DLTKcat: deep learning-based prediction of temperature-dependent enzyme turnover rates.

The enzyme turnover rate, ${k}_{cat}$, quantifies enzyme kinetics by indicating the maximum efficiency of enzyme catalysis. Despite its importance, ${k}_{cat}$ values remain scarce in databases for most organisms, primarily because of the cost of experimental measurements. To predict ${k}_{cat}$ and account for its strong temperature dependence, DLTKcat was developed in this study and demonstrated superior performance (log10-scale root mean squared error = 0.88, R-squared = 0.66) than previously published models. Through two case studies, DLTKcat showed its ability to predict the effects of protein sequence mutations and temperature changes on ${k}_{cat}$ values. Although its quantitative accuracy is not high enough yet to model the responses of cellular metabolism to temperature changes, DLTKcat has the potential to eventually become a computational tool to describe the temperature dependence of biological systems.

A fine balance of hydrophobic-electrostatic communication pathways in a pH-switching protein.

Allostery is the phenomenon of coupling between distal binding sites in a protein. Such coupling is at the crux of protein function and regulation in a myriad of scenarios, yet determining the molecular mechanisms of coupling networks in proteins remains a major challenge. Here, we report mechanisms governing pH-dependent myristoyl switching in monomeric hisactophilin, whereby the myristoyl moves between a sequestered state, i.e., buried within the core of the protein, to an accessible state, in which the myristoyl has increased accessibility for membrane binding. Measurements of the pH and temperature dependence of amide chemical shifts reveal protein local structural stability and conformational heterogeneity that accompany switching. An analysis of these measurements using a thermodynamic cycle framework shows that myristoyl-proton coupling at the single-residue level exists in a fine balance and extends throughout the protein. Strikingly, small changes in the stereochemistry or size of core and surface hydrophobic residues by point mutations readily break, restore, or tune myristoyl switch energetics. Synthesizing the experimental results with those of molecular dynamics simulations illuminates atomistic details of coupling throughout the protein, featuring a large network of hydrophobic interactions that work in concert with key electrostatic interactions. The simulations were critical for discerning which of the many ionizable residues in hisactophilin are important for switching and identifying the contributions of nonnative interactions in switching. The strategy of using temperature-dependent NMR presented here offers a powerful, widely applicable way to elucidate the molecular mechanisms of allostery in proteins at high resolution.

The S1 to S2 and S2 to S3 state transitions in plant photosystem II: relevance to the functional and structural heterogeneity of the water oxidizing complex.

In Photosystem II, light-induced water splitting occurs via the S state cycle of the CaMn4O5-cluster. To understand the role of various possible conformations of the CaMn4O5-cluster in this process, the temperature dependence of the S1 → S2 and S2 → S3 state transitions, induced by saturating laser flashes, was studied in spinach photosystem II membrane preparations under different conditions. The S1 → S2 transition temperature dependence was shown to be much dependent on the type of the cryoprotectant and presence of 3.5% methanol, resulting in the variation of transition half-inhibition temperature by 50 K. No similar effect was observed for the S2 → S3 state transition, for which we also show that both the low spin g = 2.0 multiline and high spin g = 4.1 EPR configurations of the S2 state advance with similar efficiency to the S3 state, both showing a transition half-inhibition temperature of 240 K. This was further confirmed by following the appearance of the Split S3 EPR signal. The results are discussed in relevance to the functional and structural heterogeneity of the water oxidizing complex intermediates in photosystem II.

Heat wave-induced microbial thermal trait adaptation and its reversal in the Subarctic.

Climate change predictions suggest that arctic and subarctic ecosystems will be particularly affected by rising temperatures and extreme weather events, including severe heat waves. Temperature is one of the most important environmental factors controlling and regulating microbial decomposition in soils; therefore, it is critical to understand its impact on soil microorganisms and their feedback to climate warming. We conducted a warming experiment in a subarctic birch forest in North Sweden to test the effects of summer heat waves on the thermal trait distributions that define the temperature dependences for microbial growth and respiration. We also determined the microbial temperature dependences 10 and 12 months after the heat wave simulation had ended to investigate the persistence of the thermal trait shifts. As a result of warming, the bacterial growth temperature dependence shifted to become warm-adapted, with a similar trend for fungal growth. For respiration, there was no shift in the temperature dependence. The shifts in thermal traits were not accompanied by changes in α- or ß-diversity of the microbial community. Warming increased the fungal-to-bacterial growth ratio by 33% and decreased the microbial carbon use efficiency by 35%, and both these effects were caused by the reduction in moisture the warming treatments caused, while there was no evidence that substrate depletion had altered microbial processes. The warm-shifted bacterial thermal traits were partially restored within one winter but only fully recovered to match ambient conditions after 1 year. To conclude, a summer heat wave in the Subarctic resulted in (i) shifts in microbial thermal trait distributions; (ii) lower microbial process rates caused by decreased moisture, not substrate depletion; and (iii) no detectable link between the microbial thermal trait shifts and community composition changes.

