Rapid advances inquantum computing have opened up new opportunitiesfor solving the central electronic structure problem in computationalchemistry. In the noisy intermediate-scale quantum (NISQ) era, wherequbit coherence times are limited, it is essential to exploit quantumalgorithms with sufficiently short quantum circuits to maximize qubitefficiency. The procedural construction of hardware-efficient ansätzeprovides one approach to design such circuits. However, refining theaccuracy of the global minimum by increasing circuit depth may leadto a proliferation of local minima that hinders global optimization.To investigate this phenomenon, we explore the energy landscapes ofhardware-efficient circuits to identify ground-state energies of thehydrogen, lithium hydride, and beryllium hydride molecules. We alsopropose a simple dimensionality reduction procedure that reduces quantumgate depth while retaining high accuracy for the global minimum, simplifyingthe energy landscape, and hence speeding up optimization from bothsoftware and hardware perspectives. However, the inherent limitationsassociated with current noisy intermediate-scale quantum (NISQ) devices,mainly short qubit decoherence times and low error correction,6 preclude the feasible implementation of exactalgorithms such as quantum phase estimation (QPE).7 Instead, hybrid classical–quantum algorithms moreresilient to quantum noise, such as the variational quantum eigensolver(VQE),8 have been successfully employedin actual quantum hardware in calculating the ground-state energyof various molecules.9 This approach isexpected to prevail until more fault-tolerant quantum devices supportinga larger number of implementable qubits are developed.10The intractability ofthe many-body problem continues to pose enormouschallenges in finding the ground-state energy of molecules for traditionalclassical computing.11 choosing a good circuit ansatz for the approximationis crucial. Several approaches exist in the selection of ansätze:one method involves utilizing the unitary coupled cluster (UCC) ansatzthat typically employs excitations within the electronic structureof the molecule, where single and double excitations are most commonlyused.12 However, the number of quantumgates required to implement the traditional UCC ansatz typically growsrapidly as the complexity of the target molecule increases.13 Although various methods have been developedin refining the UCC ansatz to curtail the number of excitation operatorsthat need to be implemented, for example, via the ADAPT-VQE algorithmthat selects cluster operators based on their contribution to theoverall gradient function,14 their computationalimplementation via standardized quantum gates within quantum circuitsonto contemporary quantum computers still remains difficult in practice.15 Furthermore, it has also been suggested thatthe ADAPT-VQE algorithm requires a greater number of measurementsto be made on a quantum computer compared to standard VQE.16As the VQE algorithm seeks to variationallyconstrain the upperbound for the ground-state energy of a target molecule,17 However, as the primary goal of the hardware-efficientansatz is to locate the global minimum rather than preserve the symmetriesof the molecule, a large number of gate layers may be needed to achieveconvergence. This issue becomes increasingly problematic for largersystems requiring a greater number of qubits due to the barren plateauproblem, where in the presence of noise the gradients decrease exponentiallyas the number of qubits and circuit layers increases.18 Furthermore, the inclusion of more circuit layers may leadto the introduction of numerous local minima, making global optimizationmore difficult. Finally, the increase in the number of implementedquantum gates may result in compounding of gate noise arising fromdepolarization, thermal relaxation, and dephasing errors.19A less demanding approach, which is themain focus of this study,is to employ hardware-efficient ansätze that aim to improvethe convergence of the ground-state energy of a given molecule viathe progressive introduction of more parametrized and entangling quantumgate layers. This simple, yet effective, strategy has been successfullyimplemented in quantum hardware to find the ground-state energiesof hydrogen, lithium hydride, and beryllium hydride.25 We thereforeseek to advance the exploration of hardware-efficient ansätzein computing the ground-state energies of hydrogen, lithium hydride,and beryllium hydride via the VQE algorithm using the principles ofenergy landscape theory and associated computational tools, whichhave been employed successfully in treating relatively high-dimensionalmolecular systems.29 By developing the tools necessary to analyze the solution landscapesof hardware-efficient ansätze in greater detail, we providegreater insight into the proliferation of local minima and other stationarypoints arising from VQE optimization,30 and thus design new strategies to mitigate their occurrence andensure an efficient search for the global minimum. We also devisea simple deparameterization procedure that aims to reduce the parameterspace of hardware-efficient ansätze, while still retainingthe accuracy of the global minimum, thus simultaneously acceleratingglobal optimization and reducing quantum gate noise.The employment of basin-hopping methodsto study energy landscapesarising from quantum computing is relatively scant, with a notableexample being the enhancement of Grover’s algorithm by meansof a quantum basin-hopper.231 OPTIM,32 and PATHSAMPLE33 with the base VQE algorithmused in approximating the ground-state energy of a given moleculefor a particular geometry. The general methodology begins by firstconsidering the electronic Hamiltonian Ĥe of the molecule in its second quantizedformhpq and hpqrs arethe one- and two-body integrals and â† and â are the fermionic creationand annihilation operators, respectively. Ĥe is then isospectrally mapped to a suitablequbit Hamiltonian Ĥq. We employ parity transformation with two-qubit reduction34 via the PySCF package to yield a linear combinationof Pauli strings P̂α withcoefficients gα, thus compactingthe number of encoded qubits N(36)Ĥq, and thus the ground-state electronicenergy of the molecule, E0, can then bevariationally approximated with the VQE algorithm. We evolve an initialHartree–Fock state |ψ(0)⟩ with a suitable hardware-efficientansatz for unitary operator Û(θ) and L layers by means of a quantum computerRy-parametrized rotationgates taking on the standard formL componentis composed of a parametric layer Ry rotation gates for each qubit and alinear entanglinglayer CNOT gates arearranged in a linear fashion from the first to the Nth qubitRy-linear entangling circuithas been used successfully as a shallow yet effective hardware-efficientansatz in finding the ground-state energies of various molecules viaVQE.38 qubits N ⟩= Û(θ)|ψ(0)⟩can be used to evaluate the expectation value E(θ) on a classical computer, which the variational principleimplies must be greater than or equal to E0E0 up to a certain minimum circuitlayer depth Lmin. For a given iterationnumber k with angular parameters θ(k) = {θ1, θ2,. . . , θμ, . . . ,θLN}, we employ basin-hopping22 to find the global minimum of Ek using the GMIN program with local minima characterizedby a limited-memory Broyden–Fletcher–Goldfarb–Shanno(L-BFGS) algorithm.39 During basin-hoppingglobal optimization, the energy of the succeeding iteration, Ek+1, is accepted via the Metropoliscriterion, i.e., if Ek+1 < Ek or with probabilityexp(−(Ek+1 – Ek)/T) otherwise,where T is an effective temperature in units of energy.22 If Ek+1 is not acceptedthen a random perturbation of up to 1.0 rad is performed on θ(k) and the optimization proceedsas usual. The parameter-shift rule is used to compute the analyticgradients for each angular parameter, since the only parametrizedgates are localized single-qubit Ry gates with two unique eigenvalues40eμ is the unit vector of parameter θμ. Subsequently, the updated parameters of iteration k + 1 are relayed back into the quantum computer for the computationof a new kE+1. This processbetween the quantum–classical computer interface continuesuntil a suitable convergence criterion is reached. For this study,5000 basin-hopping steps with a root-mean-squared (RMS) gradient convergencecriterion of 5 × 10–10 au anda reduced temperature of 1.0 au were used to perform global optimizationvia GMIN for the H2, LiH, and BeH2 molecules we employ the OPTIM program to locate transitionstates and characterize the corresponding pathways that connect pairsof minima. To classify each stationary point as a minimum, transitionstate, or higher order saddle point, the LN × LN Hessian of the circuit ansatz H was constructedby iterating the parameter-shift rule again from ν for Hessian element HμνH to determine the number of negative eigenvalues V. The local minima, i.e., stationary points with zero negative eigenvaluesfor their respective Hessians, can then be filtered from other stationarypoints. Double-ended connection runs between pairs of minima beginwith a doubly-nudged41 elastic band (DNEB)calculation, where candidate transition states are further refinedwith hybrid eigenvector following.45 Here, the convergence conditionfor the Rayleigh–Ritz calculation of the smallest nonzero Hessianeigenvalue was set at 10–5 au. To compare the distancebetween two fully evolved states ψ(θ(γ))and ψ(θ(δ)) with different rotationparameters, the state vector overlap Sγδ was used as a metric24 as discussed below.The final evolved state|ψis not necessary to produce a global minimum with an accurate energy.Thus, to reduce the parameter depth even further, a heuristic deparameterizationprocedure can be adopted. The most straightforward implementationis as follows: first, a parametrized Ry gate is selected and frozen by assigning the gatea fixed rotation value. A rotation amplitude of zero is typicallysought, although other standardized values such as ±π/2or ±π can also be used. The former choice is most desirablefor various reasons: it allows for the reduction of the Ry gate into a virtual identity gate thatdoes not need to be implemented in practice, thus eliminating anyassociated quantum gate noise. In terms of software, the computationalcost of optimizing the parameter associated with that gate is alsosaved. Finally, by aiming to find as many virtual identity gates aspossible, we can construct quantum circuits with more degrees of freedomfor circuit transpilation, thus potentially allowing for more efficientmapping of the quantum circuit onto actual quantum hardware and subsequentlyreducing its effective depth.46 The VQEalgorithm is then performed for the reformulated circuit ansatz. Ifthe same global minimum energy for all required bond lengths can beachieved as for the original circuit then the deparameterization ofthat Ry gate is maintained;otherwise, it is reparameterized. Another Ry gate is then chosen and deparameterized, and thisprocess continues until no more Ry gates can be frozen without degrading the accuracy, thus yieldinga refined circuit that is suitable for all molecular geometries sampled.In some cases the Hamiltonian LN –2, since for a linear ansatz as in Ry gate in sequence is the most important in varying the evolvedstate and is thus set to be parametrized by default. However, it ispractically more efficient to compare similar rotation amplitudesof global minima obtained for different bond lengths, simultaneouslypicking out multiple Ry gates that conform to the standardized values of {0, ±π/2,±π} to be deparameterized. Conversely, the