Breakup volcanism along rifted passive margins is highly variable in time and space. The factors controlling magmatic activity during continental rifting and breakup are not resolved and controversial. Here we use numerical models to investigate melt generation at rifted margins with contrasting rifting styles corresponding to those observed in natural systems. Our results demonstrate a surprising correlation of enhanced magmatism with margin width. This relationship is explained by depth-dependent extension, during which the lithospheric mantle ruptures earlier than the crust, and is confirmed by a semi-analytical prediction of melt volume over margin width. The results presented here show that the effect of increased mantle temperature at wide volcanic margins is likely over-estimated, and demonstrate that the large volumes of magmatism at volcanic rifted margin can be explained by depth- dependent extension and very moderate excess mantle potential temperature in the order of 50–80 °C, significantly smaller than previously suggested. Magmatic productivity at passive margins is controlled by mantle temperature and rifting style. The authors reveal that melt volume at rifted margins is linearly correlated with margin width and that volcanic margins may result from depth dependent extension without high temperature mantle plumes. Decompression melting at standard mantle potential temperature and full spreading rates larger than 1.5 cm/year leads to accretion of 4–8 km of magmatic crust, consistent with uniform global oceanic crustal thickness away from hotspots4. However, the processes controlling the variation of magmatism at rifted margins are not well understood and a source of controversy10. Rifted margins in terms of the thickness of early oceanic crust can to first order be characterised with three magmatic modes . (2) Margins where magmatic productivity exceeds that expected from decompression melting at normal mantle temperature, expressed in high volumes of extruded volcanics deposited as seaward-dipping sequences (SDRs), over-thickened intruded continental and oceanic crust and regions of magmatic underplating11 can be considered excess-magmatic margins (Mode 2). (3) Magma-poor (a-magmatic) margins (Mode 3) have little syn-rift magmatism, in some cases exhibiting a broad zone of exhumed mantle with little to no magmatism at the sea floor preceding formation of mature oceanic crust12. While a variety of mechanisms, including low mantle potential temperature13, low spreading rate3 and counterflow of depleted lithospheric mantle15, have been suggested as an explanation for the absence of magmatism on magma-poor margins, what controls the volume, distribution and timing of magmatism at normal- to excess-magmatic margins is incompletely understood. The voluminous magmatism at volcanic margins has commonly been explained with mantle plumes, typically with a plume head diameter in the order of 2000 km and excess temperatures ranging 100–200 °C above normal18. However, this interpretation has been challenged by the inferred lack of associated mantle plumes at some volcanic margins such as the US East Coast and NW Australian volcanic margins19. Moreover, the excess temperature required to produce ultra-thick igneous crust is often in conflict with inferences from geophysical and geochemical analysis22. Alternative models for voluminous magmatism at volcanic margins include the effects of active upwelling23, rift history10, small-scale convection25 or variation in mantle composition27.Mantle melting during the formation of mid oceanic ridges is relatively well understood and thought to be mostly a function of mantle potential temperature and spreading rate30. Narrow margins with coupled deformation in the lithosphere are expected to exhibit early and sharp rupture of both the crust and the mantle lithosphere15. In contrast at some wide margins, the stretching factor of the crust is significantly smaller than the whole lithosphere29, implying preferential removal of most of the mantle lithosphere. Similar removal of mantle lithosphere is also observed in the Basin and Range wide rift system, where syn-extensional magmatism over a wide range has been identified31. These contrasting styles of rifting are to first order controlled by crustal rheology33.Previous models of melt generation have mostly focused on seeking heterogeneities in temperature or composition of the sub-lithospheric mantle, implicitly assuming simple, uniform lithospheric extension where the crust and mantle lithosphere rupture simultaneously. However, observations have shown that rifted margins rarely experience uniform extension; rather, many margins exhibit complex tectonic styles with depth-dependent extensionHere we show that these tectonic rifting styles lead to highly contrasting magmatic outputs during passive margin formation. While narrow rifts are expected to produce mature mid-ocean ridge spreading following early crust and mantle lithosphere rupture, resulting in standard oceanic crust thickness at the COB, wide rifts are expected to lead to significant melt production beneath moderately extended crust before lithospheric rupture. By combining forward models and published observations, we provide a new conceptual and quantitative framework explaining the volume of decompression melting accreted to rifted passive margins as a function of margin width and mantle potential temperature.Tp). We explore models with varying crustal strength to investigate the role of contrasting styles of rifted margin formation on magmatism. A Wet Quartz flow law is used for the crust34, which is scaled by a viscosity-scaling factor, fc, to produce stronger or weaker crust. The melt parameterization model follows ref. 24 (see “Methods” for details). Melt parameters are calibrated by comparing predicted igneous crustal thickness with global oceanic crustal thickness3, with a mantle potential temperature of 1300 °C resulting in on average 6-km thick oceanic crust  and normal mantle potential temperature, Tp = 1300 °C, leads to narrow lithospheric breakup. The strong coupling between frictional-plastic upper crust and upper mantle lithosphere promotes narrow rupture of the whole lithosphere. The transition from the COB to normal oceanic crust is within a distance of <30 km, with predicted melt thickness  gradually increasing from 0 to ~5.5 km, in the range of normal global oceanic crust thicknesses4. Model II shows highly contrasting behaviour, with very weak crust (fc = 0.02) allowing for decoupling of upper crust and mantle lithosphere leading to highly depth-dependent extension, leaving the extended crust in contact with upwelling sub-lithospheric mantle  confirm progressive enhancement of magmatic accretion to the distal margin with increasing margin width  and margin width (W) can be parameterised to first order by V* = heffW + V0, where V0 is the intercept on the volume axis and heff is the slope of the linear curve. As we include melt volume over an initial spreading section of 50 km on each side . heff represents the average igneous crustal thickness produced during wide rifting. In our models, heff can be derived semi-analytically based on the characteristics of depth-dependent wide rifting . We limit our analyses to sections where both conjugate margins are available in order to account for possible asymmetric distribution of magmatic volumes39 and prioritize conjugate margin sections where both refraction and reflection seismic data are available  with P-wave velocities increasing from ~4.0 to ~6 km/s, (2) high-velocity (>7.2 km/s) lower crustal bodies (VLCB) interpreted as magmatic underplates at the base of the crust and (3) transitional partially intruded crust (Vintrude) between SDR and LCB. Following ref. 42, the content of igneous material in each contribution is assumed to be 50 ± 50% for SDR, 10 ± 10% for transitional crust and 100% for LCB. Total melt volume V* per unit margin length along strike is calculated by summing all contributions from both conjugate margins, together with the additional contribution over the first 50-km oceanic spreading section on each side, V* = VLCB + 0.5VSDR + 0.1Vintrude + Vspread. Errors in melt volume come principally from uncertainty of portions of igneous material in SDR and transitional intruded crustal volumes, and are calculated as Verr = 0.5VSDR + 0.1Vintrude. Estimated total melt volumes are listed in Table Volume of magmatic addition is estimated from three contributions41 Fig. : (1) ext~6 km/s,  high-vel44 suggest that the COB can be defined as either the first identified oceanic crust (COBF) or the ocean ward limit of continental crust (COBL). COBF and COBL coincide at volcanic margins, whereas they differ at a-magmatic margins with exhumed mantle. We use therefore the most distal location of continent crust (COBL) as it better captures the degree of crustal stretching of passive margins. Several proxies have been used to define the landward limit of a margin, including the location where the crust reaches a thickness of 25 km (ref. 9), the location of the onshore topographic maximum43 and the location of the innermost normal fault45. Here we use the termination of un-thinned continental crust as the landward limit of the margin, defined as the mid point of the crustal taper bounded by the location of the first crustal thinning , we may divide the melt volume–margin width space into three temperature regimes: (1) a normal-temperature regime (1280–1330 °C) with hoc in the range of 4–8 km, (2) a high-temperature regime (>1330 °C) with hoc > 8 km and (3) a low-temperature regime (<1280 °C) with hoc < 4 km  and base lithosphere (zl). The sub-lithospheric mantle follows an adiabatic geothermal gradient, 0.4 °C/km, with given potential temperature, Tp = 1300 °C, this leads to base lithosphere temperature of Tl = 1350 °C at depth 125 km. The initial geotherm in the mantle lithosphere is linear between Moho temperature, Tm = 550 °C, which is configured to be the same for all models, and base lithosphere temperature Tl. The initial temperature in the crust increases with depth from the surface, T0 = 0 °C, to the base of the crust (Tm = 550 °C), and follows a stable continental geotherm, Ar = 0.88 μW/m3, which results in a basal heat flux, qm = 20 mW/m2 that matches the heat flux in the mantle lithosphere (i.e. steady state in the lithosphere). For models with a higher or lower potential temperature, and therefore different base lithosphere temperature Tl, heat production in the crust is adjusted to match the heat flux in the mantle lithosphere. Thermal boundary conditions are specified surface temperature for the top (0 °C) and bottom (1540 °C for the reference model) boundaries, and insulated side boundaries. The value of the bottom boundary temperature is adjusted according to potential temperature. Latent heat of melting and adiabatic heating/cooling is taken into account. Thermal diffusivity, κ = k/ρcp = 10−6 m2/s.The initial temperature field, which is configured analytically, is laterally uniform, and consists of three segments delimited at Moho  and compositional depletion (X) (ref. 64)We use a parameterized melt prediction modelmentclass2pt{minim24 to be 0 on the wet solidus  and a viscosity change owing to dehydration during damp melting  describes the quantity of melt produced per unit distance of spreading. In the case of wide rifting, before final breakup, we can define the effective melt thickness, heff, as the quantity of melt produced per unit distance of extension. heff is smaller than hoc because upwelled mantle experiences lower degree of melting during continental rifting than during mid oceanic ridge spreading. The degree of melting is controlled by the height of upwelling mantle at temperatures above solidus2  with its base at a depth of ~60 km for normal mantle potential temperature  than during spreading (ds) (Supplementary Fig. heff can not be directly constrained, the ratio between Tp = 1300 °C (Supplementary Fig. Analysing the underlying physics of depth-dependent wide rifting allows us to establish the linear correlation. If all the melt generated in the melting regime forms oceanic crust immediately, then the total melt produced during each increment of spreading equals the thickness of oceanic crustAssuming constant melt productivity during rifting and spreading, respectively, Supplementary Fig. Supplementary InformationPeer Review File