Temperature dependence of pollen germination and tube growth in conifers relates to their distribution along an elevational gradient in Washington State, USA.

BACKGROUND AND AIMS: Pollen germination and tube growth are essential processes for successful fertilization. They are among the most temperature-vulnerable stages and subsequently affect seed production and determine population persistence and species distribution under climate change. Our study aims to investigate intra- and inter-specific variations in the temperature dependence of pollen germination and tube length growth and to explore how these variations differ for pollen from elevational gradients. METHODS: We focused on three conifer species, Pinus contorta, Picea engelmannii, and Pinus ponderosa, with pollen collected from 350 to 2200m elevation in Washington State, USA. We conducted pollen viability tests at temperatures from 5 to 40°C in 5°C intervals. After testing for four days, we took images of these samples under a microscope to monitor pollen germination percentage (GP) and tube length (TL). We applied the Gamma function to describe the temperature dependence of GP and TL and estimated key parameters, including the optimal temperature for GP (Topt_GP) and TL (Topt_TL). KEY RESULTS: Results showed that pollen from three species and different elevations within a species have different GP, TL, Topt_GP, and Topt_TL. The population with a higher Topt_GP would also have a higher Topt_TL, while Topt_TL was generally higher than Topt_GP, i.e., a positive but not one-to-one relationship. However, only Pinus contorta showed that populations from higher elevations have lower Topt_GP and Topt_TL and vice versa. The variability in GP increased at extreme temperatures, whereas the variability in TL was greatest near Topt_TL. CONCLUSIONS: Our study demonstrates the temperature dependences of three conifers across a wide range of temperatures. Pollen germination and tube growth are highly sensitive to temperature conditions and vary among species and elevations, affecting their reproduction success during warming. Our findings can provide valuable insights to advance our understanding of how conifer pollen responds to rising temperatures.

Temperature-dependent excitonic emission characteristics of highly crystallized carbon nitride nanosheets.

Highly-crystallized carbon nitride (HCCN) nanosheets exhibit significant potential for advancements in the field of photoelectric conversion. However, to fully exploit their potential, a thorough understanding of the fundamental excitonic photophysical processes is crucial. Here, the temperature-dependent excitonic photoluminescence (PL) of HCCN nanosheets and amorphous polymeric carbon nitride (PCN) is investigated using steady-state and time-resolved PL spectroscopy. The exciton binding energy of HCCN is determined to be 109.26 meV, lower than that of PCN (207.39 meV), which is attributed to the ordered stacking structure of HCCN with a weaker Coulomb interaction between electrons and holes. As the temperature increases, a noticeable reduction in PL lifetime is observed on both the HCCN and PCN, which is ascribed to the thermal activation of carrier trapping by the enhanced electron-phonon coupling effect. The thermal activation energy of HCCN is determined to be 102.9 meV, close to the value of PCN, due to their same band structures. Through wavelength-dependent PL dynamics analysis, we have identified the PL emission of HCCN as deriving from the transitions:σ*-LP,π*-π, andπ*-LP, where theπ*-LP transition dominants the emission because of the high excited state density of the LP state. These results demonstrate the impact of high-crystallinity on the excitonic emission of HCCN materials, thereby expanding their potential applications in the field of photoelectric conversion.

Polyparameter Linear Free Energy Relationships for Partitioning of Neutral Organic Compounds to Storage Lipids.

