Heat Oscillations Driven by the Embryonic Cell Cycle Reveal the Energetic Costs of Signaling

Flexibility and sensitivity in gene regulation out of equilibrium

Cells adapt to environments and tune gene expression by controlling the concentrations of proteins and their kinetics in regulatory networks. In both eukaryotes and prokaryotes, experiments and theory increasingly attest that these networks can and do consume biochemical energy. How does this dissipation enable cellular behaviors forbidden in equilibrium? This open question demands quantitative models that transcend thermodynamic equilibrium. Here, we study the control of simple, ubiquitous gene regulatory networks to explore the consequences of departing equilibrium in transcription. Employing graph theory to model a set of especially common regulatory motifs, we find that dissipation unlocks nonmonotonicity and enhanced sensitivity of gene expression with respect to a transcription factor's concentration. These features allow a single transcription factor to act as both a repressor and activator at different concentrations or achieve outputs with multiple concentration regimes of locally enhanced sensitivity. We systematically dissect how energetically driving individual transitions within regulatory networks, or pairs of transitions, generates a wide range of more adjustable and sensitive phenotypic responses than in equilibrium. These results generalize to more complex regulatory scenarios, including combinatorial control by multiple transcription factors, which we relate and often find collapse to simple mathematical behaviors. Our findings quantify necessary conditions and detectable consequences of energy expenditure. These richer mathematical behaviors-feasibly accessed using biological energy budgets and rates-may empower cells to accomplish sophisticated regulation with simpler architectures than those required at equilibrium.

Direct quantitative perturbations of physical parameters in vivo to elucidate vertebrate embryo morphogenesis

Physical parameters such as tissue interplay forces, luminal pressure, fluid flow, temperature, and electric fields are crucial regulators of embryonic morphogenesis. While significant attention has been given to cellular and molecular responses to these physical parameters, their roles in morphogenesis are not yet fully elucidated. This is largely due to a shortage of methods for spatiotemporal modulation and direct quantitative perturbation of physical parameters in embryos. Recent advancements addressing these challenges include microscopes equipped with devices to apply and adjust forces, direct perturbation of luminal pressure, and the application of micro-forces to targeted cells and cilia in vivo. These methods are critical for unveiling morphogenesis mechanisms, highlighting the importance of integrating molecular and physical approaches for a comprehensive understanding of morphogenesis.

Uncovering underlying physical principles and driving forces of cell differentiation and reprogramming from single-cell transcriptomics

Recent advances in single-cell sequencing technology have revolutionized our ability to acquire whole transcriptome data. However, uncovering the underlying transcriptional drivers and nonequilibrium driving forces of cell function directly from these data remains challenging. We address this by learning cell state vector fields from discrete single-cell RNA velocity to quantify the single-cell global nonequilibrium driving forces as landscape and flux. From single-cell data, we quantified the Waddington landscape, showing that optimal paths for differentiation and reprogramming deviate from the naively expected landscape gradient paths and may not pass through landscape saddles at finite fluctuations, challenging conventional transition state estimation of kinetic rate for cell fate decisions due to the presence of the flux. A key insight from our study is that stem/progenitor cells necessitate greater energy dissipation for rapid cell cycles and self-renewal, maintaining pluripotency. We predict optimal developmental pathways and elucidate the nucleation mechanism of cell fate decisions, with transition states as nucleation sites and pioneer genes as nucleation seeds. The concept of loop flux quantifies the contributions of each cycle flux to cell state transitions, facilitating the understanding of cell dynamics and thermodynamic cost, and providing insights into optimizing biological functions. We also infer cell-cell interactions and cell-type-specific gene regulatory networks, encompassing feedback mechanisms and interaction intensities, predicting genetic perturbation effects on cell fate decisions from single-cell omics data. Essentially, our methodology validates the landscape and flux theory, along with its associated quantifications, offering a framework for exploring the physical principles underlying cellular differentiation and reprogramming and broader biological processes through high-throughput single-cell sequencing experiments.

Historic obstacles and emerging opportunities in the field of developmental metabolism - lessons from Heidelberg

The field of developmental metabolism is experiencing a technological revolution that is opening entirely new fields of inquiry. Advances in metabolomics, small-molecule sensors, single-cell RNA sequencing and computational modeling present new opportunities for exploring cell-specific and tissue-specific metabolic networks, interorgan metabolic communication, and gene-by-metabolite interactions in time and space. Together, these advances not only present a means by which developmental biologists can tackle questions that have challenged the field for centuries, but also present young scientists with opportunities to define new areas of inquiry. These emerging frontiers of developmental metabolism were at the center of a highly interactive 2023 EMBO workshop 'Developmental metabolism: flows of energy, matter, and information'. Here, we summarize key discussions from this forum, emphasizing modern developmental biology's challenges and opportunities.

