How fast and how deep do animals breathe, and how does this depend on how active they are? To answer this question, one needs to dig deeply into how breathing works and what biophysical processes it involves. And one needs to think about body size.

It is impressive how nature adapts the same body plan – e.g. the skeletal structure of mammals – to various shapes and sizes. From mice to whales, also the functioning of most organs remains the same; they are just differently scaled. Scaling does not just mean “making bigger or smaller”. As already noted by Galilei, body shapes change as they are adapted to body dimensions, and the same holds for physiological variables. Many such variables, for instance, heartbeat rates, follow scaling laws of the form y~x^a, where x denotes body mass and the exponent a is typically a multiple of ¼ [1]. These unusual exponents – instead of multiples of ⅓, which would be expected from simple geometrical scaling – are why these laws are called “allometric”. Kleiber’s law for metabolic rates, with a scaling exponent of ¾, is a classic example [2]. As shown by G. West, allometric laws can be explained through a few simple steps [1]. In his models, he focused on network-like organs such as the vascular system and assumed that these systems show a self-similar structure, with a fixed minimal unit (for instance, capillaries) but varying numbers of hierarchy levels depending on body size. To determine the flow through such networks, he employed biophysical models and optimality principles (for instance, assuming that oxygen must be transported at a minimal mechanical effort), and showed that the solutions – and the physiological variables – respect the known scaling relations.

The paper “The origin of the allometric scaling of lung ventilation in mammals“ by Noël et al. [3], applies this thinking to the depth and rate of breathing in mammals. Scaling laws describing breathing in resting animals have been known since the 1950s [4], with exponents of 1 (for tidal volume) and -¼ (for breathing frequency). Equipped with a detailed biophysical model, Noël et al. revisit this question, extending these laws to other metabolic regimes. Their starting point is a model of the human lung, developed previously by two of the authors [5], which assumes that we meet our oxygen demand with minimal lung movements. To state this as an optimization problem, the model combines two submodels: a mechanical model describing the energetic effort of ventilation and a highly detailed model of convection and diffusion in self-similar lung geometries. Breathing depths and rates are computed by numerical optimization, and to obtain results for mammals of any size many of the model parameters are described by known scaling laws. As expected, the depth of breathing (measured by tidal volume) scales almost proportionally with body mass and increases with metabolic demand, while the breathing rate decreases with body mass, with an exponent of about -¼. However, the laws for the breathing rate hold only for basal activity; at higher metabolic rates, which are modeled here for the first time, the exponent deviates strongly from this value, in line with empirical data.

Why is this paper important? The authors present a highly complex model of lung physiology that integrates a wide range of biophysical details and passes a difficult test: the successful prediction of unexplained scaling exponents. These scaling relations may help us transfer insights from animal models to humans and in reverse: data for breathing during exercise, which are easy to measure in humans, can be extrapolated to other species. Aside from the scaling laws, the model also reveals physiological mechanisms. In the larger lung branches, oxygen is transported mainly by air movement (convection), while in smaller branches air flow is slow and oxygen moves by diffusion. The transition between these regimes can occur at different depths in the lung: as the authors state, “the localization of this transition determines how ventilation should be controlled to minimize its energetic cost at any metabolic regime”. In the model, the optimal location for the transition depends on oxygen demand [5, 6]: the transition occurs deeper in the lung in exercise regimes than at rest, allowing for more oxygen to be taken up. However, the effects of this shift depend on body size: while small mammals generally use the entire exchange surface of their lungs, large mammals keep a reserve for higher activities, which becomes accessible as their transition zone moves at high metabolic rates. Hence, scaling can entail qualitative differences between species!

Altogether, the paper shows how the dynamics of ventilation depend on lung morphology. But this may also play out in the other direction: if energy-efficient ventilation depends on body activity, and therefore on ecological niches, a niche may put evolutionary pressures on lung geometry. Hence, by understanding how deep and fast animals breathe, we may also learn about how behavior, physiology, and anatomy co-evolve.

References

[1] West GB, Brown JH, Enquist BJ (1997) A General Model for the Origin of Allometric Scaling Laws in Biology. Science 276 (5309), 122–126. https://doi.org/10.1126/science.276.5309.122

[2] Kleiber M (1947) Body size and metabolic rate. Physiological Reviews, 27, 511–541. https://doi.org/10.1152/physrev.1947.27.4.511

[3] Noël F., Karamaoun C., Dempsey J. A. and Mauroy B. (2021) The origin of the allometric scaling of lung's ventilation in mammals. arXiv, 2005.12362, ver. 6 peer-reviewed and recommended by Peer community in Mathematical and Computational Biology. https://arxiv.org/abs/2005.12362

[4] Otis AB, Fenn WO, Rahn H (1950) Mechanics of Breathing in Man. Journal of Applied Physiology, 2, 592–607. https://doi.org/10.1152/jappl.1950.2.11.592

