Characterising the structural dynamics of proteins and the effects of excipients are critical for optimising the design of formulations. In this work we investigated four lyophilised formulations containing bovine serum albumin (BSA) and three formulations containing a monoclonal antibody , and explored the role of the excipients polysorbate 80, sucrose, trehalose, and arginine on stabilising proteins. By performing temperature variable terahertz time-domain spectroscopy (THz-TDS) experiments it is possible to study the vibrational dynamics of these formulations. The THz-TDS measurements reveal two distinct glass transition processes in all tested formulations. The lower temperature transition,  Similar−6 and 10−12 s range and MHz/GHz frequency range, has been used to understand the dynamic relaxation processes of protein-solvent interfaces  as a model protein. We furthermore investigate the effects of adding polysorbate as well as altering the concentration on three monoclonal antibody (mAb) containing formulations. By comparing systems which contain the higher molecular weight and Y-shaped mAb versus globular BSA, we can investigate the effects of molecular weight and structure in the lyophilised formulations. We aim to provide a comprehensive understanding of the molecular dynamics of materials leading up to the glass transition temperature (22.1−1).BSA, sucrose, glycine, histidine, L-histidine monohydrate, L-arginine, polysorbate 80 (poly-oxyethylene sorbitan mono-oleate) were all purchased from Sigma-Aldrich . The mAb used, mAb1, was obtained from AstraZeneca  is a recombinant human IgG1 monoclonal antibody, with MW of approximately 144.8 kDa and extinction coefficient 1.42 mg  which was purged with dry nitrogen gas (relative humidity < 1%) to avoid moisture sorption from atmospheric water vapour. The lyophilised powder samples were pressed into 13 mm diameter flat-faced pellets, using a load of 1.5 metric tons. The resulting pellets were between 300 and 700 μm in thickness and 70 mg in weight each, and were placed between two-quartz windows. This sandwich structure was sealed in the sample holder, as described previously .2.42O and diluted to a concentration of 3–4 μm before analysis by CD. Protein concentration was calculated by measuring absorbance at 280 nm on a Nanovue spectrophotometer  using the extinction coefficient of 43,824 M−1 cm−1 (Circular dichroism spectroscopy (CD) was used to investigate the structural changes of the following formulations: F2 at 278 K and after being heated to 370 K (following a THz-TDS experiment); F4 at 278 K and after being heated to 410 K in glass vials in a dry heat block. We also analysed BSA powder  as received from the supplier. All BSA formulations were dissolved in dHM−1 cm−1 .2O and diluted to a concentration of 1 μm, calculated using the extinction coefficient of 207,360 M−1 cm−1 , l the path length (mm), c the molar concentration (M) and n the number of residues (583 amino acids for BSA and 1330 for mAb1).Samples were analysed in a 1 mm cuvette at a temperature of 303 K. CD spectra were acquired using a JASCO J-810 spectropolarimeter . Spectra were recorded over the spectral range of 250–190 nm, with a resolution of 0.5 nm, a continuous scan at 50 nm min2.5FTIR was used to examine the change in the secondary structure of neat lyophilised BSA powder at 278 K. F2 was analysed at 278 K and after being heated to 370 K. F4 was analysed at 278 K and after being heated to 410 K. F6 was analysed at 278 K and after being heated to 330 K. F7 was analysed at 278 K and after being heated to 370 K.−1. At least four spectra were measured for each formulation. The FTIR spectra of the pure excipients were recorded and subtracted from each sample spectrum, by a linear subtraction scaled to the excipient peak at 851 cm−1. The recorded spectra were normalised based on the total area under the curve. To estimate the secondary structure composition, each spectrum was smoothed using a Savitsky-Golay derivative function fitted over 14 cm−1 and the second derivative of the amide I region from 1590 to 1620 cm−1 was calculated. Ten Gaussian peaks were fitted to the second derivative spectrum and the ratio of the peak areas compared to the total area under the curve was used to estimate the secondary structure content  using an agate mortar, and pressed into 7 mm diameter self-supporting disks using a load of 10 tons. FTIR spectra were acquired using a Cary 680 FTIR spectrometer  by co-averaging 120 scans and at a resolution of 1 cm content .2.613C CP-MAS spectra were acquired using a Bruker AVANCE 400  equipped with a Bruker 4 mm CP/MAS 1H/X BB probe at room temperature, operating at a magic angle spinning (MAS) rate of 12 kHz together with the SPINAL64-proton decoupling pulse sequence .Solid-state nuclear magnetic resonance spectroscopy was used to investigate the structural changes of the unheated (278 K) and heated (370 K) samples of F2, unheated (278 K) and heated (410 K) samples of F4, unheated (278 K) and heated (330 K) samples of F6, and unheated (278 K) and heated (370 K) samples of F7. sequence  during a1H spin lock pulse time 1H pulse with 13C detection via CP. For each sample eight individual time points t were acquired .Proton spin-relaxation times in the rotating frame A is a correction factor. 13C spectra were externally referenced to the methylene signal of adamantane (δ = 38.48 ppm).To obtain 2.7The THz-TDS spectra were acquired using the methodology introduced previously . In orde2.8−1) and cooled at a rate of 3 K min−1 from room temperature to approximately 243 K. The samples were subsequently heated at a rate of 10 K min−1 to 295 K and then at 5 K min−1 to 373 K. The modulation frequency was 0.006 K s−1. The temperature and heat flow of the instrument were calibrated using indium  was used to determine the calorimetric glass transition temperature  see , support−1) of the FTIR spectrum showed an asymmetric feature centred at approximately ∼1658 cm−1, , the To investigate the structural changes on the molecular scale, When comparing the spectrum of the formulation with the one of the pure protein, no significant chemical shift differences can be observed that could imply any major changes in the structure of the protein. In contrast, the signals of the anomeric carbon atoms were clearly shifted. This can be explained by the formation of an amorphous structure of the sugar in the buffer upon freeze-drying compared to the crystalline structure of the sugar in the physical mixture. Additionally, the signal lineshapes of histidine and sucrose were found to be significantly sharper in the physical mixture compared to those observed for the formulation. This indicates phase separation of the individual components. The broad signal linewidths of both sugar and protein signals in sample F2 indicate that upon lyophilisation both components interact stronger with each other. When comparing the individual samples of lyophilised heated and unheated formulations with and without the addition of polysorbate, no significant chemical shift changes were apparent as a result of the heating or the addition of polysorbate see .Previous studies have shown that the investigation of f sugars . By comp nm (T1) . Equal rThe values of e radian . In the e radian .The individual formulations of heated and unheated BSA and buffer with and without the addition of polysorbate show no significant differences in their relaxation times. The  and BSA  are the The terahertz data further confirmed the information from the ssNMR measurements regarding the miscibility of sugar and protein phases as discussed above. There was no indication from the terahertz data that any phase separation had taken place .13C CP NMR data to detect potential structural changes in the heated and unheated samples of formulations F6 and F7 based on the acquired spectra  . Howeverbilities . However413C CP-MAS. A spectral analysis of the formulations showed no major chemical structural changes of the protein structures after heating. NMR relaxation time measurements of We have examined lyophilised BSA formulations (F1-F4) and lyophilised mAb formulations (F5-F7). By performing temperature variable THz-TDS experiments we studied the structural dynamic properties of these formulations. A monotonous increase of absorption coefficient with temperature was observed for F4, F5, and F6, while the absorption coefficient plateaus at high temperatures for F1, F2, F3, and F7. All the formulations examined exhibit three temperature regimes, with a distinct None.