We show via time resolved spectroscopic measurements how the π-bridge connections in A–π–D–π–A–π–D–π–A multichromophoric PDI systems strongly affect the triplet yield and triplet formation rate. In the planar compound, with stronger intramolecular charge transfer (ICT) character, triplet formation occurs via conventional intersystem crossing. However, clear evidence of efficient and fast intramolecular singlet exciton fission (iSEF) is observed in the twisted trimer compound with weaker ICT character. Multiexciton triplet generation and separation occur in the twisted (flexible-bridged) PDI trimer, where weak coupling among the units is observed as a result of the degenerate double triplet and quintet states, obtained by quantum chemical calculations. The high triplet yield and fast iSEF observed in the twisted compound are due not only to enthalpic viability but also to the significant entropic gain allowed by its trimeric structure. Our results represent a significant step forward in structure–property understanding, and may direct the design of new efficient iSEF materials.In this study, two analogous perylene diimide (PDI) trimers, whose structures show rotatable single bond π-bridge connection (twisted)  via time resolved spectroscopy that triplet formation proceeds via intersystem crossing in a rigid-bridged perylene diimide trimer and via efficient and fast intramolecular singlet exciton fission in the analogous flexible-bridged trimer.We show  Understanding the science and mechanism by which PDI acceptors themselves exhibit SEF can be beneficial in avoiding the extra layer to be taken up by a “SEF sensitizer” in an actual photovoltaic device, reducing the complexity, cell thickness, and greatly improving the absorption of solar photons.The scientific benefits and applications of understanding the dynamics of multiexciton triplet generation in organic chromophores cannot be overemphasized. One benefit is evaluating the actual potential impact singlet exciton fission (SEF) has on improving the power conversion efficiency (PCE) of organic solar cells.18–22 High rate of xSEF has often been associated to highly-ordered crystalline systems in comparison to their amorphous counterpart. This has been associated with a SEF assisted process – crystal lattice vibration.23 The ordered chromophores have to be in close proximity and achieve a slip-stacked or herringbone dimeric structure. This leads to them having weaker interchromophore (excitonic) interactions.24 In these solid state films, triplet formation is significantly influenced by the morphology and crystal packing, which are usually difficult to control. Hence, for devices made with xSEF chromophores where solid-state packing interactions are crucial, slight perturbations can have a drastic effect on the rate and yield of xSEF. This limits the understanding of the underlying key factors affecting the rate and efficiency of singlet fission in xSEF materials. To this regards, a more suitable approach would be intramolecular singlet exciton fission (iSEF).13,25–29 Materials capable of iSEF can overcome these challenges because each molecule undergoes SEF via through-bond interactions in multichromophoric systems – that is, not depending on intermolecular orientation, intermolecular coupling, or through-space interactions.Intermolecular SEF (xSEF) has been observed in solid state aggregates of PDI derivatives.10 Another strategy involves the covalent coupling of two xSEF chromophores where the triplet yield has been reported to be affected by the conjugation between the two chromophores.14,15,30–32 There are also reports about the effects of through–bond proximity between the chromophores on the triplet production. Campos et al.13 gave a very detailed account for pentacene dimers where the proximity of the pentacene moieties and the extent of conjugation was varied using (oligo) phenylene spacers. It was suggested that the rate of singlet fission (rate of triplet production) and the rate of recombination of the two triplets could be controlled by using spacers of varying length. In another study, Thompson et al.17 looked at how connecting two SEF chromophores to a bridge moiety at its ortho, meta or para position influences the through–bond and through-space contributions to the coupling of the compound. Intramolecular SEF was observed only in the ortho and para systems, not in the meta; and this was associated to the lack of effective conjugation, hence very weak coupling, causing predominantly radiative decay of the excited state. However, all these studies were reported for acene dimers for the end purpose of sandwiching them with organic photovoltaic (OPV) active layer materials. There are little to no studies about the effects of the π-bridge in multichromophoric OPV active layer materials themselves, e.g. PDIs, in tuning the iSEF rate or in activating/deactivating iSEF.Donor–acceptor configuration, which induces an intramolecular charge transfer character, is a molecular design strategy for iSEF molecules.15–17 structural flexibility of the covalently linked units has been proposed to be crucial in activating SEF. However, these studies lack a direct comparison with rigidly bridged units of the same chromophore in order to isolate the effects of π-bridge flexibility. This is what our current investigation seeks to illuminate – the impact of the π-bridge rotation vs. rigidity on the dynamics of triplet exciton formation, and the triplet production efficiency. Most literature studies involve dimers. Investigations about oligomeric structures, with more than two chromophores attached linearly, are very few. In the development of iSEF-OPV materials using a strong acceptor-strong donor configuration,10 the role of the flexibility/rigidity of the π-bridge in influencing the triplet production rate and efficiency, has not been investigated.The aim of this study is to investigate the unique role of the π-bridge in allowing or inhibiting triplet production (rate and yield) in oligomeric multichromophoric PDI systems. In few recent literature reports,β) position(s) with benzodithiophene (BDT) electron donor moieties, forming an A–D–A–D–A assembly. The connections between the donor and the acceptor moieties were realized via single bonds in the β compound, and through ring cyclization in the βC compound , and the cyclized βC compound achieving a planar PDI–BDT–PDI structure . These two compounds show different triplet production dynamics owing to their respective degree of electronic coupling. The photoinduced dynamics of triplet production – via iSEF or regular intersystem crossing (ISC) – was thoroughly investigated with a variety of time resolved spectroscopic techniques, employing both femtosecond and nanosecond time resolution while probing both excited state absorption and emission. The experimental spectroscopic study was carried out in a joint effort with theoretical calculations to further elucidate the excited state deactivation mechanism of the two compounds.In this work, two PDI trimers with push–pull character were synthetized see . For eacca. 60 000–70 000 M−1 cm−1 , and the βC compound has a planar PDI–BDT–PDI structure   to that of the parent PDI monomer  is enhanced by over one order of magnitude for the planar βC (ca. 300 GM) relative to the twisted β compound (ca. 10 GM). The increased two-photon absorption cross section of the planar, rigid, fused ring connected molecule, as expected, indicate its higher intramolecular charge transfer character in the excited state relative to the twisted, flexible, single bond bridged analogue. The degree of charge transfer for the β and βC excited state was further analyzed in detail with the help of quantum chemical simulations. These compounds were divided into 5 subunits/moieties, considering their acceptor(1)–donor(2)–acceptor(3)–donor(4)–acceptor(5) structure where the acceptors and the donors are the PDI the BDT fragments, respectively. The NTOs computed on the S1 geometry which describe the S1→S0 transition are shown in Fig. S31,βC (0.80 e−) is indeed higher than that of β (0.74 e−).Previous studies have observed the relationship between molecular planarity and two-photon absorption.41–47 The transient spectra of the investigated trimers at short delays following photoexcitation suggest the occurrence of intramolecular charge transfer (ICT), and no significant spectral shift was observed. It is possible that a singlet excited state with ICT character is formed very fast (within solvation).47 At longer delays this signal decays, resulting in the simultaneous formation of an ESA at 514 nm and 543 nm for β and βC, respectively. The kinetics at these wavelengths exhibit a rise (β compound (344 ps), but clearly slower for the rigid-bridged βC compound (1800 ps). Global analysis, via singular value decomposition (SVD), of the transient absorption data revealed the presence of four exponential components . Therefore, the ultrafast absorption measurements allow us to follow the triplet formation dynamics in these molecules. The triplet formation occurs fast for β (∼340 ps) and much slower for βC pointing to a different mechanisms for triplet production in the two molecules – SEF for β and ISC for βC, respectively. Additionally, triplet formation takes place slower in a less polar solvent relative to chloroform (e.g. for β in toluene triplet rise occurs in ca. 690 ps).The excited state dynamics was investigated by femtosecond transient absorption. The time resolved spectra  & S3† sht a rise . This ri48–51  and via conventional ISC for the planar/rigid-bridged βC system (φT ≪ 100%).Triplet quantum yields were also computed following the SVD analysis of the femtosecond transient absorption results1 see ESI indicateβ and βC, respectively. It is worthy to note that signals of triplet absorption have been reported for other PDI derivatives