[5] Noël F, Mauroy B (2019) Interplay Between Optimal Ventilation and Gas Transport in a Model of the Human Lung. Frontiers in Physiology, 10, 488. https://doi.org/10.3389/fphys.2019.00488

[6] Sapoval B, Filoche M, Weibel ER (2002) Smaller is better—but not too small: A physical scale for the design of the mammalian pulmonary acinus. Proceedings of the National Academy of Sciences, 99, 10411–10416. https://doi.org/10.1073/pnas.122352499

It is often the case that scientific knowledge exists but is scattered across numerous experimental studies. Because of this dispersion in different formats, it remains difficult to access, extract, reproduce, confirm or generalise. This is the case in crop science, where Mahmoud et al [1] propose to collect and assemble data from numerous field experiments on intercropping.

It happens that the construction of the global dataset requires a lot of time, attention and a well thought-out method, inspired by the literature on data science [2] and adapted to the specificities of crop science. This activity also leads to new possibilities that were not available in individual datasets, such as the detection of full factorial designs using graph theory tools developed on top of the global dataset.

The study by Mahmoud et al [1] has thus multiple dimensions:

• The description of the solutions given to this data assembly challenge.
• The illustration of the usefulness of such procedure in a case study of 37 field experiments on cereal-legume associations. The dataset is publicly available [3], while some results obtained from it have been independently published elsewhere [e.g. 4].
• The description of an algorithm able to detect complete factorial designs.
• An informed discussion of the merits of global datasets compared to alternatives, in particular meta-analyses
• A documented reflection on scientific practices in the era of big data, guided by the principles of open science.

I was particularly interested in the promotion of the FAIR principles, perhaps used a little too uncritically in my view, as an obvious solution to data sharing. On the one hand, I am admiring and grateful for the availability of these data, some of which have never been published, nor associated with published results. This approach is likely to unearth buried treasures. On the other hand, I can understand the reluctance of some data producers to commit to total, definitive sharing, facilitating automatic reading, without having thought about a certain reciprocity on the part of users and use by artificial intelligence. Reciprocity in terms of recognition, as is discussed by Mahmoud et al [1], but also in terms of contribution to the commons [5] or reading conditions for machine learning.
But this is another subject, to be dealt with in the years to come, and for which, perhaps, the contribution recommended here will be enlightening.

References

[1] Mahmoud R., Casadebaig P., Hilgert N., Gaudio N. A workflow for processing global datasets: application to intercropping. 2024. ⟨hal-04145269v2⟩ ver. 2 peer-reviewed and recommended by Peer Community in Mathematical and Computational Biology. https://hal.science/hal-04145269

[2] Wickham, H. 2014. Tidy data. Journal of Statistical Software 59(10) https://doi.org/10.18637/jss.v059.i10

[3] Gaudio, N., R. Mahmoud, L. Bedoussac, E. Justes, E.-P. Journet, et al. 2023. A global dataset gathering 37 field experiments involving cereal-legume intercrops and their corresponding sole crops. https://doi.org/10.5281/zenodo.8081577

[4] Mahmoud, R., Casadebaig, P., Hilgert, N. et al. Species choice and N fertilization influence yield gains through complementarity and selection effects in cereal-legume intercrops. Agron. Sustain. Dev. 42, 12 (2022). https://doi.org/10.1007/s13593-022-00754-y

[5] Bernault, C. « Licences réciproques » et droit d'auteur : l'économie collaborative au service des biens communs ?. Mélanges en l'honneur de François Collart Dutilleul, Dalloz, pp.91-102, 2017, 978-2-247-17057-9. https://shs.hal.science/halshs-01562241

Unlike a species tree, a gene tree results not only from speciation events, but also from events acting at the gene level, such as duplications and losses of gene copies, and gene transfer events [1]. The reconciliation of phylogenetic trees consists in embedding a given gene tree into a known species tree and, doing so, determining the location of these gene-level events on the gene tree [2]. Reconciled gene trees can be seen as phylogenetic trees where internal node labels are used to discriminate between different gene-level events. Comparing them is of foremost importance in order to assess the performance of various reconciliation methods (e.g. [3]).
A paper describing an extension of the widely used Robinson-Foulds (RF) distance [4] to trees with labeled internal nodes was presented earlier this year [5]. This distance, called ELRF, is based on edge edits and coincides with the RF distance when all internal labels are identical; unfortunately, the ELRF distance is very costly to compute. In the present paper [6], the authors introduce a distance called LRF, which is inspired by the TED (Tree Edit Distance [7]) and is based on node edits. As the ELRF, the new distance coincides with the RF distance for identically-labeled internal nodes, but has the additional desirable features of being computable in linear time. Also, in the ELRF distance, an edge can be deleted if only it connects nodes with the same label. The new formulation does not have this restriction, and this is, in my opinion, an improvement since the restriction makes little sense in the comparison of reconciled gene trees.
The authors show the pertinence of this new distance by studying the impact of taxon sampling on reconciled gene trees when internal labels are computed via a method based on species overlap. The linear algorithm to compute the LRF distance presented in the paper has been implemented and the software —written in Python— is freely available for the community to use it. I bet that the LRF distance will be widely used in the coming years!