Ry gates with more variable rotation amplitudesacross multiple molecular geometries are chosen to remain parametrizedthroughout the procedure. Overall, the flexible designation of multipleparametrized and deparameterized gates within the same run via comparisonof amplitudes across sampled bond lengths reduces the overall numberof times the deparameterization procedure needs to be implemented,thus providing substantial savings to the additional hardware andsoftware computation costs incurred from implementing the deparameterizationprocedure.If carried out in this manner, the maximum number of runs in implementingthe deparameterization procedure would be We also find that reducing the number of parametersmay lead tosimplification of the energy landscape for the refined ansatz, reducingthe number of minima. However, new stationary points, arising fromthe truncation of the stationary points in the original circuit ansatz,can also appear. Hence, it is important to compare the refined andunrefined ansätze to determine if the desired energy landscapesimplification has been achieved.33.1Ĥq operator of H2 in the STO-3Gbasis consists of five Pauli strings, where H–H bond lengthsbetween 0.1 and 5.0 Å with intervals of 0.1 Å were considered.Utilizing a modified L = 1 ansatz equipped with aCNOT gate and a Hartree–Fock initial state of –10 hartrees (Ha) of the true ground-stateenergy for all H–H bond lengths sampled. However, a local minimumwas also obtained for each case. We used OPTIM to locate the transitionstate between the two minima . Forexample, with a H–H bond length of 0.7 Å, the stationarypoints can be organized into a disconnectivity graph . Although the deparameterization procedure for circuitswith L = 4 provided an improvement in optimizationtimes, the results are not competitive with ansätze for L > Lmin. This observationcanbe attributed to the more limited deparameterization for lithium hydride,where only one gate can be frozen if we wish to maintain the accuracyof the global minimum across all Li–H bond lengths. Thus, from an energy landscape perspective, if quantumgate noise is not a significant factor then choosing a circuit ansatzwith a depth greater than Lmin may beadvantageous in computing the ground-state energy in this example.An interesting phenomenon occurs when quantum circuits with or L = 4 5a and 5b GHz CPU 1, we fouL = 4 circuitansatz, we also observe fewer local minima relative to their correspondingtransition states and higher order saddle points. To explore thisphenomenon further, we considered the Li–H bond length of 1.5Å more systematically. Using OPTIM, each stationary point wasconverged to a tighter convergence RMS gradient criterion of 10–12 au, and the pathways between local minima were analyzedfor each transition state . We then repeated the procedure until we reached the maximumreduction of the number of active parameters from 30 to 8 .The major simplification of the  GHz CPU 2 and fou42, LiH, and BeH2 via the VQE algorithm.The use of basin-hopping methods has provided a platform to largelybypass the obstacle of barren plateaux associated with variationalquantum algorithms, enabling us to obtain local minima and other stationarypoints for which we can reconstruct the energy landscape of the circuitansatz by means of disconnectivity graphs, as we have demonstratedfor BeH2 in particular. Characterizing the landscape alsoenables us to understand the efficiency with which the global minimumcan be located, complementing established descriptors such as theinnate expressibility or entangling capability of the ansatz.49 This insight is especially important for LiH,where although the circuit ansatz of depth Lmin supports a sufficiently accurate global minimum energy,it was not the best choice due to an abundance of alternative stationarypoints that hinder global optimization. Hence, it may be more efficientto choose a circuit ansatz with a few more layers to access more stateswithin the same Hilbert space, thus bypassing alternative solutionsmore effectively. For sparser Hamiltonians, we have also tested adeparameterization procedure to freeze redundant Ry gates, which can simplify the energylandscape while retaining the accuracy of the global minimum. ForBeH2, we find that deparameterization significantly reducesthe computational expense of global optimization. The reduction ofparametrized gates to virtual identity gates is also expected to beuseful in reducing the noise attributed to practical implementationof quantum gates as well as more efficient circuit transpilation,thus providing tangible benefits to both hardware and software aspects.Exploiting quantum computing to profile molecular energy landscapesis an exciting prospect, and we aim to use the methods developed hereto explore circuit ansätze for other variational algorithmssuch as UCC in future work. Finally, we also envision that our methodscan be utilized in other variational quantum algorithms where layer-basedansätze are readily employed, for example in the Quantum ApproximateOptimization Algorithm (QAOA) in solving combinatorial optimizationproblems,50 as well as quantum neural networksin trainable quantum machine learning models.51We have employed the energy landscapeframework to explore thesolution space of hardware-efficient ansätze with varying circuitdepth for H


The [FeFe]-hydrogenase I from Clostridium acetobutylicum (CaI) is a member of a large family of structurally related enzymes where interfacial electron transfer is mediated by a terminal, non-canonical, His-coordinated, [4Fe–4S] cluster. The function of His coordination was examined by comparing the biophysical properties and reactivity to a Cys substituted variant of CaI. This demonstrated that His coordination strongly affected the distal [4Fe–4S] cluster spin state, spin pairing, and spatial orientations of molecular orbitals, with a minor effect on reduction potential. The deviations in these properties by substituting His for Cys in CaI, correlated with pronounced changes in electron transfer and reactivity with the native electron donor–acceptor ferredoxin. The results demonstrate that differential coordination of the surface localized [4Fe–4S]His cluster in CaI is utilized to control intermolecular and intramolecular electron transfer where His coordination creates a physical and electronic environment that enables facile electron exchange between electron carrier molecules and the iron–sulfur cluster relay for coupling to reversible H2 activation at the catalytic site.One of the many functions of reduction–oxidation (redox) cofactors is to mediate electron transfer in biological enzymes catalyzing redox-based chemical transformation reactions. There are numerous examples of enzymes that utilize redox cofactors to form electron transfer relays to connect catalytic sites to external electron donors and acceptors. The compositions of relays are diverse and tune transfer thermodynamics and kinetics towards the chemical reactivity of the enzyme. Diversity in relay design is exemplified among different members of hydrogenases, enzymes which catalyze reversible H Histidine coordination of the distal [4Fe–4S] cluster in [FeFe]-hydrogenase was demonstrated to tune the cluster spin-states, spin-pairing and surrounding molecular orbitals to enable more facile electron transfer compared to cysteine coordination. Understanding the underlying mechanistic principles of these reactions has inspired the creation of numerous synthetic catalysts within the field of biomimetic chemistry. For example, great advances in catalyst design have been achieved through a rigorous biophysical and structural investigation of the active site of hydrogenase enzymes.1–4 Inherent to H2 formation as well as all redox catalytic reactions is the process of directing electrons to the active site at the optimal flux and reduction potential to enable efficient catalysis.5 Of equal importance is how the internal electron transfer events integrate with external redox partners. A detailed description of the biophysical features of cofactors that exist at this interface is critical to fully understand the mechanisms of intramolecular electron transfer fundamental to driving a broad range of chemical reactions in biological systems.There is broad interest in understanding reduction–oxidation (redox) enzymes that catalyze the diverse chemical transformations that comprise biological energy transformation. Many of these reactions are relevant to energy storage in energy carrier compounds such as hydrogen gas .13–15 Studies have shown that site-differentiated coordination of iron–sulfur clusters can result in changes to the redox potential (Em), geometry, and electronic properties. These properties contribute to function in electron transfer embodied in the Marcus theory for non-adiabatic electron transfer (16 The electron transfer rate constant (kET) is determined by the tunneling matrix element |TDA2|, reorganization energy (λ), the total Gibbs free energy change (ΔG0) for the electron transfer reaction, and temperature (T).Site-differentiated iron–sulfur clusters, where a canonical Cys residue is exchanged for another residue such as His, Asp, Glu, or Ser are prevalent in redox enzymes.transfer .16 The eG0 , the density of electronic states |TDA2|  and/or λ .In this context, site differentiation of iron–sulfur clusters can be envisioned as a means to control electron transfer by tuning of ΔClostridium pasteurianum (CpI) and the structurally homologous enzyme from C. acetobutylicum (CaI). These enzymes catalyze H2 activation at a conserved organometallic, iron–sulfur cluster, or H-cluster, that is integrated with a conduit of iron–sulfur clusters, termed the F-clusters. F-clusters function in the transfer of electrons between external donor–acceptor molecules and the H-cluster during catalysis. The distal end of the conduit branches, ending at a site-differentiated [4Fe–4S] cluster with 3Cys1His ligation ([4Fe–4S]His) or a [2Fe–2S] cluster  under anaerobic conditions. Both DDHis and DDCys displayed typical ligand-to-metal charge transfer bands in their absorption spectra characteristic of oxidized iron–sulfur clusters, which diminished in intensity following reduction by sodium dithionite  and recombinantly expressed in hia coli . Followie Fig. S1.