Storage lipids are an important compartment in the bioaccumulation of neutral organic compounds. Reliable models for predicting storage lipid-water and storage lipid-air partition coefficients (Kislip/w and Kislip/a), as well as their temperature dependence, are considered useful. Polyparameter linear free energy relationships (PP-LFERs) are accurate, general, and mechanistically clear models for predicting partitioning-related physicochemical quantities. About a decade ago, PP-LFERs were calibrated for Kislip/w at the physiological temperature of 37 °C. However, to date, a comprehensive collection and sufficiently reliable PP-LFERs for Kislip/w and Kislip/a at the most common standard temperature of 25 °C are still lacking. In this study, experimentally based Kislip/w and/or Kislip/a values at 25 °C for 278 compounds were extensively collected or converted from the literature. Subsequently, PP-LFERs were calibrated for Kislip/w and Kislip/a at 25 °C, performing well over 10 orders of magnitude with root-mean-square errors of 0.17-0.21 log units for compounds with reliable descriptors. Furthermore, standard internal energy changes of transfer from water or air to storage lipids for 158 compounds were derived and used to calibrate PP-LFERs for estimating the temperature dependence of Kislip/w or Kislip/a. Additionally, using PP-LFERs, low-density polyethylene was confirmed to be a better storage lipid analogue than silicone and polyoxymethylene in the equilibrium passive sampling of nonpolar and H-bond acceptor polar compounds.

Investigating Temperature-Dependent Microscopic Deformation in Tough and Self-Healing Hydrogel Using Time-Resolved USAXS.

Tough and self-healing hydrogels are typically sensitive to loading rates or temperatures due to the dynamic nature of noncovalent bonds. Understanding the structure evolution under varying loading conditions can provide valuable insights for developing new tough soft materials. In this study, polyampholyte (PA) hydrogel with a hierarchical structure is used as a model system. The evolution of the microscopic structure during loading is investigated under varied loading temperatures. By combining ultra-small angle X-ray scattering (USAXS) and Mooney-Rivlin analysis, it is elucidated that the deformation of bicontinuous hard/soft phase networks is closely correlated with the relaxation dynamics or strength of noncovalent bonds. At high loading temperatures, the gel is soft and ductile, and large affine deformation of the phase-separated networks is observed, correlated with the fast relaxation dynamics of noncovalent bonds. At low loading temperatures, the gel is stiff, and nonaffine deformation occurs from the onset of loading due to the substantial breaking of noncovalent bonds and limited chain mobility as well as weak adaptation of phase deformation to external stretch. This work provides an in-depth understanding of the relationship between structure and performance of tough and self-healing hydrogels.

Temperature Dependence of the Number of Defect-Structures in Poly(vinylidene fluoride).

Poly(vinylidene fluoride) (PVDF) is predominantly characterized by alternating CH2 and CF2 units in a polymer backbone, originating from the head-to-tail addition of monomers or regular propagation. Due, to a small extent, to inverse monomer addition, so-called defect structures occur which influence the macroscopic properties of PVDF significantly. The amount of defect structures in the material is determined by the polymerization conditions. Here, the temperature dependence of the fraction of defect structures in PVDF obtained from polymerizations between 45 and 90 °C is reported. We utilized 19F-NMR spectroscopy to determine the fraction of defect structures as a function of temperature. To derive kinetic data, the polymerization of VDF is considered a quasi-copolymerization described by the Terminal Model involving four different propagation reactions. Based on the experimentally determined temperature-dependent fractions of defect structures, the known overall propagation rate coefficient, and taking into account the self-healing behavior of the macroradical, the Arrhenius parameters of the individual propagation rate coefficients were determined using the Monte Carlo methods.

The Temperature Dependence of Hydrogen Bonds Is More Uniform in Stable Proteins: An Analysis of NMR h3JNC' Couplings in Four Different Protein Structures.

