In the hereby recommended paper [1], Delaney, Letten and Engelstädter study the appearance of antibiotic resistance(s) in a bacterial population subject to a combination of two antibiotics \( A \) and \( B \), in concentrations \( C_A \) and \( C_B \) respectively. Their goal was to find optimal values of \( C_A \) and \( C_B \) that minimize the risk of evolutionary rescue, under the unusual assumption that resistance mutations to either antibiotic are not equally likely.

The authors introduce a stochastic model assuming that the susceptible population grows like a supercritical birth-death process which becomes subcritical in the presence of antibiotics (and exactly critical for a certain concentration c of a single antibiotic): the effect of each antibiotic is either to reduce division rate (bacteriostatic drug) or to enhance death rate (bacteriocidal drug) by a factor which has a sigmoid functional dependence on antibiotic concentration. 

Now at each division, a resistance mutation can arise, with probability \( \mu_A \) for a resistance to antibiotic \( A \) and with probability \( \mu_B \) for a resistance to antibiotic \( B \).

The goal of the paper is to find the optimal ratio of drug concentrations \( C_A \) and \( C_B \) when these are subject to a constrain \( C_A + C_B = c \), depending on the ratio of mutation rates. Assuming total resistance and no cross resistance, the authors show that the optimal concentrations are given by \( C_A = c/(1+\sqrt{\mu_A/\mu_B }) \) and \( C_B = c/(1+\sqrt{\mu_B/\mu_A}) \), which leads to the beautiful result that the optimal ratio \( C_A/C_B \) is equal to the square root of \( \mu_B/\mu_A \).

The authors have made a great job completing their initial submission by simulations of model extensions, relaxing assumptions like single antibiotic mode, absence of competition, absence of cost of resistance, sharp cutoff in toxicity… and comparing the results obtained by simulation to their mathematical result.

The paper is very clearly written and any reader interested in antibiotic resistance, stochastic modeling of bacterial populations and/or evolutionary rescue will enjoy reading it. Let me thank the authors for their patience and for their constant willingness to comply with the reviewers’ and recommender’s demands during the reviewing process. 

Reference

Oscar Delaney, Andrew D. Letten, Jan Engelstaedter (2025) Optimal antimicrobial dosing combinations when drug-resistance mutation rates differ. bioRxiv, ver.3 peer-reviewed and recommended by PCI Mathematical and Computational Biology https://doi.org/10.1101/2024.05.04.592498

Insecticides are used to control crop pests and prevent severe crop losses. They are also a major cause of the current decline in biodiversity, contribute to climate change, and pollute soil and water, with consequences for human and environmental health [1]. The rationale behind the work of Malou et al [2] is that some pesticide application protocols can be improved by a better knowledge of the insects, their biology, their ecology and their real-time infestation dynamics in the fields. Thanks to a network of pheromone sensors and a mathematical method to derive the spatio-temporal distribution of pest populations from the signals, it is theoretically possible to adjust the time, dose and area of treatment and to use less pesticide with greater efficiency than an uninformed protocol.

Malou et al [2] focus on the mathematical problem, recognising that its real role in pest control would require work on its implementation and on a benefit-harm analysis. The problem is an "inverse problem" [3] in that it consists of inferring the presence of insects from the trail left by the pheromones, given a model of pheromone diffusion by insects. The main contribution of this work is the formulation and comparison of different regularisation terms in the optimisation inference scheme, in order to guide the optimisation by biological knowledge of specific pests, such as some parameters of population dynamics.

The accuracy and precision of the results are tested and compared on a simple toy example to test the ability of the model and algorithm to detect the source of the pheromones and the efficiency of the data assimilation principle. A further simulation is then carried out on a real plot with realistic parameters and rules based on knowledge of a maize pest. A repositioning of the sensors (informed by the results from the initial positions) is carried out during the test phase to allow better detection.

The work of Malou et al [2] is large, deep and complete. Its includes a detailed study of the numerical solutions of different data assimilation methods, as well as a theoretical reflection on how this work could contribute to agricultural and environmental issues.

References

[1] IPBES (2024). Thematic Assessment Report on the Underlying Causes of Biodiversity Loss and the Determinants of Transformative Change and Options for Achieving the 2050 Vision for Biodiversity of the Intergovernmental Science-Policy Platform on Biodiversity and Ecosystem Services. O’Brien, K., Garibaldi, L., and Agrawal, A. (eds.). IPBES secretariat, Bonn, Germany. https://doi.org/10.5281/zenodo.11382215

[2] Thibault Malou, Nicolas Parisey, Katarzyna Adamczyk-Chauvat, Elisabeta Vergu, Béatrice Laroche, Paul-Andre Calatayud, Philippe Lucas, Simon Labarthe (2025) Biology-Informed inverse problems for insect pests detection using pheromone sensors. HAL, ver.2 peer-reviewed and recommended by PCI Math Comp Biol https://hal.inrae.fr/hal-04572831v2

[3] Isakov V (2017). Inverse Problems for Partial Differential Equations. Vol. 127. Applied Mathematical Sciences. Cham: Springer International Publishing. https://doi.org/10.1007/978-3-319-51658-5.

Paleoproteomics is a rapidly growing field with numerous challenges, many of which are due to the highly fragmented, modified, and degraded nature of ancient proteins. Though there are established standards for analysis, it is unclear how different software tools affect the identification and quantification of peptides, proteins, and post-translational modifications. To address this knowledge gap, Rodriguez Palomo et al. design a controlled system by experimentally degrading and purifying bovine beta-lactoglobulin, and then systematically compare the performance of many commonly used tools in its analysis.

