Discovering autocatalytic chemistries that can evolve is a major goal in systems chemistry and a critical step towards understanding the origin of life. Autocatalytic networks have been discovered in various chemistries, but we lack a general understanding of how network topology controls the Darwinian properties of variation, differential reproduction, and heredity, which are mediated by the chemical composition. Using barcoded sequencing and droplet microfluidics, we establish a landscape of thousands of networks of RNAs that catalyze their own formation from fragments, and derive relationships between network topology and chemical composition. We find that strong variations arise from catalytic innovations perturbing weakly connected networks, and that growth increases with global connectivity. These rules imply trade-offs between reproduction and variation, and between compositional persistence and variation along trajectories of network complexification. Overall, connectivity in reaction networks provides a lever to balance variation  with reproduction and heredity (persistence being necessary for selection to act), as required for chemical evolution. Autocatalytic networks may have started evolution during the origin of life. Here, the authors establish a landscape of thousands of RNA networks by barcoded sequencing and microfluidics, and derive relationships between topology and Darwinian properties such as variation and differential reproduction. Theoretically, it has been shown that autocatalytic reaction networks can emerge from random pools12 and several scenarios have been proposed for how they could have supported early modes of evolution17. Although the proposed dynamics and suggested chemical embodiments differ, these scenarios have in common the possibility to form a diversity of autocatalytic systems, with evolution arising from transitions between such systems. Consistently, recent experiments indicate that RNA replicases (RNA-dependent RNA-polymerase ribozymes) may have emerged as components of such networks18, and hypercycle models propose that early replicases may have participated to networks19. The possibility for autocatalytic networks to evolve is significant as the spontaneous appearance of an RNA replicase with sufficient processivity to allow self-replication and enough fidelity to avoid an error catastrophe21 seems unlikely, given the length (>165 nt) and structural complexity of known replicases24.Autocatalytic reaction networks, where chemicals collectively catalyze the synthesis of each other, are a crucial ingredient for the emergence of evolution, as they enable the maintenance and reproduction of out-of-equilibrium chemical states. Experimentally, autocatalytic chemistries built from a broad range of molecules, including organic25. Indeed, these properties need to be mediated by chemical compositions 26 without the copying of a sequence. Furthermore, evolution in reaction networks may be constrained by trade-offs between these properties. For instance, robustness to environmental perturbations and persistence of compositions are necessary for selection to act, but must be balanced with variation to explore novel states.Nevertheless, sustaining evolution in reaction networks without template-based replication is by no means trivial, and autocatalytic networks that could support the Darwinian properties of variation, differential reproduction, and heredity are not known16 . The large-scale combinatorial screen establishes a landscape of networks from which we analyzed the growth (product accumulation or reaction yield) and fraction of catalytic species (composition) as a function of network topology. We also compare the composition of networks that differ by a single catalytic species as way to assess the susceptibility of networks to the appearance of novel catalytic species. From this, we deduce network parameters that control properties central to Darwinian evolution: reproduction, interpreted as the accumulation of autocatalytic species, and variation, interpreted as changes in species fractions. We found how these parameters depend on the specificity of the interactions between the catalysts produced during the reaction and their substrates. In turn, these molecular rules are found to impose trade-offs between the Darwinian properties they control, thus predicting how evolutionary trajectories can be constrained in a scenario where networks expand by successive accretion of novel species.Here, we develop a method to generate a wide diversity of reaction networks and measure the relationship between network topology and product formation in a prebiotically relevant experimental model of autocatalytic sets of RNAs28 of the Azoarcus bacterium, where fragments, denoted WXY and Z, assemble into noncovalent complexes that catalyze the formation of more efficient covalent ribozymes29  and target (tag), located at extremities of the WXY fragments29  and Z fragments  between measured and expected species concentrations  by adding the first order effective catalytic rates of noncovalent and covalent ribozymes measured independently for individual IGS-tag pairs , or due to environmental changes in physico-chemical conditions (extrinsic cause of variation)G and G′ differing by a single catalytic species denoted a  =  to More specifically, we compared networks n V Fig. . By defiion Fig. .33. In contrast, for covalent ribozymes only, product fractions should be predicted by eigenvector centrality, which accounts for longer catalytic chains33. Despite these differences, the in-degree centrality was found to be a good approximation of the eigenvector centrality for our dataset :n, which we call perturbation breadth, is the number of catalytic species whose formation is catalyzed by the new catalyst a added to the network; (ii) m, which we call catalytic novelty, is the number of species already present in G that catalyze the same reactions as the newly added catalytic species a ; (iii) σG, which we call the background strength, is the sum of all catalytic rates of the catalytic species of the initial reaction network, and; (iv) e is the catalytic rate of the reactions catalyzed by catalyst a (as determined by the ribozyme IGS).The predicted perturbation depends on four parameters, which characterize the initial network and the added catalytic species Fig. : (i) n, σG, e, m, and n on m = 0, Fig. σG/e . When a catalyst with the same specificity (same ribozyme IGS) as the added catalyst was already present in the network  to be combined with a low normalized background strength (σG/e ≤ 1)  Fig. . Similar 1) Fig. .σG/e combined with the weak but significant correlation between growth and σG , Eq. σG/ne). The ratio σG/ne expresses a second trade-off, between the robustness induced by the background strength of the network σG, and the variation induced by the novel species as characterized by n and e.To test the interplay between robustness and variation in scenarios where novel catalytic species would appear either spontaneouslyime Fig. . We havene must be comparable to the σG of the perturbed network, σG would roughly double after a strong perturbation, enhancing robustness to further variation. Consequently, strong variations should be followed by small ones, and result in inflexions (change in curvature) in cumulative perturbation trajectories. We quantified the corresponding inflexions by their sharpness  are prone to few but strong variations (sudden changes in composition), whereas ‘dense’ chemistries  are prone to many but weak variations   Fig. .11. Our experimental results show that connectivity in reaction networks further poses conditions on the ability for networks to evolve, as network topology modulates both growth and variation in response to the appearance of novel species. Indeed, in autocatalytic networks, Darwinian evolution is in principle possible despite the absence of template-based replication, but relies on the appearance  of catalytic species that are sustained by autocatalysis and modulate the composition of a pre-existing network15. This experiment shows that a diverse growth and variation dynamics could be generated from combinations of only a few specific interactions, raising the possibility to synthesize chemistries with the capacity to evolve based on reasonably sized spaces of chemical interactions.A first general constraint to achieve evolution in chemical networks resulted from theoretical studies, which established that the density of catalytic interactions must exceed a threshold for network self-reproduction40. Indeed, in prebiotic scenarios such as Dynamical Kinetic Stability41, evolution depends on a balance between persistence of chemical compositions, thus robustness to environmental changes, and exploration of novel compositions, thus susceptibility to perturbations. These evolutionary trade-offs and the connectivity rules imply a ‘Goldilocks’ range (neither too high not too low) in the density of catalytic interactions for evolution to be possible.What then, are the requirements for reaction networks to evolve? First, we found that network-level structures constrain properties that emerge at the level of chemical compositions. Specifically, network topology imposes trade-offs between growth (favored by higher connectivity) and variation (favored by lower connectivity), and between variation (favored by lower connectivity) and robustness to environmental changes (favored by higher connectivity). These considerations are directly relevant to scenarios where early evolution is driven by environmental heterogeneity4. In our case, catalysis from self-assembled molecules  enables the onset of self-reproduction, but leads to relaxation of chemical compositions toward states determined by the substrates, rather than by the covalent catalysts transmitted from pre-existing networks . Chemicals were purchased from Sigma–Aldrich unless specified otherwise. 4-(2-Hydroxyethyl)-1-piperazinepropanesulfonic acid (EPPS) was purchased from Alfa Aesar . Denaturing polyacrylamide gels (12%) were prepared using gel stock solution  and run in 1X Tris-Borate EDTA buffer (TBE). DNA/RNA oligonucleotides (Supplementary Data 48 (Version 0.69-6).Sequencing data processing and analysis was performed using custom software written in Python 2.7.16. The compositional landscape Fig.  was prep31. In the dsDNA template for the WXY fragments the IGS is duplicated at position 25 to allow identification by sequencing. This is done by site-directed mutagenesis and producing plasmids bearing respective IGS duplicated at 25th position (see ‘Duplication of IGS’ Supplementary Methods). For PCRs, plasmids (at 25 pg/µL) were mixed with 0.5 µM of respective primers  and purified on polyacrylamide gels. RNA concentrations were measured using Qubit® RNA HS Assay Kit . The Z fragment RNA used here was custom synthesized (PAGE purified) by IDT DNA technologies and used without further purification.RNAs were in vitro transcribed as described in ref. TM NovecTM, Product No.:98-0212-2928-5) and a fluorosurfactant . Devices were designed with AutoCAD software , with channels containing 3 M NaCl liquid electrodes50. After plasma bonding, channels were made hydrophobic by immediately flushing them with 2% 1H,1H,2H,2H-perfluorodecyltrichlorosilane  in HFE 7500 with the help of syringe. Droplet-based microfluidics experiments were performed using an inverted microscope (Nikon Eclipse Ti) as described earlier51. Flows were controlled by either syringe pumps (Harvard Apparatus Inc.) or by air-pressure control pumps .Droplet-microfluidic experiments used HFE 7500 fluorinated oil  Initial emulsions production: Using all possible 16 WXY RNA fragments (gMgWXYcNu), 24 unique different WXY fragments combinations were prepared in separate tubes , was folded in the same manner as WXY RNA, and encapsulated in 50 pL droplets using a 50 pL drop-making device (Supplementary Data B) Electrocoalescence of initial emulsions: The 5 pL droplets (containing WXY fragments) and 50 pL droplets (containing Z