Anopheles spp. Feeding alternatives to fresh blood are thus a priority for research, outdoor large-cage trials and control interventions. Several artificial meal compositions were tested and Anopheles oogenesis, egg laying and development into the next generation of adult mosquitoes were followed. We identified blood-substitute-diets that supported ovarian development, egg maturation and fertility as well as, low progeny larval mortality, and normal development of offspring into adult mosquitoes. The formulated diet is an effective artificial meal, free of fresh blood that mimics a vertebrate blood meal and represents an important advance for the sustainability of Anopheles mosquito rearing in captivity.Mosquito breeding depends on the supply of fresh vertebrate blood, a major bottleneck for large-scale production of  Most vector mosquitoes are anautogenous which means that females require a vertebrate blood meal for egg production and development4. A major bottleneck for establishing effective mosquito breeding in captivity is that production methods depend on a supply of blood from different animal sources and its quality is often variable. Current mosquito laboratory rearing strategies use as blood sources sedated or restrained live animals  or human blood. Nevertheless, foreseeing the urgent need to produce mosquitoes on a large scale, the use of large quantities of blood constitutes a drawback due to ethical concerns and logistical issues associated with demanding safety regulations. In addition, the mass rearing of mosquitoes requires a specialized animal care facility, qualified personnel, and an efficient feeding system. These facts might result in a significant hindrance since local regulations, ethical concerns, and infrastructure vary considerably between different countries. Taken together, these limitations are prompting research directed at the development of an artificial meal capable of mimicking blood in terms of producing viable mosquito eggs.Malaria elimination and the current rise of other vector-borne diseases has led to the development of several innovative mosquito control methodsin vivo with limited success in comparison to a standard vertebrate blood meal8. Successful artificial diets for vector mosquitoes, must fulfil the following requirements: (1) female mosquitoes must fully engorge when feeding, (2) the artificial diet must allow vitellogenesis to occur, (3) it must result in large egg batches, and (4) the offspring fitness should be comparable to wild mosquitoes9. Until now, little is known about artificial meals for Anopheles spp. but several studies have been published for Aedes mosquitoes. Alternative vertebrate blood-free meals for Aedes mosquitoes must supply an energy source for mosquitoes to feed (e.g. ATP9), a protein source essential for egg maturation10, carbohydrates for energy consumption, and amino acids (aa)11 that are vital for egg production. In fact, the aa composition is one of the major limiting factors of female mosquito fertility as this depends on the blood source12. Besides proteins, a blood meal might also provide lipids, particularly cholesterol13 for egg production improvement. All of these components are also probably necessary for meals targeted to Anopheles mosquitoes.Artificial diets based on the rich nutrient content of human blood have been shown to prompt female mosquito oogenesis and fertility 14. GPCRs are a large family of cell surface proteins. At least 276 receptor genes exist in the Anopheles genome, many of which are orphans and have currently uncharacterised functions15. Conserved sequence homologues of mosquito GPCRs exist in humans and their activating peptides circulate freely in blood and regulate a diversity of physiological functions including energy metabolism and reproduction. This means that during mosquito blood feeding it is likely that interactions between mosquito GPCRs and putative vertebrate peptides may occur.Insect reproduction and nutrient metabolism are also regulated by a series of neuropeptides many of which act through the activation of heterotrimeric GTP-binding protein (G protein)–coupled receptors in the presence of an internal or external stimuli17. The mosquito genome contains orphan receptor genes that have a similar sequence and may be functional homologues of some vertebrate GPCRs. The exposure of mosquitoes to human GPCR-activating peptides when they take a blood-meal raises interesting questions about co-evolution of protein-protein interactions and cross-regulation of physiological systems. In the present study we tested the hypothesis that human GPCR ligands in blood, potentially by binding to mosquito GPCRs, can stimulate egg development and viability when they take a blood meal. To test this hypothesis we formulated an artificial blood free meal for female Anopheles mosquitoes and supplemented it with physiological concentrations of several different human GPCR ligands. The effect of the formulated diet on egg development, fecundity and egg viability was compared with the vertebrate fresh blood meal. The study highlights the potential of the largely neglected field of co-regulatory mechanisms of host – vector physiology.The insect and human GPCR systems have recently been characterised using comparative genomics approaches18, luteinizing hormone releasing hormone (LHRH), which stimulates the release of luteinizing hormone (LH) and follicle-stimulating hormone (FSH) and triggers ovulation in females19 and melatonin (MT) which regulates circadian rhythms of feeding20 and peaks in the blood at dawn ; Ligands of Class B GPCRs (a.k.a. Secretin-GPCRs) glucagon-like peptide 1 (GLP1), glucagon-like peptide 2 (GLP2) and vasoactive intestinal peptide (VIP) that regulate feeding behaviour21, gut motility24, glucose and insulin metabolism26 and parathyroid hormone (PTH), calcitonin (CT) and corticotrophin releasing hormone (CRH) which regulate ion metabolism and the stress response in humans and other vertebrates and also indirectly affects feeding behaviour31; and of Class C GPCRs (a.k.a Glutamate GPCRs) the Glutamate and ɣ-aminobutyric acid (or GABA) which are two important neurotransmitters that stimulate feeding32. Two fish peptides (CT and LHRH) were also tested as they are potent activators of the human peptide receptors and have similar functions to their human orthologues34. No potential activity or physiological effect of the selected human GPCR-ligands in mosquitoes is known.Candidate molecules that circulate in human blood plasma and that stimulate different GPCRs were selected based on, a) their involved in the regulation of reproduction and nutrient metabolism in humans and b) the identification of orphan GPCRs in the mosquito genome that are sequence orthologues of human receptors Table . Human lin vivo for their capacity to trigger vitellogenin (Vg) transcription, a molecular marker of oogenesis initiation in the female mosquito fatbody35  only 6 (P1 to P6) induced up-regulation of Vg expression 24 h post-injection  providing amino acids, vitamins and carbohydrates (based on DMEM tissue culture medium ref. 12–604 F from Lonza) or to a rich liquid diet (r-liq_diet), that consisted of i-liq_diet supplemented with: a) a phagostimulant (ATP), b) proteins (BSA) essential for egg maturation and c) cholesterol . By including fertility and fecundity as well as initiation of oogenesis it was possible to directly establish the effect of the diet on successful egg production or egg laying. Fully engorged mosquitoes were maintained under optimal conditions  and egg laying observed 48 hours post-feeding. The egg number was counted 72 hours post-feeding  eggs whereas those fed on r-liq_diet laid on average 25 (±5) eggs per female. The best egg laying rates were achieved with r-liq_diet + P1 (hGLP1) (26 (±11) eggs per engorged female). Females fed on r-liq_diet + P5 (hCT) laid the lowest average number of eggs (n = 10) and this was in line with the significant reduction in percentage of egg development recorded Fig. . The datMosquito fitness is a determinant factor for the success of a mosquito colony when they are released into the wild. Colonies from each diet were maintained under standard insectary conditions, and the life cycle was followed for one generation. Larvae, pupae and adult mortality were recorded. Offspring from females fed on r-liq_diet + P2 (hGLP2), P3 (hPTH) or P6 (hGABA) showed better performances  Fig.  when com10) in which artificial blood meals only showed relative success in Aedes mosquitoes, but were of limited or no-success when applied to Anopheles mosquitoes39. Recently a successful plasma-based artificial meal was described for Anopheles mosquitoes40 but lower feeding rates and estimated reproductive potential were obtained relative to the blood-fed control. Our results demonstrate that the r-liq_diet has a similar or superior effect on mosquito fitness relative to the standard vertebrate blood meal. Diet supplementation with vertebrate peptides affected different aspects of the female mosquito physiology and the progeny suggesting that they are also biologically active in the mosquito and interfere with reproduction and fitness. The fact that human calcitonin and salmon calcitonin reduced mosquito fecundity is intriguing and novel and suggests that crosstalk between the vertebrate peptides exist as they modify the physiology of the female mosquito. Human and salmon calcitonin are two small peptides of the same family that share 50% amino acid sequence identity and the fish peptide is a more potent activator of the human calcitonin receptor than the human peptide42. In vertebrates, calcitonin regulates mineral metabolism during pregnancy and lactation and peptide levels increase in the circulation. However, the reason why these peptides decrease mosquito fecundity is currently unknown. So far, no receptor that interacts with human or salmon CT has been identified in the malaria mosquito. Nonetheless, the identification of a molecule with the potential to decrease mosquito fecundity provides the basis for the design of more effective drugs in programs to reduce and control mosquitoes or other insect populations.Except for the r-liq_diet + P5 (hCT), the results obtained from the other dietary groups were similar to the blood fed colonies, showing a considerable advance over published studies (reviewed inAnopheles species r-liq_diet (with no peptide supplementation) was administrated to A. stephensi and A. aquasalis female mosquitoes using a similar procedure to that described above and egg production assessed 24 hours post-feeding. Developing eggs were identified in 70% to 93% of the A. stephensi females and 33% to 35% of the A. aquasalis females and the number of eggs per female was 53 ± 10 and 46 ± 27, respectively.As a proof of principal and to test the capacity of the formulated fresh-blood-free diets to trigger egg development in other Anopheles mosquitoes that mimicked a standardized vertebrate blood meal. The fresh-blood-free diet formulated stimulates oogenesis and egg production and has a similar or superior effect on mosquito fitness relative to a standard vertebrate blood in Anopheles coluzzii and we reveal it can also be used to feed other anopheline species. Supplementation of the blood-free diet with the vertebrate peptides that activate GPCRs regulating reproduction and metabolism reveals that they modify mosquito physiology. The putative mosquito GPCRs activated by the vertebrate peptides remain to be characterized. Of the tested human peptides, P2 (hGLP 2), had the most notable effect when it was introduced in the blood-free artificial diet and it significantly increased VTG expression, mosquito egg production and offspring fitness relative to blood-fed mosquitoes. P2 is a 33-amino acid peptide present in enteroendocrine L-cell and released in response to nutrient intake and it stimulates cell proliferation, inhibition of apoptosis and proteolysis in the small and large intestine in human24. It belongs to a family of peptides with functions in the gastrointestinal (GI) tract, carbohydrate metabolism and appetite regulation44. The effect of human or other vertebrate GLP2 peptides in invertebrates has not yet been explored. In contrast, P5 (hCT) had an inhibitory role on mosquito reproduction. The outcome of the study indicating potential co-evolution of protein-protein interactions and physiological systems between species that interact (eg. host – parasite/vector) remains to be further explored. The use of the artificial fresh-blood-free meal herein described for mosquito rearing will help reduce costs, effort and eliminate live animal use for mosquito culture opening-up new opportunities for vector-borne diseases control.The availability of a successful blood substitute diet will allow mass production of anautogenous mosquitoes without the need for costly animal care facilities or blood or plasma supply. The development of chemically well-defined artificial diet to provide a reliable and consistent nutrition to adult mosquitoes is a breakthrough for mass rearing of mosquitoes. Herein we described a formulated diet for anautogenous female Anopheles coluzzii (former Anopheles gambiae M form) Yaoundé strain were used. The peptides calcitonin (from human), calcitonin , glucagon-like peptide 1 [1-37aa]  trifluoroacetate salt, and glucagon-like peptide 2 [1-33aa] (human) ammonium acetate salt were purchased from Bachem (Germany). The peptides parathyroid hormone (from human), oxytocin (from human), kisspeptin 10 (from human), melatonin, and neuropeptide Y  were purchased from Tocris .Except otherwise indicated, all reactions were performed at room temperature (20 °C), reagents were purchased from Sigma-Aldrich Corporation , and female mosquitoes of A. coluzzii (Yaoundé line) and Anopheles stephensi. Anopheles aquasalis were obtained from a colony at the Entomology Department Insectary of the Fundação de Medicina Tropical Dr Heitor Vieira Dourado (FMT-HVD) , that were derived from a colony established in 199545. Mosquitoes were maintained under standard insectary conditions of 26 ± 1 °C, 75% humidity and a 12 h:12 h light:dark cycle. Adult mosquitoes were fed on 10% glucose solution ad libitum until the day before feeding trials.All animal experiments were carried out in strict accordance with the Portuguese law and guidelines for the use of laboratory animals. The protocols used were approved by Direção-Geral de Veterinária, Ministério da Agricultura do Desenvolvimento Rural e das Pescas, Portugal . Mosquitoes were obtained from a laboratory colony of Mus musculus), obtained from the IHMT Animal house, were intraperitoneally anesthetized with 20% Imalgène 1000  and 10% Rompun . Female mosquitoes fed directly on healthy female CD1 mice for 30–45 min, with regular monitoring to verify that mice were anesthetized. Unfed mosquitoes were removed and fully engorged mosquitoes were kept at 26 ± 1 °C, 75% humidity. When needed, a cardiac puncture was performed on anesthetized mouse to collect 1 mL of blood for artificial blood feeding assays.Female CD1 mice  in PBS. Samples were washed twice with 0.5% Triton in PBS and incubated with 250 µM Nile Red  for one hour in the dark. Samples were washed twice with 0.5% Triton in PBS and the slides were mounted by using Vectashield with dapi  and analyzed using a Leica TCS SP5 laser scanning confocal microscope .The ovaries of 46. PCR reactions were carried out for a 10 µl final reaction volume containing 1.5 mM MgCl2 , 0.2 mM dNTPs , 0.25 µM of each gene specific primer pair and 0.5 U of DreamTaq DNA Polymerase  and the amplification products analysed on agarose electrophoresis gel.Total RNA from female fatbodies was isolated using the TRI Reagent protocol and treated with 1 U DNase for 1 min according to the manufacturer’s instructions to eliminate genomic DNA contamination. DNase I treated total RNA  was denatured at 70 °C for 10 min, quenched on ice for 5 min and used for cDNA synthesis in a 20 µl final reaction volume containing 10 µL of 2 × RT buffer mix, 1 µL of 20 × RT enzyme mix , and nuclease-free water. cDNA was synthesized for 60 min at 37 °C followed by 5 min at 95 °C to stop the reaction and hold at 4 °C. The quality and quantity of the cDNA produced was assessed by PCR amplification of the ribosomal protein S7 unit using the following protocol: 95 °C for 3 min; 35 cycles of 95 °C for 30 sec, 60 °C for 30 sec, 72 °C for 30 sec, followed by 72 °C for 5 minutes2 (coefficient of determination) were calculated for each target gene and transcript expression was normalized using ribosomal S7 subunit as reference gene.Quantitative Real-time PCR (q-RT-PCR) analysis was used to quantify the expression of Vitellogenin-1 precursor (Vg), a protein biomarker of mosquito oogenesis initiation. Vg expression levels in the fatbodies were quantified using the ΔΔCT method a) after a blood meal, b) after microinjection with the different peptides, and c) after being fed on the various artificial diets. Primers used are described in Table A. coluzzii mosquitoes were cold-anaesthetized and injected intrathoraxically with 69 nL of 10 µM peptide. For each experiment, a control group injected with PBS was included. Injections were performed using a microinjection system . The complete list of the peptides used and respective abbreviations are presented on Supplementary Information, Table Two-day-old female Mosquitoes (n = 30 approximately) were kept inside paper cups covered with a net. Each cup had a glass feeder on top connected to 2 plastic tubes for water inlet and outlet and temperature within the multiple cylindrical water-jacked plastic was kept at 37.5 °C by a constant water flow supply. Parafilm® was stretched across the mouth of the feeder and 1 mL of a pre-warmed meal was pipetted into the glass feeder. Peptides were tested at a 10 µM final concentration. Mosquitoes were allowed to feed for 60 minutes. Unfed mosquitoes were removed and fully engorged female mosquitoes were kept at 26 ± 1 °C under 75% humidity.The i-liq_diet consisted on Dulbecco’s modified Eagle’s medium . The formulation of the enriched artificial meal (r-liquid diet) is listed on Supplementary Information, Table Fatbodies were collected from pools of 30–35 mosquitoes. Tissues were dissected, transferred to RNAlater  and stored at −20 °C until RNA extraction. For the blood meal assays, mosquito fatbodies were collected at different time points . Fatbodies from females feed on 10% glucose at the same time points were used as controls. For the peptides screening experiment and artificial diet assays, mosquito fatbodies were dissected 24 h post-injection and 24 h post-feeding, respectively.Experimental feeding of mosquitoes using blood, i-liquid diet, r-liquid diet  mortality was checked daily and dead stages were removed. Although there was abundant food, the dead larvae could have been cannibalized. As the larvae resulting from females fed with different diets were in similar conditions, we assume that if it occurs, cannibalism would be similar in all groups. The number of male and female adults for each diet was recorded by the end of the experiment when all pupae have developed into adult mosquitoes. Dead adults  were counted and removed daily. Adults were maintained on water with 10% glucose solution ad libitum until the day they died. The experiment ended when all pupae developed into adult mosquitoes in all diets. Three independent replicates were performed for each diet.Eggs were collected into a water tray (23 × 15 × 6 cm) and mosquito development was followed until all pupae have emerged, for each diet. After hatching, a strict similar larval feeding regime was applied to all trays, using grounded fish food (1:1 ASTRA pond-fish-sticks and TetraMin flacs). Trays were fed approximately 13 mg every day. Water levels were kept constant throughout the experiment by addition of dHData are presented as the mean ± standard deviation of at least three independent experiments (except where otherwise indicated), and the corresponding standard deviations in histograms are represented by error bars. The Student’s t test was used to compare independent groups when data followed a Gaussian distribution, and differences were considered significant when P ≤ 0.05. The Fisher’s exact test was used to compare the differences on proportions among distinct diet-fed groups. The statistical analysis was performed on GraphPad Prism6 software.Supplementary Information


Wall-bounded shear flows transitioning to turbulence may self-organize into alternating turbulent and laminar regions forming a stripe pattern with non-trivial oblique orientation. Different experiments and flow simulations identify oblique stripe patterns as the preferred solution of the well-known Navier-Stokes equations, but the origin of stripes and their oblique orientation remains unexplained. In concluding his lectures, Feynman highlights the unexplained stripe pattern hidden in the solution space of the Navier-Stokes equations as an example demonstrating the need for improved theoretical tools to analyze the fluid flow equations. Here we exploit dynamical systems methods and demonstrate the existence of an exact equilibrium solution of the fully nonlinear 3D Navier-Stokes equations that resembles oblique stripe patterns in plane Couette flow. The stripe equilibrium emerges from the well-studied Nagata equilibrium and exists only for a limited range of pattern angles. This suggests a mechanism selecting the non-trivial oblique orientation angle of turbulent-laminar stripes. It is known from experiments and simulations that stripes of alternating laminar and turbulent regions can form in plane Couette flow. Here the authors find an exact invariant solution which captures the detail of the spatial structures of these patterns and identifies their origin. Remarkably, the flow may further self-organize into a regular pattern of alternating turbulent and laminar stripes12 also observed in Taylor-Couette17 and channel flow22. The wavelength of these stripes or bands is much larger than the gap size, the only characteristic scale of the system, and they are oblique with respect to the streamwise direction. Consequently, both the large-scale wavelength and the oblique orientation of turbulent-laminar stripes must directly follow from the flow dynamics captured by the governing Navier–Stokes equations. Experiments and numerical flow simulations reliably generate stripe patterns but a theory explaining the origin of the pattern characteristics is still missing. This is related to the Navier–Stokes equations being highly nonlinear partial differential equations, whose theoretical analysis remains challenging.The complex laminar-turbulent transition in wall-bounded shear flows is one of the least understood phenomena in fluid mechanics. In the simple geometry of plane Couette flow (PCF), the flow in a gap between two parallel plates moving in opposite directions, the transitional flow spontaneously breaks the translational symmetries in both the streamwise and the spanwise direction causing regions of turbulent and laminar flow to coexist in space23. Recent advances in numerical methods not only allow the simulation of flows but also the construction of exact equilibria, traveling waves and periodic orbits of the fully nonlinear 3D Navier–Stokes equations. These exact invariant solutions are believed to be embedded in a strange invariant set generating the chaotic dynamics of turbulent flow in the system’s state space24. Consequently, a picture emerges where turbulent flow is described as a chaotic walk between dynamically unstable invariant solutions which together with their entangled stable and unstable manifolds support the turbulent dynamics25. Exact invariant solutions are thus “building blocks” which resemble characteristic flow structures that are observed in flow simulations and experiments, when the dynamics transiently visits the exact invariant solution. A theoretical explanation of oblique stripe patterns within this dynamical systems description requires the as yet unsuccessful identification of exact invariant solutions resembling the detailed spatial structure of turbulent-laminar stripes, including their oblique orientation and large-scale periodicity.It was the early observation that an oblique turbulent-laminar pattern can be the preferred solution of the Navier-Stokes equations that motivated R. Feynman to stress the lack of “mathematical power [of his time] to analyze [the Navier–Stokes equations] except for very small Reynolds numbers”28. Like most invariant solutions of PCF found since then29, this so-called Nagata equilibrium is periodic in the streamwise and spanwise directions, repeating on the scale of the gap height. Such periodic solutions do not capture the coexistence of turbulent and laminar flow on scales much larger than the gap height and consequently cannot underly oblique stripes. Spanwise localized invariant solutions31 and doubly localized invariant solutions in extended periodic domains32 show nonlinear flow structures coexisting with laminar flow but no known invariant solution captures oblique orientation or suggests a pattern wavelength matching oblique stripe patterns.Nagata discovered the first invariant solution of PCFWe present a fully nonlinear equilibrium solution of PCF Fig. , resembl33. The numerical domain is periodic in two perpendicular dimensions along the plates (x and z) with periods of  =  in units of half the gap height. No-slip boundary conditions are imposed at the moving plates located at y = ±1. Inversion symmetry with respect to the domain center is enforced. The relative plate velocity and the associated base flow are tilted against the periodic domain dimensions at an angle of θ = 24° following Barkley and Tuckerman7. At Reynolds number Re = Uh/ν = 350, with the relative plate velocity 2U, gap height 2h and kinematic viscosity ν the flow organizes into self-sustained turbulent-laminar stripes, as shown in Fig. For direct numerical simulations (DNS) of oblique stripe patterns in PCF we use a parallelized version of the pseudo-spectral code CHANNELFLOW31. Specifically, the Nagata equilibrium was periodically extended in the spanwise direction for n = 9 periods, then sheared to align the velocity streaks with the base flow in the tilted domain and finally multiplied with a scalar window function equal to a scaled mean field of turbulent kinetic energy of the oblique stripe pattern from several DNS runs. Using the constructed velocity field as initial guess, Newton iteration yields the stripe equilibrium  =  , a symmetry also found for the mean flow of stripe patterns8. The sinusoidal amplitude modulation, the captured overhang regions and the inversion symmetry, all characteristic of the pattern’s mean flow, together with the visual comparison in Fig. The stripe equilibrium shares the small-scale wavy modulation with the Nagata equilibrium but also shows the large-scale oblique amplitude modulation of the turbulent-laminar stripe pattern. The amplitude modulation between the high-amplitude turbulent region and the low-amplitude laminar region of the equilibrium on average follows a sinusoidal profile closely resembling the pattern mean flow found in DNS at identical boundary conditions6 directions are attracting. Consequently, the dynamics is attracted towards the stripe equilibrium from almost all directions. The exponential growth rates ωr along the unstable directions are small compared to typical turbulent time scales in the flow, given by the oscillatory frequencies ωi in the spectrum of eigenvalues , intersects with the group of translations of a tilted rectangular domain, with periodicity , ifAt small scales, the stripe equilibrium reflects the wavy streak structure of the spatially periodic Nagata equilibrium. This suggests that the stripe equilibrium emerges from the Nagata equilibrium in a bifurcation creating oblique long-wavelength modulations. To identify this pattern-forming bifurcation numerically, the Nagata equilibrium needs to “fit” in an extended tilted periodic domain aligned with the wave-vector of the neutral mode creating the oblique long-wavelength modulation. The Nagata equilibrium indeed not only satisfies the streamwise and spanwise periodic boundary conditions of the commonly studied minimal flow domain but may also be periodic with respect to selected larger tilted domains. The symmetry group of the Nagata equilibrium, including all combined discrete translations over streamwise-spanwise periods  =  considered so far, the geometric condition  =  at which the Nagata equilibrium does not exist. Keeping Lz = 40 and choosing winding numbers  =  however leads to a slightly modified domain  =  in which the Nagata equilibrium with  =  exists, as displayed in Fig. ReI = 164. Its neutrally stable long-wavelength eigenmode, whose eigenvalue changes sign at ReI, is plotted in Fig. is satisfied for mentclass2pt{minimves Fig. . For thementclass2pt{minimθ, Lx)I =  to the parameters θ with the Reynolds number linear in θ, such that Lx(θ) = Lz/(n tan(θ)) for n = 9 and constant domain width of Lz = 40. The resulting bifurcation diagram demonstrates that the Nagata equilibrium Using parametric continuation we follow both the periodic Nagata equilibrium  at Re = 225 in Fig. The primary bifurcation is of pitchfork type, subcritical, forward in ion Fig. .θ, Lx)II =  along solution branch Re, θ, Lx) = . The amplitude profiles of single-pulse and double-pulse equilibria show that the single-pulse with period Lz = 40 has large modulations at Re = 350 and θ = 24°, while the modulations in the double-pulse equilibrium are reduced (Fig. λ in the range of 40 ≤ λ ≤ 60 at Re around 35010. In summary, two bifurcations successively break discrete translation symmetries of the Nagata equilibrium to create the stripe equilibrium solution.A secondary pattern-forming bifurcation occurs at (Re,  332, 23.°, 10.3 a 332, 23.°, 10.3 aced Fig. . This agz = 0 and z = 20. For the stripe equilibrium Small-scale velocity streaks carry a wavy modulation which has a streamwise phase that is clearly evident when plotting the streamwise vorticity at the midplane. We illustrate streamwise wave fronts by lines connecting vorticity maxima or minima in the spanwise direction (red/blue lines in Fig. θ = 24° against the spanwise direction and oriented exactly along the pattern wave vector (35 limits the range of angles at which oblique stripe patterns can exist.In the turbulent region of equilibrium θ = 24°. Continuation in θ for fixed pattern wavelength λ = 40 determines the range in θ for which the stripe equilibrium exists. At Re = 350, the equilibrium exists in the range 16.5° ≤ θ ≤ 26.1° before it undergoes saddle-node bifurcations (Fig. λ = 40 are observed in simulations8. At lower Re, the range of allowed pattern angles shrinks and shifts towards larger values (Fig. θ for varying Re aligns with simulations and experiments of turbulent-laminar stripes8. The finite existence range of the fully nonlinear exact equilibirum solution of the 3D Navier–Stokes equations thus appears to select the non-trivial angle at which self-organized turbulent-laminar stripes emerge in transitional shear flows.We identified equilibrium λ = 40 is limited to oblique orientations in a finite range of pattern angles around θ = 24°. The existence range agrees with simulations and experimental observations of turbulent-laminar stripes. This suggests a selection mechanism for the pattern angle and provides a route towards explaining why turbulent-laminar stripes are oblique.Experimental and numerical observations of self-organized oblique turbulent-laminar stripes in wall-bounded extended shear flows suggest the existence of exact invariant solutions underlying these patterns. We present the first such invariant solution of the fully nonlinear 3D Navier–Stokes equations in plane Couette flow that captures the detailed spatial structure of oblique stripe patterns. The stripe equilibrium emerges from the known Nagata equilibrium via a sequence of two pattern-forming bifurcations with long-wavelength oblique neutral modes. The existence of the stripe equilibrium at wavelength peer review fileDescription of Additional Supplementary FilesSupplementary Data 1


In this paper we explore the relationship between the Visual Evoked Potential (VEP), a component of the electroencephalogram elicited by visual stimuli, and cognitive functions in children growing up in an urban slum in Bangladesh. VEPs in response to pattern-reversing checkerboards were collected in 6 month-old-infants (n = 91) and 36-month-old children (n = 112). We examine variation in the amplitude and latency of the first positive component, the P1, of the VEP in relation to cognitive scores on the Mullen Scales of Early Learning and the Wechsler Preschool and Primary Scale of Intelligence. We also examine whether children’s caregiving experiences prior to the neuro-cognitive assessment explain variation in the P1 of the VEP. We find that the P1 amplitude of the VEP is related to concurrent cognitive performance in each respective cohort. We also find that the P1 amplitude at 6 months is prospectively associated with cognitive outcomes at 27 months, and the P1 amplitude at 36 months is prospectively associated with children’s IQ at 60 months. We find no associations between caregiving experiences and variation in the P1 of the VEP at 6 months, yet caregiving experience do explain variation in the P1 amplitude at 36 months. Caregiving experiences also explain variation in children’s concurrent and prospective cognitive functioning. The VEP may be used as a biomarker to index the neurobiological embedding of early adversity, which in turn may impact children’s cognitive functions. Numerous studies from both high and low-income countries have found that part of the association between poverty and poor child outcomes is driven by characteristics of the home environment including the amount of cognitively stimulating activities and language a child is exposed to5. Moreover, characteristics of the home environment have been shown to mediate some of the effects of poverty on neural outcomes that may underlie disparities in cognition, such as lower hippocampal volumes and dispersed electrophysiological activity during selective attention7. Finally, a psychosocial intervention study found that a parent-focused intervention targeting family stress regulation, responsive parenting, language use, and facilitation of child attentions was associated with altered neural responses and improved selective attention highlighting the importance of children’s social family environment for both cognitive and neurodevelopmental outcomes8. The current study utilizes the visual evoked potential (VEP) to interrogate brain functioning in a sample of children growing up in impoverished homes in an urban slum in Dhaka, Bangladesh.Growing up in a resource-poor home is a known risk factor for compromised developmental outcomes across a range of domains including executive functions, language, and memory9. The VEP is recorded non-invasively using scalp electrodes and the ease of assessment has made the VEP widely used in both clinical practice and research9. The VEP response can be observed early in life and becomes relatively mature by the first year10. The most commonly used quantification of the VEP is extraction of the amplitudes and latencies of the first three peaks, namely the first negative peak (N1), the first positive peak (P1), and the second negative peak (N2). The two later peaks, especially the P1, are generally believed to reflect higher-order visual processes compared with the early N1, which reflects the activity of afferent fibers when the sensory signal travels from the eye to the visual cortex10. Interindividual variation in the amplitude and latency of the VEP peaks has been examined mostly in relation to visual processing11, but may also reflect more global neural “efficiency” or “maturation”12. The VEP, recorded shortly after birth has, for instance, been used to make predictions about neurological and cognitive outcomes after pre- and perinatal complications including intrauterine growth restriction, maternal drug misuse during pregnancy, prematurity, and birth asphyxia14. Studies of children, adolescents, and adults have also observed relationships between VEP latencies and amplitudes and IQ, such that a higher IQ is related to faster latencies and larger amplitudes in the P1 and N2 components18.The VEP is an exogenous component of ongoing EEG, generated in the visual cortex in response to visual stimulation14. Emphasizing the importance of the early environment for the