Long channels with diameter of few tens of nanometer are produced by chemical track etching of swift heavy ion irradiated muscovite sheets. Such small apertures are most suitable e.g. as beam defining apertures for focusing systems in ion beam facilities enabling beam diameters down to a few nanometers. One of the most important parameters to consider is the interaction of the ion beam with the walls of the aperture. We report angle-resolved transmission and energy-loss measurements of MeV ion beams through ion-track-etched capillaries with very high aspect ratio of about 60. For all ion energies, the angle-resolved transmission curves measured through the channels show a significant enhancement with respect to the expected pure geometrical considerations. This broadening of the acceptance angle increases further when the kinetic energy is reduced. This effect is ascribed to low-angle scattering of the ions at the surface of the muscovite capillary walls. These results are well described by simulations applying a similar approach as used for ion beam channeling in crystals. One technique to overcome this problem is the ion track nanotechnology using swift heavy ions of kinetic energy in the MeV to GeV range. In many materials, mainly insulators, such ion projectiles produce along their trajectories a few nanometer wide track consisting of damaged, often amorphous material2. Employing a suitable chemical etching, the tracks can be converted into open channels. The diameter depends on the applied etching parameters and etching time. Given the high kinetic energy, this procedure can be used for thick films of several tens of μm3. Apertures produced by ion track etching have already been successfully used as irradiation mask for example to create a pair of close-by Nitrogen-Vacancy (NV) centres in diamond having been entangled at room temperature5. Track-etched polymer membranes were also successfully applied as templates to grow tailored nanowires6.Small and robust apertures are important for a large number of applications especially in ion beam technology. The collimation of particles like ions with energies in the keV to MeV range requires a mask of several μm thickness. Plasma etching or milling with a focused ion beam (FIB) are in principle suitable methods to fabricate tiny holes7. The latter is a very important requirement for apertures used for ion beam collimation of low MeV ions. The smoothness defines the so called transparent zone, which is a section near the edges where the ions pass through the aperture being deflected but not being stopped. If the ion beam has a certain divergence and the thickness of the sheet is high, the smoothness of the edge is even more important. Additionally, the mask material must be radiation hard and should not be degenerated when exposed to the ion beam. For highly charged ions it has been found that charging up of the channel walls leads to a focusing effect8. Furthermore, charging of pore walls was observed for ions below 100 keV9.A suitable and promising material to create small pores by means of ion-track etching is muscovite mica because of its high chemical stability. Muscovite mica has a complex crystal structure with chemical formula Compared to geometric considerations, an unexpected surplus of singly and doubly charged ions passing through the channels within small entrance angles was observed. To demonstrate our assumption of small angle scattering inside the capillaries, we performed experiments at different kinetic energies and tilt angles.2+ ions and direct irradiation of the detector. The ratio of the two measurements gives From scanning electron microscopy (SEM) micrographs Fig.  we can mThe difference between the measured yield and the porosity may have different reasons: (i) The edges of the pores are possibly not completely smooth, or slightly misaligned, (ii) there might be some residual gas or water within the pores, and (iii) the ion current measurement may be underestimated due to a detector efficiency that decreases for high ion currents. Nevertheless the transmission measurements are in the same order of magnitude as the porosities, and seem to be reasonable.α was varied in small steps and the number of ions transmitted per step was integrated. Figure α. This measurement was done for three ion energies. For further analysis we considered β as the angle of full width at half maximum (FWHM) of the transmission. The resulting values are To test transmission under different angles of beam incidence, the tilt angle entclass1pt{minimaαt is the thickness of the sheet and h is the diagonal of a pore, this can be either b or c depending on the pore orientation. ω is the corresponding angle at the diagonal, this is λ for diagonal c and κ for diagonal b. The calculated cross sections as a function of α are included in Fig. To get a qualitative understanding of the transmission behavior of the ions through the sheet, the geometric effect of rotating the capillaries with respect to the ion beam was taken into account. The capillaries have a rhombus-shaped cross section of average width of entclass1pt{minima10. Channeling is expected to be possible for ions traveling close to the wall of capillaries, because the ion trajectories form a small angle with the smooth surface walls. After etching, the inner walls are expected to consist of mono crystalline oxygen-terminated planes because they have the slowest etching rate. This planes form a rhombus with angles of 60° and 120° in the mica unit cell7, similar to the rhombus-shape of the pore cross-section observed in the SEM micrographs shown in Fig. When comparing the calculated and the experimental yield data, it is obvious that the measured curves are systematically broader, even if the maximum of the pore size distribution is taken into account. This effect increases with lower energies. Geometric effects alone can obviously not explain this broadening suggesting another effect that enhances the transmission of the ions through the capillaries. We propose this to be crystal channeling. This is a well known effect of ion implantation processes in crystals occurring if the ions move under a small angle with respect to certain specific crystal directions. The ions get deflected along the plane leading to enhanced penetration depths. In this case the potential of the crystal atoms can be