Turing’s mechanism is often invoked to explain periodic patterns in nature, although direct experimental support is scarce. Turing patterns form in reaction–diffusion systems when the activating species diffuse much slower than the inhibiting species, and the involved reactions are highly nonlinear. Such reactions can originate from cooperativity, whose physical interactions should also affect diffusion. We here take direct interactions into account and show that they strongly affect Turing patterns. We find that weak repulsion between the activator and inhibitor can substantially lower the required differential diffusivity and reaction nonlinearity. By contrast, strong interactions can induce phase separation, but the resulting length scale is still typically governed by the fundamental reaction–diffusion length scale. Taken together, our theory connects traditional Turing patterns with chemically active phase separation, thus describing a wider range of systems. Moreover, we demonstrate that even weak interactions affect patterns substantially, so they should be incorporated when modelling realistic systems. Howevhibition ,10, sinchibition –13. Suchhibition . CooperaPhysical interactions are crucial for organizing biomolecules in cells , cells iIn this paper, we study a minimal system that is capable of forming droplets as well as Turing patterns. Effectively, we add physical interactions between activator and inhibitor to a standard reaction–diffusion system. This approach allows us to quantify how interactions affect pattern formation and it unveils a range of systems that interpolate between Turing’s mechanism and patterns formed in active phase separating systems. In particular, we show how weak repulsive interactions stabilize patterns by inducing cross-diffusion, while strong interactions lead to phase separation, where coarsening is arrested by chemical reactions.. 2. 2.1A and an inhibitor I. The basic Turing model describes the dynamics of the respective fractions t,i = A, I. Here, the first term on the right-hand side describes ideal diffusion with a diffusivity matrix h ≥ 1, these reactions promote the production of A and I by activator A and suppress it by the inhibitor I, while both species exhibit linear degradation with rate k. This choice of chemical reactions allows us to independently control the typical fraction ϕ0 of components A and I, the reaction rate k, and the reaction nonlinearity h. We show in the electronic supplementary material that equation , a phase enriched in A and I will segregate from one enriched in the solvent, whereas strong repulsion (large positive χ) will lead to segregation of A from I with an equal amount of solvent in both phases. However, it is unclear how this equilibrium behaviour is modified by the active reactions described by equation −1δF/δϕi,Di are the diffusivities of the species i = A, I, which are related to the mobilities Diϕi in this multi-component system [χ = 0) and the wavelength of patterns is large compared with w. Consequently, , patterns with finite amplitudes only emerge if the reactions are sufficiently nonlinear (large h) and the inhibitor diffuses sufficiently fast (DI ≫ DA), as expected for Turing patterns [h and DI/DA change. Apparently, repulsion between A and I promotes pattern formation (χ > 0), while attraction suppresses it (χ < 0). However, very strong attraction can again lead to large amplitudes  and  in a onepatterns . This trd corroborate these observations: without interactions (middle column), the system stays either homogeneous (pink parameter set) or forms normal Turing patterns (red parameter set) with a localized activator A and a fairly homogeneous inhibitor I. By contrast, strong attraction (left column) leads to co-localization of A and I, reminiscent of phase separation, albeit with a well-defined pattern length scale. Similarly, A segregates from I for strong repulsion (right column). Taken together, we thus showed that there is an interesting interplay between stereotypical Turing patterns and interactions promoting phase separation.The corresponding volume fraction profiles shown in figure 1. 2.2w, the generalized diffusion in equation . This analysis demonstrates that without interactions (χ = 0) in dilute system , diffusion is dominated by the diagonal entries, resulting in stereotypical Turing patterns. In this case, we show analytically in the electronic supplementary material that patterns can only form when the diffusivity ratio DI/DA and the reaction nonlinearity h are sufficiently large, consistent with the literature [To understand how interactions affect pattern formation, we first analyse weak interactions , equation  imply fluxes of A opposite to the gradient of I, thus favouring the segregation of the two species and enhancing patterns [ϕA, ϕI) = 〈ϕAϕI〉 − 〈ϕA〉〈ϕI〉, where the brackets denote spatial averages in the stationary state. χ, consistent with enhanced cross-diffusion), increasing reaction nonlinearity h, and diffusivity ratio DI/DA. The more detailed stability analysis presented in the electronic supplementary material demonstrates that repulsive interactions always promote pattern formation and lower the required reaction nonlinearity h and diffusivity ratio DI/DA; see χ < 0) generally stabilize the homogeneous system. However, this behaviour only holds for moderate interactions χ since strong attraction . Based on the strong correlations between A and I seen in A and I from the solvent, while the reactions play a minor role. Indeed, we show in the electronic supplementary material that phase separation is possible in the absence of reactions when χ < χ−, where χ− = 8 arctanh(1 − 4ϕ0)/(4ϕ0 − 1) marks the binodal point for a given average fraction ϕ0 of A and I. χ− is very close to the onset of patterns, and that the resulting profiles are perfectly co-localized. Taken together, strong attraction between A and I leads to co-segregation of the two components from the solvent while the reactions barely affect the amplitude.Turing’s mechanism cannot explain patterns that form when the activator A and I should also lead to phase separation. In fact, for χ > χ+ with χ+ = 1/ϕ0, we predict that A can segregate from I spontaneously, even without reactions present; see electronic supplementary material. Figures A and I and a vanishing threshold for h and DI/DA. These numerical data indicate a continuous transition from patterns formed by reactions and diffusion (Turing patterns for weak interactions) to those formed by phase separation . Taken together, we showed that patterns can form by reactions and by phase separation with an intricate interplay between them.Strong repulsion between . 2.4h and diffusivity ratio DI/DA. By contrast, the interaction strength χ has a stronger influence: More repulsive interactions lead to patterns with shorter wavelengths, presumably because larger χ promote pattern formation. However, the strongest influence on the pattern length scale ℓ is the reaction rate k: numerical simulations and the linear stability analysis presented in k allows adjusting ℓ over several orders of magnitude with barely any changes in the pattern amplitude.We next ask what determines the length scale ℓ of the patterns. We show in the electronic supplementary material that ℓ is hardly affected by variations of the reaction nonlinearity k affects the pattern length scale ℓ, we first focus on weak interactions. In this case, interactions mainly cause cross-diffusion , the system exhibits phase separation, implying that the initial instability is dominated by short patterns of length w while the stationary state patterns may exhibit much longer length scales due to coarsening [Figure 4b shows that the linear stability analysis indeed predicts ℓ ∼ w in the region where we predict phase separation. For associative phase separation at strong attraction (χ < χ−), these patterns remain stable, and coarsening is suppressed; the variation in ℓ reflects the influence of χ on the interfacial width; see electronic supplementary material. In the contrasting case of strong repulsion (χ > χ+), patterns coarsen to the reaction–diffusion length and thus scale with k−1/2; see figure 4b. This behaviour is similar to the coarsening observed in active droplets, where the final length scale is also governed by the reaction–diffusion length [figure 4b might not represent the full stationary state since domain sizes only grow logarithmically with time in these one-dimensional systems [A and I leads to associative phase separation.To understand how the reaction rate equation  and elecarsening . Figure n length . Note th systems . However. 2.5a) and strong interactions induce phase separation. In particular, strong attraction between A and I leads to co-localization (left column) whereas strong repulsion induces anti-correlated patterns (right column). Interestingly, in both cases of phase separation droplets form instead of stripe patterns, even though both phases occupy roughly half of the space. In such a case, normal phase separating systems exhibit stripe patterns [figure 5b shows that the pattern length scales we measured in one dimension are very close to the ones measured in two-dimensional simulations for the same parameters, suggesting that the results from the simple one-dimensional system translate to the more complex two-dimensional system and also hold in higher dimensions.So far, we have focused on pattern formation in one dimension for simplicity, but many natural patterns form in planar geometries. To see whether our results hold for this relevant case, we next perform a few selected simulations in two dimensions; see figure 5patterns , but the. 3A and I co-localize) or segregative (A separates from I). Both cases exhibit patterns for a much larger range of diffusivities and reaction nonlinearities than normal Turing patterns, and the resulting length scales differ: in the segregative case of strong repulsion, patterns are governed by the reaction–diffusion length scale and thus grow larger for weaker reactions. By contrast, patterns in the associative case of strong attraction are arrested at the interfacial width. Taken together, we thus demonstrated that interactions can affect patterns substantially. Our linear stability analysis presented in the electronic supplementary material and a recent pre-print [We propose an extension to Turing patterns that takes into account physical interactions that occur naturally. Weak repulsion between activator and inhibitor enhances patterns by inducing cross-diffusion, thus amplifying local activation and global inhibition. By contrast, strong interactions lead to phase separation, which can either be associative  and  on an eq