Calcium oscillations optimize the energetic efficiency of mitochondrial metabolism

Energy transduction is central to living organisms, but the impact of enzyme regulation and signaling on its thermodynamic efficiency is generally overlooked. Here, we analyze the efficiency of ATP production by the tricarboxylic acid cycle and oxidative phosphorylation, which generate most of the chemical energy in eukaryotes. Calcium signaling regulates this pathway and can affect its energetic output, but the concrete energetic impact of this cross-talk remains elusive. Calcium enhances ATP production by activating key enzymes of the tricarboxylic acid cycle while calcium homeostasis is ATP-dependent. We propose a detailed kinetic model describing the calcium-mitochondria cross-talk and analyze it using nonequilibrium thermodynamics: after identifying the effective reactions driving mitochondrial metabolism out of equilibrium, we quantify the mitochondrial thermodynamic efficiency for different conditions. Calcium oscillations, triggered by extracellular stimulation or energy deficiency, boost the thermodynamic efficiency of mitochondrial metabolism, suggesting a compensatory role of calcium signaling in mitochondrial bioenergetics.

Dissipative scaling of development and aging in multicellular organisms

Evolution, self-replication and ontogenesis are highly dynamic, irreversible and self-organizing processes dissipating energy. While progress has been made to decipher the role of thermodynamics in cellular fission, it is not yet clear how entropic balances shape organism growth and aging. This paper derives a general dissipation theory for the life history of organisms. It implies a self-regulated energy dissipation facilitating exponential growth within a hierarchical and entropy lowering self-organization. The theory predicts ceilings in energy expenditures imposed by geometric constrains, which promote thermal optimality during development, and a dissipative scaling across organisms consistent with ecological scaling laws combining isometric and allometric terms. The theory also illustrates how growing organisms can tolerate damage through continuous extension and production of new dissipative structures low in entropy. However, when organisms reduce their rate of cell division and reach a steady adult state, they become thermodynamically unstable, increase internal entropy by accumulating damage, and age.

Thermodynamic probes of life

Nonequilibrium fluctuations reveal nonuniform heat dissipation in living cells.

Energy metabolism modulates the regulatory impact of activators on gene expression

Gene expression is a regulated process fueled by ATP consumption. Therefore, regulation must be coupled to constraints imposed by the level of energy metabolism. Here, we explore this relationship both theoretically and experimentally. A stylized mathematical model predicts that activators of gene expression have variable impact depending on metabolic rate. Activators become less essential when metabolic rate is reduced and more essential when metabolic rate is enhanced. We find that, in the Drosophila eye, expression dynamics of the yan gene are less affected by loss of EGFR-mediated activation when metabolism is reduced, and the opposite effect is seen when metabolism is enhanced. The effects are also seen at the level of pattern regularity in the adult eye, where loss of EGFR-mediated activation is mitigated by lower metabolism. We propose that gene activation is tuned by energy metabolism to allow for faithful expression dynamics in the face of variable metabolic conditions.

Energy metabolism modulates the regulatory impact of activators on gene expression

Gene expression is a regulated process fueled by ATP consumption. Therefore, regulation must be coupled to constraints imposed by the level of energy metabolism. Here, we explore this relationship both theoretically and experimentally. A stylized mathematical model predicts that activators of gene expression have variable impact depending on metabolic rate. Activators become less essential when metabolic rate is reduced and more essential when metabolic rate is enhanced. We find that in the Drosophila eye, expression dynamics of the yan gene are less affected by loss of EGFR-mediated activation when metabolism is reduced, and the opposite effect is seen when metabolism is enhanced. The effects are also seen at the level of pattern regularity in the adult eye, where loss of EGFR-mediated activation is mitigated by lower metabolism. We propose that gene activation is tuned by energy metabolism to allow for faithful expression dynamics in the face of variable metabolic conditions.

Pathway to Independence: the future of developmental biology

In 2022, Development launched its Pathway to Independence (PI) Programme, aimed at supporting postdocs as they transition to their first independent position. We selected eight talented researchers as the first cohort of PI Fellows. In this article, each of our Fellows provides their perspective on the future of their field. Together, they paint an exciting picture of the current state of and open questions in developmental biology.

Physical Constraints in Intracellular Signaling: The Cost of Sending a Bit

Many biological processes require timely communication between molecular components. Cells employ diverse physical channels to this end, transmitting information through diffusion, electrical depolarization, and mechanical waves among other strategies. Here we bound the energetic cost of transmitting information through these physical channels, in k_{B}T/bit, as a function of the size of the sender and receiver, their spatial separation, and the communication latency. These calculations provide an estimate for the energy costs associated with information processing arising from the physical constraints of the cellular environment, which we find to be many orders of magnitude larger than unity in natural units. From these calculations, we construct a phase diagram indicating where each strategy is most efficient. Our results suggest that intracellular information transfer may constitute a substantial energetic cost. This provides a new tool for understanding tradeoffs in cellular network function.

Polyploidy in Xenopus lowers metabolic rate by decreasing total cell surface area

Although polyploidization is frequent in development, cancer, and evolution, impacts on animal metabolism are poorly understood. In Xenopus frogs, the number of genome copies (ploidy) varies across species and can be manipulated within a species. Here, we show that triploid tadpoles contain fewer, larger cells than diploids and consume oxygen at a lower rate. Drug treatments revealed that the major processes accounting for tadpole energy expenditure include cell proliferation, biosynthesis, and maintenance of plasma membrane potential. While inhibiting cell proliferation did not abolish the oxygen consumption difference between diploids and triploids, treatments that altered cellular biosynthesis or electrical potential did. Combining these results with a simple mathematical framework, we propose that the decrease in total cell surface area lowered production and activity of plasma membrane components including the Na+/K+ ATPase, reducing energy consumption in triploids. Comparison of Xenopus species that evolved through polyploidization revealed that metabolic differences emerged during development when cell size scaled with genome size. Thus, ploidy affects metabolism by altering the cell surface area to volume ratio in a multicellular organism.