between 500 and 600 nm.18,37,52,53 This signal can be quenched by oxygen (either via energy transfer or electron transfer).54 The transient lifetimes change from hundreds of nanoseconds in air equilibrated solution to tens of microseconds in deaerated/nitrogen purged solution . Also, these transient species can be sensitized by higher-triplet energy donors, or are able to sensitize lower-triplet energy acceptors, such as tetracene as shown in n ← T1 transition of the trimers. As shown in β, the triplets produced upon photoexcitation decay much faster i.e. shorter lifetimes (6.0 μs), in comparison to the triplets produced in βC (40 μs). This is an evidence leaning to a SEF-induced mechanism of triplet production in the twisted β. It has indeed been observed in many SEF literature studies17,55–57 that a molecule hosting two triplet excitons usually exhibits a much faster triplet decay than one hosting a single triplet, due to the increased probability of triplet–triplet annihilation.To investigate the long-lived excited state dynamics, nanosecond transient absorption measurements were carried out . No pump Fig. S15. Quenchivia nanosecond transient absorption measurements. These experiments give important information about the triplet energy of the compounds (see ET = 1.27 eV) was successfully employed as an energy donor to sensitize the triplet of β, but relatively acted as a triplet energy acceptor to βC. This result proves that the triplet energy of the twisted β trimer is significantly lower than the triplet energy of the planar βC trimer. Our experimental results thus support the feasibility of SEF in the β compound which requires a low triplet energy for the SEF energetic condition to be fulfilled . The sensitization experiments also allowed for the accurate evaluation of triplet extinction coefficients , thus suggesting that iSEF indeed takes place in this molecule.Sensitization experiments were performed unds see . Tetraceents see , useful 28 This was performed by probing the samples at 850 nm, where linear absorption is negligible, under excitation with femtosecond pulses at 425 nm. Attenuation of the probe beam was observed for both samples: 29.7% attenuation for β at OD = 0.116 and 34.6% attenuation for βC at OD = 0.885, both under an average pump power of 4.25 mW  relative to the planar βC (∼0.3%). It has to be noted that for the case of the βC compound, the estimated triplet yield value is not accurate because of the observed phosphorescence interference at 850 nm. This analysis contains some approximations, however the result obtained for the β trimer is consistent with the triplet quantum yield accurately measured by the nanosecond transient absorption sensitization experiments. This once again confirms that the β compound thus undergo singlet exciton fission in solution, owing to its triplet yield also obtained by two-color transmission measurements to be ≫100%.Analysis of the obtained results was carried out in order to obtain an estimation of the triplet quantum yield for the two compounds. See the ESInown see . This wavia femtosecond transient absorption measurements. The much smaller time window of the FUC allows for a more accurate evaluation of the lifetime of the ultrafast components, as 1.0 ps for β and 0.2 ps for βC. Our FUC results show that the ICT is indeed faster in the rigid relative to the twisted trimer. Also, that SEF could be a CT-mediated process in the twisted trimer.10,22 However, when ICT is extremely fast it becomes competitive with SEF, as observed in the planar trimer.50Time resolved fluorescence measurements, both with femtosecond and nanosecond time resolution, have been extremely valuable in providing information about the rate constants of the ultrafast intramolecular charge transfer process and about the decay of the double triplet species, respectively. Fluorescence kinetics were acquired by femtosecond fluorescence up conversion (FUC) *. This component could be either a result of direct 1(TT)* emission,58–60 or delayed S1 fluorescence from the 1(TT)* state.1,19,23,53 Time resolved emission and/or temperature-dependent spectra obtained by photoluminescence measurements with broadband detection would be required to identify the specific mechanism of the double triplet emission. A 4.66 ns lifetime is not unusual for double triplet states as observed in the literature for perylene diimide chromophores. Wasielewski et al.18 reported a lifetime of 2.8 ns for polycrystalline thin films of slip stacked PDI, attributed to a small amount of delayed fluorescence resulting from triplet–triplet annihilation. Sean Roberts et al.53 also reported lifetime of ∼10 ns associated to the non-radiative decay of the triplet (or double triplet) excitons to the ground state.Fluorescence kinetics were also acquired by single photon counting (SPC) with nanosecond resolution . For the– 1.3 ns . For β, via ISC was predicted to be much faster for the planar βC than for its twisted analogue due to large cancellation between ΔEST and reorganization energies for β  ≥ 2 × E(T1), is met. Energies of the relaxed S1 state were predicted to be 1.30 eV and 1.89 eV for β and βC, respectively , but not in the planar βC for which it is energetically uphill by 0.59 eV (2 × 1.24 − 1.89 = 0.59).Quantum chemical simulations were performed to give an insight into triplet formation mechanisms. Triplet formation  Fig. S30. T1 stat Fig. S29 were 0.51TT), that is the kinetic feasibility, is more instrumental to judge the potentiality of SEF taking place than just the simple singlet–triplet energy gap.61 Though TD-DFT calculations were conducted to obtain the energetics of singly excited states, it is clearly stated by theorists that TD-DFT is not an ideal method for calculation of the multi-excitonic (ME) states, i.e., double-triplet states. The RAS-SF method, on the other hand, has shown to be capable of correctly describing the characters of multi-excitonic states and providing a more in-depth picture of the interactions between the locally excited singlet and multi-exciton states. Importantly for trimers like β and βC, RAS-SF is also able to compute all possible multi-exciton states, obtaining their spatial as well as their spin components , the trends and the relative energy values can still be discussed. The TT states from the RAS-SF trimer models are qualitatively described in †A recent perspective pointed out that the accessibility of double triplet state of singlet character , required to reach the multiexcitonic state from the S1 state. As shown in β compound is configuration 3. More specifically, the RAS-SF calculation shows that excitons in the lowest multi-exciton state are localized on adjacent PDI units. The two higher energy configurations (configurations 1 and 2) are within 0.02 eV of configuration 3, indicating that all TT states of β compound are easily energetically accessible. In the case of the βC compound, the lowest multi-exciton state is configuration 2 of β), suggesting a nontrivial difference in energy to access configurations 1 and 3.Krylov has shown that it is not uncommon for perylene diimide compounds to have their lowest  Table S7. This 1T1 can evolve into a triplet-paired state1(TT) in singlet fission chromophores via state crossings when the S1 and TT states are close in energy.63 Throughout this non-adiabatic transition, it is true in some cases that the singlet exciton of S1 state resides over several adjacent chromophores. This phenomenon promotes the 1(TT) formation and thus increases the SF efficiency.61 Only the couplings of the singly excited state S1 with the ME state on adjacent chromophores will be playing significant roles throughout this non-adiabatic transition. In this particular case of β compound, as suggested by the electronic configuration of its lowest TT state , kinetic accessibility, and feasibility of separation of the double triplets.Overall, quantum chemical simulations support that iSEF is the dominant pathway to generate 15–17 Those studies, however, do not report the direct comparison between rigid-bridged and flexible-bridged units of the same chromophore in order to isolate the effect of the π-bridge. In this work, we point out the key differences between planar (rigid-bridged) and twisted (flexible-bridged) systems as they relate to the efficiency and rate of triplet production upon singlet photoexcitation. The systems investigated are newly synthesized oligomeric PDI trimers. Typically, the fluorescence quantum yield of PDI monomers is around 90%, indicating that the radiative decay pathway is the most preferred. However, for these PDI trimers, especially for the flexible-bridged β trimer, the fluorescence efficiency is found to be very low suggesting a prevalent non-radiative deactivation – triplet production.In the literature, it has been proposed for multichromophoric systems that using a rotatable linker is crucial in obtaining iSEF.βC trimer, we obtain a triplet yield of 16% via triplet sensitization experiments employing a nanosecond transient absorption technique. The femtosecond transient absorption results show ultrafast intramolecular charge transfer and slow triplet formation occurring in few nanoseconds for this molecule. This rate agrees with the intersystem crossing rate predicted by quantum chemical simulations. Our experimental and computational results thus conclude that triplet production for the rigid βC trimer proceeds via regular intersystem crossing (β trimer we clearly show that the mechanism of triplet production is different and involves iSEF (via triplet sensitization as well as two-color transmission experiments. (ii) A fast triplet formation (∼340 ps) observed via femtosecond transient absorption measurements. (iii) Distinct triplet species detected via transient absorption experiments – the correlated triplet pair and the independent triplets with lifetime of 6 μs.64–66 (iv) A decay lifetime different from that of the S1 species (4.7 ns), attributed to the double triplet species. (v) Thermodynamic viability – E(S1) ≥ 2 × E(T1). (vi) Kinetic feasibility allowed by the energetic accessibility of the double triplet state from the S1 state – the rate is given as: r ≈ eES1−E1TT)−const. and a second step leading to triplet separation (from 1TT to T1). The total enthalpy and entropy change were evaluated as the sum of the changes observed in the two steps. Detailed results are reported in Table S8.