Parental feeding practices (PFPs) have been implicated in the development of children’s eating behaviours. However, evidence suggests that feeding practices may also develop in response to their child’s weight or emerging appetitive traits. We used the twin design to test the hypothesis that parents develop their feeding practices partly in response to their child’s appetite.Data were from Gemini, a population-based cohort of 2402 British families with twins born in 2007. Psychometric measures of PFPs and appetite were completed by parents when their twins were 16-months and 5-years. Within-family analyses including all twins with available data in the sample (n = 1010–1858 pairs), examined if within-pair differences in PFPs were associated with differences in appetitive traits, controlling for differences in birth weight-SDS, early feeding method and child sex. In a subsample of twin pairs who were considerably discordant for appetitive traits by ≥ 1SD (n = 122–544 pairs), the direction and magnitude of within-pair differences in feeding practices was explored.2=0.02–0.09) and 5-years (η2=0.05–0.21).Within-family variation in parental feeding practices in toddlerhood and early childhood was low (discordance ranged from 0.1 to 6% of the sample), except for pressure to eat . Within-pair differences in all appetitive traits were associated with differential use of ‘pressure to eat’ at both 16-months and 5-years. In the subsample of twins most discordant for appetitive traits, parents used more pressure with the twin expressing lower food responsiveness, lower emotional overeating, lower food enjoyment, higher satiety responsiveness, slower speed of eating, higher emotional undereating and greater fussiness in toddlerhood and early childhood . Effect sizes were small to large at 16-months (ηParents rarely varied their feeding practices between twins in toddlerhood and early childhood, except for pressure. Parents exerted greater pressure on their twin who expressed a poorer appetite compared to their co-twin, suggesting that parents develop a pressuring feeding style when their child expresses a poorer appetite or lower interest in, and enthusiasm for, eating. These findings could be used to guide interventions seeking to support parents in feeding their children in a way that nurtures the development of healthy eating behaviours.The online version contains supplementary material available at 10.1186/s12966-023-01440-2. Parents are often considered the ‘gatekeepers’ of their child’s food environment, especially during the preschool years, influencing the ‘what’, ‘when’ and ‘how’ of children’s eating through their feeding practices . As suchWhile much of the literature to date has focussed on relationships between feeding and eating behaviour from parent to child , 11, 12,only use different feeding practices with their twins (or siblings) if they are responding to different characteristics expressed by each child. Previous research using the twin design  found that parents did indeed vary their feeding practices if their twin children varied in their fussiness around food, with mothers using more pressure and instrumental feeding with the fussier twin ) of 8.2 (± 2.2) months old. The recruitment of the sample has been described in detail elsewhere [‘I use puddings as a bribe to get my child to eat his/her main course’; 16 months:α = 0.50, 5 years:α = 0.68) [‘I give my child something to eat to make him/her feel better when s/he is feeling upset’; 16 months:α = 0.85, 5 years:α = 0.80) [‘My child should always eat all of the food I give him/her’; 16 months:α = 0.65, 5 years:α = 0.64) [I limit my child’s access to sugary foods’; 16 months:α = 0.86, 5 years:α = 0.90) [‘I let my child decide when s/he would like to have his/her meal’) [‘I encourage my child to eat a wide variety of foods’; 16 months:α = 0.59, 5 years:α = 0.63) [‘I keep track of the high fat foods that my child eats’; 16 months:α = 0.72, 5 years:α = 0.73) [‘I model healthy eating for my child by eating healthy foods myself’; 16 months:α = 0.80, 5 years:α = 0.80) [‘I avoid buying unhealthy foods and bringing them into the house’; 16 months:α = 0.69, 5 years:α = 0.71) [Nine Parental feeding practices (PFPs) were reported by the primary caregiver when their children were 16 months and 5 years old –24. The  = 0.68) . ‘Emotio = 0.80) . The ‘pr = 0.64) . ‘Restri = 0.90) . The ‘Par meal’) . ‘Encour = 0.63) . ‘Monito = 0.73) . ‘Modell = 0.80) . ‘Covert = 0.71) –24.‘Given the choice, my child would eat most of the time’ 16 months:α = 0.76, 5 years:α = 0.81). Enjoyment of Food (EF) assesses a child’s subjective pleasure from eating . Emotional Overeating  and Emotional Undereating  assess the extent to which a child eats (more or less) in response to emotional stressors. Satiety Responsiveness (SR) measures a child’s sensitivity to internal cues of ‘fullness’ . Slowness in Eating (SE) refers to the speed of meal consumption . Food Fussiness (FF) examines a child’s pickiness about the flavour and texture of foods they are willing to eat . A mean score was calculated for each subscale for participants who had completed the majority of items for that scale . EUE was only measured at 5 years, it is not included in the CEBQ-T as mothers reported during the piloting of the questionnaire that their toddlers did not engage in this behaviour [Child appetite was assessed at five years using the Children’s Eating Behaviour Questionnaire (CEBQ)  and at 1ehaviour . Desire Mothers reported the gestational age of the twins at delivery (weeks) and each child’s sex. The feeding method used in the first three months of life was indicated by the mother using the following response options: “exclusive breast feeding”, “mostly breastfed, some bottle”, “equal breast and bottle feeding”, “mostly bottle feeding, some breastfeeding”, “almost entirely bottle feeding” and “entirely bottle”. Responses were dichotomised into 1 = Mostly breastfed  or 0 = mostly bottle-fed (“entirely or mostly bottle-fed for 3 months”).Primary caregivers consulted their child’s health records  when reporting birthweight and any subsequent weight measurements available at completion of the baseline (8 months), 16 months and 5 years questionnaires. Electronic weighing scales and height charts were sent to all families when the twins were aged two years to collect parent-reported height and weight measurements every 3 months. Weight (kg) data was converted into standard deviation scores (SDS) for child weight (Weight-SDS) at 16 months and body mass index (BMI-SDS) at 5 years using the UK 1990 British growth reference data , adjustiWithin-family differences between twin pairs for the seven eating behaviour appetitive traits and nine parental feeding practices were calculated by subtracting scores for Twin 2 (second born) from Twin 1 (first born) using a similar method to previous research , 16. TabWithin-pair differences in each appetitive trait, for all twins with complete data at each age, were entered into a linear regression model (continuous independent variable) to determine if this was associated with within-pair differences in each feeding practices (continuous dependent variable). Separate models were run for differences in each appetitive trait with differences in each feeding practice. The models controlled for differences between twins in birth weight SDS, early feeding method and sex. As a sensitivity analysis, models were additionally adjusted for differences in weight-SDS at 16 months  or BMI-SDS at 5 years .TableRepeated measures analysis of covariance were used to explore the magnitude of differences in feeding practices for a subsample of twins who were considerably discordant in their appetitive traits in toddlerhood (16 months) and early childhood (5 years). These analyses were used to explore differences in parental feeding practices between twin pairs who were discordant for each appetitive trait . ‘Discordant twins’ were defined as twin pairs who had a difference score ≥ 1 standard deviation (SD) of the difference score for that appetitive trait. For example, for food responsiveness at 16 months this equated to a difference score ≥ 0.43 between twin pairs  and early childhood (5 years), parents exerted greater pressure to eat on their twin who expressed lower food responsiveness, lower enjoyment of food, lower emotional overeating tendencies, higher satiety responsiveness, slower speed of eating, higher emotional undereating and was fussier around food compared to their co-twin  or BMI-SDS at 5 years . The findings for pressure to eat mirrored those observed in the main analysis, although the magnitudes of association were slightly attenuated when adjusting for child weight at measurement, but effects were still small to moderate in size Table.This is the most comprehensive study to date to use the discordant twin design to test the hypothesis that parental feeding practices are developed partly in response to children’s appetitive traits in toddlerhood (16 months) and early childhood (5 years of age). Our findings only partially supported this hypothesis. We observed that, despite considerable discordance in appetitive traits between twin pairs, parents did not vary their feeding practices between twin pairs for most feeding practices. The exception to this was pressure to eat for which considerable discordance in its use was observed. For pressure to eat, our findings supported the hypothesis that parents develop this feeding practice partly in response to their two twins expressing different appetites. In the analyses of the whole sample, we observed that within-parent variation in pressure to eat was significantly and positively associated with within-pair differences in appetitive traits in toddlerhood and early childhood – i.e. the extent to which a parent treated their two children differently with regard to pressuring them to eat, depended on how different their twin children were in their