Immunogold labeling in combination with transmission electron microscopy analysis is a technique frequently used to correlate high-resolution morphology studies with detailed information regarding localization of specific antigens. Although powerful, the methodology has limitations and it is frequently difficult to acquire a stringent system where unspecific low-affinity interactions are removed prior to analysis.We here describe a combinatorial strategy where surface plasmon resonance and immunogold labeling are used followed by a direct analysis of the sensor-chip surface by scanning electron microscopy. Using this approach, we have probed the interaction between amyloid-β fibrils, associated to Alzheimer’s disease, and apolipoprotein E, a well-known ligand frequently found co-deposited to the fibrillar form of Aβ in vivo. The results display a lateral binding of ApoE along the amyloid fibrils and illustrates how the gold-beads represent a good reporter of the binding.This approach exposes a technique with generic features which enables both a quantitative and a morphological evaluation of a ligand-receptor based system. The methodology mediates an advantage compared to traditional immunogold labeling since all washing steps can be monitored and where a high stringency can be maintained throughout the experiment. Fibrillar aggregates of the amyloid β peptide (Aβ) are considered as one of the hallmarks of AD and their ultrastructural morphology and properties have been extensively studied. The Aβ-fibrils are represented by a β-sheet polymer where the lateral assembly of several thinner filaments constitute the final fibrillar morphology –3. The fImmunogold labeling in combination with electron microscopy represents a technique used for the ultra-structural investigation of biological samples. The methodology reports the binding of e.g. an antibody to its antigen or a ligand to its receptor by conjugation to a gold particle and hence facilitates detailed structural information of the ultrastructural morphology. Immunogold techniques are however frequently hampered by the ability to remove unspecific low-affinity binding and hence to obtain a high stringency of the system. Consequently, it is often difficult to discriminate between relevant binding and non-specific interactions.D determination [Within the SPR technique, the sample for analysis is frequently attached to a surface via strong covalent bonds and the immobilized proteins can then be probed by potential interaction partners through injections into a continuous flow of the media. The methodology facilitates detailed monitoring of binding kinetics including Kmination . It is hAn SPR experiment frequently involves the acquired kinetic data from an interaction between e.g. a receptor and its ligand and in most cases this covers the required needs. The SPR technique has however been extensively used regarding the monitoring of amyloid formation –26 where1–40 readily forms fibrils under stagnant solutions in PBS and the relative proportion of fibrillar material can be monitored by using the amyloid-specific probe ThT. Figure 1–40 to a fibrillar form, where the initial lag-phase is followed by a logarithmic phase of fibril assembly, and subsequently reaches a plateau, where most of the monomeric fraction is converted to mature fibrils. Figure Aβ1–40 fibrils using both SPR and SEM a scheme of analysis to include all controls was employed. In total 2000 response units (RU) of Aβ1–40 fibrils were immobilized and then probed with ApoE until saturation binding had been acquired implicating that most of the accessible sites have been occupied  it is possible to make direct analysis by SEM. Ultra- small (diameters < 10 nm), yet non-conducting materials such as the amyloid fibrils can be distinguished from the background by the inelastic electron scattering when the electron beam hits the sample surface at low accelerating voltage. The low-energy secondary electrons, detected by the in-lens detector, provide high-resolution, surface-sensitive information, as well as compositional contrast, displaying darker shades of gray for the organic matter (fibrils) and brighter gray level for the heavier elements (gold beads). The gold-beads indirectly probing bound ApoE could be readily identified due to their strong electron scattering properties and therefore easily discriminated from the background of both the gold-surface of the CM5-chip and the immobilized fibrillar sample. Figure The results revealed a fibrillar morphology in accordance with the TEM analysis of the corresponding sample and in essence no background binding is anti-ApoE antibodies and the subsequently added protein-A coated gold-beads was observed. Figure Gold-particles have been used within the field of electron microscopy for a very long time due to their remarkable electron density and are today available in different sizes and conjugated to different linker molecules , 32. In A limiting factor regarding the traditional use of immunogold techniques is that the sample is not strongly immobilized onto the surface. This feature frequently hampers the removal of unspecific binding after probing with e.g. antibodies or ligands and it is as a consequence difficult to acquire a good signal to noise ratio since an appropriate washing is difficult to perform and monitor. Sample preparation for TEM is also frequently associated with negative staining using a water solution of uranyl-acetate having pH between 4 and 5 which also may compromise the binding and may cause dissociation of assembled protein complexes.Present work is focused on the interaction between the amyloid form of Aβ and its well-known ligand ApoE where in particular the ApoE ε4 allele is associated with a significantly increased risk of developing the disease , 33. ThrThe procedure in more general terms exposes a strategy that may be employed also in other contexts and serves as a versatile tool whenever the ultra-structural morphology is of interest in combination with binding kinetics.Interestingly, we observed an unexpected discrepancy where ApoE frequently did not bind uniformly to all fibrils within a sample. While certain fibrils were highly covered with ApoE, others in essence completely lacked bound ApoE. While this may be a technical artefact an alternative option is that ApoE may have a selective affinity for certain fibrillar morphologies. Although a single fiber follows a very high structural order, similar to the formation of a crystal, fibrils may differ from each other and Aβ samples frequently expose heterogeneous fibril morphology –3, 34. TTaken together, we have demonstrated a combinatorial immunogold-labeling approach using SPR and SEM, which allows improving the stringency of the system of analysis. The setup facilitates both quantitative and morphological evaluation where importantly an efficient binding and washing can be monitored between each step in the sequential experimental approach defining the immunogold technique. The technique is in essence applicable to most setups using SPR where an ultrastructural morphology also is of interest. A schematic illustration of the setup is shown in Fig. 1–40 peptides, were obtained from AlexoTech AB . Aβ1–40 was dissolved in 20 mM NaOH while both ApoE was dissolved in PBS. To remove potential aggregates both ApoE as well as Aβ1–40 were subjected to size-exclusion chromatography  in degassed PBS at 4 °C prior to its use. Both Aβ1–40 as well as ApoE eluted as a single peak.Recombinant lyophilized ApoE4, as well as recombinant lyophilized Aβ1–40 fibrils, freshly gel-filtrated monomeric Aβ in PBS was distributed in a 96-well microtiter plate with dark walls and clear bottom  to a final concentration of 20 μM and incubated at 37 °C in the presence of 40 μM ThT. The aggregation process was monitored by recording the ThT signal using a fluorescence microplate reader  with excitation at 440 nm and emission at 480 nm according to standard procedures [In order to prepare Aβocedures . Fibrill1–40 fibrils were sonicated for 60 s in a water bath and a total volume of 3.5 μl of fibrils was applied to 300 mesh formvar/carbon-coated, glow-discharged Ni-grids. After 1.5 min, the grid was washed in distilled water and consequently negatively stained for 15 s with 1.5% uranyl acetate . Finally, fibrils were examined under a Talos L120 TEM (FEI) microscope (120 kV) equipped with a Ceta CMOS 4 k × 4 k pixel (FEI) camera supported with the FEI TIA .Prepared Aβ1–40 monomeric peptide solution, ApoE4, Anti-ApoE  and 15 nm protein-A gold beads  were injected at a flow rate of 20 μL/min. All the steps were followed by a 5 min flow of buffer, and after the final step additionally washed by degassed distilled water for 5 min at a flow rate of 50 μL/min. Biosensor data were processed by BioLogic Software Scrubber2 and sensograms were made using GraphPad Prism 5.01.The interaction between Aβ fibrils and ApoE was monitored using a BIAcore 3000 biosensor  equipped with a CM5 sensor chip . Prior to fibril immobilization the dextran matrix on the sensor chip surface was activated with a mixture of 1-ethyl-3- (3-dimethylaminopropyl) carbodiamide (EDC) and N-hydroxysuccinimide (NHS). Aβ fibrils were immobilized at a density of 2000 response unit (RU) using standard amino coupling reagents and then deactivated according to the manufacture instruction. All SPR experiments were performed in degassed PBS at 25 °C. Fibrils were immobilized at a flow rate of 5 μL/min, whereas AβPrior to analysis the SPR chip was disassembled and mounted onto an aluminium stub using carbon adhesive tape and a copper tape is applied between the chip surface and metal stub for proper electrical grounding. The sample morphology was examined by field-emission scanning electron microscope  using an in-lens secondary electron (SE) detector at an accelerating voltage of 3 kV and probe current of 90 pA. The immobilized and Au-labelled fibrils can be directly visualized at low beam accelerating voltage without the application of a thin metal coating. Furthermore, no additional steps of sample processing are required e.g. fixation, dehydration and drying.