β twisted compound (ΔHTOT = −0.20 eV) and endothermic for the βC planar trimer (ΔHTOT = +0.59 eV). In the literature about iSEF in covalently linked dimers, only enthalpy has been considered in describing their thermodynamics. This is because covalently linked dimers can accommodate just one correlated triplet pair, hence no entropic contribution. However, for trimeric structures the role of entropy should be considered. In a covalently linked trimer, like those investigated here, the double triplet has three possible accommodations on two of its three PDIs; and in particular two equivalent accommodations on each pair of adjacent PDIs owing to molecular symmetry. In principle, the trimeric structure allows entropic gain to play a significant role in the SEF thermodynamics, as literature studies have reported for solid state films8,67 and very recently for oligomers.56 The quantum chemical simulations indeed showed the presence of three multiexcitonic states. For β, the two 1TT accommodated on adjacent PDIs of the structure, as well as that on the left-most and right-most PDI units, are energetically accessible from S1. The high triplet yield and fast iSEF rate observed inβis not only due to the enthalpic viability but also to the entropic gain (TΔSTOT= +0.028 eV) allowed by its trimeric structure. This leads to a negative total change in Gibbs energy for β (ΔGTOT = −0.228 eV), confirming the iSEF thermodynamic feasibility. On the other hand, for βC, the lowest energy 1TT state is the one for which the triplet excitons reside on the left-most and right-most PDI units whereas the two 1TT states allowing for an entropic gain are enthalpically inaccessible from S1. This leads to no entropic contribution, and since the total change in Gibbs energy is positive (ΔGTOT = +0.59 eV), iSEF is not thermodynamically feasible for the planar βC trimer.To gain a deeper insight into the thermodynamics of multiexciton generation, we obtained all the relevant enthalpic and entropic quantities for the trimers following an approach proposed by Krylov βC trimer, for the twisted β compound, weak coupling is observed because the singlet electron NTOs are localized on a single PDI unit. We suggest that the poor electronic communication among the PDI chromophores caused by the rotatable linker is crucial in permitting efficient iSEF. Our results demonstrate that the single-bond connections capable of weakening the coupling between the chromophores favor high iSEF yield. The fused ring connections induce strong coupling among the PDI units, as the singlet electron NTOs are delocalized over the planar trimer structure, and inhibit SEF completely. This is due to competition with other ultrafast processes in the planar system, such as intramolecular charge transfer.26 The two-photon absorption (TPA) cross section – a measure of intramolecular charge transfer character – is indeed enhanced by over one order of magnitude for the planar βC (ca. 300 GM) with respect to the twisted β compound (ca. 10 GM). Quantum chemical simulations confirm the higher degree of charge transfer in the excited state for βC (0.80 e−) relative to β (0.74 e−) by dividing their structure into 5 subunits of PDI acceptor and BDT donor fragments. Weak coupling among the PDI units is crucial not only for multiexciton generation but also for triplet separation. The rate of triplet separation is indeed given as: r ≈ eE5TT−E1TT)−const. as 0.006 eV. This result suggests that the interaction between two triplets in β is indeed small, and two entangled triplets can thus easily be separated into two independent triplets. However, in βC, the inter-triplet interaction energies increase by one order of magnitude, up to 0.066 eV. For the β trimer, the long-lived independent triplets are experimentally observed following their separation, and each of them is localized on a single PDI unit, as shown by the theoretical calculations. Compared to other SEF rylene derivatives reported in the literature,19,50,53 the β trimer shows a much longer triplet lifetime. This is highly beneficial for its use in solar energy conversion devices, allowing efficient extraction of multiple charge carriers per incident photon.68While strong coupling among the PDI chromophores can be inferred for the planar via time resolved spectroscopic measurements how a slight structural variation of the π-bridge of multichromophoric perylene diimide (PDI) systems strongly affects the triplet yield and triplet formation rate. Triplet formation proceeds via conventional intersystem crossing for the planar trimer as evidenced by its triplet yield of 16% and triplet production in the nanosecond timescale. On the other hand, we find clear evidence of highly efficient (170%) and fast (few hundred picoseconds) intramolecular singlet exciton fission taking place in the twisted trimer. A fused ring connection induces strong coupling among the PDI units as in the planar system and this inhibits singlet exciton fission completely due to a strong competition with other ultrafast processes, such as intramolecular charge transfer. Our results demonstrate that a rotatable π-bridge, capable of lowering the coupling between the chromophores, is necessary to activate intramolecular singlet exciton fission in multichromophoric systems. The quantum chemical simulations prove that the entropic gain allowed by multiple possibilities of accommodating the correlated triplet pair on adjacent PDIs in the twisted trimer is a crucial determinant for multiexciton triplet generation. Successive multiexciton triplet separation occurs in the flexible-bridged PDI due to weak coupling among the units, and degenerate double triplet and quintet states.Here, we report a comparative study between rigid-bridged (planar) and flexible-bridged (twisted) perylene diimide trimer systems to highlight the role of the π-bridge linker in activating intramolecular singlet exciton fission. We show All authors have given approval to the final version of the manuscript and declare no competing financial interest.SC-011-D0SC03271A-s001


There was an error in the original article . The errpermissible” fibers.”A correction has been made to Section 3, paragraph 5: “Therefore, at a standard of 2 million asbestos fibers larger than 5 microns in length per cubic meter of air would mean somewhere in the range of inhaling 16 million “The authors apologize for any inconvenience caused, and state that the scientific conclusions are unaffected. The original article has been updated.


Transcriptional terminators signal where transcribing RNA polymerases (RNAPs) should halt and disassociate from DNA. However, because termination is stochastic, two different forms of transcript could be produced: one ending at the terminator and the other reading through. An ability to control the abundance of these transcript isoforms would offer bioengineers a mechanism to regulate multi-gene constructs at the level of transcription. Here, we explore this possibility by repurposing terminators as ‘transcriptional valves’ that can tune the proportion of RNAP read-through. Using one-pot combinatorial DNA assembly, we iteratively construct 1780 transcriptional valves for T7 RNAP and show how nanopore-based direct RNA sequencing (dRNA-seq) can be used to characterize entire libraries of valves simultaneously at a nucleotide resolution in vitro and unravel genetic design principles to tune and insulate termination. Finally, we engineer valves for multiplexed regulation of CRISPR guide RNAs. This work provides new avenues for controlling transcription and demonstrates the benefits of long-read sequencing for exploring complex sequence-function landscapes. Transcriptional terminators are generally viewed as hard endpoints for transcribing RNA polymerases. Here, the authors reimagine terminators as transcriptional valves with predictable read through. They engineer and characterize 1780 valves and use them for multiplexed gene regulation. However, endogenous gene regulation is often multifaceted, employing diverse mechanisms that affect the stability and processing of DNA, RNA, and proteins to create complex regulatory programs2.The ability to precisely control when and where genes are expressed is crucial for engineering the behavior of living cells. To achieve this, bioengineers have predominantly focused on developing genetic parts to regulate transcription and translation initiation rates for genes of interest3. Although such machinery is not generally present in prokaryotes, there is a growing realization that these organisms also generate transcript isoforms by utilizing incomplete transcriptional termination6. In this case, two transcript isoforms are possible: one ending at the terminator (if termination succeeds), and the other reading through (if termination fails)  Fig. .Fig. 1Ma7 as a way of insulating multiple genetic parts and devices from each other8 and the host genome9. Engineering terminators with a variety of efficiencies, insulated from an upstream sequence, or tuned for manipulating transcript isoform ratios10 has yet to be widely explored. However, an ability to design transcript isoforms in this way could open new avenues to control the stoichiometry of multi-gene expression purely at the level of transcription. Furthermore, this regulatory approach could be more efficient and impose less burden13 than other more commonly used methods, like operons, as not all RNA polymerases (RNAPs) would need to synthesize full-length multi-gene transcripts and thus could be freed more quickly for other tasks. This approach would also be suitable for differential expression of purely RNA-based regulators  where translation into protein does not occur.The design of synthetic terminators often focuses on increasing their termination efficiency17. More recently, methods employing RNA sequencing (RNA-seq) have been used to provide a more detailed and direct measurement of termination at a nucleotide resolution by allowing for transcriptional profiles capturing RNAP flux along the DNA to be inferred. Drops in RNAP flux within these profiles can be used to measure both termination efficiencies as well as the precise location at which these events occur19.A major bottleneck when developing new genetic parts is the time and effort needed to characterize libraries of parts to understand their design principles and build predictive models of their function. For transcriptional terminators, a commonly used approach in vivo is a fluorescence assay in which two different fluorescent reporter proteins have the terminator to be tested placed between them. By comparing the ratio of fluorescence for each reporter with and without the terminator present, it is possible to indirectly quantify the fraction of transcriptional read through and the termination efficiency of the terminator20, the occlusion of adjacent ribosome binding sites due to terminator mRNA secondary structures, the impact of a terminator on the translational coupling of neighboring genes7, and transcription-translation coupling17 could all potentially play a role and affect the accuracy of the measurements made. Such differences may explain why in vitro and in vivo termination efficiencies have not been found to correlate well21. Nonetheless, insights into in vitro termination have proven useful. For example, in vitro assays using chip-based capillary electrophoresis22 have been used to identify terminators which have subsequently been used both in vitro23 and in vivo24. A bigger issue facing all of these approaches though is their limited throughput and scalability, with designs often needing to be tested separately. This severely hampers the exploration of the vast genetic design space and limits our ability to understand how terminators are effectively engineered.A challenge with all in vivo approaches is that they often need to make assumptions about