−1, absent in the DDCys spectra, that is located in the region where Fe–N stretching is expected to have a fundamental frequency (220–280 cm−1) in spectra of iron–sulfur cluster proteins  and are consistent with other [4Fe–4S] and [2Fe–2S] cluster containing proteins.25,26 When DDHis was poised at pH 5.9, below the His pKa1 (average of 6.6 in protein environments)27 the entire [4Fe–4S] cluster was partially degraded as evidenced by the attenuation of the Fe–S bands , although it has not been directly measured.19 To quantify the low reduction potentials of these [4Fe–4S] clusters, we employed square wave voltammetry (SWV) for both DDHis and DDCys .19,28 The Em of [4Fe–4S]His was −565 mV at pH 8.8, whereas substitution of His for Cys led to a Em,DDCys = −630 mV at the same pH, 65 mV lower than the native cluster. For comparison, the E+/H2H couple is −520 mV vs. SHE at pH 8.8 and 1 atm H2. Therefore, coordination by His or Cys results in Em that is favourable for transfer of electrons with C. acetobutylicum ferredoxin (Em = −480 mV at pH 8.8) during H2 oxidation.21The [4Fe–4S]His cluster has been implicated to possess a low reduction potential , however notable changes in reduction potential were found when the solution pH was increased above 10 31 . No pH dependency was observed for DDHis between pH 6–10 (above 10 . At pH 114.52)31 . This woEm and spin properties affects the reactivity of CaI, a holoenzyme mutant was generated where His coordination of the distal [4Fe–4S] cluster was changed to Cys (H93C CaI). The WT and H93C CaI hydrogenases were investigated for H2 production and uptake activities using C. acetobutylicum ferredoxin , the native electron donor/acceptor to CaI.20To determine whether altering the distal cluster 2 uptake and evolution activities were measured at pH 6 and 8.3 in both dye-linked  and ferredoxin linked assays. In all conditions, the activities were significantly altered in the H93C CaI versus WT CaI. H2 production activity was reduced 3-fold and uptake activity was decreased 5-fold in H93C CaI (Table S12 uptake) and/or reduced MV , which complements the Fd assays to inform on electron transfer events over a broader range. In this case, the electrocatalytic profiles displayed similar overall shapes, however WT CaI was significantly steeper than H93C (versus red). The more constant linear growth of H93C CaI indicates a limitation in electron transfer activity. Since the enzymes differ only in the coordination of the distal [4Fe–4S] cluster, the results are due to differences in interfacial electron exchange rates that arise from changes in the [4Fe–4S] cluster coordination.Free-energy effects on electron transfer in redox enzymes can be examined using protein film voltammetry. This technique enables access to a wide window of driving force  and [4Fe–4S]His  clusters based on their unique temperature and power properties32 and agreement with prior EPR analysis of the homologous CpI protein19 and a CpI protein fragment containing only the [2Fe–2S] cluster28  under the turnover conditions of the sample, yielding the well characterized S = ½ signal at g = 2.10, 2.04, 2.00.33 Overall, the similarity between WT and H93C spectra suggests minimal influence of the ligand alteration on the other S = ½ F-cluster and H-cluster signals. It is also noted that for all the spectra reported here, a small residual signal at g = 4.3 was observed and is thought to arise from a small Fe3+ impurity.In addition to driving force effects, the underlying electronic and magnetic properties of iron–sulfur clusters determine how they function in electron transfer. To define these properties of the [4Fe–4S]His cluster in CaI, X-band CW EPR on the DDHis and DDCys proteins were performed and used to resolve the more complex spectral properties of the WT and H93C full enzyme counterparts. When DDHis was reduced with dithionite, two luster28 . The sigluster28 . Broaden g = 5.6 . These d g = 5.6 . Both lonchanged . Similarnchanged . Like DDnchanged . Conversg = 5.6 and 5.1 are most consistent with S > ½ spin states, and are similar to EPR signals that arise from half-integer Kramer systems in other [4Fe–4S] cluster containing proteins.34–38 In the highly homologous [FeFe]-hydrogenase from CpI, low-field resonances at g = 5.80 and 4.76 were also observed in reduced samples and assigned to an undefined S = 3/2 spin system.33 Similar low-field resonances at g = 5.70, 5.55, and 5.15 were also observed for the [FeFe]-hydrogenase from Thermotoga maritima and suggest the presence of multiple S > ½ species.39 As shown in g = 5.1 were used to assign it to a ±3/2 doublet of the S = 7/2 spin system with E/D = 0.125, where D and E are the respective axial and rhombic zero-field splitting parameters , which is lost upon conversion to full Cys coordination, demonstrates that His coordination increases the overall density of states that are energetically accessible.40The low-field signals observed at s Fig. S9. This asS > ½ spin states may be sensitive to additional interactions not present in the truncated protein. One possibility is that inhomogeneous broadening of the S > ½ signals is due to a magnetic exchange interaction of the distal [4Fe–4S]His cluster with the F-cluster relay (e.g. FS4B), as has been shown for the observed S = ½ signals that are reflective of a reduced F-cluster relay.19 Evidence of magnetic interactions indicates long-range electronic interactions that extend throughout the F-cluster relay and includes the [4Fe–4S]His cluster. Together with the increased spin-states, the electronic properties of [4Fe–4S]His function to facilitate more reversible electron transport to and from the catalytic H-cluster compared to [4Fe–4S]Cys.The diminished and broadened signal intensity of the CaI EPR spectrum in the low-field region compared to DDHis suggests the 41,42 In our calculations, we considered the primary coordination sphere truncated at the Cβ carbon atom for the site-differentiated His-coordinated cubane structure in its unprotonated ([4Fe–4S]His) and protonated ([4Fe–4S]HisH) states, and compared it with the all Cys coordinated cubane structure ([4Fe–4S]Cys) . This value is considerably more negative compared to both [4Fe–4S]His (E° = −1510.82 mV) and [4Fe–4S]HisH (E° = −1297.12 mV), where the protonated version of HisH has the most positive potential. This trend is in agreement with our experimental observations of DDHis at pH < 10 having a more positive Em value than DDCys  with the His coordinated iron (Fe3) atom Fig. S11. We thusEm value. For example, in the case of the His coordinated [4Fe–4S] cluster in the [NiFe]-hydrogenase from Desulfovibrio fructosovorans a Cys substitution leads to a slight positive shift in Em.44 For CaI we demonstrated that the substitution of His for Cys leads to a small negative shift in Em of ∼65 mV. In the context of non-adiabatic electron transfer (G°) profile for electron transfer with ferredoxin and the F-cluster relay in [4Fe–4S]His versus [4Fe–4S]Cys CaI, that favours reversibility.The effect of site-differentiation on [4Fe–4S] clusters, specifically where a mixture of Cys and His coordinating residues is observed, has been shown to have differential effects on the transfer  there arTDA|. The LUMO map, which defines where electrons can localize on the [4Fe–4S] cluster, is less symmetric in [4Fe–4S]His with more of the LUMO residing in the space between CaFd and the [4Fe–4S]His cluster to enable electron exchange between the two species. The imidazole ring of [4Fe–4S]His also serves to extend the MO network for electron tunnelling closer to the nearby [4Fe–4S] cluster and includes a coordinated water. Similar extended MO networks and presence of coordinated water have been shown to greatly enhance electronic coupling and electron transfer rates between iron–sulfur clusters in complex I.45 In addition, the [4Fe–4S]His cluster has a higher density of electronic states compared to [4Fe–4S]Cys, which are energetically accessible during the reduction–oxidation events of electron transfer.40 This was observed from a stabilized S = 7/2 spin system that is lost with a change to Cys. A more symmetric spin localization ([4Fe–4S]Cys) versus the less symmetric, more delocalized ([4Fe–4S]His) cluster has been proposed to impact rate constants with donor–acceptors through spin exchange interactions.46The EPR measurements and computational modelling of CaI [4Fe–4S]His cluster demonstrate that His coordination also creates a uniquely tuned electronic structure of the cluster compared to all Cys coordination which impacts |λ) were not calculated for [4Fe–4S]His or [4Fe–4S]Cys, a recent computational study on a His-ligated distal FeS cluster in a [NiFe]-hydrogenase revealed that His-ligation did not result in significant changes to λ.47Although solvent reorganization energies (2 activation.44,47,48 The results presented here broadly inform on the functional effects of site-differentiation, and how it may be a common approach that biology employs to control electron transfer reactions within enzymes and with electron mediators. It is anticipated that this is a more general mechanism to optimize kinetics, directionality, and coupling of electron transfer in complex energy transduction systems.5 For CaI, the unique coordination of the [4Fe–4S]His cluster acts to integrate the electronic structure and physical environments to enable facile electron exchange, an advantageous property for electron transfer with ferredoxin.We have demonstrated that His ligation of the distal [4Fe–4S] cluster in CaI tunes the cluster's reduction potential, bonding and electronic properties that in turn tune the reversibility of intermolecular and intramolecular electron transfer for coupling to reversible catalytic HExperimental and computational data files that are not included in the ESIThe manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.There are no conflicts to declare.SC-013-D1SC07120C-s001


Management of diabetes during fasting is a clinical challenge. Sodium glucose co-transporter -2 inhibitors (SGLT2i) are considered safe with a low risk of hypoglycemia. However, studies on SGLT2i are scarce. This study was designed to compare the efficacy, safety, and tolerability of empagliflozin with metformin during Ramadan in comparison with sitagliptin and metformin.It was a prospective, observational study, conducted at 11 different sites all across Pakistan on an outpatient basis during Ramadan (May 2021–June 2021). including 132 patients, 88 who received metformin and sitagliptin, and 44 patients who received metformin and empagliflozin.Patients of the SGLT-2i group experienced similar symptomatic hypoglycemic episodes (15.9%) as the sitagliptin group. There was an improvement in blood sugar levels after the use of SGLT-2i (RBS 181 ± 64 before Ramadan vs 162 ± 53 after Ramadan). HbA1c also improved after the use of SGLT-2i before and after Ramadan (7.2 ± 0.8 vs 6.9 ± 0.9 for Metformin + Empagliflozin and 7.8 ± 1.5 vs 7.6 ± 1.6 for Metformin and sitagliptin). Weight and BMI improved after the use of SGLT-2i (BMI 36.5 ± 4.8 before Ramadan and 33.7 ± 2.4 after Ramadan). There were no reported cases of urinary tract infection in the empagliflozin group.SGLT-2 inhibitors combined with metformin for patients with diabetes during Ramadan fasting is as effective, safe and well tolerated as DPP4 combined with metformin. Ramadan is a lunar-based month lasting between 29 − 30 days. Fasting during the holy month of Ramadan constitutes one of the five main pillars of Islam and it is obligatory for all healthy adult Muslims to fast during Ramadan. The duration of fasting varies from 12 to 20 h, with the average fasting period being 15 h [The type of medication the patient is taking for diabetes management influences the potential risks that fasting may cause and needs careful attention within the treatment plan. Adjustments to the dose and timing of some medications may be required during Ramadan to minimize the risk of hypoglycemia, hyperglycemia and dehydration in fasting patients along with Ramadan specific diabetes education. Several observational and randomized controlled studies have been conducted on people with Type 2 diabetes mellitus (T2DM) fasting during Ramadan, focusing on the safety profile of different available oral antidiabetic agents, notably assessing the incidence of hypoglycemia episodes. –6 These Sodium glucose co-transporter-2 Inhibitor (SGLT2-inhibitor) are a newer class of oral hypoglycemic agents that have shown to be effective as monotherapy and as an add-on treatment for T2DM with significant add-on benefit regarding body weight and systolic blood pressure reduction. , 9 HowevKeeping in view the hot climate and the long fasting hours, it was need of time to determine which medications will be beneficial for fasting people with diabetes. Therefore, the present study was designed to evaluate the efficacy and safety