Intracerebral implantation of cell suspensions is finding its clinical translation with encouraging results in patients with stroke. However, the survival of cells in the brain remains poor. Although the biological potential of neural stem cells (NSCs) is widely documented, the biomechanical effects of delivering cells through a syringe-needle remain poorly understood. We here detailed the biomechanical forces  that cells are exposed to during ejection through different sized needles  and syringes  at relevant flow rates . A comparison of 3 vehicles, Phosphate Buffered Saline (PBS), Hypothermosol (HTS), and Pluronic, indicated that less viscous vehicles are favorable for suspension with a high cell volume fraction to minimize sedimentation. Higher suspension viscosity was associated with greater shear stress. Higher flow rates with viscous vehicle, such as HTS reduced viability by ~10% and also produced more apoptotic cells (28%). At 5 µL/min ejection using a 26G needle increased neuronal differentiation for PBS and HTS suspensions. These results reveal the biological impact of biomechanical forces in the cell delivery process. Appropriate engineering strategies can be considered to mitigate these effects to ensure the efficacious translation of this promising therapy. The brain especially poses a delivery challenge due to its encasement by the skull and target sites often being seated deep below functional tissue. A minimally invasive implantation procedure is therefore required. This is commonly achieved through a needle attached to a syringe and requires injection of high-density cell preparations near sites of damage by applying external force. The safety of this intracerebral implantation of cells, as well as tissue pieces, has been demonstrated in phase I clinical trials with no major side effects from the procedure4. Nevertheless, the survival of cells using this procedure indicates a poor retention and survival of cells. Cell retention/survival rates of approximately 5% of implanted cells are reported5. While the inflammatory host microenvironment around the damaged tissue may affect the survival after transplantation, cell damage may first occur during injection from the shear mechanical forces inside the needle-syringe assembly. Delivery of cells is therefore a key process to ensure efficacy of intracerebral stem cell implantation1.The clinical potential of cell therapy is driven by the biological activity of cells in restoring, repairing or replacing lost cells/tissues. However, this potential can only be realized if cells are appropriately delivered6. The biophysical properties of the suspension vehicle and cells, such as viscosity and density, interact with the syringe-needle design characteristics to determine the biomechanical forces generated by the ejection procedure. The viscosity of the suspension vehicles determines shear stress and influences the force required for ejection8. Wall shear stress affects cell function, such as the secretion of pro-inflammatory cytokines from mesenchymal stem cells (MSCs)9. In addition to the suspension vehicle and bore size, wall shear stress is modulated through the applied force to eject cells. This applied force is defined by the ejection parameters, such as the speed of ejection . Ejection parameters have been shown to affect viability of cells12. Importantly, intravenous (i.v.) and intra-arterial (i.a.) injections are into an aqueous solution (i.e. blood), whereas intracerebral injections are typically into the brain parenchyma that acts as a solid or semi-solid. Significant differences in flow/ejection rates are therefore being used for i.v. or i.a. delivery of cells through catheters (400–1200 µL/min)11 compared to intracerebral syringe-needle injections (1–10 µL/min)4. Using MSCs, it has been shown that smaller needle bore size increases apoptosis in ejected cells13. A slower flow rate attenuates this effect8. To avoid the deleterious effects of the ejection process of cells for tissue injection, it is hence essential to characterize the biomechanical forces cells are exposed to during a syringe-needle injection and to define optimal parameters.Cell delivery through a needle-syringe is achieved by suspending cells in a liquid phase vehicle. The process of suspending cells can affect their viability and affect cell clumping, as well as sedimentation3. To evaluate these biomechanical forces on NSCs, we here measured the ejection pressure for different syringe  and needle  combinations and compared 3 common suspension vehicles  using different flow/ejection rates . To determine the biological effects of these conditions, cell viability, cell membrane damage, apoptosis, and cell differentiation were measured. Based on these investigations, optimal parameters for cell delivery can be determined.Although extensive work on the intracerebral delivery of fetal tissue pieces has been performed, little work has been done on human neural stem cells (NSCs) in cell suspensions for intracerebral injection6. All solutions were sterilized using a 0.2 µm filter prior to use.A solution buffer consisting of phosphate buffered saline , a cryopreservation solution HypoThermosol , and Pluronic F68  were used as vehicles for cell suspension. We have previously reported the density  and viscosity  measurements for these solutions, as well as their performance to maintain cell suspensions5 being most commonly used in preclinical studies, whereas 50 to 250 µL syringes were used in recent clinical trials4. With respect to biomechanical forces, it is important to note that these syringes have different bore sizes (Table v) to create a pressure point (PP), exerting biomechanical effects on cells as they are ejected  were used here, as they minimize the tissue damage during insertion and provide a bolus of ejection that distributes equally in all directions  followed by pressurized air to remove all fluid from the syringe barrel. Syringes were sterilized by UV irradiation overnight. Plungers were placed in an alcohol solution followed by a sterile PBS wash and UV irradiation as above. Needle interiors were cleaned by drawing up and washing with sterile water followed by sterile PBS, and were sterilized in a Germinator hot bead dry sterilizer (CellPoint Scientific) for 5 minutes. At present, no performance criteria are found in the literature regarding the repeat use of syringes and needles. We noted that new needles require very little force for the plunger to drop in a vertical position  on a stereotactic frame (Kopf). An LCKD-1KG series subminiature compression load cell (Omega) was positioned on top of the syringe plunger Fig. . A high-ρ is the density of the vehicle (g/μL), Q is volumetric flow rate (μL/s), D is the diameter of either the needle or syringe (cm), and η is dynamic viscosity of the vehicle (kg/(m s)). Syringe-needle combinations where bore size remains the same have a homogenous flow between both compartments, as the transition zone between syringe and needle does not create a pressure point  numbers <2,100 Fig. . A unifoint Fig. . Howeverτmax is shear stress (N/m2), Q is volumetric flow rate (cm3/s), η is dynamic viscosity of the vehicle (kg/(m s)), and R is the inner radius of either the needle or syringe (m). Physiological shear stress in human arteries ranges from 1–7 N/m2 and in the venous system from 0.1–0.6 N/m2 16. In rodents, this can be up to an order of magnitude higher18. However, experiments in cortical neurons indicate that shear stress as low as 1 N/m2 for 1 hour can significantly reduce cell viability, especially with a prolonged exposure19. A shear stress of 0.5 N/m2 has been demonstrated to exert no significant effect on cortical neuron viability19 and is therefore here considered as threshold to define acceptable shear stress conditions.As the cell suspension flows through the syringe-needle barrel, it encounters the barrel wall which is immobile. The shearing force caused by interaction with the barrel wall produces a deformation of the cell suspension defined as the shear rate Fig. . The she20. In brief, the cell line was derived from the cortical region of a human fetus 12 weeks old and conditionally immortalized using cMyc-ERTAM under the control of 4-hydroxytamoxifen . In the absence of 4-OHT, NSCs will cease proliferation and undergo differentiation. NSCs were expanded on laminin  coated flasks until 80–85% confluency was reached. Recombinant human basic fibroblast growth factor  and epidermal growth factor  were used as mitogens (Table 2. Cells were tested monthly for mycoplasma using a PCR kit (Sigma) or colorimetric analysis  and found to be negative. A biophysical characterization of NSCs indicated an average cell diameter of 19.29 µm, yielding a cell volume of 3,912 µm3 and a density of 2.04 g/mL6.The human cortical neural stem cell (NSC) line CTX0E03  was cultured, as previously described in detail6. Cells were spun down with supernatant aspirated to afford suspension in a given vehicle at a 50,000 cells/µL concentration (~20% volume fraction). The following formula was used to calculate the appropriate volume of suspension vehicle to be added to the cell pellet to yield a given concentration/volume fraction:V = volume of vehicle to be added; VT = total volume of preparation; VC = total cell volume.At 80–85% confluency, cells were harvested from their flask after adding 5 mL of Accutase in a T75 flask and counted, as previously described4, 105 and 106 cells suspended in 10 μL of PBS and then subtracting the weight of 10 μL PBS alone. Once the mass of a single cell is determined, the total mass of a cell suspension can then be calculated by adding the mass of total cells in a known cell fraction (20% cell fraction in 1 mL suspension requires 5 × 107 cells) with the mass of vehicle alone. The combined mass was then divided by the total volume of suspension (1 mL) to yield the suspension density of different theoretical volume fractions. According to the random closed packing (RCP) paradigm, spheres of equal size can achieve a maximum volume fraction of 0.63621, indicating that practically a ~60% volume fraction is the highest achievable cell content and equivalent to a cell pellet.The density of a vehicle is an important measure that influences buoyancy, as well as sedimentation. The density of vehicles was determined by weighing 1 mL of each vehicle on a precision scale . The weight of the vehicle (in grams) was then divided by the total volume (i.e. 1 mL) to obtain density in g/mL. In order to measure the suspension density of different cell volume fractions, the mass of a single cell was first measured by weighing 10ηs (cP) is the dynamic viscosity of the suspension, ηv (cP) is the dynamic viscosity of the vehicle, φ is the volume fraction of the cells in the suspension, φm is the maximum volume fraction of the cells in the suspension, and ηi is the intrinsic viscosity of the medium. For spherical particles such as the cells in suspension, ηi is 2.5. Additionally, φm was defined as 1 for a suspension with no vehicle. Further, φ was calculated by dividing the target cell concentration  by the maximum concentration of cells (2.5 × 105 cells/μL).The viscosity of cell suspensions is defined by both vehicles and cells. Their relative volume fraction defines their relative weight to the overall viscosity of the suspension. The viscosity of the suspension can be calculated for different cellular fractions according to the Krieger-Dougherty equation:Fg) or lift due to the buoyancy force (Fb), which opposes Fg. The drag force (Fd) describes the fluids resistance to the cells movement. In vehicles with a density lower than cells (ρ < 2.04 g/mL), the gravitational force acts on cells to sediment. However, the angle of the barrel affects the sedimentation rate , d is the diameter of the cell (m), ρc is the density of the cell (kg m−3), ρv is density of the vehicle (kg m−3), g is gravitational acceleration at each angle of injection (m s−2), and η is the dynamic viscosity of the