fragment and reaction buffer) were reinjected into separate channels of a droplet fusion device  amplified 103 times (TREK high-voltage amplifier). Flows were regulated such that, on average, between one and five 5 pL droplets coalesce with one 50 pL droplet with a fusion frequency of ~150 Hz (Supplementary Movie C) Incubation and splitting of droplets: After collection, fused droplets were incubated at 48 °C in a thermo-block for 1 h to allow the accumulation of ribozymes. In order to dilute the MgCl2 during the reverse transcription (RT) step, these droplets (~60–65 pL) were reinjected (spaced with HFE 7500 oil containing 2% surfactant) and split by a T-junction device53 (Supplementary Data D) Droplet barcoding and RT in droplets: To sequence the RNA in each split droplet we developed a strategy combining droplet barcoding and RT in droplets, inspired by single-cell transcriptomics methods described earlier35. Here barcoded hydrogel beads are individually encapsulated in droplets with all the necessary reagents for RT and fused with RNA network containing droplets. The details of each step are as follows: (a) Barcoded hydrogel bead synthesis: Hydrogel beads were produced by co-encapsulating 10% (w/w) polyethylene glycol diacrylate (PEG-DA) 6000 , 1% (w/w) PEG-DA-700 , 400 µM of acrydite-modified dsDNA with a 4 base sticky-end  through a PTFE tubing and collected in 5 mL tube . Prior to UV irradiation, the complete experiment setup was maintained in the dark to avoid any spontaneous polymerization. The collected droplets were washed once with 4 mL hexane to break the emulsion and then the beads were washed three times with 4 mL binding-wash buffer  by centrifuging at 3000 × g for 2 min. Beads were then filtered using Steriflip 20 µm Nylon filters  and stored in binding-wash buffer supplemented with 1 mM EDTA. In contrast to earlier methods54, barcodes were built on the beads using a split-and-pool ligation strategy55 , 4 µM dsDNA adaptor with two different 4 base sticky-ends, the first being complementary to the 4 base sticky-end on the beads, and containing a BclI restriction site and the Read 2 Illumina adaptor sequence  barcodes. After the final pooling step, a partially double-stranded sequence was ligated to all the beads using the same ligation protocol . The final barcoded hydrogel bead library was washed five times with 4 mL of binding-wash buffer supplemented with 1 mM EDTA and resuspended in the same buffer. (b) Encapsulation and fusion: The barcoded beads (50 µL) were washed five times with 500 µL of binding-wash buffer by centrifuging at 11,866 × g for 1 min. Washed beads were then mixed with 2.5 µL of 10 mM dNTPs, 10 µL of 5× SuperScript III reaction buffer (Invitrogen), 2.5 µL of 100 mM dithiothreitol (DTT), 0.4% of Tween 20 (10%), 100 units of SUPERase۰InTM inhibitor  and incubated at 37 °C for 30 min to ensure diffusion of all reactants within the beads. After this, the beads were centrifuged as above and excess of liquid over the beads was removed. Then, at 4 °C, 500 units of reverse transcriptase  and 25 units of BclI restriction enzyme  were added to the beads and mixed thoroughly. These hydrogel beads together with the other reagents were encapsulated individually in ~50 pL droplets  Sequencing sample preparation: In order to block extension of the nonelongated primers, 20 µL of cDNA was mixed with 1× TdT reaction buffer (New England Biolabs), 0.25 mM CoCl2, 0.4 mM ddCTP  and 0.4 U/µL of Terminal Transferase . The reaction was carried out in 50 µL volume and incubated for 30 min at 37 °C before heat inactivation at 70 °C for 10 min. The TdT treated cDNAs were purified using magnetic beads  following the manufacturer’s protocol. Sequencing adaptors were then appended using two sequential PCR steps  was set to 50, which was found to computationally maximize the number of distinct networks formed after random droplet fusions . Once this was fixed, network diversity was further maximized based on selecting the fragment assignment  to maximize the spread (Shannon entropy) of the expected growth rate  and transient time  distributions across networks resulting from the simulation of 10,000 random droplet fusions.Azoarcus ribozyme with specific IGS-tag pair or a hairpin RNA reporter). Read 2 was used to determine the UMIs56 and the droplet barcode. The structure of read 1 and 2 is summarized in Supplementary Fig. Azoarcus ribozymes and hairpin RNA reporters based on the shape of the distribution of number of reads per UMI  and the RNA molecule identity  were prepared, each with: a distinct pair of hairpin RNA reporters at a final concentration of 5 nM, a set of 4 WXYZ ribozymes with the same IGS  but in different proportions  and 1.6 µM of Z fragment. The concentrations of WXYZ in the four sets are as follows; Set A: 10 nM WXYZ (GA), 20 nM WXYZ (CA), 30 nM WXYZ (AA), 40 nM WXYZ (UA). Set B: 1 nM WXYZ (CC), 2.5 nM WXYZ (AC), 5 nM WXYZ (UC), 91.5 nM WXYZ (GC). Set C: 0.1 nM WXYZ (CU), 0.25 nM WXYZ (UU), 0.5 nM WXYZ (AU), 99.15 nM WXYZ (GU). Set D: 0.01 nM WXYZ (UG), 0.05 nM WXYZ (CG), 65 nM WXYZ (AG), 34.94 nM WXYZ (GG). The four emulsions were mixed and then singly fused to droplets containing hydrogel beads as described above to perform droplet-level sequencing. The data was processed as above using the same thresholding strategy. We quantified the bias as the proportion of droplets containing pure  and compared to mixed populations  to extract autocatalytic rate parameters (see below), using the strategy developed by von Kiedrowski6, as described in ref. 32. The concentrations of RNA fragments were kept identical to the droplet experiments (0.1 µM of WXY and 1.6 µM of Z fragment). For this, initial rates of formation of covalent WXYZ from WXY and Z fragments were measured as a function of the different concentrations of ‘doped’ covalent WXYZ ribozymes (with same IGS and tag as the WXY fragment) added at the beginning of the reaction. To facilitate the measurements, minor amounts (0.001 µM) of radiolabeled WXY fragment (γ-32P) were also added. These radiolabeled WXY fragments were prepared using T4 Polynucleotide Kinase (New England Biolabs) and γ-32P ATP (Perkin–Elmer). For each initial condition , time courses were measured to derive the initial rate of formation of covalent WXYZ from WXY and Z fragments. In accordance with previous measurements32, the initial rate of formation of WXYZ (v0) was found to depend linearly on the concentration of the doped WXYZ. This affine relationship can be described with the following linear equation x is the concentration of the covalent ribozyme, α is the slope for an IGS/tag pair, which quantifies the WXYZ synthesis by covalent ribozymes, and β is the y-intercept, which quantifies the WXYZ synthesis by noncovalent ribozymes 30. Wobble pairs (GU and UG) and one of the mismatched IGS/tag pairs (AG) were also measured and found to have negligible values for α and β (Supplementary Fig. As earlier measurementsj, whose concentration is xj, contributes to the rate of formation of covalent catalysts from species i with the term αijxj while noncovalent catalysts contribute with the constant term βij. αij, and βij terms were measured experimentally and independently from the network experiments, for single IGS-tag pairs (Supplementary Fig. 30 determined a forward rate of 0.65 μM−1 min−1 for complex formation. Given a Z fragment concentration of 1.6 μM, this gives a characteristic time of ~1 min for complex formation compared to 1 h for covalent product formation. Second, the kinetics is valid at the beginning of the reaction but does not take into account variations in substrate concentrations. In particular, Z is a shared resource between all species which may cause nonlinearities in the kinetics. However, Z is provided in excess for all network and is not strongly depleted as the median yield of reactions is 17%, to the exception the 16 member one, where is it provided in equimolar concentration with the total WXY fragments. In this case, it should be noted that Z fragment binds to all WXY fragments with the same equilibrium constant as IGS-tag variations only affect the binding between WXY and WXYZ. Consequently, Z titration is expected to affect the overall rate of total product accumulation but not to the relative production rates between species.In a network, covalent catalysts from species Further information on research design is available in the Supplementary InformationDescription of Additional Supplementary FilesSupplementary Data 1Supplementary Data 2Supplementary Data 3Supplementary Movie 1Supplementary Movie 2Reporting Summary


We conclude that rapid and regular cycling of oxygenation levels selects for pseudohypoxia, and that this is consistent with the ecological theory of optimal defense.Tumors experience temporal and spatial fluctuations in oxygenation. Hypoxia inducible transcription factors (HIF-α) respond to low levels of oxygen and induce re-supply oxygen. HIF-α stabilization is typically facultative, induced by hypoxia and reduced by normoxia. In some cancers, HIF-α stabilization becomes constitutive under normoxia. We develop a mathematical model that predicts how fluctuating oxygenation affects HIF-α stabilization and impacts net cell proliferation by balancing the base growth rate, the proliferative cost of HIF-α expression, and the mortality from not expressing HIF-α during hypoxia. We compare optimal net cell proliferation rate between facultative and constitutive HIF-α regulation in environments with different oxygen profiles. We find that that facultative HIF-α regulation promotes greater net cell proliferation than constitutive regulation with stochastic or slow periodicity in oxygenation. However, cell fitness is nearly identical for both HIF-α regulation strategies under rapid periodic oxygenation fluctuations. The model thus indicates that cells constitutively expressing HIF-α may be at a selective advantage when the cost of expression is low. In cancer, this condition is known as  Phenotypic plasticity confers flexibility that allows an organism to survive in the face of often unpredictable and rapid changes in its environment. Many organisms, from microbes to humans, vary gene expression facultatively. In this way phenotypic expression matches demand3. In contrast, when environments are constant, or are predictably variable, an intermediate and constitutive level of expression may be favored over facultative expression5.Phenotypic plasticity, the production of alternative phenotypes in response to variable environments, is ubiquitous in nature8.Inducible or facultative defenses, such as defensive chemicals in plants, and spines and projections in zooplankton such as rotifers and cladocerans, include remarkably diverse and well-studied examples of phenotypically plastic responses to biotic and abiotic threats or stressors. Biotic threats include herbivores, predators, pathogens, and parasites. An important abiotic threat is hypoxia, a reduction in oxygen availability. Hypoxia may be either acute, intermittent, or chronic, and it may be experienced at the organismal, tissue, or cellular levels. Cells respond to hypoxia via stabilization of the Hypoxia-inducible Factor (HIF), an inducible defense against both acute and chronic hypoxia within the cellular environment. HIF is a heterodimeric α/β transcription factor that induces expression of genes that lead to tissue re-oxygenation. The evolution of inducible defenses, like HIF, appears to be favored by unpredictability of environmental conditions, reliable cues of those conditions, and a high cost of the defense10. In tumors, significant heterogeneity in oxygen levels result from both a dynamic ecosystem of blood vessels of varying functionality, and cancer cells with different tolerances to hypoxia. Within a nascent tumor ecosystem, cancer cells, which can somatically evolve, experience both acute and chronic hypoxia due to rapid growth, limited blood supply, and disorganized vascular delivery systems11. This leads to complex cycles of oxygenation and hypoxia, characterized