Exploration 3: A Search for Informative Models
(Under construction)
August 3 2026
In Exploration 2, models for the behavior of the circadian clock in blue-green algae were discussed, the only system for which behavior over a range of temperature has been studied using sloppy model techniques. In trying to understand the evolution from ectothermy to homeothermy in vertebrate, it would be useful if there were systems with data that could be compared between many widely divergent species.
The obvious species would be those most widely used for developmental studies: zebrafish (Danio rerio), African clawed toads (Xenopus laevis and tropicalis), chicken (Gallus gallus), mouse (Mus musculus). As discussed below, these all share the core principals of spatial and temporal collinearity (where the physical order of the Hox genes on the chromosome matches their activation time and location in the embryo. How this is accomplished and with what degree of accuracy likely differs among them.
They also differ greatly in the range of temperatures at which development normally occurs in vivo. As found out in Exploration 1, this range is very narrow for all mammalian species and not easily manipulated. For all of these systems there are now in vitro systems that appear to recapitulate many of processes occurring during gastrulation and organogenesis.
Thus, in searching for systems to which would be amenable to analysis by sloppy model techniques, I will first examine in vivo data to find simple systems whose temperature behavior stands out as different between the species, and then turn to in vitro systems to see if they could provide adequate data to a analyze.
As discussed in Background 6: The fossil record, a major impetus to evolution near the origin of the vertebrate lineage was two rounds of polyploidation. The lineage of fin-rayed fish, including zebrafish, underwent a further polyploidation, resulting in more Hox clusters and Hox genes, as did the lineage leading to Xenopus which occurred after their last common ancestor with the lineage leading to the amniotes. Thus, the number of Hox clusters and genes is different for the model ectotherms than for the 4 clusters and 39 (?) genes of the homeotherm species.
Although the sequential transcription of Hox clusters prior to cells entering the presomitic mesoderm prinicapally determines their anterior/posterior, there is evidence that this can undergo some 'fine tuning' prior to the fixing of the somite boundaries. As discussed in section 4 of Exploration 2, DUSP proteins may play a role in regulating the oscillation of Erk phosphorylation, which according to recent studies in zebrafish (Simsek 2024), which is important in finalizing these boundaries . The effect of temperature on this system will be the first examined across all the model systems.
Background 8 discusses the prevalence of the Uniform Temperature Performance Curve (UTPC) equation in ectotherms, where the rate of many processes as a function of temperature can be expressed as a simple function of only 3 parameters; the temperature at the maximum rate, this maximum rate, and the (higher) temperature at which the rate goes to 0.
The idea of developmental scaling is that in ectotherms many higher level developmental processes might be coordinated by having their lower level processes all being adapted. to the same UTPC. Does this actually occur in any ectotherm, and what departures from this behavior have occurred during the evolution of endothermy and homeothermy. This aspect will also be a topic for each system examined.
In the next section, I will examine some of the peculiarities of each species that may be relevant to this endeavor.
3.1 Model species
A. Zebrafish
Two rounds of whole genome duplication in early vertebrates are thought to resulted in 4 clusters each containing 13 diploid genes for a total of 52. By the time of the first tetrapod, the number is thought to have been reduced to 39. This is the number in mammals and many birds, including chicken. The whole-genome duplication that occurred in the ancestor of teleost (ray-fined) fishes have allowed them to develop unique regulatory and evolutionary plasticity. The zebrafish has 7 Hox clusters containing a total of 48 functional genes. Unlike the case for mice and humans, Hox mutations in zebrafish that cause changes in anterior/posterior expression usually not lethal to the embryo. Having multiple copies of similar genes may dampen any effect of a mutation in a single one. Also, having more copies of their initial sets of genes has allowed great plasticity due to "subfunctionalization" where initially similar copies of genes can diverge and split former "responsibilities" or to take on new responsibilities. For example, one diploid set may be only be active in early patterning while a sister set is active in later neurodevelopment. In Background 8 discussing the UTPC in ectotherms, it is discussed how adaptation to a wide range of temperatures may involve related copies of a gene being active at different parts of this range.