vehicle (kg(m s)).Cells in suspension can either sediment due to the influence of the gravitation force , Q is volumetric flow rate (m3 s−1), and R is the inner radius of either the needle or syringe (m). The velocity of the cells moving through a fluid influences the drag force (Fd) that cells are exposed to. Objects with very small Reynolds numbers (Re < 0.1) in viscous fluids are exposed to frictional Fd that can be described by Stoke’s law. The Stokes drag force exerted on cells can be calculated using Stoke’s formula for Fd that is acting at the interface between the fluid and cells:Fd is the drag force (N), η is dynamic viscosity of the vehicle (Pa s), r is the radius of the cell (m) and v is flow velocity.The mean velocity of cell suspension passing through a syringe or needle under a constant flow rate can be calculated using the following equation:To determine effects of vehicle suspension, ejection speed and needle size on cell viability, NSCs were suspended in PBS, HTS, or Pluronic at a concentration of 50,000 cells/μL (20% volume fraction) and loaded into a 10 μL Hamilton syringe  with either a 26G or 32G needle attached and ejected at 1, 5, 10 μL/min. A 1 μL volume of cells was ejected into a 0.5 mL Eppendorf tube containing 5 μL of PBS. 5 μL were taken up into a P10 pipette and added to a hemocyotmeter (Fisher). To distinguish dead from live cells, a 6 μL volume of trypan blue (Sigma) was added to visualize dead cells.22. For this, a 1 μL volume  out of a 10 μL cell suspension  was ejected onto 13 mm circular coverslips  coated with laminin containing proliferation media. A control condition consisted of ejecting 1 μL of cells from a P10 pipette (Eppendorf) using a 10 μL tip (Fisher SureOne). The 24-well plates were incubated overnight, and 24 hours after injection, supernatants were collected from each well. Triplicate biological samples were analyzed using the LDH Cytotoxicity Assay Kit (Pierce). Results were read using a microplate reader (BioTek) at 490 and 680 nm. Absorbance at 490 nm for each experimental condition was compared to absorbance for samples from wells that had total lysis (100% LDH release).The effect of mechanical stress on cell damage was investigated using lactate dehydrogenase (LDH) release https://fiji.sc).At 24 hours post-ejection, NSCs seeded on coverslips (as per above) were fixed with 4% paraformaldehyde and assayed for apoptosis using immunohistochemistry. A primary antibody consisting of a rabbit anti-Caspase-3  in PBS + 0.1% Triton X-100 was incubated with cells overnight at 4 °C followed by a goat anti-rabbit IgG Alexa Fluor 555  secondary antibody for 1 hour at room temperature. To visualize individual nuclei for cell counting, Hoechst 33342  was applied as a counterstain for 5 min prior to placing the coverslip on a microscopic slide using Vectashield for fluorescence (ThermoFisher). Using a Zeiss AxioImager M2 Fluorescence Microscope, fifteen randomly chosen images (20x magnification) were acquired. For each condition, 45 images were analyzed using Fiji version 1.49  were fixed using 4% paraformaldehyde to investigate if these different ejection conditions influence the differentiation phenotype of NSCs. Primary antibody staining was performed overnight at 4 °C with rabbit anti-Fox3  to measure neuronal differentiation and mouse anti-human Stem123  to visualize astrocytes. A goat anti-mouse IgG Alexa Fluor 488 (1:500), and also goat anti-rabbit IgG Alexa Fluor 555 (1:500) secondary antibody was applied for 1 hour at room temperature before application of Hoechst 33342 to visualize individual cell nuclei. Cell counting was performed using 45 images acquired at 20x magnification using Fiji.Graphing was performed in Prism version 7 (GraphPad). Statistical analyses and contour plots were calculated in Minitab version 17 (Minitab). One-way analyses of variance (ANOVA) compared multiple conditions for a single independent and dependent variable  with Bonferroni post-hoc testing. Two-way ANOVAs were used to determine statistical differences between more than 1 independent variable (e.g. ejection pressure) using Tukey’s post-hoc test. A p value of <0.05 was considered significant. For contour plots, dependent variables were plotted against independent variables in 5–12 equal data ranges (bin sizes) to define contour lines that span the measured values and provide an overview of the interaction of independent variables on the dependent variables.6 Pa (i.e. 1.05 MPa) was evident for Pluronic at a speed of 1 μL/min from a 10 μL syringe with a 32G needle. In contrast, ejection pressure was up to 20x higher in needles compared to syringes. The smaller bore size of needles produced significantly higher ejection pressures with a maximum ejection pressure of 2.12316 × 107 Pa (21.23 MPa) for the 1 μL/min speed of pluronic from a 10 μL syringe with a 32G needle condition. The smallest 32G needle consistently produced the highest ejection pressure for all vehicles. A 7.3-fold increase in ejection pressure was evident between the 20G and 26G needle and a further 5.4-fold increase between a 26G and 32G needle for pluronic. Additional pressure increases were evident when the smaller needles were combined with smaller syringes. The least ejection pressure was present in the larger syringe (250 μL) with a large diameter needle (20G) at a 5 and 10 μL/min ejection speed. All conditions exceed normal levels of intracranial pressure (~2 kPA) by at least 50%. The only condition where ejection pressure did not exceed the level of intracranial pressure that would require treatment (3.3 kPA)  utilized PBS with an ejection speed of 5 μL/min in a 250 μL syringe and 20G needle (3.238 kPa). However, even under these conditions the maximum pressure inside the needle exceeded intracranial pressure 15 × (47.272 kPa). A direct comparison of vehicles in a 10 μL syringe, which is the most commonly used size for preclinical studies, indicated that PBS as vehicle produced the least ejection pressure and that faster speed of ejection also lowered ejection pressure , i.e. fluid resistance, that the vehicle exerts on the cells and flow rate of the vehicles. In laminar flow conditions, Fd can be described using Stoke’s law. In most cases, Fd is negligible indicating that gravity will exert a sedimentation effect on cells . Only with HTS some Fd is exerted on cells at volume fractions >50% and a flow rate >5 μL/min. The influence of Fd is therefore negligible on the sedimentation of cells in suspensions.The cells’ speed of sedimentation is also influenced by the frictional drag force , whereas cells suspended in PBS experienced the least shear stress (0.5 N/m2). A smaller needle diameter also induces more shear stress, again indicating that a 32G needle is very narrow for cell injection (<5 cells diameter). Although exposure to shear stress is short during the uptake and ejection procedure, a prolonged (12 hours) shear stress of 1 N/m2 (10 dyn/cm2) has been associated with increased cell death19, as well as an increased influx of Ca2+ ions into neurons and astrocytes25. In contrast, 0.5 N/m2 had no effect on cell viability19.Interaction of cells with the barrel walls further exposes them to shear stress that can lead to membrane damage leading to cell lysis or apoptosis. Higher viscosities lead to higher shear stress. This was evident in the case of HTS, which produced the highest level of shear stress  does not affect the proportion of neuron subtypes28. Others have demonstrated that neurite extension in neuronal differentiation is decreased on stiffer (4.2–7.9 kPA) compared to less stiffer substrates (0.1–0.8 kPa)29, indicating the influence of biomechanical forces on differentiation, as well as neuronal function. PBS and pluronic here also showed a shift in astroglia differentiation, which has been thought to be associated with higher stiffness/shear stress30. Although these biomechanical forces exerting effects on neuronal differentiation cannot be completely eliminated from the delivery process, it is nevertheless important to minimize these if neuronal differentiation is the pivotal mechanism of recovery.Needle/transcatheter induced biomechanical forces have also been reported to influence the therapeutic potential of mesenchymal stem cells31. Suspension vehicle also affects viscosity by defining the space in between cells and guiding their potential interaction with each other. Lower viscosity vehicles, such as PBS, can support higher cell volume fractions, while maintaining a lower viscosity. Higher viscosity materials, such as HTS, in contrast, might be more favorable for lower cell volume fraction suspensions, as more viscous fluids maintain more consistent single cell suspensions by limiting agglomeration of cells32. Although uniform laminar streamline flow is retained, with increasing viscosity of the suspension, shear stress is dramatically increased. Cell fraction has a dramatic effect on the biomechanical properties of suspensions. To keep shear stress under 0.5 N/m2 requires cell suspension containing <40% cell volume fraction and a flow rate of 5 μL/min. These are important considerations for intracerebral cell transplantation.As ejection pressure and shear stress are dependent on the viscosity of the material passing through the barrel, it is critical to note that the cellular fraction in a cell suspension affects viscosity and hence influences these parameters and their influence on cell behavior. Higher cell volume fraction increases viscosity, which is consistent with other reports demonstrating rheological changes in cell suspension with varying cell concentration6. Higher cell volume fractions reduce sedimentation by increasing the suspension viscosity. A key difference for intracerebral injections in a clinical and preclinical setting is that animals are typically implanted using a vertical plane (90°) to deliver cells into the brain, whereas neurosurgeons will use a horizontal plane (0°) to administer cells. We here confirmed that sedimentation in a cannula is minimal along the horizontal plane (<5 μm/s), but there is significant sedimentation along the vertical plane (>80 μm/s). The sedimentation is further influenced by cell density and viscosity of the material. Faster sedimentation will lead to an uneven payload delivery, but can also lead to the formation of a plug that blocks the ejection33. In this case, additional pressure is required and displacement of the plug can lead to a bolus ejection, rather than convection-enhanced delivery. Careful consideration of the biomechanics of the cell suspension and measurement of applied force during delivery can potentially mitigate these delivery issues.Cell volume fraction also affects sedimentation/settling of cellsin vitro to model the in vivo process in the absence of variables that could affect measurements, such as different tissue types, as well as variability in the placement of and potential blockage of cannulas34. Ejection into a fluid allows the ejectate to freely dissipate, whereas injection into a tissue that behaves like a solid will form a cell deposit that increases resistance and ejection pressure. Haptic feedback during manual injection can allow surgeons to adjust the applied force to compensate for a tissue-based build-up of resistance to the injection. However, a comparison of injection pressure in a simulated peripheral nerve block administration by anesthesiologist found that the perception of applied force and rate of injection varied widely and generally was too high35. Defining safe ejection rates and monitoring applied force are therefore important advances that facilitate a robust implementation of convection-enhanced delivery36. The interstitial pressure inside the tissue can also lead to a reflux phenomenon38 that can lead to an expulsion of transplanted cells from the brain39. Further in vivo studies will be required to determine how ejection into tissue will affect pressure in the syringe-needle, as well as the dispersion of cells from the injection site.To ensure consistency between measures, ejections here were preformed into a fluid In vivo injection studies therefore need to determine appropriate volumes and injection speeds to define the dispersion area of the injectate40. Damaged tissue, as in the case of stroke, is likely to be more permeable than intact tissue5. Nevertheless, coverage of large areas of damage might require several injection sites and tracts to ensure an appropriate coverage of transplanted cells43. Especially in a clinical setting larger anatomical structures will require extensive areas for cells to spread. Needle length is also typically longer (15.2 cm) and hence will expose cells to shear stress for longer periods44. However, 20G needles are commonly used clinically, which will mitigate shear stress and injection pressure compared to small rodents using 26G needles. These differences further underpin key biomechanical variables in cell delivery in a clinical and small rodent setting that could have implications for the biological action of implanted cells45. Establishing efficient injection protocols therefore is likely to require both small and large animal models47.In addition to the density and viscosity of the material, the volume, as well as the speed of injection, are also likely to influence potentially adverse events. 