Conditional robustness analysis for fragility discovery and target identification in biochemical networks and in cancer systems biology

Robustness analysis for quantitative assessment of vaccination effects and SARS-CoV-2 lineages in Italy

Background

In Italy, the beginning of 2021 was characterized by the emergence of new variants of SARS-CoV-2 and by the availability of effective vaccines that contributed to the mitigation of non-pharmaceutical interventions and to the avoidance of hospital collapse.

Methods

We analyzed the COVID-19 propagation in Italy starting from September 2021 with a Susceptible-Exposed-Infected-Recovered (SEIR) model that takes into account SARS-CoV-2 lineages, intervention measures and efficacious vaccines. The model was calibrated with the Bayesian method Conditional Robust Calibration (CRC) using COVID-19 data from September 2020 to May 2021. Here, we apply the Conditional Robustness Analysis (CRA) algorithm to the calibrated model in order to identify model parameters that most affect the epidemic diffusion in the long-term scenario. We focus our attention on vaccination and intervention parameters, which are the key parameters for long-term solutions for epidemic control.

Results

Our model successfully describes the presence of new variants and the impact of vaccinations and non-pharmaceutical interventions in the Italian scenario. The CRA analysis reveals that vaccine efficacy and waning immunity play a crucial role for pandemic control, together with asymptomatic transmission. Moreover, even though the presence of variants may impair vaccine effectiveness, virus transmission can be kept low with a constant vaccination rate and low restriction levels.

Conclusions

In the long term, a policy of booster vaccinations together with contact tracing and testing will be key strategies for the containment of SARS-CoV-2 spread.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12879-022-07395-2.

Robustness: linking strain design to viable bioprocesses

Microbial cell factories are becoming increasingly popular for the sustainable production of various chemicals. Metabolic engineering has led to the design of advanced cell factories; however, their long-term yield, titer, and productivity falter when scaled up and subjected to industrial conditions. This limitation arises from a lack of robustness - the ability to maintain a constant phenotype despite the perturbations of such processes. This review describes predictable and stochastic industrial perturbations as well as state-of-the-art technologies to counter process variability. Moreover, we distinguish robustness from tolerance and discuss the potential of single-cell studies for improving system robustness. Finally, we highlight ways of achieving consistent and comparable quantification of robustness that can guide the selection of strains for industrial bioprocesses.

Mathematical Modeling and Robustness Analysis to Unravel COVID-19 Transmission Dynamics: The Italy Case

This study started from the request of providing predictions on hospitalization and Intensive Care Unit (ICU) rates that are caused by COVID-19 for the Umbria region in Italy. To this purpose, we propose the application of a computational framework to a SEIR-type (Susceptible, Exposed, Infected, Removed) epidemiological model describing the different stages of COVID-19 infection. The model discriminates between asymptomatic and symptomatic cases and it takes into account possible intervention measures in order to reduce the probability of transmission. As case studies, we analyze not only the epidemic situation in Umbria but also in Italy, in order to capture the evolution of the pandemic at a national level. First of all, we estimate model parameters through a Bayesian calibration method, called Conditional Robust Calibration (CRC), while using the official COVID-19 data of the Italian Civil Protection. Subsequently, Conditional Robustness Analysis (CRA) on the calibrated model is carried out in order to quantify the influence of epidemiological and intervention parameters on the hospitalization rates. The proposed pipeline properly describes the COVID-19 spread during the lock-down phase. It also reveals the underestimation of new positive cases and the need of promptly isolating asymptomatic and presymptomatic cases. The results emphasize the importance of the lock-down timeliness and provide accurate predictions on the current evolution of the pandemic.