Flexibility and sensitivity in gene regulation out of equilibrium

Cells adapt to environments and tune gene expression by controlling the concentrations of proteins and their kinetics in regulatory networks. In both eukaryotes and prokaryotes, experiments and theory increasingly attest that these networks can and do consume bio-chemical energy. How does this dissipation enable cellular behaviors unobtainable in equilibrium? This open question demands quantitative models that transcend thermodynamic equilibrium. Here we study the control of a simple, ubiquitous gene regulatory motif to explore the consequences of departing equilibrium in kinetic cycles. Employing graph theory, we find that dissipation unlocks nonmonotonicity and enhanced sensitivity of gene expression with respect to a transcription factor's concentration. These features allow a single transcription factor to act as both a repressor and activator at different levels or achieve outputs with multiple concentration regions of locally-enhanced sensitivity. We systematically dissect how energetically-driving individual transitions within regulatory networks, or pairs of transitions, generates more adjustable and sensitive phenotypic responses. Our findings quantify necessary conditions and detectable consequences of energy expenditure. These richer mathematical behaviors-feasibly accessed using biological energy budgets and rates-may empower cells to accomplish sophisticated regulation with simpler architectures than those required at equilibrium.

Significance Statement

Growing theoretical and experimental evidence demonstrates that cells can (and do) spend biochemical energy while regulating their genes. Here we explore the impact of departing from equilibrium in simple regulatory cycles, and learn that beyond increasing sensitivity, dissipation can unlock more flexible input-output behaviors that are otherwise forbidden without spending energy. These more complex behaviors could enable cells to perform more sophisticated functions using simpler systems than those needed at equilibrium.

Coronary conductance in the normal development of sheep during the perinatal period

Birth is associated with substantial shifts in cardiovascular physiology. Little is known about coronary vascular adaptations during this period. We used fetal and neonatal lambs to measure coronary function at late gestation (92% of term) and shortly after birth (5-6 days postnatal age). In each animal we measured unanesthetized myocardial perfusion and oxygen delivery using a circumflex artery flow probe. We used inflatable occluders and adenosine to determine coronary conductance and flow reserve. In a subset of animals, we used myocardial contrast echocardiography (MCE, anesthetized) to assess its utility as a tool for studying changes in regional myocardial perfusion in normal development. Separate age-matched animals were instrumented with aortic and coronary sinus sampling catheters to determine myocardial oxygen extraction (unanesthetized). With an average of 17 days of developmental time separating our neonatal and fetal cohorts we found that heart-to-body weight ratio was significantly greater in neonates than fetuses. In resting animals, we found significant decreases in weight-normalized perfusion of, and oxygen delivery to, neonatal relative to fetal myocardium. Similar results were seen when measuring baseline MCE-derived perfusion. Pressure-flow relationship studies revealed lower baseline and maximal coronary conductance in neonates than fetuses, with similar coronary flow reserve between groups. There was greater oxygen extraction in neonates than fetuses. Combined analysis of oxygen extraction with coronary flow suggested greater oxygen consumption by the fetal than neonatal myocardium. We conclude that, during the immediate perinatal period, cardiac growth outpaces coronary microvascular growth resulting in lower capacity for microvascular perfusion in the early neonate.

Eukaryotic gene regulation at equilibrium, or non?

Models of transcriptional regulation that assume equilibrium binding of transcription factors have been less successful at predicting gene expression from sequence in eukaryotes than in bacteria. This could be due to the non-equilibrium nature of eukaryotic regulation. Unfortunately, the space of possible non-equilibrium mechanisms is vast and predominantly uninteresting. The key question is therefore how this space can be navigated efficiently, to focus on mechanisms and models that are biologically relevant. In this review, we advocate for the normative role of theory-theory that prescribes rather than just describes-in providing such a focus. Theory should expand its remit beyond inferring mechanistic models from data, towards identifying non-equilibrium gene regulatory schemes that may have been evolutionarily selected, despite their energy consumption, because they are precise, reliable, fast, or otherwise outperform regulation at equilibrium. We illustrate our reasoning by toy examples for which we provide simulation code.

Cellular self-organization: An overdrive in Cambrian diversity?

During the early Cambrian period metazoan life forms diverged at an accelerated rate to occupy multiple ecological niches on earth. A variety of explanations have been proposed to address this major evolutionary phenomenon termed the "Cambrian explosion." While most hypotheses address environmental, developmental, and ecological factors that facilitated evolutionary innovations, the biological basis for accelerated emergence of species diversity in the Cambrian period remains largely conjectural. Herein, we posit that morphogenesis by self-organization enables the uncoupling of genomic mutational landscape from phenotypic diversification. Evidence is provided for a two-tiered interpretation of genomic changes in metazoan animals wherein mutations not only impact upon function of individual cells, but also alter the self-organization outcome during developmental morphogenesis. We provide evidence that the morphological impacts of mutations on self-organization could remain repressed if associated with an unmet negative energetic cost. We posit that accelerated morphological diversification in transition to the Cambrian period has occurred by emergence of dormant (i.e., reserved) morphological novelties whose molecular underpinnings were seeded in the Precambrian period.