2 is exerting minimum impact on cell survival and differentiation. Cell volume fractions at <40% delivered with a 26G or larger needle at <5 μL/min will achieve this using PBS, HTS or pluronic. Smaller 32G needles are unfavorable for cell injections. For vertical injections, lower (<20%) cell volume fractions will be best formulated with more viscous vehicles (>100 cP combined), whereas higher cell volume fractions (>20%) need less viscous vehicle to mitigate shear stress, as well as sedimentation during the ejection process. A horizontal injection, as commonly used in clinical settings, reduces sedimentation and requires less consideration for vehicle viscosity. The delivery process is hence a crucial step in the intracerebral implantation of cells that requires the definition of appropriate parameters to ensure the efficacious translation of this promising therapy.The therapeutic success of cell therapy is dependent on the efficient and safe delivery of cells to the brain. We here demonstrated the importance of considering the biomechanical variables that influence this process. A shear stress <0.5 N/mSupplementary Figures


The magnitudes and characteristic timescales of ring conformational fluctuations are determined as functions of flow strength and polymer concentration. Our results suggest that ring conformational fluctuations arise due to transient threading of linear polymers through open ring chains stretching in flow.Understanding the dynamics of ring polymers is a particularly challenging yet interesting problem in soft materials. Despite recent progress, a complete understanding of the nonequilibrium behavior of ring polymers has not yet been achieved. In this work, we directly observe the flow dynamics of DNA-based rings in semidilute linear polymer solutions using single molecule techniques. Our results reveal strikingly large conformational fluctuations of rings in extensional flow long after the initial transient stretching process has terminated, which is observed even at extremely low concentrations (0.025  Understanding the dynamics of ring polymers is challenging are despite recent progress, understanding of the nonequilibrium behavior of ring polymers has not yet been achieved. Here, the authors directly observe the flow dynamics of DNA-based rings in semidilute linear polymer solutions using single molecule techniques. With regards to biological molecules, it has been proposed that the topological constraints of ring (or circular) polymers can potentially inform chromatin folding and genome organization2. In the realm of synthetic polymers, ring polymer topology has been leveraged to create new sustainable materials. In recent work, synthetic ring polymers based on cyclic poly (cPPA) show high levels of purity and stability3. Interestingly, polymer degradation (depolymerization) of cPPA can be precisely triggered by heating or by applying an external chemical stimulus. In this way, cPPA serves as a promising candidate for next-generation plastics that disintegrate on demand4.Ring polymers are intriguing materials with unique properties due to a topologically enclosed macromolecular structure with no beginning or end8. Prior work has shown that ring polymer melts generally exhibit lower zero-shear viscosities7 and higher recoverable compliance compared to linear polymer melts8. However, even a small amount of linear contaminates alters the rheological response of ring polymer melts, resulting in a drastic increase in viscosity11. Moreover, ring polymer melts were found to show no apparent plateau modulus, but addition of a small fraction of linear chains causes the rubbery plateau to reappear11. Therefore, despite many efforts, a central challenge in ring polymer research lies in achieving high purity ring polymer samples that are free of linear chains. Indeed, the ‘purest as-possible’ ring polymer samples prepared by post-polymerization cyclization of linear chains still contain small fractions of linear chains, even after rigorous purification12.Achieving a clear understanding of ring polymer dynamics is important for fundamental polymer physics. Experimental efforts to study high purity ring polymer melts began many years ago. Early work focused on the properties of synthetic ring polymers based on polystyrene and polybutadiene using shear rheologyRg upon the addition of linear polymers into the background solution14. Diffusion measurements of ring DNA molecules show that although a ring polymer diffuses approximately 1.4 times faster than a linear chain in a concentrated ring polymer solution, the diffusion coefficient drops dramatically in a background matrix of linear polymers17. Interestingly, when the background linear chain concentration is well above the overlap concentration c* for linear polymers, a heterogeneous multimode diffusion is observed for rings18. Here, it is important to note that c* is defined under equilibrium conditions when the linear polymers are unstretched by flow. Moreover, ring polymers generally exhibit a markedly different molecular weight dependence of the center-of-mass diffusion coefficient compared to linear polymers in background solutions of concentrated linear polymers or melts20. Nevertheless, it is possible to use single ring polymers as tracer polymers or probes to study entangled linear chain dynamics through small angle neutron scattering (SANS) or neutron spin echo (NSE) spectroscopy22, essentially by taking advantage of the slow diffusion of rings in ring-linear blends.From this view, understanding the properties of ring-linear blends is of fundamental interest to elucidate the properties of polymeric samples with mixed chain topology. Prior work has focused on the near-equilibrium properties of ring polymers in ring-linear blends. Computational modeling has shown that ring polymers swell with an increased 23 or restricted reptation (RR), where rings relax through amoebae-like conformations in fixed obstacles formed by background linear chains24. The once-threaded model (R1) was further proposed to capture ring diffusion along a threaded linear chain20. The ‘threading’ phenomenon refers to one or more background linear chains penetrating into an open ring conformation, thereby resulting in a significant decrease in chain diffusion26. Nevertheless, in reality, the actual diffusion mechanism may rely on a combination of elements from all of these models25.The slow-down of ring polymer dynamics in entangled solutions of ring-linear blends has also been theoretically modeled. Here, the stress relaxation mechanism is modeled to include constraint release (CR) of background linear chains27. SMFM can be used to understand phenomena such as dynamic heterogeneity and molecular individualism for polymer chains in flow30. In recent years, SMFM has been used to study the dynamics of linear polymers in large amplitude oscillatory extensional flow (LAOE)32, linear polymers in semidilute unentangled solutions34, and the heterogeneous relaxation dynamics of linear polymers in entangled solutions35.Despite recent progress in understanding the properties of ring-linear blends, a large portion of prior work has focused on the near-equilibrium properties of ring polymers such as equilibrium chain conformation or center-of-mass diffusion coefficient in concentrated solutions or melts. Moreover, ensemble-level experimental methods based on bulk rheology or light scattering provide indirect measurements of the average conformational properties of ring polymers. What are the conformational dynamics of single ring polymers in ring-linear blends under nonequilibrium conditions in flow? Recent advances in single molecule fluorescence microscopy (SMFM) and microscale flow manipulation allow for the direct observation of polymer dynamics under highly nonequilibrium conditions38. In the dilute solution regime, it was found that ring polymers show a shifted coil-stretch transition (CST) and less molecular individualism compared to their linear counterparts due to a coupling between intramolecular hydrodynamic interactions (HI) and the constrained chain topology37. Despite recent work, however, we still lack a comprehensive understanding of the dynamics of ring polymers in non-dilute ring-linear blends.Single molecule techniques have been used to study the flow dynamics of ring polymers, but only in ultra-dilute solutionsλ-DNA polymers . Our results show that ring polymers exhibit large conformational fluctuations in extensional flow, even long after the initial transient stretching process has terminated. Remarkably, this behavior occurs even at low background concentrations of linear polymers, down to 0.025 c* based on the linear constituent. These large conformational fluctuations are not observed in the steady-state stretching of linear polymers in the same background solutions33, or in the steady-state stretching of ring polymers in dilute solutions (10−5c*) under similar flow conditions37. Based on these findings, we hypothesize that large fluctuations in ring polymer extension arise due to transient threading of linear polymers through partially open rings due to stretched conformations in flow.In this work, we study the relaxation dynamics and transient stretching behavior of single ring DNA polymers in background solutions of semidilute unentangled linear DNA Fig. . In partc* to 1.0 c* 2 to an exponential decay function following the cessation of flow. Here, lcirc is the maximum fractional extension (end-to-end distance) of the polymers in the two-dimensional flow plane.We began by determining the longest relaxation time of ring polymers in semidilute solutions of linear unentangled polymers ranging in concentration from 0.025 c*). In addition, a second molecular subpopulation was found to exhibit a double-mode exponential decay 2 = A exp(−t/τs) + B, where A and B are numerical constants. The fast and slow double-mode relaxation times τd,1 and τd,2 are determined from (lcirc/Lcirc)2 = A1 exp + A2 exp + B, where A1, A2, and B are numerical constants. In prior single molecule studies of linear polymer relaxation, Zhou et al.35 observed a molecular subpopulation exhibiting double-mode exponential relaxation behavior, but only in entangled solutions of linear polymers. Interestingly, here we observe multiple molecular subpopulations with single and double-mode relaxation behavior for ring polymers in background solutions of semidilute unentangled linear chains. This behavior is qualitatively different than the relaxation of linear polymers in ultra-dilute solutions (10−5c*)27, linear polymers in semidilute unentangled solutions33, and ring polymers in ultra-dilute solutions (10−5c*)37.Interestingly, our