They present comprehensive investigations of false discovery rates, open and narrow searches, de novo sequencing coverage bias and accuracy, and peptide chemical properties and bias. In each investigation, they explore wide ranges of appropriate tools and parameters, providing guidelines and recommendations for best practices. Based on their findings, Rodriguez Palomo et al. develop a proposed pipeline that is tailored for the analysis of ancient proteins. This pipeline is an important contribution to paleoproteomics and is likely to be of great value to the research community, as it is designed to enhance power, accuracy, and consistency in studies of ancient proteins.

References

Ismael Rodriguez-Palomo, Bharath Nair, Yun Chiang, Joannes Dekker, Benjamin Dartigues, Meaghan Mackie, Miranda Evans, Ruairidh Macleod, Jesper V. Olsen, Matthew J. Collins (2023) Benchmarking the identification of a single degraded protein to explore optimal search strategies for ancient proteins. bioRxiv, ver.3 peer-reviewed and recommended by PCI Math Comp Biol https://doi.org/10.1101/2023.12.15.571577

Significant progress has been made in developing computational methods to tackle the analysis of the numerous (genome-wide scale) metabolic networks that have been documented for a wide range of species. Understanding the behaviours of these complex reaction networks is crucial in various domains such as biotechnology and medicine.

Metabolic rewiring is essential as it enables cells to adapt their metabolism to changing environmental conditions. Identifying the metabolites around which metabolic rewiring occurs is certainly useful in the case of metabolic engineering, which relies on metabolic rewiring to transform micro-organisms into cellular factories [1], as well as in other contexts.

This paper by F. Mairet [2] introduces a method to disclose these metabolites, named switch nodes, relying on the analysis of the flux distributions for different input conditions. Basically, considering fluxes for different inputs, which can be computed using e.g. Parsimonious Flux Balance Analysis (pFBA), the proposed method consists in identifying metabolites involved in reactions whose different flux vectors are not collinear. The approach is supported by four case studies, considering core and genome-scale metabolic networks of Escherichia coli, Saccharomyces cerevisiae and the diatom Phaeodactylum tricornutum.

Whilst identified switch nodes may be biased because computed flux vectors satisfying given objectives are not necessarily unique, the proposed method has still a relevant predictive potential, complementing the current array of computational methods to study metabolism.

References

[1] Tao Yu, Yasaman Dabirian, Quanli Liu, Verena Siewers, Jens Nielsen (2019) Strategies and challenges for metabolic rewiring. Current Opinion in Systems Biology, Vol 15, pp 30-38. https://doi.org/10.1016/j.coisb.2019.03.004.

[2] Francis Mairet (2024) In silico identification of switching nodes in metabolic networks. bioRxiv, ver.3 peer-reviewed and recommended by PCI Math Comp Biol https://doi.org/10.1101/2023.05.17.541195

Boolean networks stem from seminal work by M. Sugita [1], S. Kauffman [2] and R. Thomas [3] over half a century ago. Since then, a very active field of research has been developed, leading to theoretical advances accompanied by a wealth of work on modelling genetic and signalling networks involved in a wide range of cellular processes. Boolean networks provide a successful formalism for the mathematical modelling of biological processes, with a qualitative abstraction particularly well adapted to handle the modelling of processes for which precise, quantitative data is barely available. Nevertheless, these abstract models reveal fundamental dynamical properties, such as the existence and reachability of attractors, which embody stable cellular responses (e.g. differentiated states). Analysing these properties still faces serious computational complexity. Reduction of model size was proposed as a mean to cope with this issue. Furthermore, to enhance the capacity of Boolean networks to produce relevant predictions, formal methods have been developed to systematically identify control strategies enforcing desired behaviours.

In their paper, E. Tonello and L. Paulevé [4] assess the most popular reduction that consists in eliminating a model component. Considering three typical update schemes (synchronous, asynchronous and general asynchronous updates), they thoroughly study the effects of the reduction on attractors, minimal trap spaces (minimal subspaces from which the model dynamics cannot leave), and on phenotype controls (interventions which guarantee that the dynamics ends in a phenotype defined by specific component values). Because they embody potential behaviours of the biological process under study, these are all properties of great interest for a modeller.

The authors show that eliminating a component can significantly affect some dynamical properties and may turn a control strategy ineffective. The different update schemes, targets of phenotype control and control strategies are carefully handled with useful supporting examples.

Whether the component eliminated does not share any of its regulators with its targets is shown to impact the preservation of minimal trap space. Since, in practice, model reduction amounts to eliminating several components, it would have been interesting to further explore this type of structural constraints, e.g. members of acyclical pathways or of circuits.

Overall, E. Tonello and L. Paulevé’s contribution underlines the need for caution when defining a regulatory network and characterises the consequences on critical model properties when discarding a component [4].

References

[1] Motoyosi Sugita (1963) Functional analysis of chemical systems in vivo using a logical circuit equivalent. II. The idea of a molecular automation. Journal of Theoretical Biology, 4, 179–92. https://doi.org/10.1016/0022-5193(63)90027-4

[2] Stuart Kauffman (1969) Metabolic stability and epigenesis in randomly constructed genetic nets. Journal of Theoretical Biology, 22, 437–67. https://doi.org/10.1016/0022-5193(69)90015-0

[3] René Thomas (1973)  Boolean formalization of genetic control circuits. Journal of Theoretical Biology, 42, 563–85. https://doi.org/10.1016/0022-5193(73)90247-6

[4] Elisa Tonello, Loïc Paulevé (2024) Phenotype control and elimination of variables in Boolean networks. arXiv, ver.2 peer-reviewed and recommended by PCI Math Comp Biol https://arxiv.org/abs/2406.02304