profile of SGLT2 inhibitor empagliflozin with metformin in comparison with DPP4 inhibitor sitagliptin with metformin in terms of hypoglycemia, dehydration and glucose control in people with T2DM observing fast during Ramadan.. Eighty-eight patients received metformin and sitagliptin (100 mg/day sitagliptin dose), and 44 patients received metformin and empagliflozin (10 mg/day empagliflozin dose). Study participants were already taking these medications for at least six weeks prior to Ramadan.This is an observational cohort study conducted at 11 different sites all across Pakistan on outpatient basis during Ramadan (May 2021–June 2021). The study included 132 patients with type 2 diabetes mellitus of ≥ 06 months durationn = 104 samples for this study, 52 samples per group, however due to expected drop out we are taking 130 samples per group and n=65 for this study.It was estimated using online sample size calculator, openepi version 3.01 for mean difference, after input the change in mean HbA1c 8.2±1.5 % vs. 7.4±1.4% in Ramadan. We required at least Patients with HbA1c ranging from 6.5–8.5% before Ramadan and eGFR > 60 ml/min were included. Patients were excluded if they were on Insulin or had contraindications for fasting such as severe renal disease, liver diseases, unstable angina, history of diabetic ketoacidosis, hypoglycemic unawareness as per IDF diabetes and Ramadan (DAR) guidelines .1c, fasting blood glucose, urine DR and kidney function tests (serum creatinine & eGFR).A detailed history followed by clinical examination was done in all patients fulfilling the inclusion criteria. Screening visit which was done at least 5 weeks prior to the start of Ramadan, the information regarding age, gender, history of diabetes, intention to fast in the forthcoming Ramadan, and diabetes related complications were obtained. Weight, height and blood pressure was taken. Body Mass Index (BMI) and blood pressure measurements were done before and after Ramadan. Each patient was provided individualized Ramadan specific education specially focusing on dietary modifications and frequent blood glucose monitoring by glucometer at different times of the day according to DAR IDF guidelines . Blood sPatients were provided with a log book to record important daily events especially hypoglycemic symptoms, and whether they required any assistance due to symptoms of hypoglycemia, time and duration of hypoglycemia, and whether the fast was broken due to any reason. If patients experienced symptoms of hypoglycemia, they were instructed to check blood glucose level using glucometer and enter the readings in their log books along with symptoms.The log book was maintained by the patients on a daily basis throughout Ramadan, irrespective of symptoms. In case of multiple episodes of hypoglycemia, each episode was documented separately. Furthermore, every patient was instructed to check blood glucose measurement before the evening meal three times per week.At the end of Ramadan , a follow up visit was done to obtain information regarding the fast-during Ramadan and any changes in medications dose and timing if required were done.Safety and tolerability of these medications during Ramadan were assessed by reported adverse events entries in log book during the study period. All reported adverse events were categorized into mild, moderate or severe and relationship to study drug by the investigator. Patients were also contacted twice weekly by phone after the completion of Ramadan to find out about the occurrence of any serious side effect.) Hypoglycemic episodes during Ramadan were assessed by self-monitoring of the blood glucose during the day according to IDF diabetes and Ramadan (DAR) guidelines for blood glucose monitoring during Ramadan [. The reported hypoglycemic symptoms in our study participants included palpitations, nausea, sweating, confusion, tremors, symptoms of dizziness, visual blurring, or intense hunger with or without biochemical confirmation. Blood glucose < 70 mg/dl on finger prick test was considered as hypoglycemia and it was considered severe episode if patient required assistance from another person or that resulted in seizure or loss of consciousness.a Ramadan . The repb) Dehydration episodesThis was assessed by symptoms of hypotension, orthostatic hypotension, postural dizziness, dehydration, syncope attack during fasting.c) Genitourinary InfectionsNumber of participants who experienced any urinary tract or genital infections.This included changes in weight and BMI after Ramadan.The study protocol was approved by the local ethical committee and all patients signed informed consent before participation.P-value less than 0.05 was considered statistically significant. All statistical calculations were performed using SPSS 25 .Results are presented as total count, percentages, mean and standard deviation. Comparison between categorical variables was done using chi-square test while numerical variables were compared using student t-test or Mann–Whitney U test. Values of weight, BMI, HbA1c and RBS were compared before and after fasting using Paired Sample T test. A The present study included 132 patients, out of which 88 received metformin and sitagliptin (Group A), and 44 patients received metformin and empagliflozin (Group B).Comparison between the two studied groups regarding the basic data including mean age, gender, duration of diabetes, BMI, HbA1c before Ramadan, antidiabetic medications, duration of hypertension and antihypertensive medications revealed no statistically significant differences (Table Hypoglycemic Episodes: Patients of SGLT-2i group experienced similar hypoglycaemic episodes (15.9%) as sitagliptin group.∙ No. of days patients fasted: There were differences between the two groups regarding the number of days patient fasted (23 ± 12 vs 18 ± 13 days).∙ p value 1.0) and hyperglycemic episodes  were observed in both groups.∙ Similarly comparable symptomatic hypoglycemic  and (RBS 181 ± 64 vs 162 ± 53).∙ HbA1c also improved after use of SGLT-2i before and after Ramadan (7.2 ± 0.8 vs 6.9 ± 0.9% for Metformin + Empagliflozin and 7.8 ± 1.5 vs 7.6 ± 1.6% for Metformin and sitagliptin).2 before Ramadan and 33.7 ± 2.4 kg/m2 after Ramadan) .The levels of BMI after Ramadan fasting showed a non-significant difference between the SGLT-2 inhibitors group and Sitagliptin group (Sodium glucose co-transporter inhibitors (SGLT2i) is an emerging class of anti-diabetic medications which primarily act by inhibiting SGLT2 receptors located on the proximal glomerular tubules leading to significant glycosuria along with osmotic diuresis. The net consequence of this mechanism is insulin independent lowering of glucose levels in addition to modest weight loss. Owing to its mechanism of action, SGLT2i are generally not associated with hypoglycemia per se; however, it is unclear whether this risk changes during prolonged ritual fasting as observed by Muslims in Ramadan. Furthermore, risk of volume depletion may be especially pronounced during fasting, manifesting in the form of postural hypotension, dehydration, dizziness, and blackout, all of which may lead to falls and other potentially serious medical consequences. Additionally, an increased risk of urinary tract infections and genital infections is recognized with the use of SGLT2i. Finally, SGLT2i are associated with rare but clinically significant complication of euglycemic diabetic ketoacidosis. The later risk is particularly observed in people rapidly lowering or stopping concurrent insulin use. Considering all of the aforementioned knowledge, there is widespread concerns and uncertainty regarding safety of SGLT2i in patients with T2D who practice ritual fasting in Ramadan. This study, therefore, aimed to ascertain safety of SGLT2i during fasting.P = 0.65). These findings are consistent with another study conducted by Wan Seman WJ et al., which compared SGLT2i with Sulphonylureas in the management of diabetes during Ramadan and observed fewer episodes of symptomatic and severe hypoglycaemia among SGLT2i users compared to Sulphonylureas [In our study, comparable rates of hypoglycemic episodes were observed in both Empagliflozin and Sitagliptin groups (4.16% vs 8.7%, nylureas , 13. SimIn terms of risk of urinary tract infections and genital infections, our study did not find statistically significant difference between two groups. Similarly, no documented episodes of euglycemic diabetic ketoacidosis were reported in either group. We screened urine for ketones as serum ketone measurement was not available as part of surveillance, no clinical manifestation in the form of diabetic ketoacidosis was observed during study period. In an observational study performed in Singapore, no increase in ketone levels was observed during Ramadan in a cohort using SGLT2i . NonetheBoth Sitagliptin and Empagliflozin were associated with reduction in HbA1c and random blood glucose values as well as weight and BMI. However, difference of weight between both groups was not observed in this study, possibly because use of SGLT2i was started before initiation of the study. This suggests that Empagliflozin retains its glucose and weight lowering properties without adverse effects in carefully selected patients who choose to fast during Ramadan.As mentioned above, no serious adverse effects were observed which could lead to discontinuation of SGLT2i in our cohort of participants using it during Ramadan fasting.Our study has number of limitations which should be taken into account while interpreting findings. As an observational study, it has inherent bias imbedded in studies of similar nature such as recall bias which cannot be excluded in this case as rate of symptomatic hypoglycemia and dehydration was dependent on patients’ reports. Secondly, this was a small sample size study which again limits extrapolation of our findings on larger population groups.  SimilarlThe strength of this study is that it is the first study of its kind to address the safety concerns of SGLT2 inhibitors during fasting in Pakistani population. In addition, we are not aware of any previous studies directly comparing SGLT2i with DPP4 inhibitors in people with T2DM who wish to fast during Ramadan. As an observational study, physicians prescribing either Sitagliptin or Empagliflozin had full professional discretion based on their clinical judgment which is in keeping with usual day to day care thus making our findings relevant to real world practice. A robust clinical follow up and periodic biochemical assessment before, during and after Ramadan was in place with high retention rate of study participants thus lending credibility to our findings.Various trials performed to demonstrate cardiovascular safety of SGLT2i class demonstrated astonishingly positive outcomes with statistically significant reduction in progression of heart failure and renal dysfunction thus setting their place in the therapeutic management of heart failure and chronic renal disease independent of glucose lower properties. We postulate that our findings add to the evidence and clinical assurance that SGLT2 inhibitors may also be used or continued for their cardio renal protective properties in people without diabetes who wish to fast during Ramadan.In people with Type 2 diabetes mellitus fasting during Ramadan, use of SGLT-2 inhibitors combined with metformin is as safe, effective and well-tolerated as DPP4 inhibitors combined with metformin. Both combinations are effective in improving weight and HbA1c. However, DPP4 inhibitors were associated with more adverse effects than SGLT-2 inhibitors.