results reveal the emergence of multiple molecular subpopulations for ring polymer relaxation in semidilute solutions. Approximately 75% of the molecular relaxation trajectories are well-described by a single-mode exponential decay , denoted as τcirc,z, and τlin,z, respectively. Absolute values of relaxation times are shown in Supplementary Table 36. This relation appears to approximately hold for the single-mode relaxation time τs for rings in semidilute linear background solutions. However, the slow double-mode relaxation time τd,2 for rings is approximately two times smaller than the longest relaxation time for linear chains, and the fast double-mode relaxation time τd,1 for rings is substantially smaller (factor of ~15) compared to linear chains at the same background solution concentrations . In brief, this quantity provides a measure of the magnitude of conformational extension fluctuations for a single chain after the initial transient stretching phase in extensional flow, averaged over the molecular ensemble for a given Wi and background solution concentration. Chain extension fluctuations are calculated for rings 〈δ〉/Lcirc and compared to fluctuations 〈δ〉/L for pure linear semidilute solutions, as shown in Fig. −5c* to 1 c*. Importantly, ring polymers show large conformational fluctuations in semidilute linear solutions, and the magnitude of chain extension fluctuations significantly increases near the coil-stretch transition (CST), corresponding to Wi ≈ 0.5. On the other hand, relatively small chain fluctuations are observed in pure linear solutions even at 1 c*. This supports the observation that chain conformational fluctuations is unique to ring polymers, which is likely due to the threading of linear chains into rings, even at low concentrations of background linear chains such that The magnitude of chain extension fluctuations is quantified in terms of an average fluctuation in fractional chain extension 〈c* semidilute linear solution at Wi = 3.0 is shown in Fig. A characteristic dynamic trajectory for a single ring polymer in a 1.0 We conjecture that large magnitude chain extension fluctuations arise due to transient threading of linear polymers in the background solution into partially stretched, open conformation ring polymers. The transport of linear chains into open ring polymers partially stretched by flow leads to repeated and continuous hooking and unhooking events of linear chains threading into ring polymer backbones, which leads to repeated cycles of transient chain extension (hooking) and retraction (unhooking) for a given ring polymer in extensional flow. From this view, threading events are highly dynamic in the presence of fluid flow.llin/L > 0.6 in 1.0 c* linear background solutions at Wi = 1.0, whereas ring polymers exhibit a broad distribution in fractional extension centered around a fractional chain extension of lcirc/Lcirc ≈ 0.3 . In brief, the autocorrelation for chain extension fluctuations was determined based on the instantaneous value of chain extension relative to the mean extension after the initial transient stretching phase in extensional flow. Ensemble-averaged autocorrelation functions for ring extension fluctuations as a function of ion Fig. , or incr Wi Fig. , the autInterestingly, the ensemble-averaged autocorrelation functions shown in Fig. 32. Here, we define average unsteady chain extension as the average value of fractional extension for accumulated fluid strains 36, ring polymers in dilute solution36, and semidilute pure solutions of linear polymers at 1.0 c* in extensional flow  due to intramolecular hydrodynamic interactions (HI) between the two strands under planar extensional flow37. Prior work also found that semidilute solutions of pure linear chains solutions exhibit slightly inhibited steady fractional extensions and a larger critical Weissenberg number at the CST (defined as Wic), which is approximately 1.6 times larger than that for linear polymers in dilute solutions33.Based on these results, it is clear that ring polymers exhibit large conformational fluctuations in semidilute solutions, even long after the initial transient stretching phase has ended. We determined an average unsteady fractional extension for ring polymers in extensional flow Fig. , analogoWic at the CST  is typically observed only at much higher solution concentrations41, in stark contrast with our findings under nonequilibrium conditions. It is known that anisotropy in molecular extension due to flow can lead to an increase in local concentration42. For instance, the overlap concentration c* is defined as c* = M/[(4π/3)R3NA], where M is the molecular weight and R is the size of the molecule. At equilibrium, R is taken as the radius of gyration for the molecule such that R = Rg. However, under nonequilibrium flow conditions, the spatial extent (or average molecular size) of linear chains in the background are much larger than the equilibrium coil size. Given an increase in molecular size due to stretching in flow, the overlap concentration in flow can be surprisingly smaller than that at equilibrium, as c* scales with chain size such that c* ~ R−343. Assuming that linear DNA polymers in the background solution are stretched to approximately 30% of the polymer contour length in extensional flow, a solution concentration of 0.025 c* at equilibrium corresponds to approximately 5 c* in extensional flow, which could conceivably result in appreciable intermolecular interactions and polymer chain threading. These arguments can be further rationalized by considering intermolecular distances in semidilute solutions. At equilibrium, linear λ-DNA molecules can be modeled as uniformly dispersed spherical particles, yielding a mean shortest distance between particles of approximately 0.5–2 μm at 0.025 c* (1.2 μg mL−1), assuming Rg ≈ 0.7 μm45. On the other hand, if the background linear DNA molecules are stretched to 30% of their contour length in extensional flow, the radius-of-gyration of the linear chains increases by a factor of 446. In this way, the process of polymer stretching in flow leads to an increase in particle size greater than the interparticle distance, thereby causing the linear chains to overlap. To this end, observation of ring polymer fluctuations provides further evidence that only a small fraction of linear chains is required to alter the rheological response of ring polymers47.Remarkably, our results show that fluctuations in ring polymer extension occur in background solutions of linear chains at concentrations as low as 0.025 Wi at the coil-stretch transition, when most of the ring polymers are appreciably stretched. Upon increasing Wi, the magnitude of chain extension fluctuations eventually plateaus for both ring and linear polymers in semidilute solutions, despite large differences in the fluctuation magnitude.The dynamic behavior of ring polymers in semidilute linear solutions starkly contrasts with the dynamics of ring or polymers in ultra-dilute solution extensional flows, where the extension fluctuations are generally largest near the coil-stretch transition. In particular, the magnitude of ring polymer extension fluctuations increases with increasing concentration of linear polymers in the background solution Fig. . Moreove27, which provides a finite time over which the hydrodynamic drag on the ring-linear polymer structure is increased, thereby resulting in ring polymer stretch to extensions larger than the mean value. On the other hand, when the linear chains finally unhook from ring chain, the enhanced hydrodynamic drag instantaneously vanishes, resulting in a decrease in fractional extension. During this process, linear chains are continually transported into open ring polymers, which results in repeated hooking and unhooking events with associated fluctuations in chain extension. However, it is important to note that the threaded states are not necessarily limited to a doubly-threaded state as illustrated in Fig. 25.Based on these results, we hypothesize that ring polymers undergo a dynamic chain threading mechanism as illustrated in Fig. Our results further reveal the existence of two molecular subpopulations for ring relaxation. One subpopulation exhibits single-mode relaxation behavior, which we attribute to ring polymers that are not associated with a threaded linear polymer. On the other hand, the emergence of a second molecular subpopulation with double-mode relaxation behavior for ring polymers suspended in a solution of semidilute linear chains likely results from interactions with threaded linear chains. The occurrence of double-mode relaxation behavior increases upon increasing background linear chain concentration, indicating higher probabilities of interactions with threaded linear chains 15. To remove any contaminating RNA, the sample is treated with RNase A, and protein is removed by phenol-chloroform extraction followed by dialysis. The sample is finally concentrated by a second isopropanol precipitation and its topology and concentration is determined using gel electrophoresis48.Double-stranded DNA constructs 45 kbp in length are prepared via replication of fosmids in λ-phage DNA  in a buffered aqueous solution with 10 mM Tris/Tris-HCl (pH 7.4) and 1 mM ethylenediaminetetraacetic acid (EDTA) is used to prepare background semidilute unentangled solution. The stock λ-DNA solution is typically provided in a concentration of 500 μg mL−1 (≈10 c*). To prepare semidilute unentangled λ-DNA solutions at different concentrations, the stock λ-DNA concentration is first measured using a UV-vis spectrophotometer  at a wavelength of 260 nm and an extinction coefficient −1 cm−1. The stock λ-DNA concentration is generally between 300–500 μg mL−1 for different batches. We then calculate the mass of DNA required at different target concentrations with a desired volume of 5 mL, which is a typical sample volume used for single molecule imaging and viscosity measurements. Next, based on the stock λ-DNA concentration, a working volume of λ-DNA solution containing the desired concentration is prepared and heated to 65 °C for 10 min followed by snap cooling to 0 °C to minimize formation of DNA concatemers. For all polymer concentrations, the stock λ-DNA working volume is concentrated to ~50 μL using a MiVac Quattro concentrator  and viscous buffer solution containing 30 mM Tris/Tris-HCl (pH 8.0), 2 mM EDTA, 5 mM NaCl and sucrose (65% w/w) is added to the working volume to 5 mL. Prepared semidilute unentangled λ-DNA solutions then undergo a series of repeated heating and mixing cycles to ensure sample homogeneity. Samples are first heated to 55 °C for 5 min and mixed (by gentle rotation) for 10 min at room temperature (20 °C). This cycle is repeated for twice followed by an overnight gentle rotational mixing procedure at 4 °C. The concentration of the semidilute unentangled λ-DNA solution is determined before each single molecule experiment using a UV-vis spectrophotometer. For λ-DNA molecules, the overlap concentration c* = 50 μg mL−1 at 22.5 °C. The final sample concentrations (in units of μg mL−1) and corresponding scaled concentrations in units of c* are tabulated in Table For all experiments, bacteriophage λ-DNA, resulting in a final labeled DNA concentration of 2 × 10−3 μg mL−1 (~10−5c*). In addition, a small amount of reducing agent β-mercaptoethanol (14 μM) and coupled enzymatic oxygen scavenging system containing glucose (50 μg mL−1), glucose oxidase (0.01 μg mL−1), and catalase (0.004 μg mL−1) are added into the entangled solution to suppress photobleaching and photocleaving of fluorescently labeled 45 kbp DNA molecules. The semidilute unentangled solution mixture is rotationally mixed for >20 min before single molecule imaging. All the solution viscosity ηs is determined using a cone and plate viscometer  at 22.5 °C.For single molecule imaging, small amounts of 45 kbp circular DNA molecules are fluorescently labeled with an intercalating dye  with a dye-to-base pair ratio of 1:4 