appetites. In the subsample of twin pairs who were considerably discordant for appetite, parents exerted more pressure to eat on their twin who expressed a poorer appetite and a lower interest in, and enthusiasm for, eating  in both toddlerhood and early childhood. The findings were largely unchanged by adjustment for child weight, indicating that the parental pressure-appetite relationship does not simply reflect parental concern around child weight. These findings indicate that parents tend to pressure their children to eat to differing extents, and that this feeding practice is developed partly in response to a child’s emerging appetite. However, the concordance for most feeding practices suggests that, in this sample of twins, most feeding practices are parent-driven rather than child-driven.Our findings support and extend previous twin and sibling research , 16, witDespite considerable discordance in appetitive traits between twin pairs, rates of discordance for all feeding practices, except for pressure to eat, were quite low. This suggests that in toddlerhood and early childhood, contrary to our hypothesis, feeding practices are not child-responsive – rather they reflect more general approaches to parenting and feeding. The low discordance for certain feeding practices  may reflect the fact that these are feeding practices that typically cannot be varied by one parent, particularly within the same eating occasion. For example, it would be difficult for a parent to model healthy eating to differing extents to two twins within the same household, without actively separating the twins during all eating occasions. In contrast, it is more feasible to pressure one twin to a greater extent than the other twin in the same eating occasion. This has also been suggested in previous research . HoweverStrengths of the current study include the large sample size and the use of psychometric measures of parental feeding practices and child appetitive traits. In addition, the twin design removes confounding from all environmental factors that are shared completely by twin pairs, thus providing powerful evidence that pressuring feeding practices are partly a response to differences in appetite expressed by each child. However, there are limitations to this study that should be acknowledged. Firstly, the measures of parental feeding practices and children’s appetite were parent-reported and subjective in nature, thus may be susceptible to desirability biases which may introduce measurement error. However, good correspondence has been shown with more objective measures of eating behaviour . FurtherThis is the most comprehensive study to use the twin design to test the hypothesis that parental feeding practices are developed partly in response to children’s appetitive traits in toddlerhood and early childhood. The findings revealed that for most feeding practices parents did not vary their feeding practices between their two twins. The exception to this was pressure to eat, for which considerable discordance was observed. Parents exerted greater pressure on the twin who expressed a poorer appetite and a lower interest in food and eating in both toddlerhood and early childhood. These findings suggest that parents adapt their pressuring feeding practices partly in response to the appetitive traits expressed by their children. Overall, however, our findings indicated that most feeding practices seem to be parent-driven behaviours, rather than a response to their child’s unique characteristics. These findings could be used to develop guidance to support parents around appropriate feeding practices to facilitate the development of healthy eating behaviours.Below is the link to the electronic supplementary material.Supplementary Material 1: STROBE Statement - checklist of items that should be included in reports of observational studiesSupplementary Material 2: Table S1 and Table S2


P < 0.05). Furthermore, the TEP produced by CBI stimulation was related to the motor inhibitory response to CBI recorded in a hand muscle (P < 0.05), but only when using the DC coil. Multisensory sham stimulation failed to modify the M1 TEP. Cerebellar conditioning produced changes in the M1 TEP that were not apparent following sham stimulation, and that were related to the motor inhibitory effects of CBI. Our findings therefore suggest that it is possible to index the response to CBI using TMS-EEG. In addition, while both F8 and DC coils appear to recruit cerebellar projections, the nature of these may be different.Cerebellar-brain inhibition (CBI) is a transcranial magnetic stimulation (TMS) paradigm indexing excitability of cerebellar projections to motor cortex (M1). Stimulation involved with CBI is often considered to be uncomfortable, and alternative ways to index connectivity between cerebellum and the cortex would be valuable. We therefore sought to assess the utility of electroencephalography in conjunction with TMS (combined TMS-EEG) to record the response to CBI. A total of 33 volunteers  participated across three experiments. These investigated EEG responses to CBI induced with a figure-of-eight  or double cone  conditioning coil over cerebellum, in addition to multisensory sham stimulation (experiment 3). Both F8 and DC coils suppressed early TMS-evoked EEG potentials (TEPs) produced by TMS to M1 ( While interactions between the cerebellum (CB) and cortex have long been recognised as critical elements of effective motor function, a large and growing body of evidence now demonstrates that cerebello-cortical (CB-C) connectivity facilitates function across a broad range of domains. This includes seemingly disparate areas such as cognition, speech and pain . The imThe application of non-invasive brain stimulation (NIBS) over CB is one of the only methods currently available for investigating CB-C in awake and behaving humans with high temporal resolution. One form of NIBS that has been extensively applied in CB research is transcranial magnetic stimulation (TMS). This technique involves application of strong magnetic pulses to the brain, which result in an induced current in underlying tissue that produces neuronal activation . An estaWhile CBI has provided valuable insight into CB physiology and function, the need for a peripheral output measure (i.e. the MEP) limits its application to characterisation of CB-M1 interactions. Given the extensive connectivity of CB with cortical regions outside of M1, and the functional importance associated with these connections, extending measures of CBI to allow investigation outside M1 would be of great benefit. To this end, there have been some initial investigations attempting to utilise electroencephalography (EEG) to record the cortical response to TMS over CB . The reA total of 33 participants  were recruited from the university and wider community to participate across three experiments. Two individuals participated in all experiments, 8 participated in two experiments and 23 participated in a single experiment. All individuals reported being right-handed, and exclusion criteria included a history of neurological or psychiatric disease, or current use of psychoactive medication. All experimentation was approved by the University of Adelaide Human Research Ethics Committee and conducted in accordance with the Declaration of Helsinki. Each participant provided written, informed consent prior to their involvement in the study. For the duration of all experiments, participants were seated in a comfortable chair with their arms supported and relaxed next to them.Surface EMG was recorded from the first dorsal interosseous (FDI) muscle of the right hand using two Ag–AgCl electrodes placed in a belly-tendon montage, with a third electrode placed above the styloid process of the right wrist used to ground the electrodes. Signals were amplified (× 300) and band-pass filtered  using a CED 1902 signal conditioner , before being digitised at 2 kHz with a CED 1401 ADC (Cambridge Electronic Design) and stored on a PC for offline analysis. Muscle relaxation was facilitated by displaying EMG signals under high gain on an oscilloscope placed in front of the participant. Signal noise associated with mains power was removed from EMG recordings using a Humbug mains noise eliminator .Within all experiments, EEG was recorded using WaveGuard caps  with 62 sintered Ag–AgCl, TMS-compatible electrodes in standard 10–10 positons, connected to an eego mylab amplifier (ANT Neuro). Electrodes were grounded to AFz and referenced online to CPz. Signals were filtered online (DC–0.26 × sampling frequency), digitised at 8 kHz and stored on a computer for offline analysis. The impedance of all electrodes was kept < 10 kΩ for the duration of each experiment. For all stimulation blocks during which EEG was recorded, auditory input was reduced by having participants listen to white noise through ear plugs, with volume set at the upper limit of comfort. In an attempt to characterise sensory input to the EEG signal during TMS, a block of shoulder stimulation involving 100 stimuli applied over the right acromioclavicular joint was collected in all experiments. While this approach is likely to only partially replicate the sensation of TMS, previous work has shown that it can account for a substantial proportion of the later TEP signal, which is thought to reflect sensory input .2 magnetic stimulator . Stimulation targeted the cortical location producing an optimal response in the right FDI. This was achieved by holding the coil tangential to the scalp at an angle of approximately 45° to the sagittal plane, oriented to induce a posterior-anterior (PA) current in M1. For CB stimulation, TMS was applied with either a conventional 70-mm F8 coil (experiment 1) or 110-mm DC coil (experiment 2) connected to a second Magstim 2002 magnetic stimulator. Stimulation targeted the right cerebellar hemisphere by holding the centre of each coil 3 cm lateral and 1 cm inferior to the inion, on the line joining the inion and right auditory meatus [TMS over M1 was applied using an F8 branding iron coil connected to a Magstim 200y meatus . Both M1Fifteen individuals  participated in a single experimental session, during which CBI was assessed using a conventional F8 coil to activate CB. Following identification of the FDI representation in M1, resting