Despite surgical and therapeutic advances, glioblastoma multiforme (GBM) is among the most fatal primary brain tumor that is aggressive in nature. Patients with GBM have a median lifespan of just 15 months when treated with the current standard of therapy, which includes surgical resection and concomitant chemo-radiotherapy. In recent years, nanotechnology has shown considerable promise in treating a variety of illnesses, and certain nanomaterials have been proven to pass the blood–brain barrier (BBB) and stay in glioblastoma tissues. Recent preclinical research suggests that the diagnosis and treatment of brain tumor is significantly explored through the intervention of nanomaterials that has showed enhanced effect. In order to elicit an antitumor response, it is necessary to retain the therapeutic candidates within glioblastoma tissues and this job is effectively carried out by nanocarrier particularly functionalized nanocarriers. In the arena of neoplastic diseases including GBM have achieved great attention in recent decades. Furthermore, interleukin-13 receptor α chain variant 2 (IL13Rα2) is a highly expressed and studied target in GBM that is lacked by the surrounding environment. The absence of IL13Rα2 in surrounding normal tissues has made it a suitable target in glioblastoma therapy. In this review article, we highlighted the role of IL13Rα2 as a potential target in GBM along with design and fabrication of efficient targeting strategies for IL13Rα2 through surface functionalized nanocarriers. The fabricated nano-conjugate system was investigated in A172 glioblastoma cell line. Results showed >80% destruction in glioma cells at a concentration of 6–600 ng/ml. The treated glioma cells were associated with high expression of IL13Rα2 levels (Rozhkova et al., Lemasson et al. used IL13Rα2 receptor targeting strategy during pre-clinical evaluation complexed with TiOIn vitro studies showed IC50 of 146 ng/ml for fabricated nanoconjugate system as compared to 349 ng/ml of drug NPs complex. Similarly, enhanced intracranial tumor accumulation of the paclitaxel loaded functionalized NPs was observed that concludes high efficiency and specificity for the glioma tumor cells (Wang et al., in vivo stability and low drug loading capacity are two associated problems with conventional NPs targeting glioblastoma. In this regard, Jiang et al. fabricated paclitaxel loaded self assembled NPs functionalized with Pep-1, glioma homing peptide for targeting glioblastoma through IL13α2R mediated endocytosis. Results showed ultrahigh drug loading capacity of 56.03% and through IL13α2R mediated endocytosis showed high cellular uptake in U87MG cells. The surface functionalized nanocarrier also showed enhanced tumor accumulation and as a whole showed significant antiglioblastoma efficacy (Jiang et al., in vitro and in vivo studies indicated higher cellular uptake and efficient tissue penetration for the fabricated surface functionalized nanocarrier system (Jiang et al., In the domain of targeted drug delivery system, surface functionalized nanocarriers have always shown significant efficacy. In this context, paclitaxel loaded PEGylated NPs were fabricated and functionalized with Pep-1. After evaluation in glioma cell line, the prepared nanoconjugated system showed increased cellular uptake as compared to drug–NPs complex. In vivo results in U87-bearing xenograft mice showed significant tumor volume reduction (Aronson et al., in vivo (Li et al., Surface modifications particularly through Pep-1 have shown promising results and thanks to its unique role of crossing the blood–brain barrier and blood–brain–tumor barrier. Cilengitide loaded Pep-1 functionalized liposome were designed and evaluated to improve its spatial distribution. The cellular uptake was enhanced to 89% from 47% after surface modification of liposome through peptide. In a nutshell, targeting IL13α2R receptor overexpressed in glioblastoma tumors various therapeutic strategies were proposed. It has been shown that IL13α2R targeting moieties were explored for antiglioblastoma effects including anti-IL13R antibodies and ligands due to their high affinity, low immunogenicity, and high biocompatibility. However, the use of functionalized nanocarriers has shown versatile outcomes in the arena of glioblastoma therapy. Such carriers provide specificity and selectivity for targeting IL13α2R receptors in glioblastoma along with efficient penetration into the tumor environment with high rate and speed. It is important to mention that precautionary and safety measure must be ensured in case of those nanocarriers functionalized with hazardous agents such as silica and titanium. Furthermore, targeting IL13Rα2 in glioblastoma using surface functionalized nanocarriers is not fully explored and needs extensive and in-depth investigation in the future.6.Immunotherapy and nanotherapy using surface functionalized nanocarriers were used recently in glioblastoma therapy to cope with certain hurdles in the way of therapeutic delivery particularly targeting IL13α2R receptors. Actually very limited data are available in this regard and to achieve efficient treatment profiles there is a need for in-depth research studies focusing safety profiles, toxicological profiles as well as clearance mechanisms for surface functionalized nanocarriers targeting IL13α2R receptors in glioblastoma in order to push these strategies toward future advancements. In addition, the fabrication of novel surface functionalized nanocarriers and further exploration of existing carriers will indeed create new opportunities in evaluation of tumor status at particular locations that will lead to the production of conceptualized personal medicines. On the other hand, it is to worth mention that as compared to limited conventional NPs clinical translation, no formulation with surface modified nanocarriers is yet reached to clinical translation side. Thus, clinical translation of functionalized nanocarriers based therapies targeting IL13α2R receptors in glioblastoma will deliberately top up the therapeutic cargoes for glioblastoma from bench top to the clinical arena.7.Glioblastoma multiforme is a lethal and aggressive brain tumor accompanied by low efficacy treatment standards. Surgery, radiation, chemotherapy, and concomitant radio-chemotherapy have been evaluated as treatment options for the treatment and management of glioblastoma. However, low efficacy of these treatment strategies has shown poor therapeutic outcome. Immunotherapy and nanotherapy have shown promising outputs in the treatment of glioblastoma providing long half-lives with sustained release effects to the therapeutic moieties at tumor side. Furthermore, the fabrication of surface functionalized nanocarriers has indeed provided certain unique features from nanotechnology platform including, low off target effects, increased retention time at tumor site, high specificity for the target and enhanced permeation to the glioblastoma tumors. IL13α2R receptors due to absence in the normal surrounding tissues and overexpression at the surface of glioblastoma tissue has made it the most potential target in the treatment of glioblastoma. In recent time, IL13α2R receptors are targeted through therapeutic moieties loaded surface functionalized nanocarriers that have shown a significant therapeutic effect showing it potential therapeutic target for GBM therapy. However, very less literature and studies are available in this regard that need further exploration for the sack of improvement in life quality of glioblastoma patients.