Long-range HNCO NMR spectra for proteins show crosspeaks due to 1JNC', 2JNC', 3JNCγ, and h3JNC' couplings. The h3JNC' couplings are transmitted through hydrogen bonds and their sizes are correlated to hydrogen bond lengths. We collected long-range HNCO data at a series of temperatures for four protein structures. P22i and CUS-3i are six-stranded beta-barrel I-domains from phages P22 and CUS-3 that share less than 40% sequence identity. The cis and trans states of the C-terminal domain from pore-forming toxin hemolysin ΙΙ (HlyIIC) arise from the isomerization of a single G404-P405 peptide bond. For P22i and CUS-3i, hydrogen bonds detected by NMR agree with those observed in the corresponding domains from cryoEM structures of the two phages. Hydrogen bond lengths derived from the h3JNC' couplings, however, are poorly conserved between the distantly related CUS-3i and P22i domains and show differences even between the closely related cis and trans state structures of HlyIIC. This is consistent with hydrogen bond lengths being determined by local differences in structure rather than the overall folding topology. With increasing temperature, hydrogen bonds typically show an apparent increase in length that has been attributed to protein thermal expansion. Some hydrogen bonds are invariant with temperature, however, while others show apparent decreases in length, suggesting they become stabilized with increasing temperature. Considering the data for the three proteins in this study and previously published data for ubiquitin and GB3, lowered protein folding stability and cooperativity corresponds with a larger range of temperature responses for hydrogen bonds. This suggests a partial uncoupling of hydrogen bond energetics from global unfolding cooperativity as protein stability decreases.

Human protein arginine methyltransferases (PRMTs) can be optimally active under nonphysiological conditions.

Protein arginine methylation is involved in many biological processes and can be enhanced in cancer. In mammals, these reactions are catalyzed on multiple substrates by a family of nine protein arginine methyltransferases (PRMTs). However, conditions that may regulate the activity of each enzyme and that may help us understand the physiological role of PRMTs have not been fully established. Previous studies had suggested unexpected effects of temperature and ionic strength on PRMT7 activity. Here we examine in detail the effects of temperature, pH, and ionic strength on recombinant human PRMT1, PRMT5, and PRMT7. We confirmed the unusual temperature dependence of PRMT7, where optimal activity was observed at 15 °C. On the other hand, we found that PRMT1 and PRMT5 are most active near physiological temperatures of 37 °C. However, we showed all three enzymes still have significant activity at 0 °C. Furthermore, we determined that PRMT1 is most active at a pH of about 7.7, while PRMT5 activity is not dependent on pH in the range of 6.5 to 8.5. Significantly, PRMT7 is most active at an alkaline pH of 8.5 but shows little activity at the physiological intracellular pH of about 7.2. We also detected decreased activity at physiological salt conditions for PRMT1, PRMT5, and PRMT7. We demonstrate that the loss of activity is due to the increasing ionic strength. Taken together, these results open the possibility that PRMTs respond in cells undergoing temperature, salt, or pH stress and demonstrate the potential for in vivo regulation of protein arginine methylation.

The carbon-quality temperature hypothesis: Fact or artefact?

Climate warming can reduce global soil carbon stocks by enhancing microbial decomposition. However, the magnitude of this loss remains uncertain because the temperature sensitivity of the decomposition of the major fraction of soil carbon, namely resistant carbon, is not fully known. It is now believed that the resistance of soil carbon mostly depends on microbial accessibility of soil carbon with physical protection being the primary control of the decomposition of protected carbon, which is insensitive to temperature changes. However, it is still unclear whether the temperature sensitivity of the decomposition of unprotected carbon, for example, carbon that is not protected by the soil mineral matrix, may depend on the chemical recalcitrance of carbon compounds. In particular, the carbon-quality temperature (CQT) hypothesis asserts that recalcitrant low-quality carbon is more temperature-sensitive to decomposition than labile high-quality carbon. If the hypothesis is correct, climate warming could amplify the loss of unprotected, but chemically recalcitrant, carbon and the resultant CO2 release from soils to the atmosphere. Previous research has supported this hypothesis based on reported negative relationships between temperature sensitivity and carbon quality, defined as the decomposition rate at a reference temperature. Here we show that negative relationships can arise simply from the arbitrary choice of reference temperature, inherently invalidating those tests. To avoid this artefact, we defined the carbon quality of different compounds as their uncatalysed reaction rates in the absence of enzymes. Taking the uncatalysed rate as the carbon quality index, we found that the CQT hypothesis is not supported for enzyme-catalysed reactions, which showed no relationship between carbon quality and temperature sensitivity. The lack of correlation in enzyme-catalysed reactions implies similar temperature sensitivity for microbial decomposition of soil carbon, regardless of its quality, thereby allaying concerns of acceleration of warming-induced decomposition of recalcitrant carbon.

Volatility of Secondary Organic Aerosol from ß-Caryophyllene Ozonolysis over a Wide Tropospheric Temperature Range.