the stability of the cellular environment and properties of the transcripts and proteins produced. However, these may not always hold: variations in mRNA stabilityIn this work, we aim to address these issues and develop new genetic parts for regulating multi-gene constructs. Rather than treating terminators as the endpoint of a transcript, we consider them as “valves” able to regulate the RNAP flux passing through a point in DNA and thus the ratio of transcript isoforms that occur Fig. . To expl25 as well as an orthogonal transcription system in vivo27. While diverse terminators are available for the native E. coli RNAP16, for T7 RNAP only a single terminator exists in the T7 phage genome28 and only a few alternatives have been characterized30. Furthermore, while termination of RNAP in model microorganisms like E. coli and S. cerevisiae has been extensively studied31, T7 RNAP termination has many unknowns such as alternative intrinsic terminators beyond those in the T7 phage genome and the bidirectionality of termination.To demonstrate how transcriptional valves might be built, we attempted to construct proof-of-concept designs for T7 RNAP. T7 RNAP was selected due to its broad use in synthetic biology, which stems from the fact that it is a single-subunit RNAP with high processivity, making it ideal for both in vitro use32. Therefore, as a basis for an initial library of transcriptional valves, we chose 13 different intrinsic terminators to act as “core terminator” elements (T). We began by selecting the single terminator from the T7 phage genome (T27)28, which has previously been characterized in vitro22. To test its possible bidirectionality, a feature that terminators for other RNAPs have been shown to exhibit7, it was included in a reverse orientation in our designs22. Beyond the native T7 phage terminator, E. coli terminators present another source of these parts and have been shown to terminate T7 RNAP in vitro33. Therefore, 11 intrinsic rho-independent terminators were selected from the E. coli genome spanning a wide range of termination efficiencies in vivo7. Finally, a negative control terminator (T33) was designed. This consisted of a random non-coding sequence generated by R2oDNA designer34 and was further verified to not contain a strong hairpin in the mRNA secondary structure using the Vienna RNAfold tool35.Specific features of a terminator, such as its hairpin structure and U-tract, can strongly influence termination efficiency17 and we reasoned that this region could be used to fine-tune the termination efficiency of a valve. We, therefore, included a “modifier” part (M) in our transcriptional valve design and developed 13 different modifier sequences  where each was a random non-coding sequence generated by R2oDNA designer34.The genetic sequence immediately upstream of a terminator-hairpin also influences terminationces Fig. . Our fir37, we generated 7 random and genetically diverse 33 bp long spacers with a nucleotide composition similar to coding regions of E. coli that could be placed at the 5′ end of a valve. Each spacer had a stop codon “TAA” at its 3′-end, though this was not utilized in our in vitro transcription assay. Taken together, our spacers, modifiers, and core terminators could be combinatorially assembled to create a total of 1183 unique designs able to regulate RNAP flux and provide valuable information regarding the design principles of transcriptional valves.To assess the robustness of each valves’ termination efficiency to local upstream genetic context, our library also included “spacer” elements (S) Fig. . These d38. E. coli cells were transformed with this pooled library and ~500,000 colonies (>400-fold library coverage) were selected from plates via scraping before their pooled DNA was extracted. Such a high fold-coverage ensured representation of each design in the sample  was then used to verify the successful combinatorial assembly of every design. This showed that all designs were present with an even distribution of parts but an uneven distribution of designs . Comparing the reference and consensus sequence for each design we found a mean of 0.6 single nucleotide polymorphisms (SNPs) per design, with 40% of designs having no SNPs  to provide full-length reads of transcript sequences41. Crucially, each transcript isoform encodes its associated transcriptional value sequence either at the 3′-end, if termination was successful, or within the body of the transcript, if transcriptional read-through had occurred—the design’s sequence, therefore, acts as an ‘intrinsic barcode’ that is present in every read. This allowed for individual reads to be attributed to a particular design without the need to separate and barcode them before preparing the sequencing library.Existing fluorescence44. Long-read dRNA-seq allows for the whole library to be directly assayed as a single pooled sample, without the need for RT, PCR or any assembly, and the data demultiplexed to simultaneously produce separate read depth profiles for each design. Finally, by comparing the ratio of transcript isoforms for each design  a termination efficiency can be calculated  step and subsequent PCR amplificationted Fig. .45) and although this gap is closing with improvements to basecallers and sequencing chemistries, analysis pipelines need to be carefully tuned and validated to ensure accurate demultiplexing of reads when dRNA-seq is used in this way.While this approach removes the need to separate and attach unique ‘barcode’ sequences to each design when characterizing the library, it does rely on each transcriptional valve having a sufficiently different sequence for each read to be accurately mapped to a single design. Read accuracy for nanopore-based dRNA-seq is, at present, lower than for standard Illumina-based short-read RNA-seq  − R(xe)]/R(xs), where R(x) is the read depth at position x in the genetic construct, and xs and xe are the start and end nucleotide position of the transcriptional valve, respectively.The final computational demultiplexing and analysis pipeline Fig.  involved48. We also developed a mathematical model that allowed us to correct for unwanted deviations between actual and measured Te (Supplementary Note R2 = 0.22), with strong terminators over-represented in the dRNA-seq data. A good reproducibility was observed for Te values between replicates (R2 = 0.99) and for terminators shared across separately assembled libraries with different part compositions , which varied in amplitude depending on the upstream modifier and spacer . We removed the final 8 nt, which have been shown to base-pair with the DNA template in the T7 RNAP transcription elongation complex51, and studied the structure with the lowest folding energy. The strongest terminators were predicted to form terminating hairpins at their 3′-end, proximal to the elongating T7 RNAP. On the contrary, T20 was found to get locked in a secondary structure involving a hairpin ending 16 nt upstream of the T7 RNAP, meaning that it remained a weak terminator despite having a long U-tract. To reach an effective terminating hairpin T20 would have to surpass a large energy barrier.Using this data, it was possible to predict RNA secondary structures at the various points of termination and assess their potential influence. To do this we simulated co-transcriptional foldingion Fig. , assuminTe is the unique double hairpin structure that can form in the core terminator at the later points of termination. The second peak in termination for T14 coincides with the last point at which this double hairpin is predicted to exist  and the negative control (T33). Each of these could have a maximum of 4 U’s in the U-tract and none were predicted to form a hairpin proximal to the U-tract, which is likely the cause of their inactivity. This showed that T27, the reverse oriented phage terminator, was not able to efficiently terminate T7 RNAP bidirectionally. The three weakest active terminators  all had only 2 U’s in their U-tract of their most common transcript isoform, saw termination at multiple separated points, and were predicted to form a hairpin proximal to the U-tract Fig. . It is nist Fig. . T15 and53. To assess this, we reviewed the possible transcripts produced by the characterized terminators and this showed that the final nucleotide of transcript variants can be either A, C, U or G. Frequently the dominant transcript terminated within a stretch of U’s though less frequently observed transcripts were found to terminate immediately after a stretch of U’s. Further investigation revealed that in some cases, upstream sequence could tune the major point of termination. For example, modifiers M10, M11, M12, and M15 showed different stoichiometries of two types of transcripts produced by T13.An ability to engineer the precise point(s) of termination and therefore dominant 3′-UTR sequences may be important in deciding gene stoichiometries in vivo as it could potentially affect mRNA degradation rates, however, this is contestedTe . However, none of these were correlated with measured Te varied from 0 to 0.94 across the library with core terminators displaying varying levels of Te and sensitivity to different modifier and spacer parts  showed little to no termination (Te < 0.05). The remaining nine E. coli terminators displayed a range of termination efficiencies for T7 RNAP with median Te varying from 0.01 to 0.91, which was heavily influenced by upstream sequence context. The variety of Te values observed would allow for a wide range of transcript isoform stoichiometries to be produced from 1:1 to 11:1. However, we were interested to know if patterns within this data might offer insight into the capacity of each terminator to be tuned or insulated. For example, valves displaying a wide range of Te values for the same core terminator would indicate that the terminator is highly tunable, while a small range of Te for a valve used with differing spacer elements would suggest that it is able to insulate its function from upstream sequence context.Overall, rts Fig. . Groupinors Fig. . We foun56. We, therefore, designed modifiers in our initial library with the aim of being able to tune the strength of a valve. Analysis of the characterization data showed that changes in upstream genetic context (both spacer and particularly modifier sequences) could significantly influence termination strength, allowing Te to be varied over a range of up to 0.68. The ability to tune each core terminator varied, with the Te of T10 being most tunable and T16 being the least. The capacity to tune terminator strength could arise from the diversity of co-transcriptional structures that form proximal to the U-tract when interacting with the modifier  than others   Fig. . This suTe . While ideally we would have used identical padding sequences, we instead chose padding sequences with identical RNA secondary structure  as these unique sequences would help ensure accurate read demultiplexing after nanopore sequencing. These motifs targeted the 5′-stem, loop and 3′-stem regions of the terminator hairpin Fig. . Two varTe. Loop-modifier interaction during termination