Zebrafish are also noted that the sequences of enhancers of those Hox genes responsible for vertebrae patterning are substantially different than those of mammals, and likely to be related to the evolutionary flexibility of teleost to adopt a wider range of Hox expression to allow varying aquatic body shapes. Fortunately, understanding of these differences can also be studied in the medaka (Japanese rice fish), another teleost species that whose early development has been widely studied. It is only distantly as distantly related to zebrafish ( last common ancestor, 110-200 mya), which is a similar time to that between the last common ancestor of teleosts and amniotes to the time of the first use of endothermy in the therapsid lineage . Of interest to this site, the two species have different temperature tolerances, zebrafish seem adapted to tropical waters (~28 C), while medaka tolerate a wide temperature range (4 C to 30C).
Toulany et al. (2023) used the machine learning architecture of Twin Networks to develop a system to determine the stage of development of an embryo from its image. This approach has been used in human facial recognition or to train a neural network to distinguish an image of a cat from that of a dog. This approach has great advantages compared to an algorithmic approach to the same task, where decisions (possibly biased) have to be made of which characteristics are most informative and then implementing their recognition. It also can deal with less than ideal images, such as a facial picture not being face-on or an embryo being rotated.
They used the "triplet" method of training. An "anchor" image (a grid 4 million pixels) is input in the neural network outputs a series of numbers (a 1256 dimension vector). A second "positive" image, likely to be similar to the anchor image is input to a second neural which has the same weighting as the first network (its twin). In this study, the positive image would be of another embryo collected with the same interval after fertilization as the anchor image. The 'distance" between the anchor vector and the positive vector would be determined. A "negative" image, an image collected in a different interval would produce a third vector when run through the twin network, and the distance between this vector and the anchor image is determined. A procedure is then used to make the same adjustments to weightings of both networks so that if run through the procedure again the distance between the anchor and positive vectors would be reduced and the distance between the anchor and the negative vectors would increase. This would be repeated with random choices of triplet images until the networks no longer make meaningful improvements in distinguishing similar from dissimilar images.
For zebrafish, the training set of images were those for development at 28.5 C with the time of image capture over the first 24 hours post-fertilization divided into 40 intervals. 28.5 C was the temperature previously used by Kimmel et al. (1995) to develop a staging timeline in zebrafish. To study the effect of temperature on rate of development, images were collected for incubation over a range of 23.0 to 35 C. Each sample image collected at time t(e)was processed through the trained network with each of 360 (reference) images from each time interval of the 28.5 C data set processed through its twin network. The so-called cosine function would be calculated for the two vectors, which is essentially a measure of how closely the direction of the two vectors match. The cosine function would be 1 if an image was compared to itself and near 0 if the two images were very different. Next to average of the cosine function would be calculated for all 360 reference images for each. The interval with the highest cosine function would be determined. This is called the developmental time, t(d) for the sample image. If t(e) is less than t(d), the would mean that up to that time, that embryo had developed faster (to a later time) than the average embryo at 28.5 C. As would expected, the results showed that at temperatures above the reference temperatures took less time to reach a particular developmental stage, and more time for temperatures below.
At each experimental temperature, a plot of all the t(d) values versus the t(e) values could be well fitted by a straight line, giving a developmental growth rate, g, at that temperature. It should be emphasized that this not a rate of growth of in size of the embryo or any particular part, but rather the rate at which the embryo progresses through a set of developmental milestones. A plot of log g versus 1/T was well fitted by a straight line with a negative slope for temperatures between 23.5 C to 31.4 C, therefore the growth rate could be fitted to the Arrhenius equation over this range with an activation energy of 65 kJ/mole. Below 23.5 C embryos do not survice. For temperatures a few degrees above 31.4 C, developmental rate did not increase. Thus, it appears that over the first 24 hours, developmental rate can be accurately described by the Universal Temperature Performance Curve (see Background 8)
Toulany performed the same analysis for Medaka, the Japanese rice fish. It is also a teleost, but very distantly related to zebrafish. The growth rate followed the Arrhenius equation over a wider range, 18-31 C.