References

[1] Maddison, W. P. (1997). Gene trees in species trees. Systematic biology, 46(3), 523-536. doi: https://doi.org/10.1093/sysbio/46.3.523
[2] Boussau, B., and Scornavacca, C. (2020). Reconciling gene trees with species trees. Phylogenetics in the Genomic Era, p. 3.2:1–3.2:23. [3] Doyon, J. P., Chauve, C., and Hamel, S. (2009). Space of gene/species trees reconciliations and parsimonious models. Journal of Computational Biology, 16(10), 1399-1418. doi: https://doi.org/10.1089/cmb.2009.0095
[4] Robinson, D. F., and Foulds, L. R. (1981). Comparison of phylogenetic trees. Mathematical biosciences, 53(1-2), 131-147. doi: https://doi.org/10.1016/0025-5564(81)90043-2
[5] Briand, B., Dessimoz, C., El-Mabrouk, N., Lafond, M. and Lobinska, G. (2020). A generalized Robinson-Foulds distance for labeled trees. BMC Genomics 21, 779. doi: https://doi.org/10.1186/s12864-020-07011-0
[6] Briand, S., Dessimoz, C., El-Mabrouk, N. and Nevers, Y. (2020) A linear time solution to the labeled Robinson-Foulds distance problem. bioRxiv, 2020.09.14.293522, ver. 4 peer-reviewed and recommended by PCI Mathematical and Computational Biology. doi: https://doi.org/10.1101/2020.09.14.293522
[7] Zhang, K., and Shasha, D. (1989). Simple fast algorithms for the editing distance between trees and related problems. SIAM journal on computing, 18(6), 1245-1262. doi: https://doi.org/10.1137/0218082

The paper [1] presents and applies a new Bayesian inference method of phylogenetic reconstruction for multiple sequence alignments in the case of low sequencing coverage but diverse copy number aberrations (CNA), with applications to single cell sequencing of tumors.

The idea is to take advantage of CNA to reconstruct the topology of the phylogenetic tree of sequenced cells in a first step (the `sitka' method), and in a second step to assign single nucleotide variants (SNV) to tree edges (and then calibrate their lengths) (the `sitka-snv' method).

The data are summarized into a binary-valued CxL matrix Y, where C is the number of cells and L is the number of loci (here, loci are segments of prescribed length called `bins'). The entry of Y at row i and column j is 1 (otherwise 0) iff in the ancestral lineage of cell i, at least one genomic rearrangement has occurred, and more specifically the gain or loss of a segment with at least one endpoint in locus j or in locus j+1. The authors expect the infinite-allele assumption to approximately hold (i.e., that at most one mutation occurs at any given marker and that 0 is the ancestral state). They refer to this assumption as the `perfect phylogeny assumption'. By only recording from CNA events the endpoints at which they occur, the authors lose the information on copy number, but they gain the assumption of independence of the mutational processes occurring at different sites, which approximately holds for CNA endpoints.

The goal of sitka is to produce a posterior distribution on phylogenetic trees conditional on the matrix Y , where here a phylogenetic tree is understood as containing the information on 1) the topology of the tree but not its edge lengths, and 2) for each edge, the identity of markers having undergone a mutation, in the sense of the previous paragraph. 

The results of the method are tested against synthetic datasets simulated under various assumptions, including conditions violating the perfect phylogeny assumption and compared to results obtained under other baseline methods. The method is extended to assign SNV to edges of the tree inferred by sitka. It is also applied to real datasets of single cell genomes of tumors. 

The manuscript is very well-written, with a high degree of detail. The method is novel, scalable, fast and appears to perform favorably compared to other approaches. It has been applied in independent publications, for example to multi-year time-series single-cell whole-genome sequencing of tumors, in order to infer the fitness landscape and its dynamics through time, see [2].

The reviewing process has taken too long, mainly because of other commitments I had during the period and to the difficulty of finding reviewers. Let me apologize to the authors and thank them for their patience as well as for the scientific rigor they brought to their revisions and answers to reviewers, who I also warmly thank for their quality work.