could alter the core terminator hairpin during its formation, at the point of termination, or both, affecting the probability of a termination event. The largest effect on Te was caused by motifs designed to interact with the stem of the terminator. We hypothesize that this is because core terminator stem base-pairing is essential for hairpin formation whereas the loop can base-pair with an interacting motif at the same time as the completing hairpin. Therefore, a motif that can base-pair with the stem could outcompete the core terminator hairpin.Characterization of this library revealed that base-pairing can significantly reduce termination efficiency in a distance-dependent manner Fig. . The motTe, while the 3′-stem interactor did not. In the case of T16 this is likely because 5 of the 8 targeted nucleotides are predicted to be concealed within the T7 RNAP (2 nt for T29 and 3 nt for T10), where they cannot base-pair at the point of termination since they are in the U-tract. This effect on Te was greater than any other drop caused by a modifier tested so far. As with previous modifiers, T10 behaved differently to T16 and T29. The 3′-stem interactor had a large effect on termination, while the 5′-stem interactor did not. This could be a consequence of the extra native sequence context between the hairpin and the motifs  resulting in a location in which the motif can base-pair with the 3′-stem. However, it may also arise from the inherent tunability of T10. In either case, the effect on Te of motifs that base-pair with terminators diminishes when they are placed far from the terminator.For the two strongest terminators  the 5′-stem interactor caused a large drop in 57. Therefore, we looked to further investigate whether RNA structure could insulate terminator function by designing and testing a library of modifiers containing secondary structure motifs . A variety of other more complex RNA secondary structures are known and one modifier containing an “elbow” (the TAR element) and one containing a pseudoknot were also designed to see any role these might play59.It has been shown that structure can stabilize the activity of genetic partsifs Fig. . To explE. coli RNAP60. We found that short hairpin structures and complex RNA structures were the best insulators of terminator function  and so our analysis is focused on understanding the influence of sequence context proximal to the core-terminator hairpin.Our results had shown that many of the relationships observed were terminator dependent, and so a final library was designed and tested to investigate variations of the core terminator part that had the greatest influence on Te Fig. . We consTe of weak core-terminators used in our initial library could be increased by increasing the number of U’s in the U-tract . For our previous designs, some native sequence context immediately upstream of the terminator hairpin (and before the modifier) is retained. Changing this decreased Te for all the terminators studied  were used as a basis for various U-tracts containing no U’s. Variants of each of these core terminators with an 8 nt tract of A, C, or G were designed. To ensure their transcripts could be distinguished after dRNA-seq we put unique non-structural RNA sequences as barcodes upstream of the core terminators (see “Methods” section). These variants were inspired by data showing that T7 RNAP can slip and terminate at sites of 8 consecutive A’s in vitrotor Fig. . The polied Fig. , indicatTe = 0.82) and tunable. The progression of minimum free energy structures predicted to form as each nucleotide is transcribed suggests that a variety of structures form approaching the point of maximum termination  revealed wide diversity in the points of termination Fig. . We founion Fig. . This ision Fig. . This naion Fig. . These iTe. The ability for T-theta to form a complex mixture of transcript variants whose ratio can be tuned by upstream sequence could arise from co-evolution of this terminator with the T7 RNA polymerase. This would result in a high capacity for tuning both transcription (via Te) and mRNA stability (via RNA degradation) following mutation of the core-terminator or upstream sequence.T-theta was also tested with a variety of upstream modifiers designed to base-pair with the core-terminator or form secondary structures. Of these, one short hairpin near to the core-terminator (M81) tuned the ratios of transcript variants depending on the upstream genetic context. Co-transcriptional simulations of this valve indicated that a variety of secondary structures can form immediately upstream of the terminating hairpin, which can extend and therefore be influenced by sequences further upstream. The effect of versatile secondary structures upstream of the valve could potentially influence the transcripts produced as well as 4, along with 3 further E. coli terminators with long U-tracts7. At least one example of a terminator with Te > 0.5 in vitro was present in the selection for each organism. This selection sought to expand the options for engineering strong T7 RNAP valves. While each of these terminators has evolved to function in different cellular contexts, we found that they behave similarly with T7 RNAP in vitro: termination invariably occurred in a region with multiple U’s in the U-tract downstream of a hairpin. These results highlight that terminators sourced from many organisms can terminate T7 RNAP and provide yet more options for core terminator parts when designing valves.Finally, strong terminators highlighted by previous studies were also characterized Fig. . These c66, few efforts have been made to rationally regulate the relative levels of gRNAs within an array. This could be important for implementing complex patterns of gene activation or repression. Promoters of varying strength have been used to achieve a similar goal67. However, promoters do not couple gRNA stoichiometries to one another in the same way as can be achieved by using transcriptional valves and are sensitive to noise and genetic context that can affect each promoter independently.The ability for our valves to control the stoichiometry of transcript isoforms makes them ideally suited for multiplexed regulation of RNA-based parts. To demonstrate how this might be achieved, we chose to focus on the expression of a CRISPR–Cas9 guide RNA (gRNA) array. While gRNAs have been co-expressed as arraysTe, the absolute termination observed was significantly lower in the array, with a decrease that correlated with proximity to the promoter. This feature has been previously observed68, though to our knowledge the cause is not fully understood. One hypothesis is that proximity to the promoter has been predicted to increase transcriptional read-through of protein “roadblocks” by virtue of an increased force from RNAP traffic, which is cumulative69, and a similar effect could be occurring in our case.We designed four arrays, each containing the same three gRNAs (complete with handles) separated by two unique valves Fig.  to give R2 = 0.93) in the Te values. However, for some terminators Te significantly decreased at the higher concentration of T7 RNAP . We found a strong correlation  can be used to tune termination efficiency, while the inclusion of sufficiently long insulating sequences (45 nt) at the 5′-end of a core terminator reduces changes in Te when the same valve is used in conjunction with different upstream coding sequences  of termination. Our newly designed valves behaved similarly at differing T7 RNAP concentrations (simulating varying transcription initiation rates) and could regulate ratios of CRISPR gRNAs by expressing them in an array interspersed with valves . However, a detailed assessment of how well these results hold or correlate to in vivo measurements would offer another interesting future direction and such a study could also be carried out in high-throughput using other sequencing-based approaches that combine fluorescence-activated cell sorting (FACS) and subsequent sequencing (Sort-seq)80 or targeted approaches based on the pull-down of specific RNAs.The focus of this work was to assess the function of transcriptional valves in vitro. This allowed us to avoid confounding factors that would be difficult to control for in vivo  that underpin the synthesis of proteins from DNA. Nature is known to regulate gene expression at multiple levels and through numerous processes to create complex regulatory programsEscherichia coli strain DH10-β (F–endA1 glnV44 thi-1 recA1 relA1 gyrA96 deoR nupG purB20 φ80dlacZΔM15 Δ(lacZYA–argF)U169, hsdR17(rK–mK+), λ–) . Cells were grown in LB Miller broth . Antibiotic selection was performed using 100 µg/mL of ampicillin .All cloning was performed using 7 was modified for use in combinatorial assembly by first mutating the gfp stop codons from “TAATAA” to “TTAGCA” using Q5 mutagenesis  and second replacing the araC gene and PBAD promoter with a consensus T7 promoter sequence  were diluted to 100 µM in TE buffer (10 mM tris(hydroxymethyl)aminomethane, 0.1 mM ethylenediaminetetraacetic acid, pH 8.0). Duplex DNA was assembled for each core terminator, modifier, or spacer variant by annealing the complementary forward and reverse oligonucleotides  in 46 µL annealing buffer , heating to 95 °C for 5 min and slowly cooling to room temperature. Duplex DNA of all variants (1 µL (1 pmol) of each) was combined, and the pool was diluted to a final concentration of 1 pmol/µL with nuclease-free water. The pooled duplex DNA (20 µL) was phosphorylated using T4 polynucleotide kinase  in 10× T4 DNA ligase buffer (2 µL) at 37 °C for 30 min; 65 °C for 20 min. Meanwhile, plasmid backbone DNA (1 µg) was digested using EcoRI-HF  and SpeI-HF  in 10× CutSmart buffer (5 µL) and nuclease-free water (35 µL) at 37 °C for 4 hr and then 80 °C for 20 min, before gel extraction . Plasmid backbone (50 fmol) was used for pooled ligation based combinatorial assembly by combining with a 5-fold excess of the aforementioned phosphorylated duplex DNA pool (containing 250 fmol of each design for insertion into the plasmid), nuclease-free water (40 µL), 10× T4 DNA ligase buffer (5 µL) and T4 DNA ligase  and incubating at room temperature for 3 hr and then 65 °C for 10 min.E. coli strain DH10-β cells  thawed on ice for 10 min and mixed gently by tapping. The mixture was left on ice for 30 min and heat-shocked at 42 °C for 30 seconds before leaving for 5 min on ice. NEB 10-beta/Stable Outgrowth Medium  was added to each aliquot and the mixture was shaken vigorously (1250 rpm) at 37 °C for 60 min. Each aliquot was then added to one 1.5 L rectangular glass dish (Pyrex) containing LB agar with ampicillin and cells were grown overnight. Following this, sufficient colonies were scraped from agar plates for >400-fold library coverage and DNA was extracted . DNA concentrations were measured using a NanoPhotometer N60 (Implen). All libraries constructed in this work are described in Supplementary Table The pooled transcriptional valve library (3 µL) was then added to each of 12 aliquots of DNA from the pooled transcriptional valve library (400 ng) was prepared for DNA sequencing using the rapid