maturation of the VEP response, a recent study in rodents found that early impoverishment (reduced sensory and motor stimulation) led to alterations in the VEP19, yet no study has followed up on this association in humans20. Building on the previously shown associations between the VEP and cognitive outcomes in children exposed to poverty and related risks, and the evidence for associations between characteristics of early stimulation (enrichment) and the VEP in rodents, the current study examines the hypothesis that psychosocial exposures related to children’s caregiving experiences predict variation in the VEP, which in turn predicts variation in children’s early cognitive outcomes  cohort N = 130) were 6 months old at the time of the VEP and first cognitive assessment and underwent a second cognitive assessment around the age of 27 months. Children from the “Performance of Rotavirus and Oral Polio Vaccines in Developing Countries” (PROVIDE) cohort (N = 130) were 36 months old at the time of the VEP and first cognitive assessment and underwent a second cognitive assessment at 60 months. Exclusion criteria limited the sample to infants and children born > = 34 weeks gestation, with no history of neurological abnormalities or traumatic brain injury, no known genetic disorders, and no known visual or auditory delays or impairments. Descriptive statistics are shown in Table 30 were 6Visual evoked potentials (VEPs) were acquired as part of a larger test battery that included resting state EEG and event-related potentials. During data collection children were seated on their caregiver’s lap in a dimly lit room in front of a monitor with an attached Tobii X2-60 eye-tracking system at a viewing distance of 65 cm from the screen. Pattern-reversal VEPs were recorded via an Electrical Geodesics, Inc.  system using a 128-channel high density HydroCel Geodesic Sensor Net  and amplified with a NetAmps 300 high-input amplifier. Data were sampled at 500 Hz. Presentation of the stimuli on the monitor was managed by E-Prime software . Stimuli were presented for 500 ms and the stimulus phase-reversal was driven by the infants’ visual fixation on the screen and monitored by the Tobii Eye-Tracking system such that stimuli reversal continued only as long as the infants’ gaze was fixated on the screen (minimum fixation time 100 milliseconds).9, the amplitude of the P1 was measured relative to the preceding N1 peak (P1 – N1 amplitude/latency), within a time window from 70–120 ms. This time window was selected after visually inspecting the waveform from each individual subject. The window was selected to be inclusive of the P1 for all subjects. A trial was rejected if electrode 75 (Oz) was marked bad, or if it contained eye blinks, eye movements, or high-frequency noise as determined by visual inspection of each segment. Because the number of trials included in the average may affect the degree of noise in the data22, we used an inclusion criterion of a minimum of 20 trials per subject,which was met for all subjects. The 6 months old infants viewed between 32 and 100 trials , and the 36-month-olds viewed between 40 and 100 trials . After preprocessing of the VEP data we had useable data from n = 91 6-month-olds and n = 112 36-month-olds.EEG signal processing was done offline in NetStation 4.5. The EEG data were filtered with a 0.3–30 Hz finite impulse response (FIR) band-pass filter and segmented from 100 ms before stimulus onset as the baseline to 300 ms following stimulus onset, and the segments were then baseline corrected. Automated artifact detection was applied to detect channels within each segment that had a voltage change exceeding 200 μV. The VEP data were extracted from the occipital midline electrode 75 (Oz), referenced to the vertex electrode (Cz) at acquisition, and re-referenced using the average reference. Data were averaged across all trials for each subject. As per the International Society for Clinical Electrophysiology of Vision standard23 at 6, 27, and 36 months, and using the WPPSI at 60 months. The MSEL is an interactive assessment of child development and provides a global measure of cognition (the early learning composite score) and 5 subscale scores: gross motor, fine motor, visual reception, receptive language, and expressive language. The MSEL was developed in the US, but has previously been used in low-income countries25. Local staff adapted the protocol by substituting unfamiliar images and questions with objects and examples that Bangladeshi children would recognize. Given the absence of local norms for children in Bangladesh we standardized children’s raw scores within the sample in each cohort and for each time point to obtain culturally and age appropriate standardized z-scores. The composite scores were computed as the z-score of the summed subscale raw scores.Children’s cognitive development was assessed using an adapted version of the MSEL27. It was administered at 60 months of age in the oldest cohort to avoid potential ceiling effects on the MSEL. Here we focus on the full-scale intelligence quotient (IQ) and two subscales, namely verbal IQ and performance IQ.Similar to the MSEL, the WPPSI is an interactive assessment that provides both a global and subscale assessments of children’s cognitive development. The WPPSI was developed and normed in the US, but has previously been used to assess cognitive outcomes in 5 year old children in Bangladesh28. The FCI uses items from UNICEF’s Multiple Indictor Cluster Survey as well as additional questions to assess stimulating activities that the mother, father, or an “other caregiver” engaged in with the child within the last 30 days  using the Family Care Indicators (FCI). The interviews were conducted by local, native staff. The FCI has been widely used in low and middle-income countries including Bangladesh29. Model A explored relationships between family care, variation in the P1 (amplitude and latency), and children’s global cognitive score . To test whether associations between variation in the VEP and global cognition were driven by specific subscales, an exploratory Model B substituted the global cognitive score for specific domain scores. Model fit was evaluated based on common guidelines with acceptable fit indicated by a non-significant X2 (p > 0.05), the confirmatory fit index (CFI) >0.95, the root mean square residual (SRMR) < 0.08, and RMSEA < 0.0630.The hypothesized multivariate model Fig.  was testIndirect effects through which family care may impact variation in the P1 (latency or amplitude), which in turn may impact children’s cognitive outcomes, were estimated using the MODEL INDIRECT command in Mplus. We bootstrapped 10,000 times with bias-corrected confidence intervals. Missing data on the independent variables was replaced using full information maximum likelihood estimation with robust standard errors. Only children with non-missing VEP and cognitive data were included in the analyses leaving n = 91 with 6 months MSEL outcomes, n = 74 with 27 months MSEL outcomes, n = 112 with 36 months MSEL outcomes, and n = 106 with WPPSI outcomes at 60 months.Visual inspection confirmed the prototypical VEP waveforms, including the N1, P1, and N2 pattern for all participants. Grand averages for the 6- and 36-month-olds are shown in Fig. Bivariate correlations between study variables are shown in Table In the 36-months-old children, we found that family care was positively correlated with the P1 amplitude at 36 months. The P1 amplitude at 36 months was also positively correlated with children’s concurrent cognitive composite score, and with three developmental domain scores, namely visual reception, fine motor, and receptive language. The P1 amplitude at 36 months was also correlated with full scale IQ, verbal IQ, and performance IQ at 60 months. There were no correlatons between P1 latencies and either familie care or cognitive outcomes.2(3) = 1.143, P < 0.614; CFI = 1.000; SRMR = 0.026; RMSEA = 0.000), and there was a positive association between the P1 amplitude and children’s cognitive composite score at 6 months. There were no associations between family care and either variation in the P1 amplitude or latency, or between family care and the cognitive composite score. There was also no association between the P1 latency and the cognitive composite score.The first set of models examined the hypothesized associations between family care and variation in the VEP and MSEL scores at 6 months. Model 1A, which included children’s cognitive composite score at 6 months as the outcome, showed good model fit (χ2(9) = 5.320, P = 0.806; CFI = 1.000; SRMR = 0.024; RMSEA = 0.000), yet none of the associations between variation in the P1 amplitude or latency and children’s developmental domain scores reached significance. Family care also showed no association with the either the P1 amplitude, P1 latency, or any of the developmental domain scores.The exploratory Model 1B, which included the five domain scores as outcomes instead of the cognitive composite score, showed good model fit (χ2(3) = 1.112, P = 0.338; CFI = 1.000; SRMR = 0.044; RMSEA = 0.041). In this model, we found that higher P1 amplitudes at 6 months were related to higher cognitive composite scores at 27 months. Similar to models 1A and 1B there were no relationships between family care and variation in the P1 amplitude or latency, or between family care and cognition.Model 2A Fig. , which i2(7) = 8.251, P = 0.311; CFI = 0.992; SRMR = 0.051; RMSEA = 0.049). In this prospective model, we found that higher P1 amplitudes were related to higher fine motor, visual reception, and receptive language scores. Moreover, a shorter P1 latency was associated with better fine motor skills.The exploratory Model 2B Fig. , which u2(3) = 4.942, P = 0.176; CFI = 0.945; SRMR = 0.044; RMSEA = 0.076). In this model, we observed a significant positive association between family care and the P1 amplitude. We also observed a positive association between the P1 amplitude and children’s cognitive composite score. Neither family care nor the cognitive composite score showed a significant relationship with the latency of the P1.Model 3A  = 10.542, P < 0.160; CFI = 0.974; SRMR = 0.038; RMSEA = 0.067). In this model, we found that the P1 amplitude showed positive associations with fine motor and visual reception. We also saw direct effects of family care on visual reception and receptive language, independent of the effects of the VEP. There were no associations between the P1 latency and either family care or cognition.The exploratory Model 3B  = 2.617, P < 0.455; CFI = 1.000; SRMR = 0.037; RMSEA = 0.000). Model 4A showed that the P1 amplitude at 36 months was positively related to full scale IQ at 60 months. Family care was positively associated with higher P1 amplitudes and greater P1 latencies, and there was a positive relationship between family care and full-scale IQ. There were no associations between P1 latencies and family care or full scale IQ. The indirect effect of family care on full scale IQ via variation in the P1 amplitude did not reach significance  = 3.806, P < 0.433; CFI = 1.000; SRMR = 0.041; RMSEA = 0.000) and showed a positive relationship between the P1 amplitude and children's verbal and performance IQ. More family care was associated with higher P1 amplitudes, greater P1 latencies, and higher verbal IQ. None of the indirect effects of family care on children's verbal or performance IQ via the P1 reached significance  has also been proposed to be the component of the VEP that is most closely related to cognitive functions10. We found significant positive associations between the amplitude of the P1 of the VEP and children’s concurrent and prospective cognitive composite score across four sets of models. Namely, we found that a higher P1 amplitude at 6 months was associated with higher cognitive composite scores at 6 and 27 months, and that a higher P1 amplitude at 36 months was associated with a higher cognitive composite score at 36 months and higher full-scale IQ at 60 months. In a set of exploratory analyses, we examined whether these associations were driven by specific subdomains of cognitive functions related to visual and attentional functions. Here we found