thresholds are determined to establish whether or not a treatment will be able to clear the infection. In addition, the virus dynamic in the host - including the time-to-peak and the final monotonically decreasing behavior - is characterized as a function of the time to treatment initiation. Simulation results, based on nine patient data, show the potential clinical benefits of a treatment classification according to patient critical parameters. This study is aimed at paving the way for the different antivirals being developed to tackle SARS-CoV-2.

Quantitative modeling of the function of kinetically driven transcriptional riboswitches.

Riboswitches are cis-acting regulatory mRNA elements in bacteria, that modulate the expression of their associated genes in response to a cognate metabolite, operating either on the level of translation or transcription. Transcriptional riboswitches have to fold into functional structures as they are being synthesized and, only if transcription rates and ligand binding kinetics match, structured transcription intermediates are enabled to undergo ligand-dependent conformational refolding as a prerequisite for ligand-mediated gene expression. Therefore, transcription rates are of essential importance for functional riboswitch-mediated gene regulation. Here, 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 as a function of 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.

In-host Mathematical Modelling of COVID-19 in Humans.

COVID-19 pandemic has underlined the impact of emergent pathogens as a major threat to human health. The development of quantitative approaches to advance comprehension of the current outbreak is urgently needed to tackle this severe disease. Considering different starting times of infection, mathematical models are proposed to represent SARS-CoV-2 dynamics in infected patients. Based on the target cell limited model, the within-host reproductive number for SARS-CoV-2 is consistent with the broad values of human influenza infection. The best model to fit the data was including immune cell response, which suggests a slow immune response peaking between 5 to 10 days post-onset of symptoms. The model with the eclipse phase, time in a latent phase before becoming productively infected cells, was not supported. Interestingly, model simulations predict that SARS-CoV-2 may replicate very slowly in the first days after infection, and viral load 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. These models can serve for future evaluation of control theoretical approaches to tailor new drugs against COVID-19.

Topological data analysis to model the shape of immune responses during co-infections.

Co-infections by multiple pathogens have important implications in many aspects of health, epidemiology and evolution. However, how to disentangle the non-linear dynamics 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 shift (few hours post co-infection) and then modulates its response to react against the secondary (bacterial) infection. Between 18 and 26 h post co-infection the nature of the immune response changes again and does no longer resembles either of the single infection scenarios.

Characterization of SARS-CoV-2 dynamics in the host.

While many epidemiological models were proposed to understand and handle COVID-19 pandemic, too little has been invested to understand human viral replication and the potential use of novel antivirals to tackle the infection. In this work, using a control theoretical approach, validated mathematical models of SARS-CoV-2 in humans are characterized. A complete analysis of the main dynamic characteristic is developed based on the reproduction number. The equilibrium regions of the system are fully characterized, and the stability of such regions is formally established. Mathematical analysis highlights critical conditions to decrease monotonically SARS-CoV-2 in the host, as such conditions are relevant to tailor future antiviral treatments. Simulation results show the aforementioned system characterization.

Cyclo(tetrahydroxybutyrate) production is sufficient to distinguish between Xenorhabdus and Photorhabdus isolates in Thailand.

Bacteria of the genera Photorhabdus and Xenorhabdus produce a plethora of natural products to support their similar symbiotic life cycles. 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) 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 also addresses the need for prioritization in high-throughput metabolomic studies and demonstrates the viability of such an approach in future research.

Multiscale model within-host and between-host for viral infectious diseases.

Multiscale models possess the potential to uncover new insights into infectious diseases. Here, a rigorous stability analysis of a multiscale model within-host and between-host is presented. The within-host model describes viral replication and the respective immune response while disease transmission is represented by a susceptible-infected model. The bridging of scales from within- to between-host considered transmission as a function of the viral load. Consequently, stability and bifurcation analyses were developed coupling the two basic reproduction numbers [Formula: see text] and [Formula: see text] for the within- and the between-host subsystems, respectively. Local stability results for each subsystem, including a unique stable equilibrium point, recapitulate classical approaches to infection and epidemic control. Using a Lyapunov function, global stability of the between-host system was obtained. Our main result was the derivation of the [Formula: see text] as an increasing function of [Formula: see text]. Numerical analyses reveal that a Michaelis-Menten form based on the virus is more likely to recapitulate the behavior between the scales than a form directly proportional to the virus. Our work contributes basic understandings of the two models and casts light on the potential effects of the coupling function on linking the two scales.

Effects of aging on influenza virus infection dynamics.

UNLABELLED: The consequences of influenza virus infection are generally more severe in individuals over 65 years of age (the elderly). Immunosenescence enhances the susceptibility to viral infections and renders vaccination less effective. Understanding age-related changes in the immune system is crucial in order to design prophylactic and immunomodulatory strategies to reduce morbidity and mortality in the elderly. Here, we propose different mathematical models to provide a quantitative understanding of the immune strategies in the course of influenza virus infection using experimental data from young and aged mice. Simulation results suggested a central role of CD8(+) T cells for adequate viral clearance kinetics in young and aged mice. Adding the removal of infected cells by natural killer cells did not improve the model fit in either young or aged animals. We separately examined the infection-resistant state of cells promoted by the cytokines alpha/beta interferon (IFN-α/ß), IFN-γ, and tumor necrosis factor alpha (TNF-α). The combination of activated CD8(+) T cells with any of the cytokines provided the best fits in young and aged animals. During the first 3 days after infection, the basic reproductive number for aged mice was 1.5-fold lower than that for young mice (P < 0.05). IMPORTANCE: The fits of our models to the experimental data suggest that the increased levels of IFN-α/ß, IFN-γ, and TNF-α (the "inflammaging" state) promote slower viral growth in aged mice, which consequently limits the stimulation of immune cells and contributes to the reported impaired responses in the elderly. A quantitative understanding of influenza virus pathogenesis and its shift in the elderly is the key contribution of this work.

Modeling the three stages in HIV infection.

A typical HIV infection response consists of three stages: an initial acute infection, a long asymptomatic period and a final increase in viral load with simultaneous collapse in healthy CD4+T cell counts. The majority of existing mathematical models give a good representation of either the first two stages or the last stage of the infection. Using macrophages as a long-term active reservoir, a deterministic model is proposed to explain the three stages of the infection including the progression to AIDS. Simulation results illustrate how chronic infected macrophages can explain the progression to AIDS provoking viral explosion. Further simulation studies suggest that the proposed model retains its key properties even under moderately large parameter variations. This model provides important insights on how macrophages might play a crucial role in the long term behavior of HIV infection.