We investigated secondary organic aerosol (SOA) from ß-caryophyllene oxidation generated over a wide tropospheric temperature range (213-313 K) from ozonolysis. Positive matrix factorization (PMF) was used to deconvolute the desorption data (thermograms) of SOA products detected by a chemical ionization mass spectrometer (FIGAERO-CIMS). A nonmonotonic dependence of particle volatility (saturation concentration at 298 K, C298K*) on formation temperature (213-313 K) was observed, primarily due to temperature-dependent formation pathways of ß-caryophyllene oxidation products. The PMF analysis grouped detected ions into 11 compound groups (factors) with characteristic volatility. These compound groups act as indicators for the underlying SOA formation mechanisms. Their different temperature responses revealed that the relevant chemical pathways (e.g., autoxidation, oligomer formation, and isomer formation) had distinct optimal temperatures between 213 and 313 K, significantly beyond the effect of temperature-dependent partitioning. Furthermore, PMF-resolved volatility groups were compared with volatility basis set (VBS) distributions based on different vapor pressure estimation methods. The variation of the volatilities predicted by different methods is affected by highly oxygenated molecules, isomers, and thermal decomposition of oligomers with long carbon chains. This work distinguishes multiple isomers and identifies compound groups of varying volatilities, providing new insights into the temperature-dependent formation mechanisms of ß-caryophyllene-derived SOA particles.

Temperature Dependence of the Beating Frequency of hiPSC-CMs Using a MEMS Force Sensor.

It is expected that human iPS cell-derived cardiomyocytes (hiPSC-CMs) can be used to treat serious heart diseases. However, the properties and functions of human adult cardiomyocytes and hiPSC-CMs, including cell maturation, differ. In this study, we focused on the temperature dependence of hiPSC-CMs by integrating the temperature regulation system into our sensor platform, which can directly and quantitatively measure their mechanical motion. We measured the beating frequency of hiPSC-CMs at different environmental temperatures and found that the beating frequency increased as the temperature increased. Although the rate at which the beating frequency increased with temperature varied, the temperature at which the beating stopped was relatively stable at approximately 20 °C. The stopping of beating at this temperature was stable, even in immature hiPSC-CMs, and was considered to be a primitive property of cardiomyocytes.

Bio-thermal response and thermal damage in biological tissues with non-equilibrium effect and temperature-dependent properties induced by pulse-laser irradiation.

Comprehension of thermal behavior underlying the living biological tissues helps successful applications of current heat therapies. The present work is to explore the heat transport properties of irradiated tissue during tis thermal treatment, in which the local thermal non-equilibrium effect as well as temperature-dependent properties arose from complicated anatomical structure, is considered. Based on the generalized dual-phase lag (GDPL) model, a non-linear governing equation of tissue temperature with variable thermal physical properties is proposed. The effective procedure constructed on an explicit finite difference scheme is then developed to predict numerically the thermal response and thermal damage irradiated by a pulse laser as a therapeutic heat source. The parametric study on variable thermal physical parameters including the phase lag times, heat conductivity, specific heat capacity and blood perfusion rate has been performed to evaluate their influence on temperature distribution in time and space. On this basis, the thermal damage with different laser variables such as laser intensity and exposure time are further analyzed.

Climate change impacts plant carbon balance, increasing mean future carbon use efficiency but decreasing total forest extent at dry range edges.

Carbon use efficiency (CUE) represents how efficient a plant is at translating carbon gains through gross primary productivity (GPP) into net primary productivity (NPP) after respiratory costs (Ra ). CUE varies across space with climate and species composition, but how CUE will respond to climate change is largely unknown due to uncertainty in Ra at novel high temperatures. We use a plant physiological model validated against global CUE observations and LIDAR vegetation canopy height data and find that model-predicted decreases in CUE are diagnostic of transitions from forests to shrubland at dry range edges. Under future climate scenarios, we show mean growing season CUE increases in core forested areas, but forest extent decreases at dry range edges, with substantial uncertainty in absolute CUE due to uncertainty in Ra . Our results highlight that future forest resilience is nuanced and controlled by multiple competing mechanisms.

Fully automated measurement system for temperature-dependent X-ray total scattering at beamline BL04B2 at SPring-8.