The stress system in the brain plays a pivotal role in keeping humans and animals from harmful stimuli. However, excessive stress will cause maladaptive changes to the stress system and lead to depression. Despite the high prevalence of depression, the treatment remains limited. PKMζ, an atypical PKC isoform, has been demonstrated to play a crucial role in maintaining long-term potentiation and memory. Recent evidence shows that PKMζ is also involved in stress response and depressive-like behavior. In particular, it was demonstrated that stress that resulted in depressive-like behavior could decrease the expression of PKMζ in the prefrontal cortex, which could be reversed by antidepressants. Importantly, modulation of PKMζ expression could regulate depressive-like behaviors and the actions of antidepressants. These data suggested that PKMζ could be a molecular target for developing novel antidepressants. Here, I review the advance on the role of PKMζ in mediating stress response and its involvement in the development of depression. Stress is a common life experience that we may come across almost daily. Humans and animals rely on the stress system in the brain to react and adapt to various stressful events and make responses. Appropriate responses to stress are essential for survival when facing life-threatening conditions . HoweverThe treatment strategy for depression includes pharmacological intervention, psychotherapy, and a combination of these two. Pharmacological intervention, such as selective serotonin reuptake inhibitors (SSRIs), is usually required for patients with moderate and severe symptoms . Generalde novo synthesis of PKMζ during LTP required many protein kinases, including phosphoinositide 3-kinase (PI3K), Ca2+/calmodulin-dependent protein kinase II (CaMKII), mitogen-activated protein kinase (MAPK), protein kinase A (PKA), mammalian target of rapamycin (mTOR), and preexisting PKMζ (in vitro (PKMζ is an isoform of the protein kinase C (PKC), which is an enzyme that has the ability to phosphorylate serine/threonine residues . There aing PKMζ . To detein vitro . Thus, tin vivo as well as abolished long-term memory in an active place avoidance task in rats  in mediating depressive-like behaviors . The stuThe causal role of PKMζ in the mPFC in depression has been implicated by studies using selective PKMζ inhibitory peptide ZIP and viruses that overexpress PKMζ or express dominant-negative mutant PKMζ . Intra-min vitro findings are consistent with our recent in vivo study, in which we showed that both fluoxetine and desipramine, a tricyclic antidepressant, reversed CUS-induced reduction in PKMζ expression in the mPFC. As mentioned before, antidepressants, including fluoxetine and desipramine, require several weeks of treatment to exert their antidepressant actions. Recent studies have indicated that the NMDA receptor antagonist ketamine has been shown to exert fast-acting and long-lasting antidepressant action. It has been demonstrated that ketamine could rescue chronic stress-induced molecular changes, morphological alterations of neurons, and microcircuit dysfunction in the prefrontal cortex (PFC)  . IntriguGenerally, anxiety is characterized by a persistent feeling of apprehension or dread, a specific reaction to stress. A great variety of behavioral models has been developed to mimic anxiety disorders . It is nConsistent with the role of PKMζ in mediating stress-induced anxiety-like behaviors, PKMζ has been demonstrated to regulate the basal level of anxiety. Genetically modified mice that lack both PKCζ and PKMζ showed reduced anxiety behavior . In contde novo synthesized PKMζ is then converted into a conformation with constitutive activity after phosphorylation by phosphoinositide-dependent protein kinase 1 (PDK1); (3) the constitutively activated PKMζ increases N-ethylmaleimide-sensitive factor (NSF)/the glutamate receptor 2 (GluR2)-dependent trafficking of AMPAR and maintains the AMPAR expression at postsynaptic sites to potentiate synaptic transmission.Evidence has illustrated the molecular mechanism underlying the role in maintaining LTP . In hipp2+ permeability and function of AMPAR , a prolyl isomerase, which has the capacity for suppressing the translation of PKMζ from mRNA . This seof AMPAR . It is oks GluR2 . As descng AMPAR . A hypotng AMPAR ; howeverRegulation of GluR2 trafficking through the interaction between PKMζ and NSF/GluR2 might also be the mechanism underlying the role of PKMζ in the PFC in depression. . These sAs described above, most work that supports the fundamental role of PKMζ in maintaining LTP and related behaviors used ZIP as a selective inhibitor of PKMζ. However, other studies have suggested that ZIP might not be an appropriate inhibitor of PKMζ.Some evidence shows that ZIP may not be able to inhibit PKMζ. In cultured 293T cells expressing PKMζ, ZIP could not reverse PKMζ overexpression-induced increase in the phosphorylation of multiple PKC substrates. In COS-7 cells co-transfected with CKAR and PKM-RFP, ZIP did not affect the baseline normalized FRET ratio. Furthermore, ZIP did not affect MAPK2 activity in brain slices transfected with PKMζ. The authors then concluded that ZIP could not inhibit PKMζ . Howevervia a pseudosubstrate-like mechanism, suggesting ZIP might exert its effects through the displacement of PKCa from targeted sites (Other studies suggested that ZIP was not selective on PKMζ. ZIP at a concentration (10 μM) could inhibit the activity of both PKCa and PKMζ . ZIP alsed sites . In a reed sites . It is oed sites . In a phed sites .2+ activity after application of ZIP and scr-ZIP in cultured hippocampal cells (in vivo (Evidence also suggested that the effects of ZIP could be attributed to ZIP-induced cellular toxicity. One study showed that both ZIP and scr-ZIP dose-dependently caused rapid cell death of cultured hippocampal neurons . These eal cells . The facal cells . In cont(in vivo . LeBlanc(in vivo .Given these critical concerns on ZIP, i.e., the ineffectiveness in some conditions, non-specificity, and neurotoxicity, it should be cautious when interpreting the results used ZIP. In particular, ZIP should not be taken as a specific inhibitor of PKMζ. Other approaches rather than ZIP should be employed to determine the causal role of PKMζ in regulating brain functions and related behaviors. These approaches may include virus-mediated downregulation or expression of PKMζ in particular brain regions or subtype of cells. For example, previous studies have used viruses to overexpress PKMζ or the negative-dominant mutant PKMζ that could competitively inhibit PKMζ activity in particular brain regions could modulate animal behaviors .Depression is a brain disorder characterized by persistently depressed mood and loss of interest. Patients usually need to take antidepressants to benefit from the treatment continually. Furthermore, some patients may stop benefiting from particular antidepressants after long-term treatment . At leasSince PKMζ has been long taken as a memory molecule, it is of great curiosity to examine whether PKMζ could be a link between depression and memory problems. Patients with depression usually suffer short-term memory loss and are at risk of long-term memory loss . As PKMζFurthermore, depression is a complicated disease that involves many brain regions . As mentSince PKMζ in the PFC was negatively associated with depression symptoms, it could be predicted that pharmacological or behavioral approaches that could elevate PKMζ expression in the mPFC might lead to stress resilience and protect subjects from experiencing detrimental consequences of stress, which thus prevents the development of stress-induced depression. Recent evidence shows that PKMζ is involved in stress response and depressive-like behaviors. PKMζ in the PFC could be a common molecule that mediates the actions of slow-acting and fast-acting antidepressants. However, the role of PKMζ in mediating stress response and depression remains largely unknown, which needs further investigation. Addressing this issue will determine whether PKMζ could be a therapeutic target for developing novel antidepressants.The author confirms being the sole contributor of this work and has approved it for publication.The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.


Epidural electrical stimulation (EES) of the spinal cord has been FDA approved and used therapeutically for decades. However, there is still not a clear understanding of the local neural substrates and consequently the mechanism of action responsible for the therapeutic effects.Epidural spinal recordings (ESR) are collected from the electrodes placed in the epidural space. ESR contains multi-modality signal components such as the evoked neural response (due to tonic or BurstDR™ waveforms), evoked muscle response, stimulation artifact, and cardiac response. The tonic stimulation evoked compound action potential (ECAP) is one of the components in ESR and has been proposed recently to measure the accumulative local potentials from large populations of neuronal fibers during EES.Here, we first review and investigate the referencing strategies, as they apply to ECAP component in ESR in the domestic swine animal model. We then examine how ECAP component can be used to sense lead migration, an adverse outcome following lead placement that can reduce therapeutic efficacy. Lastly, we show and isolate concurrent activation of local back and leg muscles during EES, demonstrating that the ESR obtained from the recording contacts contain both ECAP and EMG components.These findings may further guide the implementation of recording and reference contacts in an implantable EES system and provide preliminary evidence for the utility of ECAP component in ESR to detect lead migration. We expect these results to facilitate future development of EES methodology and implementation of use of different components in ESR to improve EES therapy.The online version contains supplementary material available at 10.1186/s42234-023-00106-5. Epidural electrical stimulation (EES) the most common type of spinal cord stimulation (SCS) has been used for several decades to manage chronic pain  understanding the fundamentals of electrophysiology recordings, particularly referencing strategy, to ESR during EES; 2) investigating changes in ECAP component morphology during shifts of the stimulation and recording leads to explore lead migration detection as an application of ECAP component in ESR; 3) investigating the mechanism of activation of local back muscles during stimulation and the detection of EMG component in ESR by the implanted leads. In all cases, we use controls, including recordings made in the animal after euthanasia , to differentiate bona-fide ECAP components from stimulation artifact and ringing induced by filtering of stimulation artifact . We used 10 domestic white swine males (6) and females (4) aged 8-12 weeks and weighing 27-46 Kg were used for this study. Animals were kept in separate cages in a controlled environment (constant temperature at 21 °C and humidity at 45%) on a 12-hour light/dark cycle with ad libitum access to water and were fed once daily. We used a swine animal model in this study because previous studies on the effect of EES in swine have demonstrated similar result to those found in the human sensorimotor system, suggesting that the swine model is a relevant translational model to humans  from selected muscles during EES. The surgical approach has been described in detail previously  was used in Python 3.7 for the offline handling and analysis of electrophysiology data. For the analysis of the impact of referencing method on stimulation artifact and ECAP component amplitude, stimulation artifact magnitude was quantified as the peak-to-peak signal of the averaged recording (median of 150-300 traces). ECAP component amplitude was quantified as the peak-to-peak signal of the averaged ESR trace between 2.1 ms and 5 ms, which is the duration immediately