that variation in the P1 amplitude at 6 months was unrelated to any specific developmental domain scores at 6 months, but prospectively associated with three developmental domain scores at 27 months, namely fine motor, visual reception, and receptive language. These findings suggest that the VEP may be related to broader developmental outcomes as opposed to being selectively related to attentional and visual functions reflected in the visual reception score. In the 36-months old children, we found that the P1 amplitude of the VEP was significantly related to concurrent visual reception and fine motor scores. The P1 amplitude at 36 months was also prospectively associated with higher verbal and performance IQ at 60 months. We saw one significant association between P1 latencies and child outcomes, namely a negative association between P1 latency at 6 months and fine motor scores at 27 months. This findings suggests that a faster P1 latency at 6 months was related to higher fine motor scores at 27 months. The finding of associations between variation in the P1 of the VEP - particularly the amplitude of the P1 - and children’s cognitive performance at all four time points supports our hypothesis that the VEP may provide a neural index of early cognitive functions.Using data from two cohorts of infants and children from Bangladesh, we examined the hypothesis that VEPs measured at 6 and 36 months were associated with concurrent and later cognitive outcomes. We focused on the P1 component because this is the most consistent feature of infants’ VEP response that while it is present from birth31. It is therefore possible that attention plays a role in the relationship between variation in the P1 and children’s cognitive outcomes. For example, infants with higher P1 amplitudes at 6 months might be better at allocating attention, which in turn facilitates the development of other high-level cognitive functions that can be detected later in life. At the neurobiological level, a larger versus a smaller P1 amplitude reflects more synchronous neural activity over the visual cortex in response to the stimulus . A large P1 amplitude could therefore reflect more focal activity around the visual cortex which, in turn, may reflect greater synaptic efficiency in this region. Focal activation and increased synaptic efficiency could be indicative of functional specialization and developmental maturation of the visual area. Moreover, the VEP is likely influenced by myelination21. Myelination occurs rapidly over the first few years of life and serves to increase conduction velocity and again, synaptic efficiency. A recent study found that rodents exposed to low levels of stimulation showed delayed maturation of VEP latencies as indicated by higher VEP latencies at P28 and P31, roughly equivalent to a human age of 33–36 months. Moreover, changes in VEP latencies were accompanied by impaired motor and memory functions, as well as structural changes in the brain reflecting delayed myelination of nerve fibers in the visual cortex19. In humans, a combined DTI and VEP study found a strong correlation between the latency of the P1 and microstructural markers of myelination/ maturation21. Although the link between myelination and the latency of a neural response such as the VEP is most clear, it could be that myelination also impacts the amplitude of the neural response. We note that the association between higher P1 amplitudes and better cognitive scores should be considered relative to children’s age. Namely, as seen in Fig. With regard to potential mechanisms linking greater P1 amplitudes to better cognitive scores, we note that a recent study found that the P1 amplitude of the VEP is a good index of infants’ spatial and sustained attention, such that enhanced spatial and sustained attention is associated with an amplified P1 peak amplitudeIn the exploratory analyses we did not see any associations between variation in the P1 of the VEP and concurrent developmental subdomain scores in the 6 months old cohort, but we did see associations between variation in the VEP at 6 months and children's domain scores for visual reception, fine motor, and receptive language at 27 months. We also observed associations between concurrent P1 amplitudes and visual reception and fine motor domain scores in the 36-months-old children, and between P1 amplitudes at 36 months and verbal and performance IQ at 60 months. These exploratory analyses suggest that associations between the VEP and children’s cognitive outcomes were non-specific, but rather driven by or reflecting broader cognitive functions. Two methodological concerns may explain the lack of findings of associations between the P1 amplitude and domain scores in the 6-month-old infants. First, the absence of an association could reflect the smaller sample size in the 6 -month-old cohort compared with the 36-month-old cohort because fewer infants had usable EEG data used to estimate the VEPs. We note, however, that P1 amplitudes assessed at 6 months did show associations with three of the five subscales at 27 months, despite the smaller sample size, possibly suggesting that the lack of findings at 6 months is not caused solely by these analyses being underpowered. Another possible explanation for the lack of associations between variation in the VEP and MSEL scores at 6 months is that we, as expected, observed less variance in performance captured by the MSEL domain scores at 6 months compared with later in development where children are assessed across more items for each domain. The MSEL may therefore not provide enough differentiation between infants at 6 months. The VEP may also be a stronger predictor of prospective compared with concurrent cognitive functions because neural changes may emerge before, and possibly contribute to, subsequent variation in behavioral outcomes.8. A psychosocial intervention study mentioned above, for instance, found that a parent-focused intervention impacted children’s neural response during selective auditory attention such that children in the parent-focused intervention group showed more selective neural responses to attended versus unattended stimuli compared with children who received a child-focused or no intervention8. Moreover, children in the family-based intervention group also showed greater improvement of selective attention suggesting that changes in the ERP may contribute to better selective attention. The fact that we only see an association between the family care and the VEP at 36 months, and not 6 months, may suggest that environmental influences on neural functioning take time to emerge. This is in line with EEG studies showing associations between socioeconomic status and EEG power in 1 year old infant32, but not in neonates33.We did not observe any concurrent associations between family care and variation in the VEPs collected in infants at 6 months of age. We did, however, see associations between family care and P1 amplitudes in the 36-month-old children. The association between family care and the VEP in the 36-months-old children is consistent with previous studies in humans relating caregiving experiences to variation in brain structure and ERP responses during auditory attentionFinally, in the 36-month-old children we explored indirect effects through which the amplitude of the P1 may impact cognitive outcomes via the effects of family care on the VEP. Only one indirect path, namely from family care to variation in the P1 amplitude at 36 months, and from the P1 amplitude to fine motor skills at 36 months reached significance. We note, however, that many of the indirect paths were approaching significance. It would therefore be interesting follow up on these indirect pathways in future research with larger samples that may enable better detection of indirect effects. Future studies may also add more age groups to further explore when the relationship between family care and P1 amplitudes begins to emerge.The findings of the current study should be considered in light of a number of limitations. First, although the sample sizes used in the four sets of models is considerable for a neuroimaging study, the sample sizes are small for SEM models. Small samples sizes may cause complex models, such as the exploratory models, to be underpowered due to the number of estimated paths. As mentioned above, this is particularly true for the 6-month-old cohort where fewer infants had usable EEG data. Second, all results should be considered correlational since neither the concurrent associations nor the prospective associations are sufficient to address causality. Examination of causal relationships would require an experimental manipulation as seen in randomized controlled trials. Although we found evidence for one indirect effect from early caregiving experience to fine motor skills via the VEP we cannot be certain about the directionality of this effect. An alternative hypothesis could be that children’s developmental status (which may correlate with the P1) may impact parenting interactions because the types of stimulating activities parents engage in with a child may depend on the child’s cognitive (or motor) abilities. Third, we have limited information about perinatal events  and although we excluded children born very preterm (< = 34 weeks gestation) or with known neurological abnormalities we cannot rule out that other perinatal complications that may correlate with both family care and the brain outcome may confound observed effects.A key aim of the current study was to explore whether the VEP can be used as an early neural marker of current and future cognitive outcomes in a community sample of infants and children living in an impoverished neighborhood in Dhaka, Bangladesh. We found consistent evidence for associations between P1 amplitudes and both concurrent and prospective cognitive functions in infants as young as 6 months. The association between the VEP and cognitive outcomes did not appear to be specific to the visual domain, but implicated visual/attention skills as well as motor and language functions.We also explored the hypothesis that early caregiving experiences may predict variation in neural responses detected by the VEP, which in turn may be associated with children’s cognitive developmental outcomes. This hypothesis was confirmed for one indirect effect whereby more frequent caregiver-child interactions were associated with a magnified P1 response (higher P1 amplitude), which in turn was associated with better concurrent fine motor skills in the 36-month-old cohort.Using the VEP as a complementary or alternative measure to cognitive functions in the assessment of children’s early development has several advantages over behavioral measures of cognition. First, the VEP may be considered a more objective assessment compared with behavioral assessments. The VEP may, for instance, be less impacted by cultural norms that can affect children’s understanding of complex instructions associated with many behavioral tasks. Moreover, a neural response like the VEP may be somewhat less impacted by subjective factors related to the person being tested  and the tester . Second, the fact that VEP predicted prospective cognitive outcomes may suggest that the VEP can be used as a screening tool to enable earlier detection of whether a child is following an expected developmental trajectory. The prospective relationships may indicate that neural changes such as altered P1 responses may predispose variation in cognitive outcomes, and that characteristics of the VEP can be used to make predictions about a child’s prospective developmental outcomes. This, in turn, would suggest that the VEP may be used to identify children who stand to benefit most from interventions to support early cognitive development. One advantage of the VEP is that it is relatively simple to assess compared with other neuroimaging tools, and thus more easily incorporated into standard clinical or research practices, even in low resource settings like urban Bangladesh. More studies are needed to confirm associations between the VEP and cognitive outcomes, and to examine when associations between the VEP and caregiving experiences emerge.