as “waves” and “tides”14. Thus, an intermittent or temporal instability in oxygen supply is a cardinal feature of tumors. We have proposed that this generates strong evolutionary selection pressures for more aggressive cancer cell phenotypes15.Oxygen levels in normoxic or hypoxic tissues encompass a wide range of values depending on several factors, including gender, time of day, tissue type, and degree of vascularization17, cell cycle arrest, a coordinated decrease in oxidative phosphorylation with an increase in glycolysis (Pasteur Effect), and secretion of angiogenic factors to promote blood vessel formation23. Although each HIF-1-3α plays some role in a cell’s response to hypoxia, those roles are best understood for HIF-1α and HIF-2α24. HIF-3α comes in a number of variants, and each seems to have a different role in cell function17. Although HIF-1α and HIF-2α are known to differ both mechanistically and physiologically, their kinetics of stabilization and transactivation are generally similar25. Here we refer to recognized roles of HIF-1α and HIF-2α (hereafter HIF-α) in response to hypoxia. HIF-α is ubiquitously and continuously expressed in all cells. In well-oxygenated environments (normoxia), HIF-α is hydroxylated and ubiquitinated and is thus recognized and degraded by proteasomes21. In an oxygen-depleted state, hydroxylation and hence, degradation of HIF-α is inhibited, promoting the transcription of genes that regulate proliferation27, cellular metabolism21, angiogenesis28 and erythropoiesis30. If well-regulated, the recruitment of blood vessels to the site of HIF-α stabilization increases the supply of oxygen. Once O2 levels return to normal (normoxia), HIF-α returns to baseline levels. It has also been observed that aggressive cancers constitutively express hypoxia-related proteins (HRPs) even in the presence of oxygen, a condition known as pseudohypoxia31. The most common manifestation of this phenotype is the fermentation of glucose under normoxia, known as “aerobic glycolysis” or the “Warburg Effect”34.Like nearly all metazoan cells, cancer cells possess mechanisms to respond to heterogeneity in the supply of oxygen, including activation of a family of hypoxia-inducible transcription factors 35. As seen in the development of some tumors, regulation of HIF-α switches from a facultative state, where the environment induces the changes in regulation, to a constitutive state, where HIF-α client proteins remain above baseline regardless of the environment31. As this phenotype is associated with cancer progression and aggressiveness, understanding the microenvironmental conditions that select for pseudohypoxia is fundamentally important. Although increased HIF-α stability is a tumor promoting condition in many cancers, there are studies showing that HIF-α may play a role as a tumor suppressor, such as murine models of AML37. In the current study however, we developed our model using a cost–benefit analysis of expressing HIF under normoxic and hypoxic conditions, and thus downstream tumor promotion or suppression was not taken into account.Maintenance of HIF-α levels under cycling hypoxia involves tradeoffs. Under prolonged hypoxia without stabilization of HIF-α, cells die. In contrast, HIF-α stabilization under normoxia comes at a non-lethal fitness cost. Accumulation of HIF-α in well-oxygenated environments costs energy and resources for the synthesis of HIF-α client proteins that may not be necessary for survival, including activating energetically inefficient glycolysis and expression of the exofacial acidifying pH–stat, carbonic anhydrase isoform 9, CA-IX38. Optimal defense theory was developed to explain allocation of resources into defenses employed by plants in response to attack by herbivores. Optimal defense theory predicts that when herbivore damage is highly probable, plants should invest in constitutive defenses, but when the probability of herbivore attack is low, plants should invest in inducible defenses.Here, we develop a mathematical model with the goal of determining a cancer cell’s optimal level of HIF-α expression with respect to differences in fluctuating levels of oxygen availability within tumor microenvironments. Specifically, we seek to determine what tumor conditions may cause the evolution of constitutive HIF-α regulation (“hard wired” HIF-α stabilization) from facultative regulation. To do so we compare the maximal expected payoff (net cell proliferation rate) between facultative and constitutive HIF-α regulation in environments with different oxygen profiles. We hypothesize that predictable and rapid cyclic fluctuations from normoxia to hypoxia will favor constitutive HIF-α stabilization based on similar ideas in optimal defense theory (ODT)31. When oxygenation levels decline, HIF-α degradation slows, and production permits HIF-α to increase at a relatively slow rate to counter the hypoxic conditions20. Upon re-oxygenation, HIF-α can be rapidly degraded. We model cellular regulation of HIF-α as the concentration of oxygen within the tumor and surrounding microenvironment changes temporally—both with regular periodicity and stochastically. The model was informed by empirical evidence for the rates of HIF-α accumulation and degradation as the cells’ microenvironment shifts between normoxia and hypoxia, and vice-versa41.Our model investigates how cells may respond to changes in oxygenation with HIF-α expression. In a perfect world, cells would instantaneously optimize HIF-α levels in response to fluctuating oxygen concentrations. As the environment shifts from normoxia to hypoxia, cells would immediately accumulate HIF-α, and vice-versa. However, attaining the appropriate HIF-α level for the current environment is not immediate. There will be time lags in upregulating or down regulating HIF-α. HIF-α production and proteosomal degradation occur continuouslyt, G(t):r is the baseline proliferation rate of a cancer cell, c is proliferation cost of using HIF-α strategy u at time t, m is the cell mortality when conditions are hypoxic, q is the fraction of time spent in normoxic conditions, k is a cell’s intrinsic tolerance to hypoxia in the absence of HIF-α stabilization, and b is the benefit of HIF-α expression u in reducing mortality when conditions are hypoxic. See Table We compared how different HIF-α regulation strategies influence cell fitness under different oxygenation environments. Here, we define a cell’s fitness by its net proliferation rate, or “payoff”. In this model, we assume that the expected payoff depends on the base proliferation rate, the metabolic cost of expressing HIF-α, and the mortality risk of not expressing HIF-α during hypoxia. We use the following expression for a cancer cell’s payoff at time We compare three HIF-α strategies across a variety of oxygenation environments: perfect, constitutive, and facultative. A perfect strategy means instantaneous HIF-α switching in response to normoxic and hypoxic conditions. While this strategy is idealized and unrealistic, it provides a useful point of comparison for the other strategies as a perfect strategy would yield the highest possible payoff. A constitutive strategy assumes that the HIF-α level is constant over time, and a facultative strategy assumes that the HIF-α levels can change at a finite rate in response to oxygen levels. Representative examples of these strategies in a fluctuating environment are shown in the Methods Fig. , along wA perfect strategy does not mean perfect fitness in all environments. Mortality and the metabolic costs of HIF-α stabilization mean that fitness declines with more time spent in hypoxic conditions. The expected payoff of the perfect strategy (see Eq.  in Methou* (see Eq. (q = 0) or always normoxic (q = 1). The payoff over different HIF-α regulation strategy values u for different fractions of time spent in normoxia q is plotted in Fig. u*. As expected, we find that the payoff is highest when HIF-α expression is lowest (u = 0) under constant normoxic conditions. With constant normoxia, as u is increased, the payoff slightly decreases, showing the minor cost of unnecessarily producing HIF-α. However, as conditions become more hypoxic with a low HIF-α expression, the mortality term dominates, and the payoff is drastically reduced into negative values where the cell cannot survive. With constant hypoxia, HIF-α needs to increase in order for G ≥ 0 for survival. The optimal values u*, shown as red dots, reflect this for all values of q in between.The optimal constitutive strategy can be found by maximizing the payoff for a constant HIF-α level, . Initially we compared the payoffs of a constitutive strategy and facultative strategy in the same environment to determine the selection coefficient, which we defined as the fitness advantage for using a facultative strategy (details in the Methods). The selection coefficients over the full range of possible umin and umax are shown in Fig. umin and umax than for shorter cycle times. Under many circumstances the difference in the selection coefficients for the two strategies are so small as to be negligible. Under such circumstances one might expect the constitutive strategy to prevail as the facultative strategy does have a lethal component, whereas the constitutive does not.We compared the optimal facultative response between two different periodicities  of full oxygenation followed by the same for deoxygenation  for u*min and u*max, respectively  and a low probability of switching (right) is shown in Fig. 41.In the simulations above, we needed estimates for the rates of upregulation and downregulation of HIF-α. We used average rates based on values in the literature from both normal and cancer cell lines. Yet, such rates will vary with cell line and the values from the literature were not collected with our model in mind. To compare to previous values and to our model, we empirically measured HIF-α upregulation and downregulation rates in two different ovarian cancer cell lines, TOV112D and A2780s. The kinetics of HIF-α stabilization were measured under 0.2% hypoxia in vitro. For TOV112D, HIF-α upregulation and stabilization required at least one hour and was maximal at 4 h  and downregulation (α1) rates of HIF-α. Using Eqs.  in 60 min and 240 min for TOV112D and A2780s cells, respectively. Similarly, we estimated the rate of HIF-α downregulation by finding values of α1 that allow HIF-a to decline to 10% of its maximum stabilization values within 1 min and 5 min for TOV112D and A2780s cells, respectively. These yielded estimates for α0 ~ 0.038 min−1 for TOV112D and α0 ~ 0.01 min−1 for A2780s and estimates of α1 ~ 2.3 min−1 for TOV112D and α1 ~ 0.46 min−1 for A2780s. We incorporated these experimentally derived rates into the model to compare the facultative and constitutive strategies in fixed interval environments. As with our previous results, we find greater selection for a facultative strategy in environments that remain in their current state of oxygenation or lack thereof for longer time periods. The superiority of the facultative strategy over the constitutive depends heavily on up- and down-regulation rates. Decreasing the rate at which HIF-α accumulates reduces the advantage of being facultative over constitutive even in environments with longer cycles. In general, the model suggests that TOV112D cells should exhibit a facultative strategy and A2780s cells a constitutive α0) and dIntra-tumoral fluctuations in oxygenation are key for empirically evaluating whether a constitutive strategy may be favored over a facultative one. Furthermore, fluctuations within a tumor may vary spatially. Thus, different regions of a tumor may select for different HIF-α levels and strategies. To gain empirical insights, we measured spatio-temporal variation in oxygen delivery in different regions of a mouse pancreatic adenocarcinoma tumor. We used in vivo MR quantification of dynamic T2* changes that are sensitive to levels of deoxy-Hb and are thus an approximation of oxygenation. Significant heterogeneity was observed