for >1 h in dark at room temperature. Trace amounts of fluorescently labeled 45 kbp DNA are then added to background solutions of unlabeled semidilute unentangled −1). Experimental images obtained using fluorescence microscopy are analyzed using an in-house Matlab code based on algorithms reported in the literature50. The Kuhn step size of fluorescently labeled DNA is taken to be 0.132 μm27, and the contour length of fluorescently labeled λ-DNA is approximately 21.2 μm. Also, the contour length of the full circular topology of fluorescently labeled Fos 45 DNA is approximately 20 μm, with the fully stretched length of the Fos 45 ring polymer equal to Lcirc = 10 μm.Single molecule fluorescence microscopy and imaging is performed using an inverted epifluorescence microscope  coupled to an electron-multiplying charge coupled device (EMCCD) camera . Labeled DNA solutions are illuminated using a 50 mW 488 nm laser  directed through a 2.2 neutral density filter , a 488 nm single-edge dichroic mirror . Fluorescence emission is collected by a 1.45 NA, ×100 oil immersion objective lens , and a 525 nm single-band bandpass filter  is used in the detection path. Finally, images are acquired by an Andor iXon EMCCD camera  under frame transfer mode at a frame rate of 33 Hz  to generate planar extensional flow, and the control layer contains a pressure-driven valve to control fluid flow. Strain rate and flow field characterization are performed using particle tracking velocimetry (PTV)31.Two-layer PDMS-based microfluidic devices are fabricated using standard techniques in soft lithography  denotes the instantaneous polymer extension, 〈ln〉 denotes the time-averaged or mean polymer extension, and N is the total number of individual trajectories in the ensemble. Here, tf is the time at which the step strain rate input is halted, corresponding to the instant at which the ring polymer just begins to relax as indicated by the dashed line in Fig. t90 is defined as the time at which the fractional polymer extension first reaches 90% of the average fractional extension at tf. Experimental data points are discrete points with a frame rate 33 Hz, hence a summation is used instead of an integral for continuous quantities. In this way, the initial transient stretching of ring polymers is discarded, and we compute the chain extension fluctuation quantities only after the initial transient phase has died out.The average fractional chain extension fluctuation quantity 〈x(t) is defined as:λ denotes the offset time, and 〈⋅〉t denotes a time-averaged quantity. To quantitatively understand the threading dynamics the linear chains into the rings, we determined the autocorrelation function for chain extension fluctuations. Here, we define fluctuations in projected extensions as the mean extension 〈l〉t subtracted from the instantaneous chain extension l(t), such that: l′(t) = l(t) − 〈l〉t. The autocorrelation function Cl′,l′ is normalized by the autocorrelation function at zero offset time λ = 0. When calculating the autocorrelation function, the initial transient stretching phase is discarded based on the same criterion as the averaged fractional fluctuation quantity such that only the fractional chain extension from t90 to tf is considered. Finally, the correlation time is determined based on the time at which the autocorrelation function reaches zero and is normalized by the fluid strain rate The autocorrelation function of a real-valued, integrable fluctuating quantity Further information on experimental design is available in the Supplementary InformationReporting SummarySource Data


The health-risk estimation indicated that total hazard quotient (HQing + HQderm) and hazard index values were below the acceptable limit, representing no non-carcinogenic risk to the residents via oral intake and dermal adsorption of water. Moreover, the results of total risk via ingestion and dermal contact showed that the ingestion was the predominant pathway. This study also presents that the carcinogenic risk for Pb, Cr, Cd and Ni were observed higher than the acceptable limit (1 × 10−6). The present study will be quite helpful for both inhabitants in taking protective measures and government officials in reducing heavy metals contamination of urban drinking water.The continuous urbanization and industrialization in many parts of the world and Iran has led to high levels of heavy metal contamination in the soil and then on the surface and groundwater. In this study, the concentrations of 8 heavy metals were determined in forty water samples along distribution drinking water of Khorramabad, Iran. The ranges of heavy metals in this study were lower than EPA and WHO drinking water recommendations and guidelines and so were acceptable. The mean values of CDI•The data analyzed in this study show a clear situation regarding the quality of drinking water in Khorramabad.•The results of this study can be used to improve and develop the quality of drinking water that directly affects the health of consumers.•The present study will be quite helpful for both inhabitants in taking protective measures and government officials in reducing heavy metals contamination of urban drinking water Specifications TableSupply of healthy drinking water is necessary to human life, and safe drinking water should not cause a remarkable risk to human health. The increasing trend of water shortage has various negative impacts on economic development, human livelihoods, and environmental quality around the world . NumerouThe geographic coordinates of the study area are 33°29′16″N 48°21′21″E in DMS (Degrees Minutes Seconds), located in the Khorramabad city, Lorestan Province in the west of Iran. Khorramabad is situated in the Zagros Mountains with a warm and temperate climate. Natural springs are the main sources of water supply in this city. At the 2016 census, its population was 373,416. Average annual rainfall in this region is 488 mm. This city stands at an elevation of approximately 1147 m above sea level . The loc3 purchased from Merck Company was used in this work. Deionized water was utilized for solution preparation and also for dilution objectives. All glassware was washed and dried in an oven at 105 °C. Sampling bottles were cleaned by rinsing in a metal-free soap and then by soaking in 10% HNO3 before sample taking. Finally, the bottles were washed with deionized water. Totally, forty water samples from 40 different sites along the distribution network were collected during 2017 in order to measure the levels of potentially toxic heavy metals such as Pb, Cr, Cd, Mo, Zn, Cu, Ba, and Ni in drinking water of Khorramabad city. These samples were then transported to the laboratory and stored at 4 °C until analysis.Analytical grade HNOThe collected samples were analyzed for eight heavy metals including Pb, Cr, Cd, Mo, Zn, Cu, Ba, and Ni using standard methods for the examination of water and wastewater . ConcentRisk assessment is defined as the methods of evaluating the probability of occurrence of any given probable amount of the harmful health impacts over a determined time period . The heaEq. 1 and Eq. 2 taken from the Environmental Protection Agency (USEPA) were applied to determine the Chronic Daily Intake (CDI) via ingestion and dermal absorption routes, respectively ,36.(1)CDThe HQ for each heavy metal was estimated using the ratio of computed mean daily intake  of a metal ingested with contaminated water to the reference oral dose (RfD) through oral ingestion and dermal absorption for the residents. The sum of all HQs gives an estimation of total potential health risks or HI. The calculation of the HI caused by water is presented as (Eq. 3):The values of the RfD and cancer slope factor for different metals are listed in To estimate the total potential non-carcinogenic health impacts caused by exposure to a mixture of heavy metals in water, the HI for several heavy metals was computed according to the EPA guidelines for health risk assessment ,38 usingThe computed HI is compared to standard values: there is the possibility that non-carcinogenic impacts may occur in the residents when HI > 1, while the exposed person is unexpected to experience evident harmful health impacts when HI < 1 .The probable cancer risks due to exposure to a specified dose of heavy metal in drinking water can be computed using the ILCR . The ILC−6 and <10−4 for a single carcinogenic element and multi-element carcinogens [The permissible limits are considered to be 10cinogens .The minimum, mean, and maximum levels of heavy metals  present in water samples in the distribution network of Khorramabad city are presented in The heavy metal contamination in water distribution network can increase human health risks through various exposure routes. In the present work, non-carcinogenic and carcinogenic health risks caused by oral ingestion and dermal contact were explored. Based on total) in mg/kg-day are 1.00E-04 for Pb, 11.60E-04 for Cr, 1.34E-05 for Cd, 1.60E-05 for Mo, 1.48E-03 for Zn, 2.13E-04 for Cu, 2.55E-03 for Ba, and 1.09E-04 for Ni. Therefore, the mean values of CDItotal of heavy metals concentrations for adults were found in the order of Zn > Ba > Pb > Ni > Cr > Cu > Cd > Mo.Human health risk assessment comprises the determination of the nature and magnitude of adverse health effects in humans who may be exposed to toxic substances in a contaminated environment. In the present work, exposure and risk assessments were carried out based on the USEPA methodology. Human exposure to heavy metals principally occurs via pathways of drinking water, food, inhaled aerosol particles and dust . The degAs seen in Moreover, to estimate the total potential non-carcinogenic impacts induced by more than one metal, the HQ computed for each metal is summed and expressed as a Hazard Index (HI) . The meaHeavy metals , Cd, and Ni) can potentially enhance the risk of cancer in humans ,46. Long−6 is considered as insignificant and the cancer risk can be neglected; while an ILCR above 1 × 10-4 is considered as harmful and the cancer risk is troublesome. For the total of all heavy metals through all exposure routes, the acceptable level is 1 × 10-5 [-3) and nickel has the lowest chance of cancer risk (mean ILCR 9.16 × 10-5). The results of this research present that there was a cancer risk from the contaminants to residents through the cumulative ingestion and dermal contact routes in the drinking water of the region.For one heavy metal, an ILCR less than 1 × 101 × 10-5 . Among atotal of heavy metals concentrations in adults were found in the order of Zn > Ba > Pb > Ni > Cr > Cu > Cd > Mo. The HQs for those routes of this work decline in the following order: ingestion > dermal adsorption, meaning that ingestion is the dominant pathway of exposure to every receptor. The mean values of HI through ingestion and dermal adsorption as wells as total HI were obtained to be 3.31E-03, 2.15E-06, and 3.32E-03, respectively. Among all the studied heavy metals, chromium has the highest chance of cancer risks (mean ILCR 6.54 × 10−3) and nickel has the lowest chance of cancer risk (mean ILCR 9.16 × 10-5). The present study will be quite helpful for both inhabitants in taking protective measures and government officials in reducing heavy metals contamination of urban drinking water.This study was conducted to evaluate the health risks of exposure to heavy metals along with the water distribution network of Khorramabad city in Iran. Risk assessment relevant for the present study comprises computations of carcinogenic and non-carcinogenic risk of water through ingestion and dermal contact pathways. The maximum and minimum concentrations of heavy metals measured were related to Ba (81.31 mg/L) and Cd (0.43 mg/L), respectively. The order of the heavy metals toxicity according to mean concentrations measured in drinking water of the studied area was: Ba > Zn > Cu > Cr > Ni > Pb > Mo > Cd. Themean values of CDIThe authors of this article declare that they have no conflict of interests.