Data-driven approaches in materials science demand the collection of large amounts of data on the target materials at synchrotron beamlines. To accurately gather suitable experimental data, it is essential to establish fully automated measurement systems to reduce the workload of the beamline staff. Moreover, the recent COVID-19 pandemic has further emphasized the necessity of automated and/or remote measurements at synchrotron beamlines. Here, the installation of a new sample changer combined with a high-temperature furnace and a fully automated alignment system on beamline BL04B2 at SPring-8 is reported. The system allows X-ray total scattering measurements of up to 21 samples at different temperatures (from room temperature to 1200°C) to be conducted without any human assistance.

Temperature dependence, accuracy, and repeatability of T1 and T2 relaxation times for the ISMRM/NIST system phantom measured using MR fingerprinting.

PURPOSE: Before MR fingerprinting (MRF) can be adopted clinically, the derived quantitative values must be proven accurate and repeatable over a range of T1 and T2 values and temperatures. Correct assessment of accuracy and precision as well as comparison between measurements can only be performed when temperature is either controlled or corrected for. The purpose of this study was to investigate the temperature dependence of T1 and T2 MRF values and evaluate the accuracy and repeatability of temperature-corrected relaxation values derived from a B1 -corrected MRF-fast imaging with steady-state precession implementation using 2 different dictionary sizes. METHODS: The International Society of MR in Medicine/National Institute of Standards and Technology phantom was scanned using an MRF sequence of 2 different lengths, a variable flip angle T1 , and a multi-echo spin echo T2 at 14 temperatures ranging from 15°C to 28°C and investigated with a linear regression model. Temperature-corrected accuracy was evaluated by correlating T1 and T2 times from each MRF dictionary with reference values. Repeatability was assessed using the coefficient of variation, with measurements taken over 30 separate sessions. RESULTS: There was a statistically significant fit of the model for MRF-derived T1 and T2 and temperature (p < 0.05) for all the spheres with a T1 > 500 ms. Both MRF methods showed a strong linear correlation with reference values for T1 (R2 = 0.996) and T2 (R2 = 0.982). MRF repeatability for T1 values was ≤1.4% and for T2 values was ≤3.4%. CONCLUSION: MRF demonstrated relaxation times with a temperature dependence similar to that of conventional mapping methods. Temperature-corrected T1 and T2 values from both dictionaries showed adequate accuracy and excellent repeatability in this phantom study.

Thermal variation in gradient response: measurement and modeling.

PURPOSE: Many aspects and imperfections of gradient dynamics in MRI have been successfully captured by linear time-invariant (LTI) models. Changes in gradient behavior due to heating, however, violate time invariance. The goal of this work is to study such changes at the level of transfer functions and model them by thermal extension of the LTI framework. METHODS: To study the impact of gradient heating on transfer functions, a clinical MR system was heated using a range of high-amplitude DC and AC waveforms, each followed by measuring transfer functions in rapid succession while the system cooled down. Simultaneously, gradient temperature was monitored with an array of temperature sensors positioned according to initial infrared recordings of the gradient tube. The relation between temperatures and transfer functions is cast into local and global linear models. The models are analysed in terms of self-consistency, conditioning, and prediction performance. RESULTS: Pronounced thermal effects are observed in the time resolved transfer functions, largely attributable to in-coil eddy currents and mechanical resonances. Thermal modeling is found to capture these effects well. The keys to good model performance are well-placed temperature sensors and suitable training data. CONCLUSION: Heating changes gradient response, violating time invariance. The utility of LTI modeling can nevertheless be recovered by a linear thermal extension, relying on temperature sensing and adequate one-time training.

Evaluating the Arrhenius equation for developmental processes.

The famous Arrhenius equation is well suited to describing the temperature dependence of chemical reactions but has also been used for complicated biological processes. Here, we evaluate how well the simple Arrhenius equation predicts complex multi-step biological processes, using frog and fruit fly embryogenesis as two canonical models. We find that the Arrhenius equation provides a good approximation for the temperature dependence of embryogenesis, even though individual developmental intervals scale differently with temperature. At low and high temperatures, however, we observed significant departures from idealized Arrhenius Law behavior. When we model multi-step reactions of idealized chemical networks, we are unable to generate comparable deviations from linearity. In contrast, we find the two enzymes GAPDH and ß-galactosidase show non-linearity in the Arrhenius plot similar to our observations of embryonic development. Thus, we find that complex embryonic development can be well approximated by the simple Arrhenius equation regardless of non-uniform developmental scaling and propose that the observed departure from this law likely results more from non-idealized individual steps rather than from the complexity of the system.