within the tumor both in the mean Fig. A and the44. For this reason, the evolution of constitutive HIF-α regulation has drawn wide interest across many biological disciplines, including cancer. Herein, we developed a theoretical model to explore the conditions under which constitutive versus facultative HIF-α orchestration of the cellular response to temporal changes in oxygen supply will optimize a cell’s fitness, as measured by the net growth rate, or payoff. Our modeling indicates, unsurprisingly, that the perfect matching strategy for HIF-α regulation in response to fluctuating oxygenation levels always delivers a greater payoff than either the facultative or the constitutive strategies. However, cellular transcriptional and translational machinery has significant inertia and is unable to instantaneously respond to fluctuations in oxygenation and thus unable to provide a perfect match. Thus, it must respond either facultatively or constitutively. Under facultative regulation, the upper and lower bounds for rates of HIF accumulation are critical for calibrating the rate at which the cancer cells stabilize their oxygen environment. Our model predicts that the upper bound should be set very high to rapidly respond to hypoxia. Conversely the lower bound insures a non-zero level of stabilization. This increased baseline level of stabilization for the facultative strategy is only slightly below what would be expected with constitutive regulation of HIF-α. Importantly, this demonstrates the larger penalty of not upregulating HIF-α quickly enough when the environment becomes hypoxic than the cost incurred of needlessly stabilizing HIF-α during normoxia. Thus, cells constitutively expressing HIF-α may be at a selective advantage under some conditions, with little cost.Facultative regulation of HIF-α in response to fluctuating levels of oxygenation is ancestral and highly conserved across phylaOur model indicates that facultative expression of HIF-α always promotes a greater payoff than constitutive expression. Importantly, however, the difference in the payoffs between facultative and constitutive HIF-α expression depends on the nature of the fluctuations between normoxia and hypoxia. With short cycling times, the difference between facultative and constitutive HIF-α stabilization is small and perhaps negligible, so facultative expression may be indistinguishable from constitutive regulation. In contrast, long cycling times or stochastic fluctuations favor facultative HIF-α regulation.38 predicts deployment strategies for these plant defenses. ODT states that: (1) defenses should be preferentially invested in those tissues that most affect individual fitness, and (2) the reliance on an inducible defense should depend on the probability or predictability of attack  and/or constitutive defenses against herbivores or pathogens. Optimal defense theory (ODT)ack Fig. . When th45. Hence, ODT predicts that cells should regulate HIF-α expression constitutively. In our simulations, when oxygenation states switch rapidly at fixed intervals, we found that payoffs are virtually identical between facultative and constitutive HIF-α regulation  in malignant cancers, indicating that this provides a fitness advantage regardless of the trajectory used to acquire this phenotype31.Our review of the literature on the dynamics of up- and down-regulation rates, and confirmed by our own experiments indicate that HIF-α response dynamics vary considerably between experimental cell lines (our results above)49: (1) understanding the switch-like behavior of the HIF-α response to fluctuating O250; (2) analysis of the role of molecular elements of the microenvironment during the HIF-α response51; (3) elaborating how asparaginyl hydroxylase factor inhibiting HIF-1 (FIH) affects the HIF-α response54); and (4) capturing the temporal dynamics of the HIF-α response54. All of these modeling studies have helped elucidate the core elements that shape the activity and the dynamics of the HIF-α response to cycling hypoxia. Our model, in contrast, addresses the conditions that select for the evolution of constitutive regulation of HIF-α from the ancestral facultative regulation. Our model examines the consequences of different HIF-α regulation strategies on cell fitness within the complex and dynamic tumor ecosystem. We find that constitutive HIF-α regulation is favored when the probability of hypoxia is high—a finding that is consistent with ecological models of defenses to biotic threats like predation and herbivory.Previous mathematical models of hypoxia and HIF-α regulation fall into four general categories55, thus increasing the fitness of the pseudohypoxic phenotype. A second limitation is that the study investigated only the kinetics of stabilizing HIF-1α. There are at least two other HIF-α proteins, each with different activation kinetics and portfolios of client proteins. Moreover, the kinetics of the transcriptional and translational machinery induced by HIF-α are not known with certainty, and presumably do not respond instantaneously. Knowledge generated by investigating these limitations will improve subsequent models.The current study is the first of its kind to apply ecological defense theory to the expression of stress responses (e.g. HIF) in cancer cells. Hence, it is not without its limitations. First, the endpoint for our simulations to model fitness was simply net growth rate, as represented by our payoff function. There are many other components to fitness that were not considered in this study. For example, the expression of some pseudohypoxic gene products, e.g. CAIX or VEGF, may confer upon cells additional selection advantages, such as an increased ability to invade and colonize adjacent tissues2 levels. With facultative regulation, HIF-α levels change in response to environmental fluctuations in oxygen at fixed rates of accumulation (slow) and degradation (fast). It is important to note that we use “HIF-α” to represent the constellation of cellular responses to hypoxia. While the transcription factor HIF-1α is undoubtedly central to this, we do not wish to imply that its levels are solely responsible for a cell’s fitness under different conditions of oxygenation.We modeled three different strategies by which a cell can respond to the presence or withdrawal of oxygen in an environment: perfect, constitutive, and facultative Fig. . If a ceY ∈ , describe the level of oxygenation in the cell’s tumor microenvironment. In all scenarios, we assume that the environmental switch between fully oxygenated (Y = 1) or deoxygenated (Y = 0) is effectively instantaneous whereas the accumulation and degradation of HIF-α is based on intrinsic rates. Let u(t) be the HIF-α response of a cell at time t whether it has a perfect, constitutive, or facultative response, where u ∈ . For the fixed interval environment, normoxic (Y = 1) and hypoxic (Y = 0) periods switch back and forth at fixed time intervals. A perfect, constitutive, and facultative response to these changing oxygen profiles will exhibit different HIF-α expression levels.  = r − cu, and the payoff during hypoxia, GH(u) = r − cu- m(1-q)/(k + bu), so that the total payoff is:With the constitutive strategy, HIF-α levels remain constant and do not change in response to the temporal fluctuations in oxygen. When q. Therefore, the optimal constitutive strategy value, u*, can be calculated analytically by maximizing expected G with respect to u. We take the first order necessary condition for this optimum, u*, resulting in:The optimal value for HIF-α expression depends only on the fraction of time spent in each state, c, the cell’s intrinsic tolerance to hypoxia in the absence of HIF-α stabilization, k, and the fraction of time spent normoxic, q. HIF-α production increases with cell mortality when conditions are hypoxic, m. The relationship between optimal HIF-α production and the benefit of HIF-α expression, u, in reducing mortality when conditions are hypoxic, b, is hump shaped. If HIF-α expression is ineffective  then there is no point, and if HIF-α expression is extremely effective (large b) then little is needed. The u* can then be substituted into the payoff G to determine the maximal payoff available to the constitutive strategy given the micro-environmental and fitness parameters:The constitutive level of HIF-α production declines with its proliferation cost, α0, and when the environment is fully oxygenated the cell degrades HIF-α at a finite rate α1 (1). We allow a baseline production of HIF-α (umin) even under normal oxygen conditions and assume that the cell targets a maximum accumulation of HIF-α (umax) in an oxygen-depleted environment (2). We assume that the changes in expression occur at a rate proportional to the difference between some desired level and the current level, such that:Under the facultative strategy, when the environment is depleted of oxygen, we assume that the cell accumulates HIF-α at a finite rate u(t) requires that the expected payoff be calculated as the cumulative payoff over the normoxic and hypoxic periods, TN and TH, respectively. Because the HIF-α fluctuations become periodic, the total cumulative payoffs can be averaged over a cycle separated into the time spent in normoxia and the time spent in hypoxia:For the facultative strategy, the dynamic The payoff can be analytically solved to:T = TN + TH,where The payoff for the facultative HIF-α strategy in a stochastic environment is calculated similarly. But, because the HIF-α dynamics cannot settle into a dynamic equilibrium, the payoff is calculated over discretized time intervals and then taken as an average over the entire simulation.u*min and u*max that maximize a cell’s payoff. For stochastic environments, a search space was created by linearly separating 250 values between 0 and 1. These values were used to create combinations of umin and umax for which 0 ≤ umin < umax ≤ 1. After u(t) was computed for each combination of umin and umax, the payoff, G(u(t)), was calculated as an average of all payoff values at each time point. The combination of umin and umax that produced the maximum averaged payoff was considered optimal. For a given PN→H = PH→N, we ran 10 replicate runs for 2000 time units. With this number of time units, the estimated values of u*min and u*max were very similar across replicate runs (standard error of the mean < 0.01).Constrained optimization by linear approximation (COBYLA) was used to determine values of GF, and the payoff for constitutive expression, GC, normalized by the payoff for constitutive expression, SC = (GF-GC)/GC.We define the selection coefficient (SC) as the fitness advantage for using a facultative rather than a constitutive strategy. We calculated the SC as the difference between the payoff for facultative expression, 2 and at 37 °C in a humidified atmosphere.A2780s and TOV112D ovarian cancer cells were obtained through American Type Culture Collection (ATCC). Cells were grown in RPMI supplemented with 10% fetal bovine serum (FBS). For both normoxic and hypoxic treatment environments, all cells were grown in 5% CO2:94.8% N2:5% CO2. Reoxygenation was performed by transferring flasks or plates containing cells from the hypoxic chamber to an incubator under atmospheric conditions at 5% CO2. For time points shorter than 4 h, media pre-equilibrated under hypoxic conditions was used. Then, the hypoxic media was added to the cells inside a hypoxic (0.2% O2) working chamber within the Biospherix complex.A Biospherix X-Vivo Hypoxia Chamber was used to incubate cells under hypoxic conditions. For hypoxic conditions, cells were incubated at 0.2% OWestern blots were performed on A2780s and TOV112D ovarian cancer cells to validate the expression of HIF at the protein level at different time points. Cells grown in hypoxic chambers were frozen at the time points mentioned in the results section and harvested all together by lysing in Radioimmunoprecipitation assay buffer (RIPA buffer) containing 1 × protease inhibitor cocktail (Sigma-Aldrich). For each sample, a 30 