Wilkes Land in East Antarctica remains one of the last geological exploration frontiers on Earth. Hidden beneath kilometres of ice, its bedrock preserves a poorly-understood tectonic history that mirrors that of southern Australia and holds critical insights into past supercontinent cycles. Here, we use new and recently published Australian and Antarctic geological and geophysical data to present a novel interpretation of the age and character of crystalline basement and sedimentary cover of interior Wilkes Land. We combine new zircon U–Pb and Hf isotopic data from remote Antarctic outcrops with aeromagnetic data observations from the conjugate Australian-Antarctic margins to identify two new Antarctic Mesoproterozoic basement provinces corresponding to the continuation of the Coompana and Madura provinces of southern Australia into Wilkes Land. Using both detrital zircon U–Pb–Hf and authigenic monazite U–Th–Pb isotopic data from glacial erratic sandstone samples, we identify the presence of Neoproterozoic sedimentary rocks covering Mesoproterozoic basement. Together, these new geological insights into the ice-covered bedrock of Wilkes Land substantially improve correlations of Antarctic and Australian geological elements and provide key constraints on the tectonic architecture of this sector of the East Antarctic Shield and its role in supercontinent reconstructions. The bedrock also exerts important controls on the evolution of the Antarctic ice sheet3, underlying some of East Antarctica’s largest and most vulnerable glacial drainage basins  which together have the potential to contribute up to 3 m of global sea level rise in a warming climate4. However, due to thick ice cover and very limited rock exposure/sampling, our understanding of the age and composition of the Wilkes Land interior is inferred from the largely unconstrained projection of Australian geological counterparts into Antarctica1 and ages of detrital grains from glacio-marine sediments offshore of East Antarctica6.The interior of Wilkes Land remains one of the most remote and unexplored sectors of the Precambrian East Antarctic Shield. Revealing ice-covered geology in this region is critical to understanding the assembly and breakup of the Nuna/Columbia, Rodinia and Gondwana supercontinents of which Wilkes Land was a centrepiece7. The Wilkes province  also documented in the Nornalup Zone of the Albany Fraser Orogen of southwestern Australia10. The Mawson Craton  comprises the Archean to Paleoproterozoic rocks in Terre Adélie and George V Lands and has geological affinities with the Gawler Craton of South Australia2 , underlying most of the combined Vanderford-Totten-MUIS continental ice sheet, is only characterised by sparse legacy geological data13 and remains vastly underexplored. This region is interpreted to be the Antarctic extension of the unexposed Coompana and/or Madura provinces of southern Australia7 20 and extends into East Antarctica  and contains quartz (~33%), K-feldspar (~19%), plagioclase (~43%) as well as biotite, orthopyroxene, amphibole, ilmenite and magnetite (~5%), with accessory apatite and zircon , interpreted to represent the crystallisation age of this sample  ratios in the range 0.28206–0.28216  values between −0.53 and +4.87. A single outlier (spot 019) yielding Hfi ratio of 0.28101 and εHfi of −36.74 was excluded from the interpretation.Sample CI-814A2, the main rock type exposed at Chick Island, is a coarse-grained orthopyroxene-bearing granodiorite  modal classification of Streckeisencon Fig. . Zircon con Fig. . Under ccon Fig. . Thirty-ple Fig. . These zple Fig. . Twenty-Two xenoliths hosted in the granodiorite bedrock (samples CI-810A and CI-814B) have a granitic composition and contain igneous microstructures characterised by a lack of recrystallisation and the presence of interstitial igneous green amphibole. Samples contain quartz (~38%), K-feldspar (~24%), plagioclase (~33%) as well as amphibole and orthopyroxene (~5%) and accessory apatite and zircon Fig. . The app207Pb/206Pb weighted average age of 1154 ± 13 Ma  with individual apparent 207Pb/206Pb ages spread along Concordia bet]ween c. 1412 Ma to c. 1294 Ma  during post-crystallisation modification  basement at depth.Zircon grains in sample CI-814B are 70–200 μm long and have aspect ratios that vary from 1:1–1:4. Many of the larger zircon grains show medium to high CL response Fig.  with oscion Fig.  and yiel28 and is characterised by large areas of low to moderate magnetic intensity (<−300 nT) associated with the c. 1610–1490 Ma plutons of the Toolgana and Undawidgi Supersuites   overlap in age and Hf signature with zircon from the Coompana Province, and the more radiogenic xenocryst group , though displaying variable Pb loss possibly from c. 1420 Ma, overlap the isotopic signature of the more juvenile Madura Province  to intersect the coast in the proximity of the Chick Island outcrop  having aspect ratios from 1:2–1:3 and indicating an overall local sourcing of sediments. U–Pb zircon ages from the three samples reveal similar age peaks and have a statistically similar detrital distribution according to the performed Kolmogorov–Smirnov (K-S) test   amongst the fine-grained interstitial muscovite Fig.  inset. Ties Fig. . The wel232Th/208Pb ages ranging between c. 639–490 Ma  and higher U (1664 ppm) is interpreted as a detrital relict. A single analysis obtained from sample PRR-27979 yielded an apparent 232Th/208Pb age of 577 ± 17 Ma  of post-depositional authigenic monazite formation/hydrothermal alteration. An age of c. 633 Ma (average of two oldest 232Th/208Pb ages in samples PRR-21185 and PRR-27976) is therefore considered a minimum deposition age for the sandstone samples. The age of the single detrital monazite core also further constrains the maximum deposition age of the sandstones to 1038 ± 16 Ma.The observed spread in 32 indicate that the sandstone erratics were likely eroded from inland areas of the Vanderford ice catchment and transported to their present locations during a former expansion of the Vanderford Glacier25  depositional age range for at least part of the basin. This is further supported by the lack of Pan-African aged (c. 600–500 Ma) detrital zircon which instead are consistently present in younger Australian Palaeozoic to Cenozoic sedimentary deposits34. This age range broadly corresponds to the deposition of the Neoproterozoic sedimentary sequences in the eastern Officer Basin35 of southern Australia , as well as isotopically-similar granitic rocks found in the Wilkes Province  the c. 1600–1470 Ma detrital zircon age and εHf38  which is also interpreted to reflect a dominantly Mesoproterozoic sediment source form interior Wilkes Land36.In Australia, the southerly extension of the eastern Officer Basin in the Coompana and Madura provinces is poorly known and concealed by the Mesozoic and Cenozoic cover of the Bight and Eucla basins. Two sandstone samples from the Mallabie-1 drill hole in the Coompana Province are tentatively linked to the eastern Officer Basin and yield similar age spectra to our sandstone erratic samples38 Fig. . While wOur new zircon U–Pb–Hf and monazite U–Th–Pb geochronology, combined with regional age data and aero-geophysical observations have allowed us to interpret the age and composition of bedrock in interior Wilkes Land and test tectonic models.7. The improved geometrical correlation between basement provinces of Wilkes Land and southern Australia will be fundamental in further understanding the Mesoproterozoic evolution of Australo-Antarctica and as such, inform plate tectonic models for the amalgamation of Nuna and Rodinia and the configuration of Gondwana.We provide the first geological evidence for the Antarctic counterparts of the Mesoproterozoic Coompana and Madura provinces, previously only documented in southern Australia and resolve the geometry of these conjugate Mesoproterozoic basement provinces in both a Rodinia and Gondwana configuration. The addition of these two new Antarctic provinces confirm the presence of a progressively westerly-younging sequence of juvenile magmatic arc-related rocks retreating away from the Mawson Craton and provides additional evidence for a subduction-driven Mesoproterozoic evolution of Australo-Antarctica as supported by recent tectonic models36. However, due to the limited geological samples available, we are unable to define the extent of the newly identified Neoproterozoic Sabrina Basin outside the confines of the Vanderford ice catchment region. It therefore remains unclear whether the Neoproterozoic Sabina Basin formed an Antarctic extension of the larger Centralian Superbasin or constitutes a different Neoproterozoic Antarctic basin sharing provenance similarities with the Officer Basin. Furthermore, we do not exclude the presence of a younger Mesozoic or Cenozoic basin phase in the Sabrina Sedimentary Basin as previously hypothesised by Aitken et al.11, which could overlie older sedimentary sequences as seen in southern Australia with the overlap of the Bight and Eucla basins over the Officer Basin.New