motor threshold (RMT) was defined as the lowest stimulus intensity producing an MEP ≥ 50 µV in at least 5 out of 10 consecutive stimuli during complete relaxation of the right FDI . PeripheWhile central measures of CBI using EEG also utilised a CB conditioning stimulus set at 100% RMT and an ISI of 5 ms, the intensity of test stimulation over M1 was instead set to the 100% RMT intensity. This was intended to reduce the likelihood of generating MEPs, as the associated muscle twitch produces sensory input that can confound the TEP . Three sFifteen individuals  participated in a single experimental session, during which CBI was assessed using a DC coil to activate CB. Following identification of the FDI hotspot and RMT, a block of 30 stimuli  was again used to assess peripheral measures of CBI. The location of all stimulation, in addition to the intensity of test stimulation over M1 and ISI, were all the same as applied in experiment Control) involved electrical stimuli (200-µs square wave) generated by a DS7A stimulator . These were applied to the scalp via cup electrodes that were temporarily glued in place ~ 25 mm apart , over the same location targeted in experiments 1 and 2. The intensity of electrical stimulation was set at 6 mA for all participants, as pilot testing revealed that higher intensities resulted in a sensation that was clearly distinguishable from real TMS . In addition, auditory stimulation from both air and bone conduction was provided by holding the wing of the DC coil against the EEG cap (directing the generated magnetic field away from the head), directly above the stimulating electrodes, and discharging it in time with electrical stimulation. Stimulation intensity was set at 52% MSO for all participants, as this was the average maximum tolerable intensity identified in experiment Fifteen individuals  participated in a single experimental session, during which we attempted to differentiate sensory- from transcranially evoked elements in central CBI recordings. To achieve this, we used a realistic sham condition involving multisensory stimulation to replicate the sensation of real CB TMS, but without generating transcranial activation of cerebellar tissue. Stimulation conditions and protocol were the same as those applied in experiments 1 and 2, and M1 stimulation used real TMS set at 100% RMT. In contrast, all stimulation over CB  using EEGLAB  and TESAcorr.As both conditioning and test stimuli utilised during central measures of CBI are able to produce TEPs, changes in the TEP produced by the second (test) stimulus may be obscured by summation with the TEP generated by the first (conditioning) stimulus. To reduce the impact of this confound on our data, we implemented a subtraction procedure for the paired-pulse condition within each experiment. As described previously , 49, thit-tests were used to compare peripheral CBI, test MEP amplitude, test MEP intensity and central CBI conditioning intensity between experiments 1 and 2. One-sample t-tests were used to assess the effects of conditioning stimulation on the test MEP during peripheral measures of CBI (relative to 100%). Data are displayed as means ± standard deviation and P < 0.05 was considered significant. Bonferroni correction was used to adjust for multiple comparisons and normality was assessed using Kolmogorov–Smirnov tests.One-way analysis of variance (ANOVA) implemented in SPSS  was used to compare age and RMT between all experiments, whereas independent samples Z-scores using Fisher’s transform, and significance was assessed using one-sample permutation tests with the null hypothesis that Z-scores were equal to zero [P values with the tmax method [Z-scores were subsequently transformed back to the original coefficient (rho) for display.All statistical analysis of EEG data was completed in Matlab (R2018b) using custom scripts and the Fieldtrip toolbox . As an i to zero . Family-x method , 51 and corr. Clusters were defined as at least two neighbouring electrodes demonstrating a difference between conditions with a P value < 0.05 and 10,000 iterations were used. Comparisons were made within 3 time periods associated with commonly investigated TEP components N16 (16–21 ms), P30 (22–38 ms) and N45 (39–65 ms). In an attempt to identify relationships between peripheral and central measures of CBI recorded in experiments 1 and 2, Spearman’s rank correlations were used to correlate MEP inhibition with TEP amplitude recorded within each electrode during the CB + M1corr condition. In an attempt to allow for fluctuations in the amplitude of the TEP generated by the M1 test stimulus, this analysis was also repeated using the difference between the M1 TEP  and the CB + M1corr TEP (referred to as ‘Diff’ in results). Multiple comparisons were again accounted for using cluster-based permutation analyses .Cluster-based permutation analyses were used to compare TEP waveforms generated by M1 stimulation with those generated by CB alone and CB + M1F2, 42 = 3.9, P = 0.03), with post hoc comparisons showing that the experiment 3 cohort was older (~ 4 years on average) than the experiment 1 cohort (P = 0.03). Table F2, 42 = 1.8, P = 0.2), test MEP amplitude , test MEP intensity  or the CB conditioning intensity used to assess central measures of CBI . In contrast, measures of peripheral CBI were significantly more inhibited in experiment t28 = 3.7, P < 0.001). Characteristics of EEG pre-processing within each experiment are shown in Table All sessions were completed in full and without adverse reaction. Age was significantly different between experiments , 22 and 38 ms (negative cluster: P = 0.03) and 39 and 65 ms . The response to CB + M1corr was smaller compared to M1 alone from 22 to 38 ms  and 39 to 65 ms (negative cluster: P = 0.02), suggesting suppression of the M1 TEP by CB stimulation. Correlation analysis failed to identify any significant relationship between peripheral measures of CBI assessed with MEPs and either CB + M1corr or Diff conditions , 22 and 38 ms (positive cluster: P = 0.04) and 39 and 65 ms (negative cluster: P = 0.04). The response to CB + M1corr was smaller relative to M1 alone from 22 to 38 ms (negative cluster: P = 0.02), suggesting that suppression of M1TEPs following CB stimulation was also present using a DC coil. Correlation analysis found that the magnitude of peripheral CBI assessed with MEPs was negatively related to the CB + M1corr response from 39 to 65 ms   Fig.  such thaControl). Grand average waveforms and associated scalp topographies for each stimulation condition are shown in Fig. Control alone from 22 to 38 (negative cluster: P = 0.009) and 39 to 65 ms (negative cluster: P = 0.0003). We could not find any evidence for differences between the M1 alone and CBControl + M1corr conditions, suggesting that sensory input resulting from CB stimulation is not responsible for M1 TEP suppression.In experiment The aim of the current study was to investigate if it is possible to record central indices of CBI using EEG. To achieve this, we used EEG to record TEPs generated by stimulation applied to M1 and CB in isolation, in addition to during the application of bifocal stimulation required to measure CBI. Stimulation to CB was also applied with two different approaches that are commonly utilised in the literature, involving different TMS coils. Our results suggested that the TEPs produced by stimulating M1 in isolation were significantly modified when conditioned by stimulation over CB. Furthermore, this modulation was not apparent when real conditioning TMS over CB was replaced with multisensory control stimulation. In addition, we also found that the EEG response to CBI was related to the magnitude of inhibition observed in peripheral measures of CBI, but only when assessed using a DC coil. Although preliminary, these results provide the first neurophysiological evidence of CBI at the cortical level.corr conditions. Given the subtraction procedure we applied for CB + M1corr TEPs, the low correlation observed within this condition likely stemmed from removal of TEP components related to sensory input. For CB alone, previous work has shown that multisensory sham stimulation targeting CB in isolation produces strong correlations with real stimulation from ~ 50 ms [In keeping with a growing literature , 52–55,  ~ 50 ms . The low ~ 50 ms , compariControl stimulation . Consequently, it could be suggested that variations in sensory input within each experiment could contribute to differences in the response to CB stimulation. Given that variations in both somatosensory and auditory input appear to primarily modify the later TEP peaks [Multisensory sham stimulation in experiment ion Fig. . ImportaEP peaks , 54, whicorr conditions. Furthermore, these changes were related to peripheral measures of CBI recorded in experiment In contrast to experiment 3, experiments 1 and 2 both identified significant differences in TEP amplitude when comparing the M1 and CB + M1While the focality of an F8 coil is preferred when stimulating M1, the greater distance between the stimulating coil and the CB has meant that many studies investigating CBI have opted to apply conditioning stimulation using a DC coil, which penetrate deeper than their F8 counterpart . HoweverIn support of this, the results of experiment 1 suggested that applying CB conditioning stimulation with an F8 coil was able to alter the amplitude of the M1 TEP Fig. . HoweverIf effects of the F8 coil on the M1 TEP were not driven by the mechanisms thought to produce CBI (i.e. activation of hand representations in lobules V and VIII) , what caIn conclusion, the current study attempted to identify central indices of CBI using bifocal TMS-EEG. We found that conditioning stimulation over CB suppressed the amplitude of early peaks within the M1 TEP, but that these changes were not apparent in a multisensory sham control experiment. While the extent of some of these changes were related to peripheral measures of CBI produced when using a DC coil to condition CB, this relationship was not present when an F8 coil was used for conditioning. Our results suggest that it is possible to record TMS-EEG indices of CB-C using the bifocal CBI paradigm, but that variations in how CB is activated (via different conditioning coils) may result in activation of different pathways.