μg aliquot was loaded onto pre-cast polyacrylamide-SDS gels from BioRAd that were then transferred onto nitrocellulose. Membranes were incubated with primary antibodies against HIF-1α , Tubulin  or β-Actin  overnight at 4° C, followed by fluorescent-conjugated secondary antibodies (IRDye® 800CW Goat anti-MouseIgG and IRDye® 8680CW Goat anti-rabbit IgG). An Odyssey chemiluminescence-fluorescence system was used for protein detection. Proteins detected ran at the expected molecular weights, as verified using molecular weight standard markers.56. Panc02 mouse pancreatic adenocarcinoma cells were implanted subcutaneously into a C57BL/6 mouse. When the tumor reached a volume of ~ 1500mm3, as measured by calipers, the animal underwent MR imaging with a 7 T/30 cm Bruker Biospec® imaging spectrometer as follows. Mice were anaesthetized using 3% isoflurane and subsequently maintained with 1.5–2% isoflurane mixed with 100% oxygen. Anatomical images were acquired using T2-weighted coronal and axial scans to identify the middle of the tumor and facilitate outlining the tumor. To capture the spatial and temporal dynamics of oxygenation, quantitative T2* mapping was then performed continuously every 55 s for 18 series . A monoexponential function was fitted for each voxel at each time-point  to reconstruct the local T2* magnetic resonance time, which is modulated by changes in deoxyhaemoglobin levels in the blood, hence reflecting the fluctuations in blood oxygen level.In vivo measurements of oxygenation fluctuations were obtained by Intrinsic Susceptibility Magnetic Resonance Imaging (IS-MRI)All procedures were in compliance with the ARRIVE guidelines and with the Guide for Care and Use of laboratory Animal Resources (1996), National Research Council, and approved by the Institutional Animal Care and Use Committee (IACUC), at the University of South Florida under the protocol 4778.Supplementary Information


Scientific Reports 10.1038/s41598-020-58247-5, published online 28 January 2020Correction to: The original version of this Article contained errors in the Abstract.“Haptic interface technologies for virtual reality applica have been developed to increase the reality and manipulability of a virtual object by creating a diverse tactile sensation.”now reads:“Haptic interface technologies for virtual reality applications have been developed to increase the reality and manipulability of a virtual object by creating a diverse tactile sensation.”“The results also indicate that the contact force applied to a virtual object during manipulation can be a function of the perceived object weight p = 0.005 for Experiment 1 and p = 0.2 for Experiment 2.”now reads:“The results also indicate that the contact force applied to a virtual object during manipulation can be a function of the perceived object weight (p = 0.005 for Experiment 1 and p = 0.02 for Experiment 2).”These errors have now been corrected in the PDF and HTML versions of the Article.


L compared to moderate to high water users. Repeated water stress also resulted in legacy effects on plant stomatal behavior, increasing stomatal sensitivity  even when the seedling was returned to well-watered conditions. These results indicate that stomatal strategies are dynamic and change with climate and competition stressors. Therefore, incorporating mechanisms that allow for stomatal behavioral changes in response to water limitation may be an important step to improving carbon cycle projections in coupled climate-Earth system models.A better understanding of plant stomatal strategies holds strong promise for improving predictions of vegetation responses to drought because stomata are the primary mechanism through which plants mitigate water stress. It has been assumed that plants regulate stomata to maintain a constant marginal water use efficiency and forego carbon gain when water is scarce. However, recent hypotheses pose that plants maximize carbon assimilation while also accounting for the risk of hydraulic damage via cavitation and hydraulic failure. This “gain-risk” framework incorporates competition in stomatal regulation because it takes into account that neighboring plants can “steal” unused water. This study utilizes stomatal models representing both the water use efficiency and carbon-maximization frameworks, and empirical data from three species in a potted growth chamber experiment, to investigate the effects of drought and competition on seedling stomatal strategy. We found that drought and competition responses in the empirical data were best explained by the carbon-maximization hypothesis and that both drought and competition affected stomatal strategy. Interestingly, stomatal responses differed substantially by species, with seedlings employing a riskier strategy when planted with a high water use competitor, and seedlings employing a more conservative strategy when planted with a low water use competitor. Lower water users in general had less stomatal sensitivity to decreasing Ψ L; Stomata are small pores on plant leaves that control the rate at which carbon is gained and water is lost. Stomata are the primary mechanism through which plants can mitigate water stress  and ofteN) over time while limiting transpiration (E). “Optimal” stomatal behavior occurs when δAN/δE  is equal to a constant λ (or 1/λ in some formulations)  . Under tterature . This thterature .L ], at a given ΨL and set of environmental conditions. With this model, hydraulic cost or risk to the plant increases with declining ΨL. The steepness of this cost function indicates different plant physiological strategies for dealing with water stress. Plants with cost functions with steeper slopes follow a “water saver” strategy, and close stomata earlier as ΨL declines (More recent studies have proposed and employed a “gain-risk” carbon maximization (CM) hypothesis that optimizes stomatal conductance based on photosynthetic gain versus the cost or risks to the hydraulic continuum associated with decreases in ΨL . The carpetition . Under tdeclines . Plants declines .TLP), leaf photosynthetic rate , and hydraulic conductivity of different plant tissues (K). In addition, plants balance competitive capacity with the risk of hydraulic damage to xylem tissue, which can result in a long-term reduction in photosynthesis ; (3) Do plants change their stomatal behavior following drought; and (4) Is stomatal behavior explained by concomitant changes in other hydraulic metrics? Critically, answers to these questions will significantly advance our understanding of stomatal behavior because our experiment allows us to directly examine the effects of competition on stomatal strategy.Moving forward, critical questions remain about the efficacy of different optimization hypotheses (CM vs. WUE) and whether stomatal strategy is an inherent and constrained trait with little plasticity or whether plants behavior changes with environmental conditions and competitive environment. While several studies have investigated optimized stomatal behavior in response to drought alone , our undPopulus tremuloides, Populus angustifolia, and Pinus ponderosa  seedlings were planted with a competitor or alone and subsequently subject to multiple periods of water stress. We describe the design and measurements briefly here, full details are in Kerr et al. (unpublished). We chose these species because they co-exist in natural stands where competition is likely to occur, and they employ a spectrum of water use strategies ranging from high/profligate water users (cottonwoods), to intermediate (aspen), and low/conservative (pine) (We conducted a growth chamber experiment in which e (pine) . Each see (pine) . There we (pine) . As one e (pine) . Therefo–2 s–1 photosynthetic photon flux density, and 400 ppm ambient carbon dioxide (CO2). Photoperiod for the growth chamber was set to closely match that of the greenhouse, where the seedlings were initially grown, with lights on from 6:00 to 19:15 using EYE HORTILUX ceramic metal halide 315 W grow lamp lights. During the predrought treatment period, we weighed a subset of pots and calculated a baseline average water volume to be given daily. Then we imposed three water limitation treatments sequentially – a low soil moisture treatment, an elevated vapor pressure deficit (VPD) treatment, and a combination of both simultaneously – on the seedlings. We took gas exchange and hydraulic measurements during the control predrought period, each treatment period, and a subsequent a post treatment recovery period. Each drought treatment lasted 5 days and seedlings were allowed to recover for 3 days in between treatments by returning to both baseline watering and growth chamber conditions. During the soil drought, we gave seedlings 50% of the water they were receiving during the predrought baseline period. During the elevated VPD treatment, watering was returned to the predrought water regime, and relative humidity was reduced from ∼75% to ∼45%. For the combination drought, reduced watering to 25% of their daily water and reduced relative humidity to 45% to impose the most significant water stress   for the optimality criterion (N) as the smallest of two limiting factors; rubisco limitation (wc) and light limitation (wj).We fitted our data with a stomatal optimization model that uses well-established equations for modeling photosynthesis, hydraulic conductivity, and water transport and can use either λ  or θ is the xylem conductance function. Conductance is calculated by Equation 5where Ψmax is the whole plant maximum xylem conductance. In our modeling framework, Kmax was unknown, thus we estimated Kmax assuming that plants want to maximize productivity without compromising the hydraulic system. Thus, calculated to maximize the difference between measured predawn and calculated midday ΨL while not exceeding the median water potential where 50% of maximum hydraulic conductivity is lost (P50), and satisfy the remaining equations (Eqn. 1–5) according to the methods in 1 and λ, the estimated Kmax resulted in a midday ΨL that exceeded P50 with ΨL = −3.00 MPa (P50 = −2.69 MPa) and ΨL = −1.35 MPa (P50 = −1.31 MPa), respectively.where C and B Weibull curve parameters were estimated from the stem vulnerability curves  using a bootstrapping method , P is leL. Importantly, the MXTE differs between the WUE and CM optimality theories as shown by Equations 6 and 7:To understand how plants balance carbon gain versus risk/cost during water stress, we used an optimality equation that relies on measurements of stomatal conductance to estimate a “shadow cost” (or risk to future plant performance) function for both the WUE and CM theory. As described in andwhere λ is the constant marginal water use efficiency, E is transpiration, θ is the cost/risk term.We linearized the derivative of the cost function such that1 and β0 are parameters fitted using observational stomatal conductance measurements. The linearized form of the derivative is advantageous in that it (i) distinguishes between the increasing versus decreasing responses of δθ/δΨ to decreases in ΨL in the CM and WUE hypotheses, respectively, and (ii) minimizes unconstrained parameters. This linear marginal cost function implies a parabolic form of the cost/risk function with declining water potential  and each planting group (competition and no competition), for a total of eight different fitting groups per model. For the CM model, we found that the best β1 and β0 often covaried, leading to an equifinality issue (eq. 8). Therefore, we ran a series of MCMCs (∼50) each using a different fixed value of β0 in order to estimate β1. For each of the eight fitting groups, we determined the range of initial β0 values  for each planting group using an initial value of β1 = 0.1. This value was chosen because a positive β1 represents a marginal increase in cost of damage with decreasing ΨL, so it is physiologically realistic, but is still a relatively uninformed initial guess. When running the series of MCMCs, our range and increment of β0 values  algorithm was used to