Notch ankyrin domain: evolutionary rise of a thermodynamic sensor

Notch signalling pathway plays a key role in metazoan biology by contributing to resolution of binary decisions in the life cycle of cells during development. Outcomes such as proliferation/differentiation dichotomy are resolved by transcriptional remodelling that follows a switch from Notch^on to Notch^off state, characterised by dissociation of Notch intracellular domain (NICD) from DNA-bound RBPJ. Here we provide evidence that transitioning to the Notch^off state is regulated by heat flux, a phenomenon that aligns resolution of fate dichotomies to mitochondrial activity. A combination of phylogenetic analysis and computational biochemistry was utilised to disclose structural adaptations of Notch1 ankyrin domain that enabled function as a sensor of heat flux. We then employed DNA-based micro-thermography to measure heat flux during brain development, followed by analysis in vitro of the temperature-dependent behaviour of Notch1 in mouse neural progenitor cells. The structural capacity of NICD to operate as a thermodynamic sensor in metazoans stems from characteristic enrichment of charged acidic amino acids in β-hairpins of the ankyrin domain that amplify destabilising inter-residue electrostatic interactions and render the domain thermolabile. The instability emerges upon mitochondrial activity which raises the perinuclear and nuclear temperatures to 50 °C and 39 °C, respectively, leading to destabilization of Notch1 transcriptional complex and transitioning to the Notch^off state. Notch1 functions a metazoan thermodynamic sensor that is switched on by intercellular contacts, inputs heat flux as a proxy for mitochondrial activity in the Notch^on state via the ankyrin domain and is eventually switched off in a temperature-dependent manner.

Developmental energetics: Energy expenditure, budgets and metabolism during animal embryogenesis

Developing embryos are metabolically active, open systems that constantly exchange matter and energy with their environment. They function out of thermodynamic equilibrium and continuously use metabolic pathways to obtain energy from maternal nutrients, in order to fulfill the energetic requirements of growth and development. While an increasing number of studies highlight the role of metabolism in different developmental contexts, the physicochemical basis of embryogenesis, or how cellular processes use energy and matter to act together and transform a zygote into an adult organism, remains unknown. As we obtain a better understanding of metabolism, and benefit from current technology development, it is a promising time to revisit the energetic cost of development and how energetic principles may govern embryogenesis. Here, we review recent advances in methodology to measure and infer energetic parameters in developing embryos. We highlight a potential common pattern in embryonic energy expenditure and metabolic strategy across animal embryogenesis, and discuss challenges and open questions in developmental energetics.

Glycolytic flux-signaling controls mouse embryo mesoderm development

How cellular metabolic state impacts cellular programs is a fundamental, unresolved question. Here, we investigated how glycolytic flux impacts embryonic development, using presomitic mesoderm (PSM) patterning as the experimental model. First, we identified fructose 1,6-bisphosphate (FBP) as an in vivo sentinel metabolite that mirrors glycolytic flux within PSM cells of post-implantation mouse embryos. We found that medium-supplementation with FBP, but not with other glycolytic metabolites, such as fructose 6-phosphate and 3-phosphoglycerate, impaired mesoderm segmentation. To genetically manipulate glycolytic flux and FBP levels, we generated a mouse model enabling the conditional overexpression of dominant active, cytoplasmic PFKFB3 (cytoPFKFB3). Overexpression of cytoPFKFB3 indeed led to increased glycolytic flux/FBP levels and caused an impairment of mesoderm segmentation, paralleled by the downregulation of Wnt-signaling, reminiscent of the effects seen upon FBP-supplementation. To probe for mechanisms underlying glycolytic flux-signaling, we performed subcellular proteome analysis and revealed that cytoPFKFB3 overexpression altered subcellular localization of certain proteins, including glycolytic enzymes, in PSM cells. Specifically, we revealed that FBP supplementation caused depletion of Pfkl and Aldoa from the nuclear-soluble fraction. Combined, we propose that FBP functions as a flux-signaling metabolite connecting glycolysis and PSM patterning, potentially through modulating subcellular protein localization.

Non-Interventional and High-Precision Temperature Measurement Biochips for Long-Term Monitoring the Temperature Fluctuations of Individual Cells

Monitoring the thermal responses of individual cells to external stimuli is essential for studies of cell metabolism, organelle function, and drug screening. Fluorescent temperature probes are usually employed to measure the temperatures of individual cells; however, they have some unavoidable problems, such as, poor stability caused by their sensitivity to the chemical composition of the solution and the limitation in their measurement time due to the short fluorescence lifetime. Here, we demonstrate a stable, non-interventional, and high-precision temperature-measurement chip that can monitor the temperature fluctuations of individual cells subject to external stimuli and over a normal cell life cycle as long as several days. To improve the temperature resolution, we designed temperature sensors made of Pd-Cr thin-film thermocouples, a freestanding Si3N4 platform, and a dual-temperature control system. Our experimental results confirm the feasibility of using this cellular temperature-measurement chip to detect local temperature fluctuations of individual cells that are 0.3-1.5 K higher than the ambient temperature for HeLa cells in different proliferation cycles. In the future, we plan to integrate this chip with other single-cell technologies and apply it to research related to cellular heat-stress response.