This hydrolytic transformation wasfound to be catalytic with respect to hydroxide and bromide ions aswell. We have also demonstrated that, among the wide variety of seleniumspecies present in the acidic aqueous solution, the best result canbe obtained by considering HSeO3– as the kinetically active species towardbromine. The proposed mechanism containing 10 acid–base equilibriawith known equilibrium constants, the above-mentioned initiating equilibrium,and the hydrolysis of SeO3Br– is ableto fit all 49 kinetic absorbance–traces simultaneously, takinginto account properly the most important characteristics of the measureddata at strongly acidic conditions. Furthermore, this kinetic modelwas further extended by the direct reactions of hypobromous acid withselenium(IV) species suggested previously with reasonably modifiedrate coefficients to describe the pH dependence of the apparent second-orderrate coefficients over the pH = 1–13 range, providing a usefultool to predict more accurately the kinetic behavior of selenium(IV)species in water treatment process conditions.The bromine–selenite reaction at strongly acidicconditionswas investigated by monitoring the absorbance–time traces atthe isosbestic point of the bromine–tribromide system at aconstant ionic strength (0.5 M adjusted by sodium perchlorate) andtemperature. Despite the simplicity of the stoichiometry, the kineticswas found to be very complex. Although the formal kinetic orders ofthe reactants bromine and selenite are strictly 1, that of the hydrogenion varies from −2 to less than −3 and notably dependson the initial bromide concentration as well. The bromide ion alsoinhibits the reaction, making the whole system as a sound exampleof efficient autoinhibition. We have clearly shown that the inhibitoryeffect of the bromide ion cannot be explained quantitatively by eitherexclusively considering the unreactivity of the tribromide ion overelemental bromine or driving the reaction via hypobromous acid formedfrom the well-known hydrolysis of bromine in aqueous solutions. Insteadof that, bromonium ion transfer initiating equilibrium is suggestedbetween the selenium(IV) and bromine species to produce bromide ionand SeO In contrast to that, selenite may also be harmfulwhen reaching a critical level in fresh waters3 or in soils5 due to a severe accumulation process.Besides, selenium is also an important trace element for human beings,essential for fine functioning of many enzymes in relevant biochemicalprocesses, but the range between the dietary deficiency, treatmentefficiency, and toxicity might be quite narrow. Up to 0.3 mass %,it induces the apoptosis of malignant cells, but above that levelit may directly lead to healthy cell death.6 The proposed daily dose of selenium for a healthy adult was foundto be 55 μg7 necessary for the buildupof essential selenoproteins. In addition, research clearly showedthat an additional portion of 140–200–300 μg ofselenium uptake8 has a preventive effect in thecase of lung cancer,7 prostate cancer,9 and osteosarcoma6 orhelps to recover the insufficient functioning of reproductive organs.10 At the same time, selenium(IV) may behave asan antioxidant11 and a prooxidant;12 thus this duality may also play a crucial rolenot only in the prevention but also in the cancer treatment proceduresas well.13 Therefore, it seems to be ofspecial importance to unravel the mechanistic details of those reactionsin aqueous solutions, where selenium-containing species are involved.It is evident that an adequate and reliable answer could only be expectedto these problems if the mechanistic details of the reactions of seleniumspecies in aqueous conditions would be well-elucidated. Surprisingly,however, there is limited information available in the literatureabout the redox transition of selenite ion. One possible explanationof this fact is that aqueous selenite solution may contain multiplespecies in commensurable amounts, from which it is not easy to findthe kinetically active one. It is well-known that depending on thepH and the concentration selenium(IV) may be found in various formsin aqueous conditions.15 At low total selenite concentration,depending on the pH, SeO32–, HSeO3–, and H2SeO3 may be present overwhelminglyin the solution, but at a higher total concentration , the dimerization of differently protonated forms ofselenium(IV) might also occur16 providinga straightforward possibility for all species involved to be kineticallyactive reactants. Our preliminary experiments in the selenite–bromatesystem have revealed that the formation of bromine during the courseof this reaction is somewhat delayed and its characteristic sigmoidal-shapedprofiles suggested an appearance of the autocatalysis-driven clockreaction17 meaning that the rate of thereaction between the clock species (bromine) and selenite should becommeasurable with that of the formation of bromine from the bromide–bromatereaction. It straightforwardly means that the title reaction couldeasily be followed by conventional UV–vis spectroscopy providinga promising possibility to determine its apparently complex kineticsand mechanism. A survey of the literature has revealed that the titlereaction was first studied by Dikshitulu and Babu18 using the in situ generation of bromine from N-bromosuccinimide and bromide ion. They have found that the rateof the reaction is retarded by hydrogen and bromide ions as well,and both the monomeric and the dimeric forms of selenite can be treatedas reactive species toward bromine, with the latter one being morereactive. The inhibitory effect of bromide ion was interpreted bythe decreased reactivity of Br3– as compared to that of bromine. Ourrecent series studying the kinetics of the oxidation of iodine withvarious sulfur-centered reducing agents, however, has clearly revealedthat the formation of trihalide ion along with its decreased reactivitytoward the reactants may only play a marginal role in the appearanceof halide ion inhibition, if it plays a role at all.24 In all of these cases, it is rather the consequence of the initiatingequilibrium of a halonium ion transfer process from the halogen tothe sulfur-center of the substrate molecule yielding halide ion anda short-lived intermediate being responsible for this kinetic effect.On the basis of the sulfur–selenium chemical analogy, similarbehavior seems to be soundly conceivable. Moreover, because halideion is a product of these reactions, this phenomenon should ratherbe called autoinhibition. More recently, Liu et al. published a comprehensivestudy on the oxidation of selenite by various oxidants including bromine.25 Actually, not bromine but hypobromous acid wasused as an oxidizing agent, although it is out of question that brominewas also present in their study because hypobromous acid was preparedupon oxidizing excess of bromide ion by hypochlorous acid.25 They have found that the following rate lawis valid over a relatively wide pH range:T represents thetotal selenium(IV) concentration, and k12″, k13″, and k22″ were found to be 2300 ± 600, 74 000± 3000, and 820 ± 30 M–1 s–1, respectively. The main problem with this outcome is that k13″ and k22″ are kinetically indistinguishable fromeach other due to the rapidly established protonation and deprotonationequilibria of selenous acid and hypobromous acid. Because p Ka,HOBr = 8.8,26 one may easily see that thelast two terms of –1 s–1 with k13″ = 74 000 ± 3000 M–1 s–1, it is at least questionableas to whether the second term of kapp values  in each cuvette. The reaction was monitored by a Zeiss S600diode array spectrophotometer at the wavelength range of 400–900nm, and every kinetic run contained at least 1000 absorbance–timedata pairs originally. All of the solutions kept in the cell holderof the instrument were thermostated at 25.0 ± 0.1 °C.Altogether 49 kinetic experimentswere performed at different initial concentrations. The concentrationranges used in these experiments were as follows: 0.49–4.9mM, 1.1–6.8 mM, 0–31.2 mM, and 0.85–1.70 in thecases of selenite, bromine, bromide ion, and the pH, respectively.The solutions were delivered into the cuvette by the following order:first the perchlorate and the buffer solutions were introduced froman Eppendorf pipet, followed by the bromine solution. The measurementswere initiated at that time to determine precisely the initial bromineconcentration taking into consideration its volatility. After a well-definedtime-point, finally the selenite solution was added to initiate thereaction from a fast-delivery pipet. All of the measurements werefollowed up to at least 95% stoichiometric conversion to gain completeinformation about the whole course of the reaction.28 The absorbance–timetraces pp–q)–(2 (mono- and binuclear) species (βpq) is defined as follows:I = 1.0 M as well as at I = 0.3 M ionic strengthin sodium perchlorate medium are summarized in the upper part of Table S1. Because our measurements were carriedout in I = 0.5 M sodium perchlorate medium, we estimatedthe corresponding formation constants from Barcza and Sillén’sreport.14 On the basis of these data, onecan easily arrive at the following sequence of equilibria providingthe correct distribution of selenium(IV) species present in the aqueoussolution:Ki values are also presented in Table S1, and these ones served as a starting point to adjustthe forward and reverse rate constants for Figure S1). Even though the monomeric forms are the majorspecies under our experimental conditions meaning the relative amountof selenous acid (H2SeO3) and hydrogen-selenite(HSeO3–) varies 75–96% and 3–20%, especially at lower pH’sthe dimeric forms (H4(SeO3)2 and 4(SeO3)2 canalmost reach 7%; meanwhile, at the lowest acidity that of The most comprehensive equilibrium study of selenium(IV) specieswas reported by Barcza and Sillén in 1971 at various media.32 providing quitea diverse equilibrium constant of K7 =(0.67–12) × 10–9 M2 for thereaction given below:33 has clarified that not just application of differentionic strengths may provide a significant change in K7 values, but 33 has provided the value of K7 = 6.06× 10–9 M2 at an ionic strength of0.5 M and showed that the following process should also be consideredin establishing the kinetics and mechanism of the title reaction underour experimental conditions:K8 = 4.17 × 10–7 M–1. Consequently, the principle of detailed balancing34 provides an equilibrium constant of Ka1 = K7/K8 = 0.0145 M for the first acid dissociation constant of phosphoricacid, resulting in the value of pKa1 =1.84. Thus, if any small pH change is taken into consideration duringthe course of the title reaction, the acid