calculate the posterior probability density function (PDF) of β0 values  that wou0 values  was chosL becomes more negative. We used linear models and the Akaike Information Criterion (AIC) score for all three species to assess model performance and determined that the CM model more skillfully predicted stomatal conductance compared to the WUE model for all three of our species. Thus, for subsequent analyses we used only the CM model.For the WUE model, for each of the eight planting groups, we ran MCMCs with an initial guess of λ = 0.1. For some fitting groups, no solution to the system of equations could be found at small λ values so we gradually increased our initial guess by increments of 0.1 until a solution could be obtained. When proposing the next step running the MCMCs, we confine lambda to the positive parameter space as a negative value would imply a decrease in cost as Ψcmax during the predrought and post drought recovery periods, we used the predrought measured Vcmax values for the predrought and three drought periods and the post drought measured Vcmax for the post drought recovery treatment period .When investigating effects of competition between planting groups, we performed one fit using all the stomatal conductance measurements for each planting group taken across the five treatment periods for the CM only. When looking at effects of treatment period within a planting group, we performed separate fits using the subset of stomatal conductance measurements taken at each treatment period; predrought, soil drought, VPD drought, combination soil and VPD drought, and post drought recovery. Because we only calculated V–2 s–1 photosynthetic photon flux density, 400 ppm ambient CO2, and relative humidity matching that of the growth chamber for the current treatment period. Predawn leaf water potential (ΨPD) was measured for each seedling using a Scholander-type pressure chamber before the growth chamber lights turned on (between the hours of 0400 and 0600)  . Samplescmax was determined from constructing A-Ci curves using a Li-6400 open gas exchange system and settings of 25°C leaf temperature, 1200 μmol m–2 s–1 photosynthetic photon flux density, 400 ppm ambient CO2, and relative humidity matching that of the growth chamber. We also calculated the ΨTLP in the predrought and recovery periods using the pressure-volume method  score to assess relative model performance.1 values over time (treatment periods), comparisons of β1 values between planting groups, and the interaction between time and planting group using R package (nparLD)   with β0 R2WUE = 0.38, R2CM = 0.46)    , cottonw = 0.54) , and pin = 0.35) . The CM 1 and the post hoc Tukey HSD pairwise test indicated that competitor identity, in addition to competitor presence, had an effect on β1. Specifically, a high water use competitor, such as aspen and cottonwood, resulted in a riskier stomatal strategy than when aspen were grown alone or with a pine  indicating cottonwood seedlings’ stomatal behavior was more conservative under competition. Interestingly, pines had the opposite response: pines under competition employed a riskier stomatal strategy, had a small β1 value (p < 0.0001), and a cost function with a shallower slope  for all three species. For aspen and cottonwoods, all treatment periods pairwise comparisons were significant (p < 0.01) indicating that both drought presence and type resulted in shifts in β1. Pines saw less of an effect of treatment periods on β1, likely due to the fact that pines experienced less severe water stress compared to aspens and cottonwoods (as verified through ΨPD). However, pine recovery β1 were significantly different from predrought β1, VPD drought β1, and combination drought β1 (p < 0.0001), indicating that there was an effect of water stress on pine stomatal behavior.Planting group, treatment, and their interaction all had an effect on β1 . Repeate1 values during the predrought period, but all four planting groups β1 values were significantly different in the post-drought recovery period, indicating that there was an effect of competitor identity on changes in β1 following drought treatments (p < 0.0001). Within each of the aspen planting groups, recovery β1 values were significantly different from all other time periods providing further evidence that drought affected stomatal behavior (p < 0.0001). High water use competitors, such as the case when aspen competed with aspen (AxA) or cottonwood (AxC), resulted in larger recovery β1, while the aspen grown alone and aspen competing with pine resulted in a smaller recovery β1  and their recovery β1 values were largest, indicating that repeated drought treatments led to a shift toward a more conservative stomatal strategy. Competitors also affected how seedlings responded to each sequential drought: solo cottonwoods and competing cottonwoods had different β1 values during all treatment periods . Contrary to patterns seen in the other species and planting groups, pine competing with aspen (PxA) saw a statistically significant larger β1 in the predrought period than the drought and post drought treatment periods. Within treatment periods, pines without a competitor and pines with a competitor were always significantly different (p < 0.05), indicating an effect of planting group on stomatal strategy . Larger β1 values were correlated with less negative TLP, PLC, and less negative ΨPD for cottonwoods  and lower drought tolerance (less negative TLP) are associated with a shift toward a more conservative stomatal strategy. In addition, cottonwoods had less negative ΨPD in the recovery period, which is indicative of lower water stress, but also larger β1, further supporting evidence of hydraulic damage and increased cost even at less negative ΨL. The pines, the only gymnosperm, had non-significant but slightly negative correlations between β1 and TLP, PLC, and ΨPD and showed less variation in these variables, both within planting groups and across treatment periods (1 and hydraulic metrics.Shifts in the shadow cost (MXTE) and pricing hydraulic risk in response to both competition and drought were explained by competitor species and adjustments in physiological traits. The angiosperm species had a positive correlation between PLC and βc damage . The rel periods . This ma1 would make it more difficult for trees to prepare for future drought events as they are forgoing carbon even under low atmospheric demand, due to increased stomatal sensitivity. Therefore, avoiding damage to hydraulic tissue and the increased carbon cost of recovering hydraulic conductivity could favor the selection for plants to become more conservative following drought periods (Increased stomatal sensitivity following drought events could have important impacts on productivity, even under well-water conditions, preventing plants from photosynthesizing and repairing hydraulic damage sustained during drought . This ph periods . Some of periods . For exa periods . InvestiPD, and leaf gas exchange in plant communities after natural drought has not been as thoroughly investigated (L declined may help to explain the lag in gas exchange recovery following drought events, even when ΨL return to predrought levels (Prosopis velutina due to the increase in stomatal limitation even without changes to leaf biochemistry (While there have been a number of studies addressing the role of physiological traits and mechanisms affecting plant response during drought , the recstigated . The shit levels . Indeed,hemistry , which mL and had a larger shift to conservative strategies after drought had ended. Crucially, we show that drought and water stress, even on short term timescales, can have lasting effects on plant stomatal behavior even when the plants returned to favorable environmental conditions. As current climate models assume perfect plant recovery from water stress, there is a need to better describe and incorporate these stomatal behavior changes and plant recovery in order to better predict ecosystem fluxes and forest response to a changing climate.Here, we provide evidence that the CM hypothesis accurately predicts plant stomatal strategies in complex environmental and competitive stress scenarios. Further, overall stomatal behavior and shifts in stomatal strategy in response to drought were species-specific. Interestingly, higher water users showed increased sensitivity to changes in ΨThe datasets generated for this study are available on request to the corresponding author.All authors designed the experiment and carried out the data interpretation. WA developed the model. KK and NZ were involved in data collection. NZ performed the analyses. NZ wrote the manuscript with contributions from all other authors.The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Since the discovery of functional brown adipose tissue (BAT) in adult humans, research on BAT gained a new popularity to combat obesity and related comorbidities. To date, however, methods to quantify BAT thermogenesis are often either highly invasive, require advanced equipment, are time consuming or of limited sensitivity. Here we present a simple yet highly effective and minimally invasive protocol for the Precise Unravelment of Non-shivering brown fat thermoKinetics (PUNK) in mice using infrared thermography in combination with Vaseline to brush up the fur between the shoulder blades. We also use physiological and molecular readouts including indirect calorimetry, qPCR and Western Blots to test our protocol. Our study demonstrates that Vaseline before thermography vastly advances the reproducibility and quality of BAT infrared pictures or videos, as it exposes the skin above the BAT for a direct line of sight for the infrared camera and thereby circumvents the well-known problems associated with shaving and anaesthesia. We subsequently validate that this approach does not affect physiological and molecular BAT function, but instead leads to more robust and less variable results when comparing for instance norepinephrine stimulation tests or knockout animals. Taken together, the PUNK protocol for BAT thermography quickly and effectively improves scientific outcomes of this method, and can be easily added to existing paradigms. Consequently, it safes money, time and experimental animals, thereby putting the 3R’s principles of animal welfare into practice. Although the uncoupling protein 1 (UCP1) is crucial for BAT function, several recent studies have shown that the magnitude of Ucp1 mRNA expression is not a suitable read-out to estimate BAT or beige fat activity5, highlighting the need for reliable in vivo techniques to quantify BAT thermogenesis in a physiologically meaningful manner.Active brown adipose tissue (BAT) is currently discussed as an important target to combat obesity and metabolic dysfunction, as it burns extra calories as heat and extracts glucose as well as fatty acids from the blood stream to fuel cellular metabolism6, whereas other techniques that are commonly used to estimate BAT activity, like PET-CTs, fMRIs or 13C-MRS scans, determine BAT non-shivering thermokinetics indirectly from BAT metabolism or blood flow (reviewed by7). Here, the animals need to be anaesthetised and are exposed to potentially harmful radiation during these measurements, which makes it difficult, if not impossible, to conduct longitudinal studies. Infrared thermography has been successfully used in many rodent studies to directly measure BAT thermogenesis10, however there is an ongoing debate on whether to anesthetize the animals and/or remove their fur during the measurements to gain more reproducible results14. These procedures not only increase the burden for the animals but in case of anaesthetised animals lead to an underestimation of the maximum BAT temperature, which reduces the quality of scientific outcomes. Moreover, shaving can induce stress and inflammation in the affected skin areas and alters the conductivity of the area covering the BAT, thereby potentially inducing a thermogenic gene program in subcutaneous white and