barcoding kit following the standard protocol . DNA samples were sequenced for 48 h on FLO-MIN106 flow cells. Generated FAST5 files were basecalled using guppy version 3.1.5. BLASTN version 2.2.31 (with the same parameters as for dRNA-seq demultiplexing) was used to align sequencing reads to reference sequences. DNA sequencing reads were demultiplexed by selecting the best alignment to a design based upon maximum bitscore for each sequencing read. Sequencing reads with no alignment to a design, or alignments to multiple designs with the same maximum bitscore were excluded from further analysis. Part and design frequencies were calculated relative to the total number of annotated sequencing reads.46. Racon version 1.482 with parameters: -m 8 -x -6 -g -8 -w 500, was used to polish the plasmid sequence and refine the consensus sequence produced. The polished and reference sequences were then aligned using Multiple Alignment using Fast Fourier Transform (MAFFT) version 7 with parameters: --localpair --maxiterate 1000. Finally, a script was used to count the average number of single nucleotide polymorphisms per design. Annotated plasmid sequences are available in Supplementary Data We used demultiplexed sequencing reads to generate a consensus sequence for each design and assess DNA assembly fidelity. Demultiplexed sequencing reads for each design were aligned to the plasmid encoding the design using minimap2 version 2.17E. coli Poly(A) Polymerase  with 10× reaction buffer (2 µL), RNase inhibitor murine  and 2 µL adenosine triphosphate, ATP (10 mM) at 37 °C for 30 min. The reaction was stopped by proceeding to RNA purification with elution in 15 µL . Polyadenylated RNA (1 µg) was prepared using the direct RNA sequencing kit following the standard protocol  with inclusion of the reverse-transcription step and flow cell priming kit EXP-FLP002 (Oxford Nanopore Technologies). RNA samples were sequenced using MinKNOW version 20.06.5 for 48 hr on FLO-MIN106 flow cells.DNA from the pooled transcriptional valve library (1 ug) was linearized using AatII (10 units) in 10× CutSmart buffer (5 µL) and nuclease-free water (40 µL) at 37 °C for 30 min and then 80 °C for 20 min. Duplicate reactions were purified  and eluted in nuclease-free water (12 µL). In vitro transcription was performed using HiScribe™ T7 High Yield RNA Synthesis Kit . The following reagents were combined: T7 RNA Polymerase mix (2 µL), adenosine triphosphate (2 µL), guanosine triphosphate (2 µL), cytidine triphosphate (2 µL), uridine triphosphate (2 µL), kit reaction buffer (2 µL), the RNA calibration strand (0.5 µL) and the linearized DNA pool (250 ng) at 37 °C for 35 min. Synthesized RNA was diluted 20-fold in nuclease-free water and purified . The purified RNA (10 µg) was then poly-adenylated using 83. BLASTN parameters were selected based upon simulated nanopore RNA-seq data: -outfmt 6 -gapopen 5 -gapextend 2 -reward 2 -penalty -3 -evalue 1 -word_size 4 -max_target_seqs 1000000 -max_hsps 1. Python and Bash scripts were then used to match each sequencing read to a design based upon the best alignment . Sequencing reads with no alignment to a design, or alignments to multiple designs with the same maximum bitscore were excluded from further analysis. Part and design frequencies were calculated relative to the total number of annotated sequencing reads.First, dRNA-seq data in FAST5 format was basecalled using guppy version 3.1.5 in high-accuracy mode. Next, the design sequences (not including plasmid backbone) were aligned to all basecalled sequencing reads using BLASTN version 2.2.3146 to generate a sequence alignment (SAM) file. Using pySAM84, the SAM file was refined by removing sequencing reads that did not contain a full design sequence and terminated between the start of the spacer and 20 nt into the core terminator as defined by a general feature format (GFF) file for each plasmid sequence bearing a design. Reads from two identical sequencing runs were pooled to calculate final Te values. Termination efficiencies were calculated based upon the read depth on either side of the valve (see main text for details) which was further corrected by subtracting the predicted Te deviation (Supplementary Note Parsed reads were then mapped to a plasmid sequence encoding the appropriate design using minimap2 version 2.1785. A query structure that the tool would accept was submitted: “(……………………………..)”. Then the output sequences were trimmed 1 nt at either end and any sequences with a non-zero folding energy, a restriction enzyme recognition site for EcoRI, SpeI, or AatII, or a site with 4 or more adjacent identical nucleotides were removed. The remaining sequences were used to fill the gaps required for testing base-pairing and structural modifier sequences in the modifier at different distances from the core-terminator.All regions to provide padding in modifiers were designed using RNAInverse version 2.5, which can generate RNA sequences with a specific RNA structure86. Since the array would result in multiple guides per transcript, the RNA transcripts would have to be processed following transcription to separate them and make them functional. The same strategy used by Santos-Moreno et al. was used: inclusion of Csy4 recognition sites around each gRNA.Valve designs used in the arrays consisted of particular sets of spacer, modifier, and core-terminator sequences. The guide sequences were selected from the CRISPRlator construct designed by Santos-Moreno et al.87. The 3′-cytidine was omitted as it falls outside of the hairpin and the Csy4 recognition site used by Santos-Moreno et al. omitted it, yet it is recognized by the enzyme. Instead of using the same CRISPR handle for each gRNA we selected a unique handle for each gRNA from the non-repetitive examples in Reis et al.63. Three handles with dissimilar sequences and high functionality were used. These handles are compatible with dCas9sp. While gRNAs are often transcribed with a terminator sequence, this was omitted as valves were used to regulate transcription instead.Due to limitations on the number of repetitive sequences that can be effectively synthesized, measures were taken to reduce sequence homology. Csy4 recognition sites were shortened to 15 nt, which includes all but the 3′-cytidine of the shortest functional recognition site to be characterizedAt the start and end of each array was a short 15–25 nt randomly generated sequence to allow for PCR amplification and serve as a buffer for restriction enzyme cleavage. Finally, around each gRNA-handle and each valve we included unique single-cutter restriction sites to facilitate modification of the arrays. The complete array sequences were ordered as gBlock gene fragments (Integrated DNA Technologies).E. coli Poly(A) Polymerase (10 units), with RNase inhibitor murine (0.5 µL), 10× E. coli Poly(A) Polymerase Reaction Buffer (2 µL) and ATP . The reaction was incubated at 37 °C for 35 min and stopped by purification with the Zymo Clean & Concentrate 25 kit. Following nanodrop quantification, polyadenylated RNA transcripts (1 µg) were prepared for sequencing using the nanopore kit SQK-RNA002 with inclusion of the reverse-transcription step, flow cell priming kit EXP-FLP002 (Oxford Nanopore Technologies) and sequenced in duplicate on FLO-MIN106D (Oxford Nanopore Technologies) flow cells using MinKNOW version 20.06.5 for 48 h.DNA arrived freeze-dried in tubes and was solubilized as follows. The tubes were solvated in nuclease-free water (8 µL), briefly vortexed, incubated at 50 °C for 15 min, cleaned up , and eluted in nuclease-free water (10 µL). After measuring the concentration by nanodrop, all four arrays were pooled (62.5 ng of each) along with the RNA calibration strand (0.5 µL) and transcribed using the NEB HiScribe™ T7 In Vitro Transcription Kit protocol and reagents . The mixture was mixed thoroughly by tapping and incubated at 37 °C for 30 min. 10 µL of the reaction product was diluted 5-fold with nuclease-free water and purified using the Zymo Clean & Concentrate 25 kit , eluting in nuclease-free water (25 µL). Following RNA quantification (Nanodrop), 10 ug of this RNA was diluted to a total volume of 13.5 µL with nuclease-free water and polyadenylated using 88. SBOL Visual diagrams were generated using the DNAplotlib Python package version 1.089 which were then annotated and composed with OmniGraffle version 7.9.2.Computational analyses were executed using Python version 3.5 using the packages NumPy version 1.18.5, SciPy version 1.5.4, Pandas version 1.0.5, and matplotlib version 3.2.2. All genetic diagrams are shown using Synthetic Biology Open Language Visual  notationFurther information on research design is available in the Supplementary InformationDescription of Additional Supplementary FilesSupplementary Data 1Supplementary Data 2Reporting Summary


Using simulationsand theory, we examine the enthalpy and entropyof hydrophobic hydration which exhibit minima in supercooled water,contrasting with the monotonically increasing temperature dependencetraditionally ascribed to these properties. The enthalpy/entropy minimaare marked by a negative to positive sign change in the heat capacityat a size-dependent reversal temperature. A Gaussian fluctuation theoryaccurately captures the reversal temperature, tracing it to water’sdistinct thermal expansivity and compressibility influenced by itsmetastable liquid–liquid critical point. The insolubility of nonpolarspecies in aqueous solution underlies a range of biological assemblyphenomena, from the formation of lipid membranes to the folding ofproteins to the stabilization of hierarchical supramolecular complexes.As such, the hydrophobic effect, which is the tendency of nonpolarsubstances to aggregate in water driven by their insolubility, hasbeen the subject of scientific scrutiny not only to understand biologicalfunction but also to harness hydrophobic assembly phenomena to engineersynthetic nanotechnologies that mimic biology. The simplest solutesstudied to gain insight into the origins of the insolubility of nonpolarspecies in water are the noble gases and alkanes, which benefit frombeing purely nonpolar so that analyses are not complicated by thepresence of ionic or polar contributions to their hydration.cAi is the concentrationof A inphase i (= w or ig), L is the Ostwald partition coefficient, kBT is the product of Boltzmann’sconstant and the temperature, and μAex is the excess chemical potential orfree energy associated with placing the solute within the liquid.In addition to μAex being large and positive for nonpolar species indicativeof their poor solubility in water, the dissolution of simple nonpolargases is marked by a number of characteristic thermodynamic signaturesassociated with hydrophobic hydration:2 (1) the hydrationenthalpy (hAex = −T2 ∂(μAex/T)/∂T|P) at roomtemperature is negative, favoring dissolution; (2) the hydration entropy(SAex = −∂μAex/∂T|P) at room temperature is more significantly negative, dominatingthe positive hydration free energy; and (3) the entropy and enthalpyare increasing functions that are expected to reverse roles and changesign at elevated temperature, indicative