dissociation process ofphosphoric acid must be included with the above-mentioned pKa1 value not to violate the principle of detailedbalancing, which is surprisingly not such an uncommon phenomenon inestablishing the complex mechanism as pointed out recently by Stanburyand Hoffman.35Thehydrolytic equilibrium of aqueous bromine solution has already beenstudied by several independent research groups,3618 on the title system. To clarify that this equilibrium alone is insufficientto explain quantitatively the bromide inhibition, K9 was reported between the range of 16.8–19.2M–1 depending on the experimental conditions.39 The value of 18.1 M–1 was chosen in this Articlebecause that value was determined at the same experimental conditions(at I = 0.5 M ionic strength in the presence of phosphoricacid/dihydrogen-phosphate buffer).39It is also well-knownthat in the presence of bromide ion bromine reacts to form tribromideion in a rapidly established equilibrium:+- and bromide inhibition with changing formalkinetic orders suggested by the initial rate studies shown below.The stoichiometry of the title reactioncan be expressed by the following simple equation:Figure S2). At thesame time, the product bromide ion has a strong inhibitory effectas indicated in 18The log–log plots of theinitial rates calculated from two series of experimental absorbance–timetraces by varying the initial concentrations of selenium(IV) and bromine,respectively, meanwhile keeping other conditions unchanged, have clearlyrevealed that the formal kinetic orders of the reactants are equalpurely to unity see S2. At thA can be consideredas a function of [H+] and even that of other rate coefficientsdiscussed later.As it is clearly seen, the inverse of the initialrate plottedagainst the initial bromide concentration provided a perfect straightline with a notable intercept at a constant pH. Consequently, therate of ka and A shown in Furthermore, the effect of the hydrogen ionconcentration on thereaction rate is even more complex as it is visualized in K9 was set to 18.1 M–1 with the forward (k9) and reverse (k–9) rate coefficients adjusted to 1.81 × 109 M–1 s–1 and 108 s–1, respectively, and the apparent second-order rate coefficient (ks) was fitted to minimize the average deviationbetween the measured and calculated data in a series of kinetic runswhere the pH, the initial bromine, and the initial selenium(IV) concentrationswere all fixed and the initial bromide concentration was varied. Sucha simplification makes it possible to focus just on the quantitativedescription of the bromide inhibition without considering the complexspeciation of selenium(IV) and the bromine hydrolysis. We have determined ks = 0.067 ± 0.003 M–1 s–1 by the least-square fit, but Figure S3 clearly indicates the inappropriateness of the model.We, therefore, concluded that the bromide inhibition cannot be describedquantitatively by just supposing the unreactivity of tribromide ionover elementary bromine in the title reaction.Our firstprobe for the quantitative description of the bromide inhibition wasbased on Dikshitulu and Babu’s report when 25 shown in K1–K9 equilibrium constants and k12″, k13″, and k22″ rate constants shown in the k12″, k13″, and k22″ rate coefficientsby a nonlinear least-square fit. An almost reasonable average deviationwas found (0.00745 absorbance unit), and the measured and calculateddata are illustrated in Figure S4. Thisfigure clearly shows that the model is not capable of describing correctlythe bromine and the pH dependencies, where systematic errors may beseen. For the sake of correctness, however, it should also be emphasizedthat bromide inhibition seems to be described significantly betteras compared to Dikshitulu and Babu’s report. As also expected,the result was quite insensitive for k22″, but k12″ = 795 M–1 s–1 and k13″ =2.23 × 1011 M–1 s–1 could be calculated. The latter value, however, significantly exceedsthe diffusion-controlled limit for second-order reactions in aqueoussolutions; therefore, it cannot be realistic, from which we concludedthat this model is also insufficient to describe quantitatively ourkinetic data.As a next step,we tried to use the kinetic model proposed by Liu et al.32–, HSeO3–, H2SeO3, H4(SeO3)2, –8% of the total selenium concentration, respectively,the very strong hydrogen ion inhibition observed in this system mayrequire these reactions to be included as well. The complete kineticmodel used in this calculation is represented in From these preliminary calculations,one can easily conclude that it seems to be plausible to considerhypobromous acid as the kinetically active species toward selenium(IV).Therefore, as a first step to improve the kinetic model, we have takeninto consideration the reactions of SeOFigure S5. As it is seen, although the average deviation mayseem to be almostsound, still one can easily notice systematic errors especially inthe case of bromide dependence. In addition to that, two kinetic parameters species should rapidly be equilibrated with bromine toproduce bromide ion by a bromonium ion transfer process to the substratemolecule as an initiating step.The result is also illustrated in n can be 1, 2, and3, when SeO32–, HSeO3–, and H2SeO3 are supposed to be the kineticallyactive species, respectively. This step must be supplemented by thehydrolysis of SeO3Br– to satisfy thestoichiometry of the reaction established:kR4,i and kR4,(i+5) values were initially included at the beginningof the fitting procedure, but the number of the necessary but fittedkinetic parameters to give a correct quantitative description wasreduced significantly to two by the end of these calculations. Forthe sake of completeness, we should emphasize that steps 1–10indicated in The initiating step of thetitle reaction may be summarized as follows: seethe 1, sugges seethe 15. Ofco32–, HSeO3–, or H2SeO3 is considered as the kineticallyactive species, the rate equation of the hydrolysis of SeO3Br– may easily be simplified as follows:2SeO3 asthe lone kinetically active species would lead to systematic deviationsbetween the measured and calculated data. Therefore, we have concludedthat under our experimental circumstance, H2SeO3 cannot be the kinetically active species. Third, in each kineticmodel, we have found that the rate coefficient of the backward processof the initiating equilibrium should be large enough to treat SeO3Br– as a short-lived intermediate. As aresult, from our calculations, besides the absolute value of kR2 , actually the kR2–/kR4,2 and kR2–/kR4,10 ratioscan be calculated, but not their absolute values. This phenomenonmay be readily understood when discussing the overall rate law ofthe title reaction 2, respectively, as the kinetically active species. One mayeasily miss the initiating equilibrium between m = 1); however,the concentration of this species in strongly acidic conditions isvery low, which means that the title reaction cannot be driven viathis pathway by realistic rate coefficients. Of course, To check whether the dimeric speciesmight also play a decisive role in determining the kinetics of thetitle reaction, we have performed further calculations where onlythe dimer forms of selenium(IV) were taken into consideration to initiatethe reaction. Therefore, the following initiating equilibrium wasestablished between selenium-containing species and bromine:3Br– (indicated by 4(SeO3)2 leads to almost the same, but a notably higher average deviationas compared to that of the previous models focusing on the exclusivereactivity of monomeric species. Third, even though to reach thisaverage deviation requires one more parameter to be fitted, the resultsobtained were not perfect, and systematic deviation may be observedbetween the experimental and calculated data especially at the seriesbelonging to the bromide dependence at middle pH’s and to theselenite dependence. As a result, these calculations clearly showedthat supposing just one kinetically active dimeric selenium(IV) speciesis not enough to describe quantitatively the measured kinetic traces.Therefore, in the next calculation procedure, we have tried to usemultiple dimeric Se(IV) species as kinetically active reactants. Inthis case, however, according to the principle of detailed balancing,34 the following equations must necessarily hold: KR5/KR6 = K5 and KR5/KR7 = K5K6, which means that kR6– = kR6kR5k5/(k–5kR5–) and kR7– = kR7kR5k5k6/(k–5k–6kR5–) equalities should always be fulfilled during thecalculation process. Using these conditions, the simultaneous evaluationof the kinetic curves clearly revealed that KR7 equilibrium can safely be removed fromthe model, and the values of the kinetic parameters obtained are givenin the final column of Figure S6). Moreover, the average deviation obtained from models 5–8is notably higher as compared to those calculated by models 1–4;thus it appears to be evident that the kinetically active speciesunder our experimental conditions are the monomeric forms of seleniteion. The only remaining question is whether any of the dimeric formsof selenite might play any role in determining the kinetics of thetitle reaction along with the monomeric form or not.From 32–, HSeO3–, KR1, KR2, KR5, and KR6 equilibria. It should be noted that KR7 can readily be eliminatedon the basis of the previous calculations mentioned in the previoussubsections. According to the principle of detailed balancing,34 the following relationships were per se introducedamong the equilibrium constants: KR1/KR2 = K1, KR1/KR5 = K4, and KR1/KR6 = K5K4 establishingthe equations between the corresponding rate coefficients necessaryto hold, such as kR2– = kR2kR1–k1/(kR1k–1), kR5– = kR5kR1–k4/(kR1k–4), and kR6– = kR6kR1–k5k4/(kR1k–5k–4), during the course of the whole calculationprocess. In other words, it means if kR1– is fixed by any reason and the equilibria belongingto the KR1, KR2, KR5, and KR6 constantsare involved in the chemical model, then kR2–, kR5–, and kR6– cannot be set arbitrarily; they have to be necessarily calculatedfrom the above-mentioned equations, otherwise the principle of detailedbalancing is violated. In the kinetic model, these equilibria mustbe followed by the hydrolysis of SeO3Br–  canbe expressed by the following equation:K1–K6, thisequation may be rearranged as follows:3–], and the positive root is given asThe total selenium(IV) concentration ([Se(IV)]A[Se(IV)]/B2 <1 inequality holds, 3– and H2SeO3 . Applying the steady-stateapproximation for species SeO3Br––]0 < 0.02 M inequalities are fulfilled,then ka is fairly constant, which soundlyexplains why the inverse of the measured initial rate was found tobe