Opposing motors provide mechanical and functional robustness in the human spindle

At each cell division, the spindle self-organizes from microtubules and motors. In human spindles, the motors dynein and Eg5 generate contractile and extensile stress, respectively. Inhibiting dynein or its targeting factor NuMA leads to unfocused, turbulent spindles, and inhibiting Eg5 leads to monopoles; yet, bipolar spindles form when both are inhibited together. What, then, are the roles of these opposing motors? Here, we generate NuMA/dynein- and Eg5-doubly inhibited spindles that not only attain a typical metaphase shape and size but also undergo anaphase. However, these spindles have reduced microtubule dynamics and are mechanically fragile, fracturing under force. Furthermore, they exhibit lagging chromosomes and a dramatic left-handed twist at anaphase. Thus, although these opposing motors are not required for spindle shape, they are essential to its mechanical and functional robustness. This work suggests a design principle whereby opposing active stresses provide robustness to force-generating cellular structures.

Forward and feedback control mechanisms of developmental tissue growth

The size and proportions of animals are tightly controlled during development. How this is achieved remains poorly understood. The control of organ size entails coupling of cellular growth and cell division on one hand, and the measure of organ size on the other. In this review we focus on three layers of growth control consisting of genetic patterning, notably chemical gradients, mechanics and energetics which are complemented by a systemic control unit that modulates growth in response to the nutritional conditions and coordinates growth between different organs so as to maintain proportions. Growth factors, often present as concentration dependent chemical gradients, are positive inducers of cellular growth that may be considered as deterministic cues, hence acting as organ-intrinsic controllers of growth. However, the exponential growth dynamics in many developing tissues necessitate more stringent growth control in the form of negative feedbacks. Feedbacks endow biological systems with the capacity to quickly respond to perturbations and to correct the growth trajectory to avoid overgrowth. We propose to integrate chemical, mechanical and energetic control over cellular growth in a framework that emphasizes the self-organizing properties of organ-autonomous growth control in conjunction with systemic organ non-autonomous feedback on growth.

Fractal Pennes and Cattaneo-Vernotte bioheat equations from product-like fractal geometry and their implications on cells in the presence of tumour growth

In this study, the Pennes and Cattaneo-Vernotte bioheat transfer equations in the presence of fractal spatial dimensions are derived based on the product-like fractal geometry. This approach was introduced recently, by Li and Ostoja-Starzewski, in order to explore dynamical properties of anisotropic media. The theory is characterized by a modified gradient operator which depends on two parameters: R which represents the radius of the tumour and R0 which represents the radius of the spherical living tissue. Both the steady and unsteady states for each fractal bioheat equation were obtained and their implications on living cells in the presence of growth of a large tumour were analysed. Assuming a specific heating/cooling by a constant heat flux equivalent to the metabolic heat generation in the tissue, it was observed that the solutions of the fractal bioheat equations are robustly affected by fractal dimensions, the radius of the tumour growth and the dimensions of the living cell tissue. The ranges of both the fractal dimensions and temperature were obtained, analysed and compared with recent studies. This study confirms the importance of fractals in medicine.

Cost-precision trade-off relation determines the optimal morphogen gradient for accurate biological pattern formation

Spatial boundaries formed during animal development originate from the pre-patterning of tissues by signaling molecules, called morphogens. The accuracy of boundary location is limited by the fluctuations of morphogen concentration that thresholds the expression level of target gene. Producing more morphogen molecules, which gives rise to smaller relative fluctuations, would better serve to shape more precise target boundaries; however, it incurs more thermodynamic cost. In the classical diffusion-depletion model of morphogen profile formation, the morphogen molecules synthesized from a local source display an exponentially decaying concentration profile with a characteristic length λ. Our theory suggests that in order to attain a precise profile with the minimal cost, λ should be roughly half the distance to the target boundary position from the source. Remarkably, we find that the profiles of morphogens that pattern the Drosophila embryo and wing imaginal disk are formed with nearly optimal λ. Our finding underscores the cost-effectiveness of precise morphogen profile formation in Drosophila development.

Close to Optimal Cell Sensing Ensures the Robustness of Tissue Differentiation Process: The Avian Photoreceptor Mosaic Case

The way that progenitor cell fate decisions and the associated environmental sensing are regulated to ensure the robustness of the spatial and temporal order in which cells are generated towards a fully differentiating tissue still remains elusive. Here, we investigate how cells regulate their sensing intensity and radius to guarantee the required thermodynamic robustness of a differentiated tissue. In particular, we are interested in finding the conditions where dedifferentiation at cell level is possible (microscopic reversibility), but tissue maintains its spatial order and differentiation integrity (macroscopic irreversibility). In order to tackle this, we exploit the recently postulated Least microEnvironmental Uncertainty Principle (LEUP) to develop a theory of stochastic thermodynamics for cell differentiation. To assess the predictive and explanatory power of our theory, we challenge it against the avian photoreceptor mosaic data. By calibrating a single parameter, the LEUP can predict the cone color spatial distribution in the avian retina and, at the same time, suggest that such a spatial pattern is associated with quasi-optimal cell sensing. By means of the stochastic thermodynamics formalism, we find out that thermodynamic robustness of differentiated tissues depends on cell metabolism and cell sensing properties. In turn, we calculate the limits of the cell sensing radius that ensure the robustness of differentiated tissue spatial order. Finally, we further constrain our model predictions to the avian photoreceptor mosaic.