zircon and monazite data from sandstone erratics demonstrate the presence of Neoproterozoic sedimentary rocks in the Sabrina Sedimentary Basin that are equivalent in age and provenance to the eastern Officer Basin of Australia and Beardmore Group in the Transantarctic Mountains. The occurrence of sedimentary rocks of this age was previously unknown for this sector of East Antarctica and has broader implications for understanding the Rodinia-to-Gondwana transition during the Neoproterozoic. Similarities in age and provenance between our sandstone erratics and the Beardmore Group in the Transantarctic Mountains suggest that Neoproterozoic sedimentary rocks may have once covered a large sector of East Antarctica, forming an extensive platform basin on the proto-pacific rifting Rodina margin40 and geothermal heat flow41 across the Australian-Antarctic margin, with potential implications for ice sheet models that simulate past and future Antarctic ice sheet behaviour.Our improved geological correlation between southern Australia and Wilkes Land, and interpretation of age and composition of subglacial bedrock, can also help inform estimations of the spatial distribution of crustal radiogenic heat productionLocation of samples used in this study is given in Supplementary Table 2 on a spot size of 29 μm. Elements measured include 49Ti, 56Fe, 90Zr, 178Hf, 202Hg, 204Pb, 206Pb, 207Pb, 208Pb, 232Th and 238U with each element being measured sequentially every 0.16 s with longer counting time on the Pb isotopes compared to the other elements. The international glass standard NIST610 was ablated at the beginning and end of the analytical session to correct for mass bias on the 207Pb/206Pb ratio. Each run consisted of 30–50 analyses of our unknowns, bracketed by 4–6 analyses of the primary reference zircon standard 9150042 used to correct for mass bias, machine drift and down-hole fractionation on the Pb/U and Pb/Th ratios, and 4 analyses (two each) of secondary standards TEMORA 143 and GJ-144/Plesovice45 to provide an independent control to assess accuracy and precision. Full tabulation of U–Pb isotopic data of unknowns and standards is reported in Supplementary Table et al.46. The degree of metamictisation was also determined in igneous zircon by using U and Th concentrations and 207Pb/206Pb ages to calculate the dose of α-events for each zircon grain. Zircon grains were classified as ‘highly crystalline’ when alpha dose was <3 α/mg × 1015, ‘moderately damaged’ when >3 and < 8 α/mg × 1015 and ‘highly metamict’ when >8 α/mg × 101547. U–Pb Tera-Wasserburg plots of igneous zircons were constructed using isoplotR48. Error ellipses on Tera-Wasserburg plots are calculated at the two-sigma level. 207Pb/206Pb data are used for all age determinations. The quoted analytical uncertainties on individual analyses are given at the 2r level. Weighted mean ages are calculated to their 95% confidence level using analyses that are ≤±10% discordant (within 2r uncertainty of concordia). Probability density plots (PDP) of detrital zircon were calculated with DensityPlotter49 using 207Pb/206Pb ages and their 1σ uncertainties for data ≤±5% discordant. Histogram bin size in all PDPs is 20 Myr. Two-sample Kolmogorov–Smirnov (K-S) tests were performed on the detrital zircon age data using the online statistics calculator of Kirkman50 to determine if the samples were derived from different sources by comparing the distance between the cumulative age distribution curves.U–Pb zircon ages were collected at the University of Tasmania, Australia using laser ablation-inductively coupled plasma-mass spectrometry (LA-ICP-MS). U–Pb zircon analyses were performed in two different sessions on an Agilent 7900cs quadrupole ICPMS with a 193 nm Coherent Ar–F gas laser and a Resonetics S-155 ablation cell at the School of Earth Sciences, University of Tasmania. Each analysis was pre-ablated with 5 laser pulses to remove any surface contamination then the blank gas was analysed for 30 s followed by 30 s of zircon ablation at 5 Hz and 2 J/cmet al.51 describe the methodology in detail. A blank gas was analysed for 60 s followed by 120 s of ablation at 5 Hz and 2 J/cm2 and a beam diameter of 40–50 µm (depending on the size of the zircon grain). Zircon CL images were used to ensure that Hf isotope analyses were contained within the same domain analysed for U–Pb. Our samples were measured in two analytical sessions. Zircons from the Mud Tank carbonatite locality were analysed together with the samples in each session to monitor accuracy of the results. Most data and the mean 176Hf/177Hf value are within 2 standard deviations (SD) of the recommended value [0.282522 ± 42 (2σ)]52. Temora zircon was also run as an independent check on the accuracy of the Yb correction. Temora zircon has an average 176Yb/177Hf ratio of 0.04, which is similar to the mean 176Yb/177Hf ratio of zircon in this study. The average 176Hf/177Hf ratio for Temora is consistent with the published value for the Temora standard [0.282687 ± 24 (2σ)53]. The initial 176Hf/177Hf (Hfi) value in zircon is calculated using the measured 176Hf/177Hf and apparent 207Pb/206Pb age. Calculation of εHfi values employed the decay constant of Scherer et al.54 of 1.865 × 10–11. Full tabulation of zircon Hf isotopic data of unknown and standards is presented in Supplementary Table 176Hf/177Hf and εHfi plots were constructed in Microsoft Excel®; zircon U–Pb and Hf isotopes from our samples are compared to a compilation of Australian and Antarctic isotopic data  at GEMOC, Macquarie University . Griffin in situ U–Th–Pb monazite dating were mounted with epoxy resin in ~12 mm thick x 25 mm diameter steel cylinder and polished using a 0.25 µm diamond polishing lap. Monazite grains were identified in rock chip laser mounts using Sparse Phase Liberation-Lite analysis (SPL-LT). Representative images of monazite grains selected for geochronology were taken using a FEI Quanta 600 SEM. Grains were also imaged using high contrast BSE imaging to detect zoning within the grains on a Hitachi SU-70 Field Emission Scanning Electron Microscope (FE-SEM).Rock chips for in situ U–Th–Pb analyses following the analytical procedures reported in Halpin et al.55 on the same LA-ICP-MS system used to collect U–Pb detrital zircon ages. Pre-ablation and ablation times follow the monazite methodology highlighted in Halpin et al.55 with operating conditions of 5 Hz and ∼2 J/cm2 on a spot size of 9 μm. Elements measured include 27Al, 31P, 43Ca, 140Ce, 172Yb, 202Hg, 204Pb, 206Pb, 207Pb, 208Pb, 232Th and 238U. The international glass standard NIST610 was used as a primary standard for trace element quantification assuming stoichiometric Ce in monazite and as a primary standard for the 207Pb/206Pb ratio correction factor for monazite. The down hole fractionation, instrument drift and mass bias correction factors for Pb/U and Pb/Th ratios on monazite grains were calculated using two analyses on the primary standard (14971-Mon–in-house standard) and one analysis on each of the secondary standard monazites RGL4B56, Bananeira57, and 94–22258 analysed at the beginning of the session and every 16–20 unknowns using the same spot size and conditions as used on the samples. Following the recommendations of Seydoux-Guillaume et al.30, Grand’Homme et al.59, 208Pb/232Th ages are preferred to the 206Pb/238U ages in all age determinations due to common Pb contamination and the relatively high Th/U ratio of monazite. Results are presented graphically in a 206Pb/238U vs 208Pb/232Th modified concordia plot. Uncertainties on individual spot ages are 1σ. Full tabulation of U–Th–Pb isotopic data of monazite unknowns and standards and modified concordia plot are reported in Supplementary Table et al.46 and Halpin et al.55. Age calculations. 206Pb/238U vs 208Pb/232Th modified Concordia diagrams were made in Microsoft Excel®.Monazite grains from each of the three sandstone erratic samples were investigated for 60 and the comparable Australian dataset available from Geoscience Australia in conjunction with geological data to match the aeromagnetic signature of the Coompana/Madura provinces and interior Wilkes Land in the Gondwana full-fit (c. 160 Ma) plate reconstruction framework of Aitken et al.7 and identify broad basement domains and lineaments. Our interpretation of Antarctic aeromagnetic data builds on the most recent tectonic model of Wilkes Land of Aitken et al.11 and preliminary interpretation of the 2015 Coompana aeromagnetic survey28 based on the most recent drillhole data available from the Coompana Province. We reproduce the Late Mesoproterozoic reconstruction of the Rodinia configuration (c. 1130–1040 Ma) of Aitken et al.7 with reversal of approximately 330 km of sinistral offset on the Mundrabilla-Frost Shear Zone to reconstruct the geometry of the Madura/Coompana and Antarctic conjugate provinces across Australia-Antarctica.We use the most recent magnetic anomaly map of the Antarctic (ADMAP-2)Supplementary Figures S1-S2Supplementary Table S1Supplementary Table S2Supplementary Table S3Supplementary Table S4Supplementary Table S5