perfectly linear as a function of bromide concentration  may be defined asox]T = [Br2] + [Br3–] + [HOBr] + [OBr–], and [Se(IV)]T standsfor the total selenium(IV) concentration given in Figure S7 clearly shows that the calculated kapp values are clearly overestimated at lower pH’s by inclusionof steps I and II with the given rate coefficients. Another indicationthat k12″ and k13″ are overestimated may be seenin Figure 2b of ref  and bromide ions followed bythe hydrolysis of this short-lived intermediate. Even though hypobromousacid is also capable of a bromonium ion transfer process shown byTroy and Margerum40 and considering thisspecies as the reactive form of a bromine-containing compound insteadof bromine also accounts for the inhibitory effect of bromide ion;this conceivable route can easily be ruled out under strongly acidicconditions by the fact that the rate coefficient of the selenite–hypobromousacid reaction would significantly exceed the diffusion-controlledlimit of second-order reactions in aqueous solution to describe themeasured kinetic traces simultaneously. Furthermore, we have shown,providing the results of numerous alternative kinetic models, thateven though several selenium species are present under our experimentalcircumstances, the kinetically active form can safely be assumed asHSeO3–. Any further trials to include more than one selenium species askinetically active reactants failed to show significant improvementin the average deviation between our measured and calculated data.In this Article, we have clearly demonstratedthat the initialstep of the selenite–bromine reaction at strongly acidic conditionsis a bromonium transfer process leading to an equilibrium betweenthe bromine molecule and selenium(IV) species to form bromoselenate, butcombining the chemical information obtained at strongly acidic conditionsand reported in the pH range of 5–12 by Liu et al.25 made it possible to refine these parameters.The kinetic model that we developed is thus capable of providing auseful and more accurate tool working already in the range of pH =1–13 to predict the fate of selenium species during water treatmentprocesses.A more important consequence of our present work is that the kineticmodel working at strongly acidic conditions can readily be extendedby the direct reactions of the monomeric forms of selenium(IV) specieswith hypobromous acid proposed by Liu et al.Last, our present work still provides a general butstraightforwardprocedure of how to avoid violation of the fundamental rule of detailedbalancing when more than one kinetically active form of rapidly equilibratedspecies should be taken into consideration to obtain meaningful kineticmodels. Avoiding violations of the principle of detailed balancingis much more important than one might think. Even in environmentallyrelevant kinetic problems, numerous incorrect examples were recentlylisted in ref .Where,


We found that all four cell types in the superficial layers of the superior colliculus received monosynaptic (direct) input from V1. Wide-field neurons were more likely than other cell types to receive primary visual cortex input. Our results provide information on the cell specificity of the primary visual cortex to superior colliculus projection, increasing our understanding of how visual information is processed in the superior colliculus at the single cell level.The superior colliculus is a critical brain region involved in processing visual information. It receives visual input directly from the retina, as well as via a projection from primary visual cortex. Here we determine which cell types in the superficial superior colliculus receive visual input from primary visual cortex in mice. Neurons in the superficial layers of the superior colliculus were classified into four groups – Wide-field, narrow-field, horizontal and stellate – based on their morphological and electrophysiological properties. To determine functional connections between V1 and these four different cell types we expressed Channelrhodopsin2 in primary visual cortex and then optically stimulated these axons while recording from different neurons in the superficial superior colliculus using whole-cell patch-clamp recording  Visual information in mammals is processed by two main brain areas, the visual cortex and the superior colliculus (SC). Whereas the visual cortex receives visual information solely via the thalamus, the SC receives visual input directly from the retina, as well as via a projection from primary visual cortex . In rodeMuch work has been done recently to uncover the circuits underlying SC-mediated defensive behaviours in mice . Less atin vitro. To visualize dendritic morphology SC neurons were filled with biocytin and their dendritic trees reconstructed post hoc based on confocal fluorescence images. Using methods similar to the earlier work by The current study builds on earlier work showing that there are four main cell types with distinct morphological and electrophysiological properties in the superficial layers of mouse SC. Specifically, these are wide-field, narrow-field, stellate and horizontal neurons . To deteAll protocols involving animals were approved by the Australian National University Animal Experimentation Ethics Committee. The mouse line used in this study was C57BL6/J .Mice at 4 weeks age were anesthetized with isoflurane (3% in oxygen) in an induction chamber and then transferred to a stereotaxic frame where anaesthesia was continued via a close-fitting nosepiece (1% isoflurane in oxygen). Anaesthesia was confirmed by the absence of a response to a foot pinch. Ear bars together with a nose clamp were used to stabilize the head. A rectal probe coupled to a feedback-controlled heating pad was used to maintain body temperature at 37°C. The scalp was shaved and the remain hair removed with hair-removal cream. After cleaning with antiseptic, an incision was made along the midline of the scalp to expose the skull and a small craniotomy (0.5 mm diameter) made using a dental drill over V1 in the left hemisphere .Viral injections were made using a glass pipette (tip diameter ~ 20 μm) back-filled with silicone oil and tip-filled with 2 μL of adeno-associated virus (AAV) containing ChR2 (AAV1-hSyn.ChR2(H134R)-eYFP.hGH; AddGene). A total volume 350 ~ 450 nL was injected into V1 at a depth of 350 μm to 750 μm in 23 nL increments, with a two-minute delay between injections. After viral injection, the pipette was slowly removed and the scalp sutured. To prevent infection, antiseptic was applied to the wounded area. Mice were injected subcutaneously with 0.2 mL Meloxicam (0.1 mg/mL) for pain management, recovered in a warm cage with wet food and water and were monitored for 3 days (twice per day) to make sure that they fully recovered from surgery.2, 3.10 mM Na-pyruvate, 2.50 mM NaH2PO4, 0.50 mM CaCl2 (pH = 7.4). Brain slices (300 μm thick) containing the left V1 and SC were cut in a coronal plane using a Leica Vibratome 1000S. Slices were transferred to warm (35°C) incubating solution of composition:  for 30 min, which was then allowed to gradually cool to room temperature for another 30 min before being used for recording.Brain slices of the left hemisphere containing V1 and SC were prepared 3 to 4 weeks after viral injection of ChR2. Mice (age 7 to 8 weeks) were deeply anesthetized with isoflurane (3% in oxygen) and immediately decapitated. The brain was rapidly extracted and immersed in an ice-cold cutting solution of composition: 100 mM Choline Chloride, 11.60 mM N-ascorbate, 7 mM MgCl3, 3 mM KCl, 1.25 NaH2PO4, 2 mM CaCl2, 1 mM MgCl2 and 25 mM glucose . The region of SC containing V1 projections was identified by the presence of green fluorescent. Whole-cell somatic recordings were performed under visual control using a 60x objective on an Olympus BX50 microscopy equipped with differential interference contract optics and infrared illumination . All recordings were made in current-clamp mode using a current clamp amplifier (Dagan BVC-700A). To characterize electrophysiological properties of SC neurons, hyperpolarizing and depolarizing current steps of 1,000 ms duration  were applied via the somatic recording pipette. Voltage signals were filtered at 10 kHz and digitized at 20 or 50 kHz using an A-D converter  under the control of Axograph acquisition software  running on an Apple Macintosh computer (iMAC-i7). Axograph was used for both data acquisition and primary analysis.During recording slices were continuously perfused with oxygenated, heated (34°C) artificial cerebral spinal fluid (ACSF) of composition: 125 mM NaCl, 25 mM NaHCOmination . Patch pFull-field optogenetic stimulation was performed with 470 nm blue light pulses (2 ms duration) via an LED light source  attached to the epifluorescence port of the microscope. A GFP (green fluorescent protein) filter cube (Chroma) was inserted into the light path to direct 470 nm LED light onto the brain slice. For each neuron we averaged the response to 10 trails of LED stimulation at different intensities .In some experiments, one or more the following pharmacological agents was added to the ACSF perfusing the slice: The sodium-channel blocker tetrodotoxin , the potassium-channel blocker 4-aminopyridine , the α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptor blocker 6,7-dinitroquinoxaline-2,3-dione  and the N-methyl-D-aspartate (NMDA) receptor blocker amino-5-phosphonovaleric acid .Fluorescence labelling was used to obtain the morphology of recorded neurons . RecordeVQ1, VQ2) and left and right horizontal quadrants  was calculated, where VQ1 = polar angle 45 to 135 degrees, VQ2 = polar angle 225 to 315 degrees, HQ1 = polar angle 135 to 225 degrees, HQ2 = polar angle 315 to 45 degrees relative to the pia (polar angle 0 or 180 degrees). Dendritic orientation index (DOI) was calculated by subtracting the total dendritic length in vertical (VQ1 + VQ2) from horizontal (HQ1 + HQ2) quadrants, divided by the total dendritic length in all quadrants.Scholl analysis and polar plots of dendritic length were performed on reconstructed neurons. Total dendritic length in the upper and lower vertical quadrants  from the lower quadrant (VQ2) and applying a threshold. All the neurons above the threshold were classified as wide-field neurons. We then calculate the DIO of the remaining neurons, with neurons with a DOI above a threshold classified as narrow-field and those below classified as stellate neurons (see Results).Morphological classification proceeded as follows. First, neurons were classified as horizontal based on a negative We determined the following electrophysiological