Physical bioenergetics: Energy fluxes, budgets, and constraints in cells

Cells are the basic units of all living matter which harness the flow of energy to drive the processes of life. While the biochemical networks involved in energy transduction are well-characterized, the energetic costs and constraints for specific cellular processes remain largely unknown. In particular, what are the energy budgets of cells? What are the constraints and limits energy flows impose on cellular processes? Do cells operate near these limits, and if so how do energetic constraints impact cellular functions? Physics has provided many tools to study nonequilibrium systems and to define physical limits, but applying these tools to cell biology remains a challenge. Physical bioenergetics, which resides at the interface of nonequilibrium physics, energy metabolism, and cell biology, seeks to understand how much energy cells are using, how they partition this energy between different cellular processes, and the associated energetic constraints. Here we review recent advances and discuss open questions and challenges in physical bioenergetics.

Improved bounds on entropy production in living systems

Living systems maintain or increase local order by working against the second law of thermodynamics. Thermodynamic consistency is restored as they consume free energy, thereby increasing the net entropy of their environment. Recently introduced estimators for the entropy production rate have provided major insights into the efficiency of important cellular processes. In experiments, however, many degrees of freedom typically remain hidden to the observer, and, in these cases, existing methods are not optimal. Here, by reformulating the problem within an optimization framework, we are able to infer improved bounds on the rate of entropy production from partial measurements of biological systems. Our approach yields provably optimal estimates given certain measurable transition statistics. In contrast to prevailing methods, the improved estimator reveals nonzero entropy production rates even when nonequilibrium processes appear time symmetric and therefore may pretend to obey detailed balance. We demonstrate the broad applicability of this framework by providing improved bounds on the energy consumption rates in a diverse range of biological systems including bacterial flagella motors, growing microtubules, and calcium oscillations within human embryonic kidney cells.

Gene Regulation and Cellular Metabolism: An Essential Partnership

It is recognized that cell metabolism is tightly connected to other cellular processes such as regulation of gene expression. Metabolic pathways not only provide the precursor molecules necessary for gene expression, but they also provide ATP, the primary fuel driving gene expression. However, metabolic conditions are highly variable since nutrient uptake is not a uniform process. Thus, cells must continually calibrate gene expression to their changing metabolite and energy budgets. This review discusses recent advances in understanding the molecular and biophysical mechanisms that connect metabolism and gene regulation as cells navigate their growth, proliferation, and differentiation. Particular focus is given to these mechanisms in the context of organismal development.

A Micromachined Picocalorimeter Sensor for Liquid Samples with Application to Chemical Reactions and Biochemistry

Calorimetry has long been used to probe the physical state of a system by measuring the heat exchanged with the environment as a result of chemical reactions or phase transitions. Application of calorimetry to microscale biological samples, however, is hampered by insufficient sensitivity and the difficulty of handling liquid samples at this scale. Here, a micromachined calorimeter sensor that is capable of resolving picowatt levels of power is described. The sensor consists of low-noise thermopiles on a thin silicon nitride membrane that allow direct differential temperature measurements between a sample and four coplanar references, which significantly reduces thermal drift. The partial pressure of water in the ambient around the sample is maintained at saturation level using a small hydrogel-lined enclosure. The materials used in the sensor and its geometry are optimized to minimize the noise equivalent power generated by the sensor in response to the temperature field that develops around a typical sample. The experimental response of the sensor is characterized as a function of thermopile dimensions and sample volume, and its capability is demonstrated by measuring the heat dissipated during an enzymatically catalyzed biochemical reaction in a microliter-sized liquid droplet. The sensor offers particular promise for quantitative measurements on biological systems.

Bistable, Biphasic Regulation of PP2A-B55 Accounts for the Dynamics of Mitotic Substrate Phosphorylation

The phosphorylation of mitotic proteins is bistable, which contributes to the decisiveness of the transitions into and out of M phase. The bistability in substrate phosphorylation has been attributed to bistability in the activation of the cyclin-dependent kinase Cdk1. However, more recently it has been suggested that bistability also arises from positive feedback in the regulation of the Cdk1-counteracting phosphatase PP2A-B55. Here, we demonstrate biochemically using Xenopus laevis egg extracts that the Cdk1-counter-acting phosphatase PP2A-B55 functions as a bistable switch, even when the bistability of Cdk1 activation is suppressed. In addition, Cdk1 regulates PP2A-B55 in a biphasic manner; low concentrations of Cdk1 activate PP2A-B55 and high concentrations inactivate it. As a consequence of this incoherent feedforward regulation, PP2A-B55 activity rises concurrently with Cdk1 activity during interphase and suppresses substrate phosphorylation. PP2A-B55 activity is then sharply downregulated at the onset of mitosis. During mitotic exit, Cdk1 activity initially falls with no obvious change in substrate phosphorylation; dephosphorylation then commences once PP2A-B55 spikes in activity. These findings suggest that changes in Cdk1 activity are permissive for mitotic entry and exit but that the changes in PP2A-B55 activity are the ultimate trigger.