beige adipocytes in the underlying BAT area15. Consequently, a reliable and minimally invasive protocol to quantify BAT thermogenesis in rodents is urgently needed, which avoids the problems associated with shaving or anaesthesia.Infrared (IR) thermography is a method that directly measures BAT heat production and subsequently UCP1-mediated uncoupling of the mitochondrial respiratory chain in vivoHere we present a new protocol for the Precise Unravelment of Non-shivering brown fat thermoKinetics (PUNK), which eliminates of the necessity of using anesthetics or shaving in infrared thermography, and leads to more stable and conclusive scientific results.Wild-type male C57BL/6NCr mice were purchased from Charles River and homozygous male UCP1 knockout (UCP1-KO) and wild-type (WT) littermates (genetic background C57BL/6 J) were obtained from our breeding colony at the animal facility of the University of Lübeck. Animals (3–5 months) were single housed on a constant 12-h light/12-h dark cycle at 23 ± 1 °C and cages were equipped with cotton nestlets. Unless otherwise stated animals had free access to food and water . All procedures were approved by the MELUND Schleswig-Holstein (Germany), and all methods were carried out in accordance with relevant guidelines and regulations. The required sample size was calculated from previous studies using G*Power version 3.1.9.4. , with power (1 − β) set to 0.80, and a significance level α of 0.05. No inclusion or exclusion criteria were set, animals were randomly assigned to groups and RO was aware of the group allocation.https://www.flir.de/products/flir-tools/).Infrared pictures were taken with a hand-held camera  on freely moving animals to minimize stress . The17, afterwards they were filmed for another 60 min. Maximum iBAT temperature was scored within the first 30 min after NE injection using the IRBIS3 software .Infrared videos of animals without (−) and with (+) Vaseline were recorded with a 5s interval using a VarioCAM hr head camera . Measurements were carried out on fasted (2 h) animals in a temperature-controlled chamber at 23 °C. Vaseline (~ 10 mg) was applied right before the experimental start, the cotton nestlets were removed and the animals were placed back in their home cage to reduce stress. Baseline iBAT temperature and maximum iBAT temperature before injection were calculated in a 10-min period of reduced activity. Since this period was not always immediately prior to injection, a continuous time axis was omitted in Fig. Rectal body temperature was measured with a thermal probe  and taken as an estimate of core body temperature.2 (ml O2/h)), the RQ and the caloric equivalents given by18  = (4.44 + 1.43 * RQ) * VO2 (ml O2/h)). Furthermore, resting metabolic rate at 23 °C (RMR) was determined in the inactive phase of mice (lights on) and over a 1-h interval of consistently low oxygen consumption rates and without physical activity.To detect possible changes in metabolic rate caused by Vaseline application or the resulting decreased thermal insulation of the fur (resp. increased heat conductance), 3 months old C57BL/6NCr wild-type mice (N = 6) were measured via indirect calorimetry using an open respirometry system . First, the animals were acclimated to a temperature-controlled chamber (23 ± 0.5 °C) and energy expenditure, food and water intake, respiratory quotient (RQ = carbon dioxide produced/oxygen consumed) and activity was measured simultaneously at 20-min intervals. After the animals got used to the climate chamber Vaseline was applied to one group of animals  Vaseline), whereas the control group received a sham treatment  Vaseline). Daily energy expenditure  was calculated over 24 h using the metabolic rate (VOhttps://www.tse-systems.com/product-details/phenomaster).Resting metabolic rate at thermoneutrality  was calculated from the lowest mean oxygen consumption over a period of 1h in a postabsorptive (fasted for 6 h) and non-moving animal after Vaseline application (~ 10 mg). Data were analyzed with TSE PhenoMaster software V6.5.3 . Heat capacity (J/(gK), calculated assuming ρ = 1.0 g/cm3) was calculated subsequently.Skin samples still containing fur were dissected from the interscapular area of C57BL/6NCr wild-type mice (N = 6) and analyzed using a transient hot bridge instrument  to validate whether Vaseline changes the conductivity of the fur and increases heat loss over the skin surface. One group of animals received the Vaseline (~ 10 mg) 24 h before the measurement, whereas the skin of the other group was first measured without Vaseline and then directly after Vaseline application (~ 150 mg). A Kapton sensor type A was used to heat the sample, and the resulting temperature change was measured to determine heat conductivity (W/(m*K), reference range skin = 0.21–0.41)19) or a mouse anti-OxPhos antibody cocktail  followed by a peroxidase-conjugated secondary antibody ). Then antigens were visualized using an ECL Plus Western blotting detection system  and band intensity was quantified using Image Lab software 6.1 . Data were normalized to total protein load and controls (without (−) Vaseline).To determine whether Vaseline treatment changes the molecular signature of brown adipocytes, iBAT samples of animals without and 24 h after Vaseline (N = 6) treatment were analyzed. For protein isolation snap-frozen iBAT samples were used and protein concentrations were determined using Pierce BCA Kit . For immunological detection 20 µg of iBAT (not pre-heated to 98 °C) were separated on a 12% SDS polyacrylamide gel and transferred onto a polyvinylidene fluoride membrane . Membranes were probed with a rabbit anti-UCP1 polyclonal antibody  and cyclophilin D (Cyclo). The expression of uncoupling protein 1 (Ucp1), β3-adrenergic receptor (Adrb3) and deiodinase 2 (Dio2) were measured and results were calculated using the ∆∆CT method, and standard curves were recorded to correct for PCR efficiency. Primer sequences are available on request.RNA isolation was performed following the manufacturer’s instructions using RNeasy Lipid Tissue Mini Kit . Subsequent cDNA synthesis was performed using the Molecular Biology RevertAid Strand cDNA Kit  with anchored oligo (dT)18 primers. Quantstudio Applied Biosystems  and SYBR green PCR master mix  were used for qPCR analysis. The most stable reference genes were determined with geNorm version 3.4p values of less than 0.05 were considered significant, and the respective levels of significance are *p < 0.05, **p < 0.01, ***p < 0.001.GraphPad Prism 7 software was used to analyze the data . Values are represented as mean, box plot (min. to max.), mean ± SD (in vivo experiments) or mean ± SEM , as indicated in figure legends. Statistical testing was performed using Student’s t-test with Welch’s correction, paired Student’s t-test, 1-way or 1-way repeated measures ANOVA with Tukey’s post-hoc test, 2-way or 2-way repeated measures ANOVA with Bonferroni’s post-hoc test where indicated. The quality and reproducibility of iBAT IR-pictures taken from freely moving mice is highly dependent on (a) the activity level of the animal, (b) the quality of the fur and (c) the time it takes an experimenter to photograph the animal in the correct position Fig. A. All thBased on these results, our aim was to develop a method that minimizes the disturbing effect of the fur on iBAT IR-temperature without influencing the conductivity for a long time (like shaving) and to establish a rapid and minimal invasive method for quantifying BAT thermogenesis using infrared thermography, which we termed Precise Unravelment of Non-shivering thermoKinetics (PUNK) protocol. Brushing up the fur with a minimum amount of Vaseline ~ 10 mg) indeed minimized the effect of the fur on iBAT temperature and led to more stable and reproducible measurements , β3-adrenergic receptor (Adrb3) and deiodinase 2 (Dio2)) 24 h after Vaseline application as well as UCP1 and OxPhos protein as a read-out for thermogenesis and mitochondrial power , DEE, RMR at 23 °C and 30 °C (BMR) or the respiratory quotient .To validate whether the PUNK protocol facilitates a more precise detection of differences in iBAT activity compared to IR pictures taken without Vaseline, we analyzed iBAT temperature of UCP1-KO mice (no active BAT) and wild-type (WT) mice after NE injection  was barely visible in animals without Vaseline  or mental disorders, leading to confounding effects in IR thermography of BAT thermogenesis.Infrared pictures of the hairy or shaved skin covering the inter-scapular area are commonly taken to measure iBAT thermogenesis25. However, shaving creates “thermal windows” and given that the thermal conductivity of the insulating surface  is the most notable physiological factor affecting heat flow between an animal and its environment9, shaved mice perceive their environment as much colder (for instance nude mice perceive 20 °C as 10 °C)22. Subsequently, BAT is recruited, browning of WAT is induced and metabolism is increased by up to 50% 23, or needs to be applied repeatedly for longitudinal studies, given that the fur grows back rapidly28.To circumvent these problems, several studies employed shaving their animals to eliminate the possibly disturbing effect of the fur6. However, anaesthesia is invasive and body temperature needs to be maintained to avoid effects of body cooling. Thus, performing long-term measurements or longitudinal studies is almost impossible, especially when considering that volatile anaesthetics such as halothane or isoflurane inhibit BAT activity30. Consequently, the absolute magnitude of BAT temperature can never be obtained from anaesthetized animals, and techniques requiring anaesthesia such as 18F-FDG PET/CT scans will suffer from similar problems. Moreover, it has been shown that in BAT 18F-FDG uptake can occur independently of UCP1 function31, which can therefore only provide a rough approximation of true BAT thermogenesis In contrast, implanted probes for precise determination of iBAT temperature, which are fixed close to the Sulzer’s vein, allow the recording of absolute iBAT temperature (reviewed by9). However, this method is rather invasive due to the required surgery and thus more complex and error-prone, and often not feasible for larger cohorts of animals. The most critical point of infrared thermography is the influence of ambient temperature on surface temperature thermography33. Skin temperature is strongly dependent on ambient temperature and control over ambient temperature is absolutely required to obtain reliable and comparable results.As an alternative to shaving, anaesthesia can be used to improve the reproducibility of IR thermography measurements and to reduce the number of animals required34, as it facilitates an automated analysis of IR videos. With Vaseline the BAT is consistently the hottest spot in the IR pictures over the entire time frame of the experiment, thus eliminating the need for manually scoring large numbers of IR pictures. Importantly, good science goes always hand in hand with good animal welfare. Whilst infrared thermography is commonly classified as a non-invasive method by national animal welfare committees and therefore often does not require an animal ethical application, add-on procedures like shaving and anaesthetizing are invasive and cause distress to the animals. Therefore, in addition to providing data of higher quality, our PUNK protocol also provides a simple way to adhere to the 3R’s guiding principle for a more ethical use of animals in BAT research.Consequently, our PUNK protocol provides an enormous advantage over previously used infrared techniques, as the animals do not need to be anesthetised or shaved. Yet it allows the performance of highly robust and reproducible measurements, increasing the statistical power of obtained results and thus reducing the required number of animals. Therefore, the PUNK protocol can be used as a complementing technique to the common gold standard of measuring NST capacity, namely indirect calorimetrySupplementary Information 1.Supplementary Video 1.