properties. Resting membrane potential (parameter 1) and input resistance (parameter 2) measured at steady state during long  hyperpolarizing current pulses. Sag in the membrane voltage back to the resting membrane potential during long  hyperpolarizing current pulses (parameter 3). The sag ratio was defined as the steady-state voltage at the end of hyperpolarizing current pulses divided by the peak voltage during hyperpolarizing current injections (−200 pA). The sag width, defined as time elapsed from the peak hyperpolarization during hyperpolarizing current injections (−200 pA) and development of the sag to half of its maximum amplitude (parameter 4). The amplitude of the rebound depolarization following cessation of long hyperpolarizing current injections  (parameter 5), defined as the rebound potential. The maximum number of rebound spikes evoked at the cessation of long hyperpolarizing current injections  (parameter 6). Action potential (AP) properties were measured from the first AP evoked by the lowest current injection which caused the neuron to fire APs regularly. AP threshold was defined as the membrane potential at which the slope of the AP reached 50 mV/ms (parameter 7). The voltage reached at the peak of the AP (AP height) measured from AP threshold (parameter 8). AP half-width, defined as the width of the AP at half AP height (parameter 9). The AP afterhyperpolarization measured as the voltage difference between AP threshold and the maximum hyperpolarizing potential after an AP (parameter 10). The maximum firing rate for the largest, positive current injection was also determined (parameter 11).Hierarchical clustering, also known as hierarchical cluster analysis, was performed in MATLAB using the 11 electrophysiological parameters described above, as well as the distance of the soma of the recorded neuron from the SC surface (parameter 12). Prior to hierarchical clustering, each parameter was normalized to give a range between 0 and 1. Hierarchical clustering starts by treating each cell as a separate cluster. It then repeatedly identifies clusters with similar properties and merges them. This continues until all the clusters are merged. The output of hierarchical clustering is a dendrogram, which shows the Ward’s linkage distance between clusters. Ward’s linkage distance is calculated from the average squared Euclidian distance between cluster centres.To determine whether a recorded SC neuron responded to optogenetic stimulation or not, we used non-parametric, receiver operating characteristic (ROC) analysis. SC neurons that showed a response to optogenetic stimulation were considered as “responders”, whereas those that did not show a response were considered as “non-responders”. ROC analysis estimates whether an ideal observer could classify whether a response was recorded in one of two possible conditions (here optogenetic stimulation or not). In each cell we compared the amplitude of the response 20 ms after optogenetic stimulation onset (“light”) with that observed 20 ms prior to optogenetic stimulation (“baseline”). Trials were filtered using a running (100 point) average prior to measurement of “baseline” and “light” response amplitude to remove noise. The overlap between “baseline” and “light” distributions was quantified by applying criterion levels ranging from the minimum to the maximum. Plots of the fraction of “baseline” and “light” responses above a given criterion level were used to generate ROC curves for each cell. The area under the ROC curve (AUC) represents a measure of separability between the “baseline” and “light” distributions. Statistical significance of the obtained AUC curves was determined by bootstrap analysis. 1,000 synthetic ROC curves were calculated based on values drawn randomly drawn from the “baseline” and “light” data set for each cell. The fraction of synthetic ROC curves with AUC values greater than that experimentally observed indicates the level of significance. If the observed AUC value was greater than 95% of the synthetic AUC values, we classified the cell as a “responder”. Conversely, if the observed AUC value was less than 95% of the synthetic AUC values, the neuron was classified as a “non-responder”.p < 0.05. Results were presented as mean values ± the standard error of the mean (SEM), unless otherwise stated. In the figures, a statistical difference of p < 0.05 is indicated by one asterisk; p < 0.01 by two asterisks and p < 0.001 by three asterisks. Non-significant difference is indicated by “ns”.For statistical comparison of properties between different cell types, an ANOVA was first used to determine whether there was an overall difference. If a difference was observed, a pairwise multiple comparison post-hoc test using Tukey’s method was used to determine which groups were different. Statistical variance for the post-hoc test was estimated from the variability across all groups. Statistical significance was set at To characterize the V1 projection to the SC fluorescently-tagged ChR2 (AAV1-hSyn.ChR2(H134R)-eYFP.hGH) was injected into V1 in one hemisphere of 4-week-old mice. After waiting 3 to 4 weeks for viral expression, a band of fluorescence could be visualized in V1 with less intense fluorescence in the SC , left. CTo determine whether neurons in V1 expressed ChR2 we made whole-cell recordings from the somata of pyramidal neurons in V1 . Action To confirm that responses in SC neurons were synaptic rather than due to ChR2 self-expression we bath applied the AMPA and NMDA glutamate antagonist DNQX and APV. In all cases, optogenetic responses were essentially abolished in the presence of DNQX and APV and recovered after washing out . These en = 39). This result indicates that all SC neurons that responded to optogenetic activation under control conditions received direct, monosynaptic input from V1.Finally, we tested if synaptic responses were monosynaptic. To do this we bath applied the sodium channel blocker TTX together with the potassium channel blocker 4-AP . TTX wiln = 21). To characterize their dendritic morphology, we determined the total dendritic length in the upper and lower vertical and right and left horizontal quadrants for each cell (n = 4). For the remaining neurons (n = 17) we subtracted the total dendritic length in the lower vertical quadrant from that in the upper vertical quadrant. If the total dendritic length in the upper vertical quadrant was five times greater or more than that in the lower vertical quadrant we classified neurons as wide-field (n = 5). We then re-examined the DOI of the remaining neurons (n = 12) and again applied a threshold (in this case 0.2), with all neurons with a DOI less than this value classified as stellate neurons (n = 7). The rational here is that neurons with a circular/spherical dendritic tree, such as stellate neurons, would be expected to have similar dendritic lengths in all four quadrants and therefore a DOI close to zero. By default, the remaining neurons, which had a DOI above 0.2, were classified as narrow-field neurons (n = 5).As the four main cells types in the superficial SC have previously been characterized based on their dendritic morphology, we reconstructed the dendritic morphology of a subset of recorded neurons following filling with biocytin and fluorescence labelling ; n = 21.ach cell , where tach cell ; n = 4. de-field ; n = 5.  neurons ; n = 7.  neurons ; n = 5.n = 153). In total, twelve different parameters were used for this cluster analysis (see Methods). Based on the earlier work by n = 5) and horizontal neurons (n = 4) were grouped into the same class based on morphological and electrophysiological properties (as well as soma depth) was 100%  had the largest sag ratio in response to hyperpolarizing current injections (n = 24) also had somata located primarily in deeper regions of the SGS (n = 27) had somata located primarily in the upper SGS (n = 17) were also located more superficially in the upper SGS . This result is similar to a recent study reporting that on average 43% of neurons in the superficial SC receive V1 input . Also coThe dendrites of wide-field neurons extend laterally as well as to the dorsal surface of the SC see . This moEPSPs properties of V1 input to the superficial SC were similar across the different cell types , althougFinally, the finding that a significant proportion of neurons in each cell type did not receive V1 input, despite the fact that activation of V1 input could generate action potentials in all four cell types except horizontal cells (which are thought to be inhibitory), suggests that the interconnectivity between excitatory neurons within the superficial SC is sparse. Alternatively, across the different cell types there may be separate, but interconnected, populations: One population which receives V1 input, and another that does not .Previous work indicates that the SC plays a critical role in the generation of defensive behaviours in mice in response to threatening visual stimuli. When mice are presented with visual stimuli representing the rapid approach of a predator, or stimuli representing a predatory cruising overhead, mice exhibit escape or freezing behaviours, retrospectively, with the type of defensive behaviour dependent on the stimulus .While there is evidence that the direct retinal projection to the SC is involved in the generation of escape behaviours to looming stimuli , other w+) SC neurons in the superficial SC provide excitatory input to the parabigeminal nucleus (PBG), evoking escape behaviours in freely moving mice  input from V1. Wide-field neurons were more likely than other cell types to receive V1 input, with this input being the most powerful. Furthermore, our data suggest that within each cell type there may be different populations: Those that receive monosynaptic V1 input and those that do not. This data provides cell specificity of the V1 to SC projection, increasing our understanding of how visual information is processed in the superior colliculus at the single cell level.The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.The animal study was approved by Australian National University Animal Experimentation Ethics Committee. The study was conducted in accordance with the local legislation and institutional requirements.SJ: Formal analysis, Investigation, Writing – original draft, Writing – review & editing. SH: Formal analysis, Investigation, Methodology, Supervision, Writing – review & editing. GS: Conceptualization, Funding acquisition, Methodology, Project administration, Resources, Supervision, Writing – original draft, Writing – review & editing.