REFERENCES

[1] Sohrab Salehi, Fatemeh Dorri, Kevin Chern, Farhia Kabeer, Nicole Rusk, Tyler Funnell, Marc J Williams, Daniel Lai, Mirela Andronescu, Kieran R. Campbell, Andrew McPherson, Samuel Aparicio, Andrew Roth, Sohrab Shah, and Alexandre Bouchard-Côté. Cancer phylogenetic tree inference at scale from 1000s of single cell genomes (2023). bioRxiv, 2020.05.06.058180, ver. 4 peer-reviewed and recommended by Peer Community in Mathematical and Computational Biology. 
https://doi.org/10.1101/2020.05.06.058180

[2] Sohrab Salehi, Farhia Kabeer, Nicholas Ceglia, Mirela Andronescu, Marc J. Williams, Kieran R. Campbell, Tehmina Masud, Beixi Wang, Justina Biele, Jazmine Brimhall, David Gee, Hakwoo Lee, Jerome Ting, Allen W. Zhang, Hoa Tran, Ciara O’Flanagan, Fatemeh Dorri, Nicole Rusk, Teresa Ruiz de Algara, So Ra Lee, Brian Yu Chieh Cheng, Peter Eirew, Takako Kono, Jenifer Pham, Diljot Grewal, Daniel Lai, Richard Moore, Andrew J. Mungall, Marco A. Marra, IMAXT Consortium, Andrew McPherson, Alexandre Bouchard-Côté, Samuel Aparicio & Sohrab P. Shah. Clonal fitness inferred from time-series modelling of single-cell cancer genomes (2021).  Nature 595, 585–590. https://doi.org/10.1038/s41586-021-03648-3

Reprogramming of cellular networks is a well known challenge in computational biology consisting first of all in properly representing an ensemble of networks having a role in a phenomenon of interest, and secondly in designing strategies to alter the functioning of this ensemble in the desired direction.  Important applications involve disease study: a therapy can be seen as a reprogramming strategy, and the disease itself can be considered a result of a series of adversarial reprogramming actions.  The origins of this domain go back to the seminal paper by Barabási et al. [1] which formalized the concept of network medicine.

An abstract tool which has gathered considerable success in network medicine and network biology are Boolean networks: sets of Boolean variables, each equipped with a Boolean update function describing how to compute the next value of the variable from the values of the other variables.  Despite apparent dissimilarity with the biological systems which involve varying quantities and continuous processes, Boolean networks have been very effective in representing biological networks whose entities are typically seen as being on or off.  Particular examples are protein signalling networks as well as gene regulatory networks.

The paper [2] by Loïc Paulevé presents a versatile tool for tackling reprogramming of Boolean networks seen as models of biological networks.  The problem of reprogramming is often formulated as the problem of finding a set of perturbations which guarantee some properties on the attractors.  The work [2] relies on the most permissive semantics [3], which together with the modelling assumption allows for considerable speed-up in the practically relevant subclass of locally-monotone Boolean networks.

The paper is structured as a tutorial.  It starts by introducing the formalism, defining 4 different general variants of reprogramming under the most permissive semantics, and presenting evaluations of their complexity in terms of the polynomial hierarchy.  The author then describes the software tool BoNesis which can handle different problems related to Boolean networks, and in particular the 4 reprogramming variants.  The presentation includes concrete code examples with their output, which should be very helpful for future users.

The paper [2] introduces a novel scenario: reprogramming of ensembles of Boolean networks delineated by some properties, including for example the property of having a given interaction graph.  Ensemble reprogramming looks particularly promising in situations in which the biological knowledge is insufficient to fully determine all the update functions, i.e. in the majority of modelling situations.  Finally, the author also shows how BoNesis can be used to deal with sequential reprogramming, which is another promising direction in computational controllability, potentially enabling more efficient therapies [4,5].

1. Barabási A-L, Gulbahce N, Loscalzo J (2011) Network medicine: a network-based approach to human disease. Nature Reviews Genetics, 12, 56–68. https://doi.org/10.1038/nrg2918
2. Paulevé L (2023) Marker and source-marker reprogramming of Most Permissive Boolean networks and ensembles with BoNesis. arXiv, ver. 2 peer-reviewed and recommended by Peer Community in Mathematical and Computational Biology. https://doi.org/10.48550/arXiv.2207.13307
3. Paulevé L, Kolčák J, Chatain T, Haar S (2020) Reconciling qualitative, abstract, and scalable modeling of biological networks. Nature Communications, 11, 4256. https://doi.org/10.1038/s41467-020-18112-5
4. Mandon H, Su C, Pang J, Paul S, Haar S, Paulevé L (2019) Algorithms for the Sequential Reprogramming of Boolean Networks. IEEE/ACM Transactions on Computational Biology and Bioinformatics, 16, 1610–1619. https://doi.org/10.1109/TCBB.2019.2914383
5. Pardo J, Ivanov S, Delaplace F (2021) Sequential reprogramming of biological network fate. Theoretical Computer Science, 872, 97–116. https://doi.org/10.1016/j.tcs.2021.03.013