of a large positive hydrationheat capacity increment (cAex = ∂hAex/∂T|P = T∂sAex/∂T|P). These thermodynamic signatureshave long been attributed to nonpolar solutes inducing a clathrate-likeordering of waters in their hydration shell,1 although this is a subject of ongoing debate.5 To gain a deeperunderstanding of the role of water structure on moderating nonpolarsolute hydration, studies have pushed into the metastable supercooledwater regime (T < 0 °C) where liquid waterpresents a more pristine hydrogen bond network order as its densitydecreases below the temperature of maximum density at 4 °C. Surprisingly,Souda experimentally found that butane and hexane can be taken upand incorporated into amorphous solid water glasses.6 Paschek subsequently demonstrated from simulations thatthe hydration heat capacity of water changes sign from positive tonegative values in supercooled water at atmospheric pressure, givingrise to minima in the hydration enthalpy and entropy.7 Galamba similarly observed a sign reversal in the hydrationheat capacity increment from simulations of alkanes spanning ethaneto tetracontane in supercooled water.8 Notably,Galamba found that the hydration enthalpy minimum shifted from −40to −20 °C from ethane to tetracontane, indicating a solutesize dependence for this effect. An earlier report by Dill and co-workershinted at the possibility of sign reversal of the hydration heat capacityat lower temperatures for a two-dimensional description of water,although this was not elaborated on.9 Pascheksurmised that, in the supercooled regime, argon hydration shell watersmore closely resembled the bulk low-density liquid, minimizing thehydration entropy penalty. Galamba, on the other hand, noted thatthe enthalpy/entropy minimum nearly coincides with the temperatureat which the difference in tetrahedral order between low-density andhigh-density water is greatest, suggesting that this behavior arisesfrom the behavior of supercooled water itself. These observationsmerit deeper study to clarify the origin of the reversal of the temperaturedependence of hydrophobic hydration and its relationship to the propertiesof supercooled water. Here we report a molecular simulation and statisticalthermodynamic analysis in terms of water’s equation-of-statethat provides an alternate perspective on the origins of the reversalof the temperature dependence of hydrophobic hydration in supercooledwater.The distribution of a solute (A) between water (w) and an idealgas (ig) phase is governed by the Ostwald solubility10 Water was simulated using theTIP4P/2005 force field11 over the temperaturerange of −65 to 100 °C in 5 °C increments at 1 atmpressure. Structural and dynamic properties of the solvent indicatethat it remains a liquid over the simulation time even in the supercooledregime. Solute excess chemical potentials were evaluated using Widomtest particle insertion.13 The solutes consideredwere helium (He), neon (Ne), argon (Ar), krypton (Kr), xenon (Xe),and methane (Me), modeled using Lennard-Jones (LJ) potentials optimizedto aqueous solubilities14 along with theirrepulsive Weeks–Chandler–Andersen (WCA) cores.15 In addition, the solubilities of hard sphere(HS) solutes with radii R (indicating the solvent-excludedsize) of up to 3.6 Å were evaluated. Further computational detailsare provided in the Supporting Information.We performed molecular simulations of simple gas hydrationin waterfrom deeply supercooled temperatures to the normal boiling point.Isothermal–isobaric ensemble simulations were conducted usingGROMACS.TsAex) of Ar in water are reported in Thmin. The interrelationship betweenthe enthalpy and entropy through the heat capacity dictates that theentropy exhibits a minimum at the exact same temperature as the enthalpy, although multiplication by the temperature results in theminimum in TsAex occurring at a temperature slightly higherthan Thmin .The excess chemical potential, enthalpy, and entropy multipliedby the temperature i, where T0 = 298.15 K is a reference temperature and ai represents parameters fitted to simulation.The accuracy of this polynomial can be verified by comparison againstour simulation results for the excess chemical potential, enthalpy,entropy, and heat capacity for the Ar-like solutes in To gain insight into the originsof the enthalpy minimum, we firstconsider the role of solute–water attractive interactions onAr’s hydration thermodynamics.  results 1d. AboveThmin determined from the polynomialfits to our simulation hydration free energies is reported in R < dww/2 ≈1.4 Å, where dww is water’seffective diameter), Thmin is practically independent of solutesize and equal to −50 °C within the simulation error.Beyond this radius, Thmin systematically increases from −50to −30 °C for the largest solutes considered. No differenceamong the LJ, WCA, and HS enthalpy minimum temperatures is observedwithin the simulation error bars when compared on the basis of thesolute size, indicating that attractive solute–water interactionsplay almost no role in this effect. The increase in Thmin with solutesize is in qualitative agreement with the shift reported by Galambafor alkanes of increasing length.8 We notethat the solute size dependence indicated in Thmin for the smallest solutes falls below the homogeneous nucleationtemperature of ice (−38 °C),17 our results along with those reported by Galamba8 suggest that Thmin can rise above this temperature forreasonably sized solutes.The solute size dependencefor Thmin plateau for R < dww/2.18 For HS solutes, the excess chemicalpotential is determined from the probability of observing a solute-sizedcavity in water devoid of water oxygens, p0/(R). For spherical observation volumes so smallthat at most one water oxygen could be observed within its boundary,the excess chemical potential of a solute of that size is exactlyThmin values obtained by utilizing the simulationwater densities in Supporting Information for fittings of simulatedwater’s equation-of-state properties used in our theoreticalexpressions). In the limit of a solute of zero size (R = 0), Thmin is observed when ∂2ρ/∂T2|P = 2ρα/T, where α = −∂ ln ρ/∂T|P is the solvent’sthermal expansion coefficient. (See the Supporting Information for the derivation.) Given that α is typicallya small number, when α is divided by the temperature, ∂2ρ/∂T2|P is expected to be nearly zero at Thmin, suggestingthat the enthalpy minimum is almost coincident with a minimum in α.While for most liquids α is a positive, monotonically varyingfunction of temperature, α for water famously becomes negativebelow its temperature of maximum density. The decrease in αcontinues well into the supercooled regime until −52.5 °Cfor TIP4P/2005 water , it is only a weakly varying function of the solute radius, yieldingan essentially flat plateau for R < dww/2. In addition, we include scaled particle theory predictionsfor Thmin for solutes larger than dww/2 in Thmin from point-like to infinitely sized solutes.Scaled particle theory provides insight into the origin of the 05 water 3a, below minimum 2, greatedww/2, multibodycorrelations between water molecules must be accounted for when evaluatingthe chemical potential. In the case of information limited to waterpair correlations embodied in the water oxygen–oxygen radialdistribution function, information theory predicts that solvent occupationfluctuations within solute-sized observation volumes are best describedby a discrete Gaussian form.20 Assumingthat the discrete Gaussian can be approximated using a continuousfunction, the excess chemical potential of an HS solute in water isn⟩ =ρ(4πR3/3) is the average numberof waters residing within an observation sphere determined by theproduct of the solvent number density and volume, while χ =,lending confidence to the accuracy of this theory applied to simplenonpolar solutes.IGFT accurately predicts the chemical potential of the 3.2 ÅHS solute over the entire range of temperatures simulated and providesan excellent prediction of the solute’s hydration enthalpy,entropy, and heat capacity 1c,d. MosThmin is semiquantitativelycapturedby IGFT (22). This compressibilitymaximum is reflected in the maximum in kBTρκT near −35 °C in TIP4P/2005water . Given that the prefactor of this term,essentially corresponding to the chemical potential multiplied bythe temperature, is a monotonically increasing function of temperature,the enthalpy minimum is controlled by the sum within the parentheses,α + ∂ln χ/∂T|P. Given that α is solely a solvent property,the solute size dependence of Thmin follows from the size dependenceof ∂ln χ/∂T|P as dictated by dww/2R ≈ 1), the compressibilitycontributions cancel and χ effectively depends only on the solventdensity. As a result, the minimum in ∂ ln χ/∂T|P nearly coincides with the minimumin α. On the other hand, χ is equal to kBTρκT for a solute of infinite size (dww/2R = 0) so that the minimum in ∂ln χ/∂T|P is dictated by theinflection point in kBTρκT at −20 °C  to those approximately 3.6 Å in radius. The maininputs into IGFT are water’s density and compressibility. Water’sstructure enters only through the effective diameter of water, assumedhere to be temperature-independent, that dictates the point at whichpair correlations begin to contribute to density fluctuations withina spherical observation cavity and does not invoke liquid water’sthree-dimensional hydrogen-bonded network. Within the context of IGFT,water’s ramified structure contributes only through its impacton its equation-of-state, which is not insignificant in supercooledwater. The solute size dependence of Thmin results fromthe interplay between the minimum in α and the inflection pointbetween the maximum in kBTρκT at supercooled temperatures and itsminimum above the melting point of water. The inflection in kBTρκT is tied to the maximum in κT, which can be traced to the metastablesecond liquid–liquid critical point found from simulationsof TIP4P/2005 water22 and strongly believedfor real water based on current evidence.24 As such, IGFT marks the change in the sign of the hydration heatcapacity increment with respect to the unique equation-of-state propertiesof liquid water in the supercooled regime. This is not to say thatatomic nonpolar solutes do not disrupt low-density water’shydrogen bond network under supercooled conditions. Rather, thesestructural imperfections accompany the normal Gaussian fluctuationsthat open suitably sized cavities in which the solute could reside.Extrapolation of the hydration enthalpies of the simple gases to temperatures below −60 °C suggests that the enthalpywill cross zero to become positive, spurred by their dramaticallynegative heat capacities (e.g., 25In conclusion,we have demonstrated that the classic signaturesof hydrophobic hydration are not inviolable but can exhibit a significantnegative heat capacity increment in the supercooled regime to reversethe supposed characteristic temperature dependence of the hydrationenthalpy and entropy. While it has been previously proposed that thisreversal is a result of the nonpolar solutes breaking down the increasinglyperfected structure of supercooled low-density water,es e.g., 1d. Below