Mitotic transitions are accompanied by drastic changes in the phosphorylation state of proteins. Kamenz et al. demonstrate biochemically that the major mitotic phosphatase PP2A-B55 is regulated by incoherent feedforward and double-negative feedback loops to promote rapid and switch-like mitotic entry and exit.

Entropy Production in Exactly Solvable Systems

The rate of entropy production by a stochastic process quantifies how far it is from thermodynamic equilibrium. Equivalently, entropy production captures the degree to which global detailed balance and time-reversal symmetry are broken. Despite abundant references to entropy production in the literature and its many applications in the study of non-equilibrium stochastic particle systems, a comprehensive list of typical examples illustrating the fundamentals of entropy production is lacking. Here, we present a brief, self-contained review of entropy production and calculate it from first principles in a catalogue of exactly solvable setups, encompassing both discrete- and continuous-state Markov processes, as well as single- and multiple-particle systems. The examples covered in this work provide a stepping stone for further studies on entropy production of more complex systems, such as many-particle active matter, as well as a benchmark for the development of alternative mathematical formalisms.

Monitoring and modeling of lymphocytic leukemia cell bioenergetics reveals decreased ATP synthesis during cell division

The energetic demands of a cell are believed to increase during mitosis, but the rates of ATP synthesis and consumption during mitosis have not been quantified. Here, we monitor mitochondrial membrane potential of single lymphocytic leukemia cells and demonstrate that mitochondria hyperpolarize from the G2/M transition until the metaphase-anaphase transition. This hyperpolarization was dependent on cyclin-dependent kinase 1 (CDK1) activity. By using an electrical circuit model of mitochondria, we quantify mitochondrial ATP synthesis rates in mitosis from the single-cell time-dynamics of mitochondrial membrane potential. We find that mitochondrial ATP synthesis decreases by approximately 50% during early mitosis and increases back to G2 levels during cytokinesis. Consistently, ATP levels and ATP synthesis are lower in mitosis than in G2 in synchronized cell populations. Overall, our results provide insights into mitotic bioenergetics and suggest that cell division is not a highly energy demanding process.

ATP drives most cellular processes, although ATP production and consumption levels during mitosis remain unreported. Here, the authors combine metabolic measurements and modeling to quantify ATP levels and synthesis dynamics, revealing that ATP synthesis and consumption are lowered during mitosis.

Chemical Embryology Redux: Metabolic Control of Development

New studies of metabolic reactions and networks in embryos are making important additions to regulatory models of development, so far dominated by genes and signals. Metabolic control of development is not a new idea and can be traced back to Joseph Needham's 'Chemical Embryology', published in the 1930s. Even though Needham's ideas fell by the wayside with the advent of genetic studies of embryogenesis, they demonstrated that embryos provide convenient models for addressing fundamental questions in biochemistry and are now experiencing a comeback, enabled by the powerful merger of detailed mechanistic studies and systems-level techniques. Here we review recent results from studies that quantified the energy budget of embryogenesis in Drosophila and started to untangle the intricate connections between core anabolic processes and developmental transitions. Dynamic coordination of metabolic, genetic, and signaling networks appears to be essential for seamless progression of development.

Reclaiming Warburg: using developmental biology to gain insight into human metabolic diseases

Developmental biologists have frequently pushed the frontiers of modern biomedical research. From the discovery and characterization of novel signal transduction pathways to exploring the molecular underpinnings of genetic inheritance, transcription, the cell cycle, cell death and stem cell biology, studies of metazoan development have historically opened new fields of study and consistently revealed previously unforeseen avenues of clinical therapies. From this perspective, it is not surprising that our community is now an integral part of the current renaissance in metabolic research. Amidst the global rise in metabolic syndrome, the discovery of novel signaling roles for metabolites, and the increasing links between altered metabolism and many human diseases, we as developmental biologists can contribute skills and expertise that are uniquely suited for investigating the mechanisms underpinning human metabolic health and disease. Here, we summarize the opportunities and challenges that our community faces, and discuss how developmental biologists can make unique and valuable contributions to the field of metabolism and physiology.

Sub-nanowatt microfluidic single-cell calorimetry

Non-invasive and label-free calorimetry could become a disruptive technique to study single cell metabolic heat production without altering the cell behavior, but it is currently limited by insufficient sensitivity. Here, we demonstrate microfluidic single-cell calorimetry with 0.2-nW sensitivity, representing more than ten-fold enhancement over previous record, which is enabled by (i) a low-noise thermometry platform with ultralow long-term (10-h) temperature noise (80 μK) and (ii) a microfluidic channel-in-vacuum design allowing cell flow and nutrient delivery while maintaining a low thermal conductance of 2.5 μW K⁻¹. Using Tetrahymena thermophila as an example, we demonstrate on-chip single-cell calorimetry measurement with metabolic heat rates ranging from 1 to 4 nW, which are found to correlate well with the cell size. Finally, we perform real-time monitoring of metabolic rate stimulation by introducing a mitochondrial uncoupling agent to the microchannel, enabling determination of the spare respiratory capacity of the cells.

Calorimetrically measuring the heat of single cells is currently not possible due to the sensitivity of existing calorimeters. Here the authors present on-chip single cell calorimetry, with a sensitivity over ten-fold greater than the current gold-standard.

