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

Galtier [1] introduces “Aphid,” a new statistical method that estimates the contributions of gene flow (GF) and incomplete lineage sorting (ILS) to phylogenetic conflict.  Aphid is based on the observation that GF tends to make gene genealogies shorter, whereas ILS makes them longer.  Rather than fitting the full likelihood, it models the distribution of gene genealogies as a mixture of several canonical gene genealogies in which coalescence times are set equal to their expectations under different models. This simplification makes Aphid far faster than competing methods. In addition, it deals gracefully with bidirectional gene flow—an impossibility under competing models. Because of these advantages, Aphid represents an important addition to the toolkit of evolutionary genetics.

In the interest of speed, Aphid makes several simplifying assumptions. Yet even when these were violated, Aphid did well at estimating parameters from simulated data. It seems to be reasonably robust.

Aphid studies phylogenetic conflict, which occurs when some loci imply one phylogenetic tree and other loci imply another. This happens when the interval between successive speciation events is fairly short. If this interval is too short,  however,  Aphid’s approximations break down, and its estimates are biased. Galtier suggests caution when the fraction of discordant phylogenetic trees exceeds 50–55%. Thus, Aphids will be most useful when the interval between speciation events is short, but not too short.

Galtier applies the new method to three sets of primate data. In two of these data sets  (baboons and African apes), Aphid detects gene flow that would likely be missed by competing methods. These competing methods are primarily sensitive to gene flow that is asymmetric in two senses: (1) greater flow in one direction than the other, and (2) unequal gene flow connecting an outgroup to two sister species.  Aphid finds evidence of symmetric gene flow in the ancestry of baboons and also in that of African apes. The data suggest that ancestral humans and chimpanzees both interbred with ancestral gorillas, and at about the same rate.  Aphid’s ability to detect this signature sets it apart from competing methods.

References

[1]   Nicolas Galtier (2023) “An approximate likelihood method reveals ancient gene flow between human, chimpanzee and gorilla”. bioRxiv, ver. 3 peer-reviewed and recommended by Peer Community in Mathematical and Computational Biology.  https://doi.org/10.1101/2023.07.06.547897

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

In “Estimating dates of origin and end of COVID-19 epidemics”, Bénéteau et al. develop and apply a mathematical modeling approach to estimate the date of the origin of the SARS-CoV-2 epidemic in France. They also assess how long strict control measures need to last to ensure that the prevalence of the virus remains below key public health thresholds. This problem is challenging because the numbers of infected individuals in both tails of the epidemic are low, which can lead to errors when deterministic models are used. To achieve their goals, the authors developed a discrete stochastic model. The model is non-Markovian, meaning that individual infection histories influence the dynamics. The model also accounts for heterogeneity in the timing between infection and transmission and includes stochasticity as well as consideration of superspreader events. By comparing the outputs of their model with several alternative models, Bénéteau et al. were able to assess the importance of stochasticity, individual heterogeneity, and non-Markovian effects on the estimates of the dates of origin and end of the epidemic, using France as a test case. Some limitations of the study, which the authors acknowledge, are that the time from infection to death remains largely unknown, a lack of data on the heterogeneity of transmission among individuals, and the assumption that only a single infected individual caused the epidemic. Despite the acknowledged limitations of the work, the results suggest that cases may be detected long before the detection of an epidemic wave. Also, the approach may be helpful for informing public health decisions such as the necessary duration of strict lockdowns and for assessing the risks of epidemic rebound as restrictions are lifted. In particular, the authors found that estimates of the end of the epidemic following lockdowns are more sensitive to the assumptions of the models used than estimates of its beginning. In summary, this model adds to a valuable suite of tools to support decision-making in response to disease epidemics.

References

Bénéteau T, Elie B, Sofonea MT, Alizon S (2021) Estimating dates of origin and end of COVID-19 epidemics. medRxiv, 2021.01.19.21250080, ver. 3 peer-reviewed and recommended by Peer Community in Mathematical and Computational Biology. https://doi.org/10.1101/2021.01.19.21250080