Contrary to some modeled reconstructions, our findings indicate an asymmetric LIS topography with higher ice on Keewatin Dome (~3200 m) and thinner ice in the prairies along the Plains divide (1700–2100 m) during LGM. The resiliency of icy permafrost to past warm intervals preserved relics of the LIS; these ice-marginal landscapes, now poised for thaw, should uncover more valuable clues about the conditions of the last major ice sheet on Earth.The Laurentide Ice Sheet (LIS) occupied a large part of North-America during the late Pleistocene. Determining the proper surface geometry and elevation of the LIS is of central importance to estimate global changes in sea-level and atmospheric circulation patterns during the late Pleistocene and Holocene. Despite largely disappearing from the landscape during the late Holocene, LIS remnants are found in the Penny and Barnes ice caps on Baffin Island (Canada) and ongoing permafrost degradation has been exposing relics of the LIS buried along its northern margin since the late Pleistocene. Here, we use the δ The models predict largely conflicting ice configurations, from a single dome centered near Hudson Bay7 to an ice sheet with multiple ice accumulation centers8, with significant differences in ice elevations (in the order of ±1000–2000 m in some places). These different LIS configurations translate into large uncertainties in modeling late Wisconsinan climate9 and melt-water contribution8. A reason for the large uncertainties in LIS topography is that the glacio-isostatic models are being calibrated to relative sea level curves and paleo lake shorelines  and subsequent models are adjusted as more of these data are becoming available12. However, to improve our assessment of the impacts of the LIS to global changes in climate and sea-level during late Pleistocene and Holocene , determination of its surface geometry and elevation from other methods is required, especially from actual remnants of the LIS.The maximum and recessional limits of the LIS have been defined using empirical data18O-elevation relation. This approach was used to reconstruct Holocene changes in ice surface elevation for the Greenland Ice Sheet and Agassiz Ice Cap17, with the findings used to infer an increased contribution from Greenland Ice Sheet to sea level change17. For the former North American late Wisconsinan ice sheets, this approach is challenged by the fact that the ice had largely disappeared from the landscape by 3–4 ka BP; nonetheless, remnants of late Wisconsinan LIS ice are still found in Penny and Barnes ice19 , with ice sourced during the LGM further up the flow-line and connecting it to the higher Keewatin Dome (3200 m)23. These elevations were derived from a glacial model using ideal ice rheology that is insensitive to unknowns parameters, the spatial extent of grounded LIS ice, yield shear stresses and the ice frozen to the bed of Hudson Bay at LGM2; no independent assessment of the reconstructed elevations using the δ18O-elevation relation was made.In glaciated places with poor known boundary conditions , an alternative approach for the reconstruction of elevation of glaciers is to use the δ24. Such sites have been discovered near the northern maximum limit of the LIS, including: (1) Peel Plateau, NWT, Canada; (2) Richards Island, NWT; (3) north-west Victoria Island, NU, Canada; (4) south-west Bylot Island, NU, Canada . The sites extend across the northern margin of the LIS which allows us to determine the elevation at key sectors: Foxe and Keewatin domes, Mc’Clintock and Plains ice divides. Our findings are compared to the various modeled LIS configurations during the late Wisconsinan, including Fisher-1985, Tarasov-2012, ICE5G, ICE6G, NAICE and an alternative version of the Fisher-1985 LIS elevation model2.In addition to the LIS remnants in Penny and Barnes ice caps, climate warming in the Canadian Arctic has been increasing thermokarst activity and buried relics of the LIS are being exposed along headwall of thaw slumps and other natural exposurescluding:  Peel Pla18O records of Penny and Barnes ice caps have been correlated with other ice cores in Arctic Canada and Greenland and cover most of the Wisconsinan glaciation19. Near the bottom of Penny Ice Cap, late Pleistocene-age ice has average δ18O of −31.2 ± 1.2‰  with the overlying Holocene-age ice having average δ18O of −23.7 ± 0.6‰. On Barnes Ice Cap, late Pleistocene-age LIS ice is exposed along the western margin in a distinctive bubble-rich white band that spreads over 200 m22. This band of white ice has average δ18O of −34.3 ± 2.4‰ , much lower than the average of −22.6 ± 1.7‰ in the Holocene-age blue ice18. At Barnes and Penny ice caps, the shift in δ18O between modern and LGM ice (δ18O[modern-LGM] = 12–15‰) greatly exceeds that expected due to changing air temperatures only 27.The four buried LIS sites consist of ice that was stranded or buried shortly after the LIS reached its maximum extent at ~21–17 ka BP28 and within the Tutsieta Lake Phase recessional limit dated to 15 k cal yr BP29. The ice sheet had receded from the region by 13.5 k cal yr BP based on 14C ages obtained from remains of steppe bison near Tsigehtchic30. In this region, a major ice lobe flowed north-northwest along the Mackenzie Valley with the Mackenzie Through and Bear Lake ice streams likely bringing LIS ice from the more southerly Plains ice divide14.On the Peel Plateau Fig. , buried −1). The white ice also has the lowest δ18O values , whereas the other three ice types have slightly higher δ18O values, ranging from −31.2 to −27.3‰  clear ice with mm-size spherical gas inclusions; (2) sub-vertically banded clear ice and fine sediments; (3) bubble-poor blue ice; (4) white ice rich in spherical gas inclusions, similar to the bubble-rich white ice band on Barnes Ice Cap. The four ice types were characterized by a Ca-Na-Cl geochemical facies  with low cation contents. Together with the stratigraphic context, the ice was inferred by ref33 to be buried LIS ice .Along the shore of YaYa Lake, massive ice was identified by radar and borehole drilling beneath 7-m of glaciofluvial sand34. Former ice margins suggest that the north-west sector of Victoria Island represented the maximum extent of the LIS8; however, a revision of the extension of the ice based on 14C of marine molluscs suggest that the LIS extended across Banks Island35, such that northern Victoria Island and the Jesse Moraines along the east coast of Banks Island represent a recessional phase of the LIS36. The LIS likely occupied north-west Victoria Island near 21–18 ka BP and the ice had receded by 14–12 ka BP36. On the Prince Albert Peninsula, the LIS originated from the Mc’Clintock ice divide and was likely transported by the Mc’Clintock Channel and possibly the Collinson Inlet ice streams14.On the Prince Albert Peninsula on north-west Victoria Island, late Wisconsinan tills are cored by buried LIS ice34 identified buried LIS ice beneath 1-m thick till extending 60–450 m laterally. The englacial ice, which contained a small amount of dispersed sediments, had a sub-vertical banding with alternating bubble-rich and bubble-free ice and its δ18O averaged −30.1 ± 1.4‰  with ice flowing northward from the Lancaster Sound ice stream40. Radiocarbon age of shells in nearby marine sediments indicate the region was deglaciated near 9860 ± 140 14C BP41.Buried LIS ice was discovered in the Qarlikturvik Valley on southwest Bylot Island37. The ice had a clear to whitish appearance, similar to the late Pleistocene-age white ice band on Barnes Ice Cap. The buried ice contained many small spherical and coalescing gas inclusions. The ice was dominated by Ca2+, Na+, Mg2+ cations and their concentration was low and within the range of ice sampled from the nearby C-93 glacier . Further, the ~4‰ difference between the δ18O record of the LIS remnants cannot solely be explained by regional temperatures or major moisture source differences because the δ18O composition of modern precipitation is strongly zonal and varies by less than 1‰ along latitudes of 67–72°; late Pleistocene δ18O precipitation records from 154 empirical proxy data showed a similar zonal distribution43. However, like Penny and Barnes ice caps20, the difference in Δ18O[modern-late Wisconsinan] for the buried LIS sites is higher than expected for their latitudes  to a deep ice core at the head of its flow line near the center of the ice sheet (Pakitsoq site and GISP2 ice core)26; such ice transport and preservation of δ18O record was also incorporated in 3D isotope stratigraphy models44 . The modern δ18O-elevation slope cannot be directly transferred to different climate periods, but empirical proxy data suggest that the δ18O-elevation relation during the late Pleistocene changed by −0.05‰43, providing a late Pleistocene δ18O-elevation relation of −0.67 ± 0.03‰ per 100 m. The increase in slope value during the colder late Pleistocene is similar to that reported from modern-day Antarctica . Applying the late Pleistocene δ18O-elevation correction and accounting for the 5–7‰ shift in δ18O of precipitation during the late Wisconsinan along the latitudes of our sites  allows us to define the LIS surface elevation in their source area during the late Wisconsinan  suggest surface ice elevations of 1900–2000 m and 2500 ± 100 m. For Barnes Ice Cap, the late Wisconsinan and LGM δ18O values are much lower , suggesting surface ice elevations for most of the last glacial period of 2200–2400 m and near 3200 ± 100 m during the LGM , the ice likely originated at similar elevation to most of the last glacial ice preserved in nearby Barnes Ice Cap (2150–2350 m). The ice at Barnes and Penny ice caps and on south-west Bylot Island would have been sourced from Foxe Dome for much of the late Wisconsinan, hundreds of km from their modern location. The very low values near −40‰ on Barnes Ice Cap and near −36‰ on Penny Ice Cap would suggest ice sourced at LGM at higher elevation and connecting it to the 3200 ± 100 m Keewatin Dome23  were measured from foraminifer shells in the Gulf of Mexico and linked to LIS meltwater sourced from the Keewatin Dome draining through the Mississippi River watershed51. On north-west Victoria Island, the buried LIS ice (δ18O = −30.1 ± 1.4‰) that flowed from the Mc’Clintock ice divide likely originated from ice sourced at surface elevations of 1500–1900 m. Finally, the buried LIS ice on the Peel Plateau (δ18O = −31.2 ± 0.6‰) and Richards Island (δ18O = −32.4 ± 1.1‰) suggests ice sourced from the Plains ice divide at surface elevations of 1700–2100 m. The Peel Plateau and Mackenzie Delta region have its highest divide at the Plains divide because the transition between the hard-frozen beds of the Canadian Shield and the deforming soft-beds of the prairies translates into a very sharp change in flowline direction 27, we performed a frequency distribution analysis of the late Pleistocene age δ18O records of GISP2, Penny and Barnes ice caps . Additionally, the variance in δ18O for the late Wisconsinan ice was assessed for the GISP2 and Penny δ18O records and standard deviations of 1.1 to 1.4‰ were calculated. As such, random sampling of buried late Wisconsinan ice does not have δ18O values that would deviate greatly from LGM-age ice . Increasing the uncertainties in δ18O to 3‰ would translate into an elevation error of 500 m.The δaps Fig. ; the lik18O records of six LIS remnants sites indicate an asymmetric LIS during the LGM, with ice surface elevations near 2200–2400 m on Foxe Dome, 3200 ± 100 m on the Keewatin Dome and 1700–2100 m along the Plains ice divide  with the mapped glacial limits in the south-eastern Mackenzie Mountains where the LIS reached maximum elevation of ~1550 m52 (descending in elevation to 750 m in the Richardson Mountains)28; (2) surface exposure age near 21 kyr for elevations >1400 m in the western Mackenzie Mountains53; and (3) reported δ18O values from other buried glacier ices and segregated ices in northwestern Canada, which are all greater than −34‰ (mainly in the −32 to −28‰ range)54. The ICE5G, ICE6G and NAICE models generally predicted too much ice in the Keewatin Dome and/or Plains ice divide. Given some uncertainties in our approach and in geophysical models, we highlight differences in the order of 1000 m between these various paleo-elevation reconstructions at LGM. For example, the ICE5G model55 has similar ice elevations for the Foxe Dome and along the Mc’Clintock and Plains ice divides, but it has a much thicker Keewatin Dome (~4000 m). Conversely, the ICE6G model6 has similar ice elevations for the Keewatin and Foxe domes, but increased ice elevation along the Plains ice divide (2800–3200 m). The NAICE model4 also has much higher ice elevation along the Plains ice divide (~2500–3000 m).Together, the paleo-elevation reconstruction derived from the δide Fig. , and the18O records from LIS remnants in glaciers and permafrost to derive surface elevation of the LIS provides valuable constraints to modeling efforts. Our δ18O-derived paleo-elevations have decent fit with the Fisher-1985 glacial model and the Tarasov-2012 glacio-geophysical model and supports the estimated LIS ice volume at LGM of ~21.1 × 106 km3 . Some of the latest modeled glacio-geophysical LIS elevation reconstruction are generally found to be over-estimating its surface elevation near the LGM on the Keewatin Dome and along the Plains ice divide, although these may also relate to uncertainties in our ice-age estimates and the dynamic nature of the LIS. There are probably other remnants near former ice-marginal extents of past ice sheets in North-America and Siberia that contain information that would help reconstruct their interior geometry and global-scale impacts. Given that the ongoing climate warming and associated thermokarst is exposing new sites that potentially contain LIS relics in permafrost24, these should be found and sampled before they melt away as they contain key information about the conditions prevailing for the last major ice sheet on Earth .The concept of using δ28.Distinguishing between buried glacial ice and other massive ice types in permafrost is usually based on cryostratigraphy and combines detailed physical, geochemical and isotopic measurements of the ice and may also include analyses of occluded gases, while its chronology usually relies on the age of the surrounding sedimentsThe buried ice on the Peel Plateau and Bylot Island were sampled in summer 2016 and 2012, respectively. At both sites, a cryostratigraphic approach was used to describe the exposed ice and the overlying sediments. Samples of ice were collected using either an ice pick or a portable core-drill. All samples were shipped and stored in our laboratories until analyses.18O/16O) and hydrogen (D/H) were determined using a Los Gatos Research high-precision liquid water analyzer coupled to a CTC LC-PAL autosampler. The results are presented using the δ-notation (δ18O and δD), where δ represents the parts per thousand differences for 18O/16O or D/H in a sample with respect to Vienna Standard Mean Ocean Water (VSMOW). Analytical reproducibility for δ18O and δD was ±0.3‰ and ±1‰, respectively.The stable isotope ratios of oxygen  at the University of Ottawa. Solutes are expressed in mg L17; (2) the δ18O-elevation relation adjusted for late Pleistocene conditions43; and (3) the concept of an ice sheet flow-line model that predicts that the margins of ice sheets contain ice that originate from their local accumulation area at much higher elevation56.The approach used to derive the surface elevation of the LIS during the late Wisonsinan for sites along its northern margin combines: (1) the stable isotope-based paleo-altimetry method used to reconstruct Holocene changes in surface elevation of the Greenland Ice Sheet and Agassiz Ice Cap56. The latter was observed on Greenland Ice Sheet where the δ18O record of ice sampled along a horizontal transect from the western edge (Pakitsoq site) was remarkably similar to that of the GISP2 δ18O ice core record situated near the center of its accumulation area due to ice resurfacing in the ablation zone26. The ice-flow on Greenland Ice Sheet was successfully modeled using a 3D transport model fitted with δ18O data from ice cores44. In fact, both Pakitsoq and Barnes Ice Cap exposed late Pleistocene-age ice near their margins over a horizontal distances of ~200–500 m; with Holocene-age ice above it . The steeper slope in Arctic region is attributed to colder-drier conditions and near adiabatic lapse rate with little mixing of air masses as they gain elevation; this is particularly the case on large ice sheets. In the lower latitudes, vertical advective mixing is much stronger and the mixing of air masses reduces the δ18O-elevation slope.The δ18O of precipitation during the late Wisconsinan is largely affected by changes in air temperature, site elevation, seasonal distribution in amount of precipitation and atmospheric circulation, the latter two relate to changes in moisture source. The effect of a change in zonally-averaged air temperature during the late Wisconsinan, including a shift in the position of sea-ice front, was associated with a latitudinal-dependent shift of 3–10‰ in δ18O of precipitation, with the higher latitudes experiencing a greater shift21. This trend was also observed in 154 late Pleistocene δ18O proxy records43. The modern δ18O-elevation slope cannot be directly transferred to other and different climate periods, such as the cooler late Pleistocene. However, based on empirical data, ref.43 suggested that the global δ18O-elevation relation during the late Pleistocene changed by −0.05‰ per 100 m. We therefore use a late Pleistocene δ18O-elevation relation of −0.67 ± 0.03‰ per 100 m for Arctic regions. This late Pleistocene δ18O-elevation slope is nearly identical to that observed in the colder Antarctica . Changes in seasonal distribution in amount precipitation and atmospheric circulation can be assessed from the D-excess parameter, which can provide clues into changes in distance to moisture source 57. Examining the D-excess record of Penny Ice Cap  and north-western  sectors of the LIS have more uncertainty. The D-excess values of the buried white ice on the Peel Plateau are within the range of that on Penny and Barnes ice caps and also of that calculated in modern-day precipitation at nearby sites 58. Therefore, if there was a change in distance to moisture source, it is not reflected in the D-excess values. However, to truly assess source distribution changes, one would have to do a trajectory tracing of ancient climates over the proposed ice sheet geometries. The biggest unknown relates to the age of the sampled buried ices. We ascribed to the four buried LIS ice a near LGM-age (29–19 ka BP)27 based on the existing chronologies of the timing of advance and retreat of the LIS in these areas. The LIS reached its maximum extent at ~21k-17 ka BP8 and had receded from these regions by 10–14 ka BP1. This timing of retreat of the LIS at the sites provides a minimum age constraints for the sampled ice with the actual age at each site being dependent on the ice flow rate in the ice sheet. The uncertainty in the age of the sampled buried LIS sites is the biggest uncertainty when comparing reconstructed paleo-elevations derived from the δ18O-elevation relation to those from various glaciological and geophysical models that have reconstruction for specific times because the LIS topography is evolving over time.The δCap Fig.  shows va2. It uses a simple plastic ice model that is insensitive to unknown parameters and uses as inputs the margins of the ice sheet, present-day topography and an assumed yield shear stress. References60 showed that elevation estimates using this model are good to 6% on present-day Greenland, with ridges and domes having smaller errors. No assumptions are made in advance about ice divides and accumulation centers. At the time of its publication in 1985, some uncertainty still existed about northern and northeastern LIS margins, thus ref.2 presented the LIS surface elevation for the minimum-concept of grounded ice margins. The maximum-concept of ice margins was produced at that time also and is shown in Fig. 6 km3). Note that the Cordilleran and Innuitian ice sheets have not been included in these reconstructions so their volumes are not included.The reconstruction of late Wisconsinan LIS surface elevation at 18 ka is from ref.Supplementary information