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Posts

Future Blog Post

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Blog Post number 4

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Blog Post number 3

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Blog Post number 2

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Blog Post number 1

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publications

Mathematical foundations of antibody aﬃnity maturation

Balelli, I.

Available in Hal, 2016

PhD Thesis manuscript. Supervisors: Milišić, V., Wainrib, G., Zaag, H. Antibody affinity maturation is a key process in adaptive immunity : it is a mechanism which allows B-cells to produce high affinity antibodies against a specific antigen. We developed and studied a mathematical framework which allows to pattern the learning process to whom B-lymphocytes are submitted during an immune response. In particular, we model antibody traits as N-length binary strings. Antibody-antigen affinity is naturally characterized using the Hamming distance: therefore the N-dimensional hypercube vertex set defines the affinity landscape of B-cell traits. Our aim is to propose and analyze a mathematical model of the division-mutation-selection process of B-cells during an immune response. Besides the biological motivations, the analysis of this learning process brought us to build a mathematical model which could be relevant to model other evolutionary systems, but also gossip or virus propagation. Our method is based on the complementarity between probabilistic tools and numerical simulations.

Branching random walks on binary strings for evolutionary processes in adaptive immunity

Balelli, I., Milišić, V., Wainrib, G.

Available in arXiv, 2018

In this article, we study branching random walks on graphs modeling division-mutation processes inspired by adaptive immunity. We apply the theory of expander graphs on mutation rules in evolutionary processes and obtain estimates for the cover times of the branching random walk.

Random walks on binary strings applied to the somatic hypermutation of B-cells

Balelli, I., Milišić, V., Wainrib, G.

Published in Mathematical biosciences, 2018

This paper establish a mathematical framework based on random walks on graph to introduce and evaluate the mutation mechanism at the basis of the evolutionary process leading to antibody maturation.

Multi-type Galton-Watson processes with affinity-dependent selection applied to antibody affinity maturation

Balelli, I., Milišić, V., Wainrib, G.

Published in Bulletin of mathematical biology, 2019

Inspired by antibody affinity maturation, the interactions between division, mutation and selection are analysed, assuming that the observed population can be classified according to fitness levels with respect to a target trait. An optimal selection rate has been identified, which allows to maximize the number of high affinity B-cells selected at a given generation.

Dynamics of the humoral immune response to a prime-boost Ebola vaccine: quantification and sources of variation

Pasin, C., Balelli, I., Van Effelterre, T., et al.

Published in Journal of virology, 2019

In this paper data from three phase 1 trials of a 2-doses vaccine against Ebola virus performed by the EBOVAC1 Consortium are analyzed. A mathematical model based on ODEs is used to characterize the dynamics of the humoral response after the second dose immunization up to 1 year of followup: it allows to estimate the durability of the antibody response and the influence of different factors on the dynamics of the humoral response.

Viral rebound kinetics following single and combination immunotherapy for HIV/SIV

Prague, M., Gerold, J. M., Balelli, I., et al.

Available in BioRxiv, 2019

In this paper we conduct a detailed analysis of the kinetics of viral rebound after immunotherapy in the context of HIV infection. We use mathematical models combined with rigorous statistical fitting to quantify the impact of these interventions on viral dynamics, and provide a framework for understanding the relative contributions of different mechanisms for preventing viral rebound and highlight the multifaceted roles of TLR7-agonists for HIV/SIV cure.

A model for establishment, maintenance and reactivation of the immune response after vaccination against Ebola virus

Balelli, I., Pasin, C., Prague, M., et al.

Published in Journal of theoretical biology, 2020

This article describes the biological motivation and the development of a mechanistic model of the humoral immune response to multiple vaccine injections. A theoretical analysis is proposed, as well as a calibration with clinical data generated by the EBOVAC project.

Parameter estimation in nonlinear mixed effect models based on ordinary differential equations: an optimal control approach

Clairon, Q., Pasin, C., Balelli, I., et al.

Available in arXiv, 2021

We present a parameter estimation method for nonlinear mixed effect models based on ordinary differential equations (NLME-ODEs). The proposed method aims at regularizing the estimation problem in presence of model misspecifications, practical identifiability issues and unknown initial conditions, using a control theory approach.

A Probabilistic Framework for Modeling the Variability Across Federated Datasets of Heterogeneous Multi-View Observations

Balelli I., Silva S., Lorenzi M.

Published in Lecture Notes in Computer Science, 2021

In this paper we propose a new Bayesian framework for federated learning of heterogeneous multi-modal biomedical data. An application to a large database (including medical imaging and clinical scores) on patients with Alzheimer disease shows that the proposed model allows high quality data reconstruction, compared to current auto-encoding methods and federated learning schemes.

A Differentially Private Probabilistic Framework for Modeling the Variability Across Federated Datasets of Heterogeneous Multi-View Observations

Balelli I., Silva S., Lorenzi M.

Published in Journal of Machine Learning for Biomedical Imaging, 2022

This paper is an extension of the work presented at the Information Processing in Medical Imaging 2021 conference: we introduce formal differential privacy guarantees compatibly with the proposed federated Bayesian framework and Expectation Maximization optimization scheme.

Fed-MIWAE: Federated Imputation of Incomplete Data via Deep Generative Models

Balelli I., Sportisse A., Cremonesi F., Mattei P. A., Lorenzi M.

Available in HAL, 2023

In this work we propose a novel pipeline for federated preprocessing, based on the deep latent variable model MIWAE for missing data imputation: we show that performing the imputation task taking advantage of the federated network is highly beneficial in term of generalizability and robustness.

A causal discovery approach for streamline ion channels selection to improve drug-induced TdP risk assessment

Al-Ali S., Llopis-Lorente J., Mora M. T., Sermesant M., Trénor B., Balelli I.

Available in HAL, 2023

Torsade de Pointes (TdP) is an extremely serious drug-induced cardiac side effect, which is related to abnormal repolarizations in single cells, and the minimum set of ion channels needed to correctly assess TdP risk is still an open question. In this work, we propose to apply the causal discovery method ICA-Linear Non-Gaussian Acyclic Model (ICA-LiNGAM) to uncover the relations across the 7 ion channels identified by the Comprehensive in vitro Proarrhythmia Assay (CiPA) initiative as potentially related to the induction of TdP. We identify I\(_{Kr}\), I\(_{NaL}\) and I\(_{CaL}\) as the ones which directly affect TdP-risk assessment, and suggest that I\(_{Na}\) perturbations could potentially have a high impact on proarrhythmic risk induction.

Book chapter: Integration of Multimodal Data

Lorenzi M. , Deprez M., Balelli I., Aguila A.L., Altmann A.

Published in Springer US, 2023

This chapter focuses on the joint modeling of heterogeneous information, such as imaging, clinical, and biological data. This kind of problem requires to generalize classical uni- and multivariate association models to account for complex data structure and interactions, as well as high data dimensionality.