Contribution of increasing plasma membrane to the energetic cost of early zebrafish embryogenesis

How do early embryos allocate the resources stored in the sperm and egg? Recently, we established isothermal calorimetry to measure heat dissipation by living zebra-fish embryos and to estimate the energetics of specific developmental events. During the reductive cleavage divisions, the rate of heat dissipation increases from ∼60 nJ · s-1 at the two-cell stage to ∼90 nJ · s-1 at the 1024-cell stage. Here we ask which cellular process(es) drive this increasing energetic cost. We present evidence that the cost is due to the increase in the total surface area of all the cells of the embryo. First, embryo volume stays constant during the cleavage stage, indicating that the increase is not due to growth. Second, the heat increase is blocked by nocodazole, which inhibits DNA replication, mitosis, and cell division; this suggests some aspect of cell proliferation contributes to these costs. Third, the heat increases in proportion to the total cell surface area rather than total cell number. Fourth, the heat increase falls within the range of the estimated costs of maintaining and assembling plasma membranes and associated proteins. Thus, the increase in total plasma membrane associated with cell proliferation is likely to contribute appreciably to the total energy budget of the embryo.

Ordered patterning of the sensory system is susceptible to stochastic features of gene expression

Sensory neuron numbers and positions are precisely organized to accurately map environmental signals in the brain. This precision emerges from biochemical processes within and between cells that are inherently stochastic. We investigated impact of stochastic gene expression on pattern formation, focusing on senseless (sens), a key determinant of sensory fate in Drosophila. Perturbing microRNA regulation or genomic location of sens produced distinct noise signatures. Noise was greatly enhanced when both sens alleles were present in homologous loci such that each allele was regulated in trans by the other allele. This led to disordered patterning. In contrast, loss of microRNA repression of sens increased protein abundance but not sensory pattern disorder. This suggests that gene expression stochasticity is a critical feature that must be constrained during development to allow rapid yet accurate cell fate resolution.

A Theoretical Framework for Evolutionary Cell Biology

One of the last uncharted territories in evolutionary biology concerns the link with cell biology. Because all phenotypes ultimately derive from events at the cellular level, this connection is essential to building a mechanism-based theory of evolution. Given the impressive developments in cell biological methodologies at the structural and functional levels, the potential for rapid progress is great. The primary challenge for theory development is the establishment of a quantitative framework that transcends species boundaries. Two approaches to the problem are presented here: establishing the long-term steady-state distribution of mean phenotypes under specific regimes of mutation, selection, and drift and evaluating the energetic costs of cellular structures and functions. Although not meant to be the final word, these theoretical platforms harbor potential for generating insight into a diversity of unsolved problems, ranging from genome structure to cellular architecture to aspects of motility in organisms across the Tree of Life.

Energy dissipation bounds for autonomous thermodynamic cycles

How much free energy is irreversibly lost during a thermodynamic process? For deterministic protocols, lower bounds on energy dissipation arise from the thermodynamic friction associated with pushing a system out of equilibrium in finite time. Recent work has also bounded the cost of precisely moving a single degree of freedom. Using stochastic thermodynamics, we compute the total energy cost of an autonomously controlled system by considering both thermodynamic friction and the entropic cost of precisely directing a single control parameter. Our result suggests a challenge to the usual understanding of the adiabatic limit: Here, even infinitely slow protocols are energetically irreversible.

Lessons from equilibrium statistical physics regarding the assembly of protein complexes

In order to carry out their functions, most proteins assemble into multicomponent complexes. In the process of assembly, complexes need to discriminate their specific components from a mixture of hundreds of different proteins present in the cell. To assess some of the implications of this requirement, we develop a minimal model of self-assembly based on equilibrium statistical physics. We argue that the need to assemble reliably imposes fundamental constraints on the characteristics of complexes, which we support with analysis of available structural and compositional data. Our work constitutes only a step toward future theory of protein complex assembly, which will have to incorporate also nonequilibrium and kinetic aspects of this fundamental and rich, yet theoretically neglected, problem.

Cellular functions are established through biological evolution, but are constrained by the laws of physics. For instance, the physics of protein folding limits the lengths of cellular polypeptide chains. Consequently, many cellular functions are carried out not by long, isolated proteins, but rather by multiprotein complexes. Protein complexes themselves do not escape physical constraints, one of the most important being the difficulty of assembling reliably in the presence of cellular noise. In order to lay the foundation for a theory of reliable protein complex assembly, we study here an equilibrium thermodynamic model of self-assembly that exhibits 4 distinct assembly behaviors: diluted protein solution, liquid mixture, “chimeric assembly,” and “multifarious assembly.” In the latter regime, different protein complexes can coexist without forming erroneous chimeric structures. We show that 2 conditions have to be fulfilled to attain this regime: 1) The composition of the complexes needs to be sufficiently heterogeneous, and 2) the use of the set of components by the complexes has to be sparse. Our analysis of publicly available databases of protein complexes indicates that cellular protein systems might have indeed evolved so as to satisfy both of these conditions.

Measuring the Energetic Costs of Embryonic Development

What are the thermodynamic costs of development? In this issue of Developmental Cell, Rodenfels et al. (2019) demonstrate that the high energetic cost of coordinated cell division that is regulated by phospho-signaling gives rise to a measurable periodicity in the heat dissipated during zebrafish embryogenesis.