following the stimulation artifact while encompassing the entire ECAP signal. Note that recording setup starts recording ~ 1.3 ms before stimulation is delivered. For the analysis of referencing method on stimulation artifact and ECAP component amplitude, stimulation artifact and ECAP component amplitude for LTR reference was normalized to 1 for each subject to account for subject-to-subject variability and enable cohort-based analysis. Shapiro-Wilk’s test was used to test the samples from n = 5 subjects for normality to satisfy the assumption of the subsequently used one sample or paired t-test (two-tailed α = 0.05).The pyeCAP package  test was used to test for changes in ECAP latency and amplitude from different electrodes.This study was not pre-registered and so all findings should be considered exploratory and not confirmatory.Figure n = 5 subjects) and REF9 (0.998 ± 0.051 SE) had higher stimulation artifact magnitudes (P < 0.001 for DIFF compared to LTR and REF9)  and with REF9 (1.029 ± 0.051 SE) compared to the DIFF referenced recordings (0.737 ± 0.069 SE) (P < 0.005 for DIFF compared to LTR)  was compared with local tissue reference (LTR) and reference on contact 9 (REF9), which is the recording contact furthest from the stimulation contacts. Figure F9) Fig. A and C. The ESR trace recorded using REF9 has an additional inflection in its morphology due to the ‘subtraction’ of the same ECAP component recorded concurrently on the reference and the recording electrode (Ch1) Fig. B.These data suggests that LTR recordings provide the clearest representation of the neural activity (no ECAP subtraction effects). However, is prone to common mode artifact contamination  and requires an additional electrode in non-neural tissue. LTR could be implemented clinically with reference to the metal external of the implantable electronics. DIFF reference was most robust to common mode artifact but also resulted in diminished neural signal magnitude. REF9 provided a middle ground with ease to implement and a clear representation of the neural activity with minimal ECAP component subtraction effects from the reference electrode. For the rest of this study, LTR was used as it provided the best representation of underlying neural activity and could be virtually re-referenced to both REF9 and DIFF.Figure β-fiber and A α-fiber conduction velocity ranges. Figure Quantifying the conduction velocity of the ECAP component is useful to determine the underlying fiber types recruited. The Aβ-fiber type is known to have a conduction velocity in the range of 35-80 m/s   was 0.462 ± 0.117 ms, 0.598 ± 0.171 ms, 0.890 ± 0.136 ms, and 1.145 ± 0.155 ms, respectively . ECAP component strength, as measured by AUC, were normalized to respective stimulation amplitudes. For each rostral shift, ECAP strength was measured as percent change from the baseline position , − 67.7 ± 5.6% (from position I to III), and − 85.6 ± 11.0% (from position I to IV). As the distance between the stimulation and recording contacts increased, there was a larger reduction in ECAP strength, and the change was significant across all groups (p < 0.001). These data show significant changes in ECAP latency and strength with lead migration, suggesting that the migration of one lead relative to the second implanted lead could be detected by changes in ECAP morphology.Lead migration is a common complication that leads to reduced long-term efficacy of EES  Fig. A. The foI’) Fig.  while thI’) Fig. . Stimulap < 0.001)   , paravertebral muscle’s rostral part (PVR), paravertebral muscle’s caudal part (PVC), gluteus (G), quadriceps (Q), bicep femoris (BF). Additional recording with needle electrodes inserted in the intercostal muscles across the skin without dissection (IMS) were also collected. Results shown in Fig. β fibers in dorsal column) and consequently appears at a delay of ~ 0.1 ms between adjacent contacts, while an EMG signal appears simultaneously on adjacent recording contacts  when compared to the DIFF-V referenced recordings (0.278 ± 0.123 SE) (P < 0.005 for DIFF compared to LTR)  when compared to REF9-V referenced recordings (.965 ± 0.287). The variability in REF9-V could be a result of variation in LTR reference electrode placement across subjects.Figure The ESR collected from the implanted leads in the epidural space captures the stimulation evoked neural and myogenic response of tissue around the recording electrode during EES. Existing work has shown the utility of the ECAP component in continuously adjusting stimulation amplitude to prevent overstimulation and an excessive sense of paresthesia to the patient , differential reference of two neighboring channels (DIFF), and reference to one of the contacts on the lead. The results showed that LTR provided the best recordings of ESR, with consistent ECAP component latency between contacts, consistent morphology, and large signal amplitude compared to other referencing methods Figs.  and 3. UDaily activities of patients include walking, sitting, standing, twisting, and bending over. These actions can all lead to small temporary movement of the leads in the epidural space resulting in suboptimal stimulation. In addition, these movements can cause a permanent lead migration, leading to loss of efficacy in EES therapy . The results on the activation of evoked EMG signals on both the EES leads and needle electrodes inserted directly in muscles provide preliminary insights on addressing target engagement during EES for optimal neural substrate activation. Future studies should investigate and isolate the different neural substrates activated during EES. In addition, advanced evoked response signal processing algorithms should be explored to carefully distinguish the components of stimulation artifact, evoked EMG responses, and ECAP components present in the ESR to make stimulation evoked responses a reliable objective measurement for EES based therapies.Additional file 1: Supplementary Fig. 1. Lead movement for animal subject S3 shown in Fig. Supplementary Fig. 2. X-Ray images of location used for stimulation.


This expectation is based on small-scale experiments and model simulations based on such observations. However, this combined effect has never been confirmed through actual observations at the nationwide or regional scale. We present the first evidence that warming and drought in the world’s leading wheat-producing countries offset the benefits of increasing [CO2] to wheat yield in the last six decades. Using country-level wheat yield census observations, [CO2] records, and gridded climate data in a statistical model based on a well-established methodology, we show that a [CO2] rise of ~ 98 μmol mol−1 increased the yield by 7% in the area of the top-twelve wheat-producing countries, while warming of 1.2 °C and water depletion of ~ 29 mm m−2 reduced the wheat grain yield by ~ 3% and ~ 1%, respectively, in the last six decades (1961–2019). Our statistical model corroborated the beneficial effect of [CO2] but contrasted the expected increase of grain yield under drought. Moreover, the increase in [CO2] barely offsets the adverse impacts of warming and drought in countries like Germany and France, with a net yield loss of 3.1% and no gain, respectively, at the end of the sampling period relative to the 1961–1965 baseline. In China and the wheat-growing areas of the former Soviet Union—two of the three largest wheat-producing regions—yields were ~ 5.5% less than expected from current [CO2] levels. Our results suggest shifting our efforts towards more experimental studies set in currently warm and dry areas and combining these with statistical and numerical modeling to improve our understanding of future impacts of a warmer and drier world with higher [CO2].Future atmospheric carbon-dioxide concentration ([CO Continuous elevation in [CO2] level and more frequent and intense heatwaves and droughts, already observed in many agricultural areas2, are expected to have a tremendous impact on crops, with significant implications for global food security4.The atmospheric concentration of carbon dioxide  or free-air carbon dioxide enrichment (FACE) experiments11. The primary conclusion from almost all such studies is that C3 crops (such as wheat) increase their yield under elevated [CO2]15. The increase in yield is mostly via enhanced net carbon assimilation rate (A)16, decreased stomatal conductivity18, and reduced transpiration19, which improves crop water productivity, defined as the ratio of crop yield to its water use20. Thus, under elevated CO2 C3 crops such as wheat are expected to increase their relative yield even higher under drought21, though this does not necessarily mean absolute yield gain. Moreover, an increase in yield under different water regimes may affect growth processes such as grain protein content differently22.While the effects of warming and drought on wheat (and other crops) have been documented at various scales, the interactive effect of [CO2] on soil water saving and yield under dry conditions23, current models use the aforementioned mechanisms to simulate crop response to future [CO2] and climate scenarios on the regional and global-scale27. After years of simulating crop response to warming and drought without considering the effect of [CO2], modelers have been recently called to include such an effect claiming that “uncertainties in the effects of elevated [CO2] on crops have narrowed”28. However, a few FACE sites have studied the benefits of elevated [CO2] under warming and drought, and the effects have yet to be validated on a larger scale.Though some have challenged this beneficial effect of [CO2] on wheat yield. Leveraging six decades of recorded atmospheric [CO2] data and census observations of country-level yields, we provide estimates of yield variation due to temperature, water deficit, rainfall distribution, and [CO2], showing that the beneficial effect of [CO2] on wheat yield diminishes under increased water deficit conditions, with major losses during the last six decades occurring mainly in leading wheat-producing countries.Here, we analyze nationwide census wheat yield data obtained from the world’s largest wheat-producing countries from 1961 to 2019 to assess the individual and combined effects of climate and  of −1, from 315.9 μmol mol−1 in 1961 to 413.4 μmol mol−1 in 2019  in the twelve countries during the last six decades , maximum (Tmax), and mean (Tmean) temperatures, as well as seasonal water deficit (PET-P), and rainfall distribution on wheat yield. Climate variables were obtained from the TerraClimate data set32, while monthly records of [CO2] from the Mauna Loa station were used to model the effects of CO2 , and (4) the interaction between [CO2] and climate variables (T + W + C + interactions).Table Tmean had a consistently significant effect on yield , with increases in Tmean during the growing season leading to reduced wheat yields (negative effect) in all four models. This negative effect weakened  when the water deficit variable was included in the model (T + W) but strengthened again  when [CO2] was further incorporated (T + W + C and T + W + C + interactions models). The negative effect of water deficit suggests a reduction in annual yield when the evaporation demand is greater than precipitation because of reduced rainfall or increased evaporative demand. Rainfall distribution is an important variable in predicting wheat yields33. In our models, rainfall distribution had a negative effect on yield , indicating that rainfall distribution might be an important predictor of yield in some but not all places.Among the temperature measures, only 2] had the most substantial effect on yield, with a net beneficial effect in both T + W + C and T + W + C + interaction models. This effect was two and four orders of magnitude higher than T and W, respectively , consistent with previous experimental studies34. Interestingly, the water deficit 2] interaction was positive suggesting that a rise in [CO2] increases