B. African clawed frog
Xenopus laevis is the most widely used amphibian for developmental studies. A similar study of temperature dependence to that above was performed by Crapse et al. (2021), but with the timing determined manually for 12 stages between the 3rd cleavage and the end of the neurala stage over a range of temperatures from 12 to 26 C. The temperature dependence up to the late gastrula phase gave an activation energy of around 65 kJ/mole, but was higher around 92 kJ/mole for late gastrula to late neurala.
A peculiarity of Xenopus laevis evolutionary history has complicated the connection of specific genes to developmental processes. 34 mya its ancestor split into two distinct lineages. 18 mya matings occurred between theses lineages. The offspring were initially infertile, but then whole chromosome doubling occurred which allowed pairing at meiosis, resulting in fertile offspring, so-called allotetraploids.
To illustrate the implications of this, consider the Hox genes. Prior to these events, this lineage would have had 2 copies of each of the initial 4 Hox clusters present in early vertebrates, as is the case in Xenopus tropicalis. By 34 mya each cluster will have diverged considerably from each other. After the doubling of the chromosomes, the ancestors of Xenopus laevis had 8 clusters, with each cluster having a nearly similar partner cluster. This has complicated identification of which genes are active during development.
C. Crocodilians
Crocodilians are closest living relatives from birds, having diverged about 245 mya. Unlike birds, which have a highly variable number of cervical, thoracic, and lumbar vertebrae, they have since that time conserved the ancient archosaur body plan, with 8-9 cervical vertebrae, 10-11 thoracic vertebrae, and 5 lumbar vertebrae.
The archosaurs arose in the late Permian, about 255 mya, with features distinct from lizards. Their legs are situated more under their bodies, allowing breathing while running. The early archosaurs transitioned from a sprawling lizard-like posture to an upright stance and developed a four chambered heart. This allows the heart to produce a higher systemic blood pressure while protecting delicate pulmonary tissue, and prevents mixing of oxygenated blood with deoxygenated blood. They likely had some degree of endothermy.
The lineage leading to crocodilians split from that leading to birds in the early Triassic, about 245 mya, and diverged into several different lifestyles during the Triassic and Jurassic, including the Neosuchia, which adapted to being a semi-aquatic ambush predator. The heart was modified to allow longer dives and they reverted to being more ectothermic. This was the only crocodillian lineage to escape the Cretaceous/Mesozoic extinction event.
In extant crocodilians, gastrulation occurs within the maternal oviducts and is completed by the time of egg-laying when the embryo is in the early neurala stage. Before egg-laying temperature fluctuation of the embryo is moderated compared to the ambient temperature by the mass and behavioral thermal regulation of the mother but can fluctuate between 2 and 5 C daily. For those species in which the egg is deposited in a nest of mud and decaying plant matter, daily temperature typically fluctuates 1 to 3 C, and 4 to 6 C in those deposited in sand pits. Average temperatures of individual eggs can vary depending on position in the nest and microclimate (sunny or shady), and there can be rapid declines in temperature during a heavy rainstorm.
Gestation in crocodilians is thus generally exposed to greater temperature variations than birds, and even more so than mammals,
Green et al. (2014) compared the genomes of the American alligator, the saltwater crocodile, and Indian gharial, that diverged around mya . They observed an exceptionally slow rate of genome evolution. They then estimated the mutation rates for ultraconserved sites (UCEs)
Bergeron et al. (2023) estimated the mutation rates across vertebrate lineages.
3.2 ERK pathways
The central hypothesis that is being examined in this site is that as a consequence of the evolution of homeothermy in mammals, small changes in anterior-posterior patterning during gastrulation, which can result in inconsequential appearance of cervical ribs, can result in later lethal events in organogenesis.
In trying to examine this hypothesis in detail, I have decided to concentrate on the ERK (extracellular signal-regulated kinases) involved processes for the following reasons:
ERKs play a central role in determining somite boundaries,
ERKS are involved in formation of many tissues and organs, in particular the circulatory system,
Several rare human genetic disorders have some symptoms (Rauen 2013) that overlap those observed in miscarriages associated with cervical ribs (Background ),
The ERK pathway has already been examined using sloppy system methodology.