Application of conditional robust calibration to ordinary differential equations models in computational systems biology: a comparison of two sampling strategies

Mathematical modelling is a widely used technique for describing the temporal behaviour of biological systems. One of the most challenging topics in computational systems biology is the calibration of non-linear models; i.e. the estimation of their unknown parameters. The state-of-the-art methods in this field are the frequentist and Bayesian approaches. For both of them, the performance and accuracy of results greatly depend on the sampling technique employed. Here, the authors test a novel Bayesian procedure for parameter estimation, called conditional robust calibration (CRC), comparing two different sampling techniques: uniform and logarithmic Latin hypercube sampling. CRC is an iterative algorithm based on parameter space sampling and on the estimation of parameter density functions. They apply CRC with both sampling strategies to the three ordinary differential equations (ODEs) models of increasing complexity. They obtain a more precise and reliable solution through logarithmically spaced samples.

CRA toolbox: software package for conditional robustness analysis of cancer systems biology models in MATLAB

Background

In cancer research, robustness of a complex biochemical network is one of the most relevant properties to investigate for the development of novel targeted therapies. In cancer systems biology, biological networks are typically modeled through Ordinary Differential Equation (ODE) models. Hence, robustness analysis consists in quantifying how much the temporal behavior of a specific node is influenced by the perturbation of model parameters. The Conditional Robustness Algorithm (CRA) is a valuable methodology to perform robustness analysis on a selected output variable, representative of the proliferation activity of cancer disease.

Results

Here we introduce our new freely downloadable software, the CRA Toolbox. The CRA Toolbox is an Object-Oriented MATLAB package which implements the features of CRA for ODE models. It offers the users the ability to import a mathematical model in Systems Biology Markup Language (SBML), to perturb the model parameter space and to choose the reference node for the robustness analysis. The CRA Toolbox allows the users to visualize and save all the generated results through a user-friendly Graphical User Interface (GUI). The CRA Toolbox has a modular and flexible architecture since it is designed according to some engineering design patterns. This tool has been successfully applied in three nonlinear ODE models: the Prostate-specific Pten^−/− mouse model, the Pulse Generator Network and the EGFR-IGF1R pathway.

Conclusions

The CRA Toolbox for MATLAB is an open-source tool implementing the CRA to perform conditional robustness analysis. With its unique set of functions, the CRA Toolbox is a remarkable software for the topological study of biological networks. The source and example code and the corresponding documentation are freely available at the web site: http://gitlab.ict4life.com/SysBiOThe/CRA-Matlab.

Electronic supplementary material

The online version of this article (10.1186/s12859-019-2933-z) contains supplementary material, which is available to authorized users.

Reverse phase protein array (RPPA) combined with computational analysis to unravel relevant prognostic factors in non- small cell lung cancer (NSCLC): a pilot study

In this work high throughput technology and computational analysis were used to study two stage IV lung adenocarcinoma patients treated with standard chemotherapy with markedly different survival (128 months vs 6 months, respectively) and whose tumor samples exhibit a dissimilar protein activation pattern of the signal transduction. Tumor samples of the two patients were subjected to Reverse Phase Protein Microarray (RPPA) analysis to explore the expression/activation levels of 51 signaling proteins. We selected the most divergent proteins based on the ratio of their RPPA values in the two patients with short (s-OS) and long (l-OS) overall survival (OS) and tested them against a EGFR-IGF1R mathematical model. The model with RPPA data showed that the activation levels of 19 proteins were different in the two patients. The four proteins that most distinguished the two patients were BADS155/136 and c-KITY703/719 having a higher activation level in the patient with short survival and p70S6S371/T389 and b-RAFS445 that had a lower activation level in the s-OS patient. The final model describes the interactions between the MAPK and PI3K-mTOR pathways, including 21 nodes. According to our model mTOR and ERK activation levels were predicted to be lower in the s-OS patient than the l-OS patient, while the AMPK activation level was higher in the s-OS patient. Moreover, KRAS activation was predicted to be higher in the l-OS KRAS-mutated patient. In accordance with their different biological properties, the Moment Independent Robustness Indicator in s-OS and l-OS predicted the interaction of MAPK and mTOR and the crosstalk AKT with p90RSK as candidates to be prognostic factors and drug targets.