the negative effect of water deficit on yield, contrary to prior studies35.Among all variables, atmospheric  interaction (p > 0.1) when India was excluded from the analysis  and no gain  in yield, respectively, at the end of the sampling period relative to the 1961–1965 baseline. These two countries experienced the worst temperature rise and intense drought conditions in their wheat-growing areas at the end of the 2010s  in both regions, and a water deficit of 21.5 mm decade–1 (p < 0.05) in China and 6.1 mm decade–1 (p < 0.1) in RUK , an area that corresponds to over 78% of the global wheat harvested area, during the last six decades. Both warming and drought-induced water deficits were significant in this area, negatively affecting yields. Climatic changes triggered large year-to-year and spatial variability in yield, with up to 45% of the variation occurring in highly productive countries such as the United States, Canada, the United Kingdom, Turkey, Australia, and Argentina7. A temperature increase of 1 °C was associated with a decline in wheat yield between 4.1% and 6.4% by three independent methods8. Our results based on census data are more conservative, showing a yield  reduction of 37. Morever, including the warm year of 1961 in the baseline might have resulted in a slight underestimation of the temperature effect in our analysis. Our analysis also shows that the mean temperature is the only temperature measure affecting yield. In contrast, temperature extremes  had no significant effect on the yield , which might result in an overestimation of yield under future climate scenarios according to our analysis. Models that include [CO2] effects rely on equations derived from experimental observations showing average reductions in stomatal conductance of 18 and evapotranspiration of 2] levels of + 100 μmol mol−1 to + 150 μmol mol−113. These reductions suggest that water-use efficiency will improve under a future increase in [CO2]20 increasing the drought tolerance of C3 crops, like wheat. Though CO2 has been shown to offset the negative effect of heat stress34, our results indicate that the interaction might be more complex under extreme drought conditions than previously suggested.Most of the studies that analyze changes in regional wheat yield due to climate variations use process-based crop models–1 showed that exposure to elevated [CO2] of + 150 μmol mol−1 did not affect yield and photosynthetic rate of wheat in almost all sites (with the only exception of the USA site)41. In general, the lack of a CO2 effect on yield was explained by an unchanged assimilation rate, concluding that the effect of CO2 on yield is highly dependent on local environmental conditions , acclimation capacity, and cultivar. An eight-year FACE experiment in a dry environment showed significant variation in soybean (C3 crop) yield under elevated [CO2]. These variations were attributed to the amount of water in the soil available to the crop throughout the growth period23. In contrast to previous expectations21, it was found that high [CO2] did not necessarily conserve water in the soil via decreased stomatal conductance but may have even caused losses in some years, with water losses leading to lower yields. Surprisingly, the effect of [CO2] on soil water was not correlated with its effect on midday stomatal conductance . A greater canopy temperature due to reduced cooling via lower transpiration and a greater leaf area index  were both suggested to cause the unexpectedly greater water losses observed in drought years. These negative water and energy balances offset the beneficial effect of [CO2] on stomatal conductance, leading to net losses in soil water content and, consequently, grain yield.A recent study involving five FACE facilities in Germany, Italy, China, Australia, and the USA under relatively dry conditions with total rainfall during the growing season ranging between 141 and 347 mm year2] under climate scenarios. In fact, FACE experiments conducted in different locations may not be comparable due to differences in soil and climate conditions and because of a different response of the cultivars, usually bred under different climates. Since FACE experiments are expensive and thus rarely performed, results from the few FACE facilities are usually extrapolated to unrepresented areas. However, extrapolating FACE results to currently dry and warm regions like Africa and the Middle East, for example, might be a challenge in the absence of prior FACE experiments in such regions. The inclusion of FACE as well as other long-term [CO2] enrichment experiments in these regions that are already experiencing severe warming and drought  may enhance our understanding of crop response to elevated [CO2] in cold and humid areas susceptible to future drier and warmer conditions and potential shift towards dryland-controlled mechanisms42. Studying the response of different lines bred under warm and dry conditions is also recommended to analyze crop breeding adaptation to altered environmental and climate conditions43.These results, as well as those from our study, suggest that conclusions from previous FACE experiments should be carefully re-examined in light of local growing conditions and cultivars used in the experiments. Variations in the results of FACE experiments conducted at different locations pose a great challenge to the study of crop response mechanisms to elevated [CO2] impacts on crops. Comparing these results with model simulations or long-term fixed experiments data could deepen our understanding of the underlying mechanisms of crop response to climate and future elevated [CO2] at the regional and global scales. Moreover, six decades of census observation data may be leveraged to examine simulation model performance under actual [CO2] rise of almost 100 μmol mol−1. The combination of statistical analysis, like the one presented here, and simulation modeling or long-term fixed experiments data could also shed light on the various roles of agrotechnology, local environment, and cultivar in affecting wheat production, with important implications for climate change adaptation efforts. To notice is that our model currently assumes a linear rise of [CO2] and would require an adjustment to a non-linear increase in [CO2] to predict wheat response under future emission scenarios.An obvious next step should be the use of biophysical simulation models to compare their attribution to the present statistical analysis. We expect this call to precipitate such participation and analysis from various groups worldwide dealing with the study of climate and [CO2] is non-linear, the beneficial effect of [CO2] on photosynthesis reaches a steady state around −144. These are the levels expected by 21001. It is likely that [CO2] will no longer cushion the impact of warming and drought by the end of this century. An atmosphere with a doubled concentration of CO2 will no longer increase photosynthesis while corresponding warming between 1.0 and 3.7 °C, accompanied by more frequent and intense droughts, will likely have a detrimental effect on global food security. Further, a substantial body of work suggests that a CO2-rich atmosphere decreases food quality by reducing protein and mineral contents45, with alarming consequences for human nutrition. Establishing a commonly-shared protocol for FACE-like experiments and expanding FACE studies to warmer and drier areas such as Africa and the Middle East is essential to increase our understanding of the impact of climatic and environmental conditions on crop yield and quality for appropriate adaptation and mitigation strategies.Finally, since the response of C3 plants to  data collected from the Mauna Loa station since 1958 were downloaded from NOAA Global Monitoring Laboratory website (https://gml.noaa.gov/ccgg/trends/data.html) and averaged over the duration of the country-specific growing season period. Growing seasons are determined according to the reported sowing, maturity, and harvest dates of wheat in each country or country-specific region   using only temperature variables (T), (2) temperature and water-related  variables (T + W), (3) including [CO2] (T + W + C), and (4) the interaction between [CO2] and climate variables (T + W + C + interactions). The complete log-linear regression model is as follows:i,t and [CO2]i,t denote wheat seed yield (in tons ha–1) and mean seasonal [CO2] (in μmol mol−1) in location (country) i and year t. Transformation to log yields and log [CO2] results in normally distributed values and highly proportionate to the effects of climate variables and [CO2] on yield  calculated as the balance between evaporative demand (PET) and water supply as rainfall (P)—in location i and year t, respectively.We used a well-established methodology to predict the logarithm of wheat seed yield based on climatic and environmental factors using a multivariate log-linear regression Ci), as well as country-specific trends . Accounting for these controls is necessary to isolate potential influences of exogenous changes in the climate variables on wheat yields. For i,t, we used a quadratic time trend in yields for each specific country30.Based on previous statistical studies of changes in yield due to climate, we included country-specific time-invariant controls  2] to changes in yield over time. We do so by calculating the percent change between predicted yields from our main regression model and predicted yields from a counterfactual scenario using the years 1961–1965 as the baseline. Though the year 1961 was exceptionally warm in some countries  holding temperature variables , and (3) water deficit (PET-P) at the 1961–1965 average level, and (4) maintaining all climate variables (temperature and water deficit) as well as [CO2] at the 1961–1965 average level, to measure the individual and overall impacts of climate and [CO2] on the yield of each major wheat producer. We added the countrywide percent changes to determine the total impact of climate and [CO2] on yields in the shared cropped area of the top 12 global wheat-producing countries.We used the estimates derived from the T + W + C statistical model to assess the contribution of climate variables (temperature and water deficit) and [CO2] on yield via its effect on temperature and water deficit. Also, our model assumes linear relationships, while some of the interactions might be non-linear in nature. Our models include country-specific effects and country-quadrate trends to predict yields under the counterfactual scenarios. We controlled for such effects assuming that they were independent of climate and [CO2] trends specifically, and were mostly related to agrotechnological advances, changes in country-specific policies, and other local-changing factors such as economic and population growth30. While this is likely to be true for most cases, minor effects of climate and [CO2] might have been eliminated thereby resulting in dependence on model specifications. Also, significant yield losses may be caused by weather extremes at short periods of days and even hours when the wheat reaches a crucial developmental stage while our analysis is confined to average seasonal conditions. Warming is expected to shorten the growth season (rapid phenology)46 and decrease the yield production potential as crops absorb less radiation. However, it can be expected that breeders can overcome this through late phenology breeding. [CO2] is uniformly distributed across the globe, and thus we used a single-point measurement to represent [CO2] levels in the different wheat-producing countries. Despite seasonal variations in [CO2] among the countries because of differences in the growing season periods, such variations are relatively small and likely underestimate the real effect of [CO2] on yield in some places.There are various caveats associated with our analysis. Since we used a multivariant regression model, we were unable to determine the indirect effect of [COSupplementary Information.