Synaptic proteins play an important role for the regulation of synaptic plasticity. Numerous studies have identified and revealed individual synaptic protein functions using protein overexpression or deletion. In neuropathic pain nociceptive stimuli conveyed from the periphery repetitively stimulate neurons in the central nerve system, brain and spinal cord. Neuronal activities change the turnover (synthesis and degradation) rate of synaptic proteins. Thus, the analysis of synaptic protein turnover rather than just expression level change is critical for studying the role of synaptic proteins in synaptic plasticity. Here, we analyzed synaptosomal proteome in the anterior cingulate cortex (ACC) to identify protein turnover rate changes caused by peripheral nerve injury. Whereas PKCγ levels were not altered, we found that the protein’s turnover rate decreased after peripheral nerve injury. Our results suggest that postsynaptic PKCγ synthesized by neuronal activities in the ACC is translocated to the postsynaptic membrane with an extended half-life. External stimuli can change the efficacy of synaptic transmission, referred to as synaptic plasticity that underlies normal and pathophysiological brain functions including learning, emotion, cognition and pain. The study of synaptic protein function is critical for understanding how synaptic plasticity is regulated. The majority of studies on synaptic protein function have manipulated protein levels through deletion, reduction, and/or overexpression in cultured cells and/or animal models. In order to sustain synaptic function proteins have a finite life time that ranges from a few hours to months , 2 causeNeuropathic pain is a disease known to be induced by abnormal signal intensification in parts of a pain signaling circuit such as spinal cord or supraspinal level without external injury. Many studies have shown that the anterior cingulate cortex (ACC) plays a role in the affective mode of pain including neuropathic pain , 7. It i14N diet for 10 days for food pellet adaptation. Following ligation of the common peroneal nerve (CPN) with a wax coated braided suture the animals were switched to a 15N bacterial diet. After 7 days, mice were decapitated and the crude ACC synaptosomal P2 fraction was purified for LC-MS analysis. SDS polyacrylamide gel electrophoresis showed that approximately 70% of all synaptic proteins had a molecular weight of less than 90 kDa with no significant expression level difference between sham and nerve injury group . We therefore decided to analyze turnover rather than expression level differences of these proteins induced by peripheral nerve injury. Following in-gel tryptic digestion and peptide extraction we calculated the 15N-labeled peptide fraction (LPF) using the in-house developed ProTurnyzer software [p < 0.01, HSP60, p < 0.05). While CH60 has been shown to be one of the components in proteolytic machinery at synapse and thus may play a role in protein turnover regulation [p > 0.05). This result shows a region-specific change of PKCγ turnover rate after peripheral nerve injury. We next examined PKCγ level changes in the ACC after peripheral nerve injury using Western blot. The ACC tissue was dissected from naïve and nerve injury-operated mice 1, 3 or 7 days after surgery and PSD fraction prepared by sucrose gradient centrifugation. PKCγ levels in PSD fraction of the ACC showed a significant change over time  = 2.915, p < 0.05; posttest, * p < 0.05) showing enhancement 1 day after nerve injury and then returning to basal level. However, total PKCγ showed no significant change over time. Also, no significant changes were found in PSD fraction of the hippocampus  = 2.126, p > 0.05).To examine synaptic protein turnover rates we used a partial stable isotope metabolic labeling method Fig. a. Brieflgulation , mitochoIn this study, we assessed the turnover rate of ACC synaptic proteins smaller than 90 kDa and identified PKCγ that showed a smaller turnover rate after peripheral nerve injury. The PKCγ isoform has the unique feature of neuron specific expression where it is localized in the soma, dendrite and axon. In the synapse, PKCγ is exclusively located in the postsynaptic site (dendritic spine), but not in the presynaptic terminal , 13. IntThe present study is the first one that examines the brain region-specific role of PKCγ in neuropathic pain. PKCγ-deficient mice show a diminished neuropathic pain phenotype after peripheral nerve injury . In the Additional file 1: Table S1. The LPF profiles of synaptic proteins smaller than 90 kDa in the ACC and hippocampus of the sham and nerve-injured mice. Red indicates p < 0.05 in unpaired t-test. The hippocampal P2 fraction was examined as a negative control.


Single-molecule fluorescence energy transfer (FRET) detection has become a key technique to monitor intra- and intermolecular distance changes in biological processes. As the sensitive detection range of conventional FRET pairs is limited to 3–8 nm, complement probes are necessary for extending this typical working range. Here, we realized a single-molecule FRET assay for a short distance range of below 3 nm by using a Cy2–Cy7 pair having extremely small spectral overlap. Using two DNA duplexes with a small difference in the labeling position, we demonstrated that our assay can observe subtle changes at a short distance range. High sensitivity in the range of 1–3 nm and compatibility with the conventional FRET assay make this approach useful for understanding dynamics at a short distance. Single-molecule fluorescence energy transfer (FRET) has been widely used to provide structural and dynamic features of biomolecules ,2,3. ThiTo reach the detection range below the lower limit, single-molecule techniques for observing distance changes occurring at short distances have been developed and used to solve a wide range of biological problems ,9,10,11.In this study, we demonstrate that single-molecule FRET assay can be used to observe the subtle conformational changes over a short distance, in contrast to conventional FRET, by employing a cyanine dye pair (Cy2–Cy7), which has an extremely small spectral overlap between donor emission and acceptor absorption a. Small R0) for both dye pairs were calculated using the following Equation:2κ is the dipole orientation factor, DΦ is the fluorescence quantum yield of the donor, J(λ) is the spectral overlap integral of donor emission and acceptor absorption, AN is Avogadro’s number and n is the refractive index of the medium −1. All data processing was conducted using custom scripts written in Matlab .Finally, we obtained time courses of FRET efficiency E of each molecule from its donor and acceptor intensities  is the rotation angle between the dyes and φ is the angular separation of the dyes for Δn = 0. Based on DNA constructs used in this study, we assumed L = 0, d = a = 2 nm and φ = 240°. According to this model, the distances between donor and acceptor fluorophores in the two DNA constructs were estimated to be 1.10 (3BP_DNA) and 2.62 nm (5BP-DNA), respectively. To test whether the use of the Cy2–Cy7 pair in single-molecule FRET measurements differentiates these two DNA constructs, unlike the conventional Cy3–Cy5 pair, we prepared the DNA duplexes labeled with each FRET pair and performed single-molecule FRET measurements.To demonstrate the ability to use the Cy2–Cy7 pair for single-molecule FRET measurements experimentally, we prepared two DNA duplexes, 3BP_DNA and 5BP_DNA, which have different labeling positions, as depicted in 0R value of Cy2–Cy7, we determined that the inter-dye distances for 3BP_DNA and 5BP_DNA are 1.49 and 2.48 nm, respectively, which confirms the ability of the Cy2–Cy7 pair to explore the short distance range with high accuracy. These results are in good agreement with the values predicted by the structural model prediction, supporting the conclusion that the single-molecule FRET method using the Cy2–Cy7 pair enables us to accurately observe the subtle conformational changes even at a short distance range.For quantitative understanding of inter-dye distance changes, we obtained FRET histograms of the two DNA constructs for the Cy3–Cy5 pair b or Cy2–In this work, we demonstrated a single-molecule FRET assay that can observe the small conformational changes of biomolecules at a short distance range below the lower limit of conventional FRET pairs by using the Cy2–Cy7 pair, of which the spectral overlap between donor emission and acceptor absorption is extremely small. In contrast to the other methods for monitoring short distance changes, our approach is readily available for single-molecule FRET applications by replacing a conventional FRET pair with the Cy2–Cy7 pair. A proof-of-concept experiment using a cylindrical model for DNA duplexes showed that our method can reliably observe distance changes at a short distance range. We anticipate that our single-molecule FRET assay proposed here will be useful for describing the subtle conformational dynamics of protein domains with advanced labeling techniques ,23,24. T