assumed to be continuous because at high ion velocities, the potential of the single atoms averages to a smooth potentialZ2 is set to 8 for oxygen. If the ions are assumed to penetrate the first layer of atoms and get scattered at an arbitrary position in the crystal, again the stoichiometric average of 9.43 has to be considered. However, this would lead just to small deviations that have no influence on the interpretation of the data.To simulate channeling, two different scattering possibilities, axial and planar, can be considered. In the axial case, we assume a straight row of atoms on which the ions are scattered. This leads to a mixture of scattering events at the different atomic constituents of mica, with an atomic number of 9.43 as stoichiometric average. Under planar scattering the ion gets deflected under a small angle on the oxygen planes dominating the wall of the pore. So the atomic number of the target atoms 10:Z1 denotes the atomic number of the projectile ion which is 7 for nitrogen, Z2 is in the planar case 8 for oxygen and −2 is the atomic areal density in the plane according to the data given in11. Furthermore α is the Thomas-Fermi screening radius:To describe the deflection angle 10:d is the distance between the ions in a row of atoms. Due to the complicated crystal structure of muscovite, there are many different possibilities for scattering atoms in a row. Therefore the calculation was simplified by taking the muscovite density of 2.83 d = 2.23 Å. The mixing of the characteristic angles for the elements of the mica crystal is assumed to happen in a way that the characteristic angle is calculated for every element and then averaged over all characteristic angles in the following way:i is the index for each element and ki is the stoichiometry of mica.For axial channeling, the deflection angle 10:M denotes the atomic mass in atomic units and the target temperature T is in our measurements room temperature. According to12, the Debye temperature for oxides and silicates is in between 800 and 1200 K. Under this condition, the thermal movement has an amplitude of Yp) or axial (Ya) channeling10:ρ.The distance between ion and target atom is the main parameter for the deflection behavior. This distance varies due to thermal motion of the target atoms. For stronger thermal amplitudes, larger distances between ions and target surface are needed for stable channeling. The thermal movement can be estimated as followsTo compare the calculated and experimental values, we need to consider the geometric effect and the channeling distribution. Under perfect alignment of the capillary axis along the ion beam direction, the ions will not interact with the pore wall. When tilting, the geometric open cross-section gets smaller and some ions collide with the walls. For these collisions there is a certain probability for channeling and thus back scattering of ions from the pore wall, depending on the tilt angle. This leads to the ion transmission as a function of the tilt angle:β of the yield vs. tilt angle is deduced by solving The FWHM angle 0.5 Fig. . The meaentclass1pt{minimaα, the energy loss increases and the transmission becomes very small. Experimentally, this situation becomes difficult due to the small number of detected ions and the corresponding large statistical uncertainties. To estimate the energy loss, the ion trajectories were simulated as a straight path in the pores until the ions hit the wall. For the incidence angle α, the number of scattering events S can be calculated by: t is the thickness of the muscovite sheet and d is an effective radius equal to the radius of a circle with the same area as the pore, which is about (60 ± 2) nm. To calculate the energy loss for each scattering event, the kinematic formula from Rutherford-back-scattering experiments was used13:Ein is the incident ion energy and M1 and M2 denote the mass of projectile and target atoms, respectively. Calculation yields just a very small energy loss in the range of 1.5% of the incident ion energy. This energy loss is smaller than the respective experimental error and this further strengthens the assumption of crystal channeling. For angles so large that the pore is geometrically closed, the ions need to penetrate the material for a certain distance if no guiding is assumed. This would lead to a significant energy loss.Planar channeling seems to describe the trajectory of the ions rather well for MeV energies and low charged ions. Furthermore, the energy loss of the ions while traveling trough the pores was recorded in dependence of the tilt angle. For larger tilt angles et al.9 and Zhang et al.8 that charging of nanopores influences the transmission of low-energy ions and could also lead to a guiding effect, it is expected that electric effects get more pronounced for ions with greater charges or lower energies. For ions with several 100 keV charging up becomes less important. The experimental data are in good agreement with calculations for axial and planar channeling. Track-etched channels in muscovite sheets are shown to be radiation hard and ideal nanoapertures for ion beams in the MeV regime. This opens new fields of applications such as mapping of radiation hardness by means of ion beam induced current (IBIC) measurements with high lateral resolution or targeted irradiation of single bio cells. Moreover, nanochannel collimation is a suitable, low cost alternative to microprobe systems for low current applications or single ion implantation.Transmission experiments of MeV light ions through high-aspect ratio nanochannels in mica show unexpected transmission yields when tilting, which can not be explained by geometric means. We ascribe this effect to channeling of ions within the surface walls of the capillaries. We provide evidence that charging effects are not influencing the pathway of single and double charged ions in the MeV range. The potential along the capillary is constant and the electric field inside the pore is negligible. Additionally, we coated the surface of the mica sheet with a metal layer. Knowing from Wang 3. The irradiations where performed with Samarium ions under normal beam incidence and a kinetic energy of 1.6 GeV corresponding to a range of 90 μm in mica14. Since each individual ion creates a track, the number of tracks is controlled by the applied ion fluence. For this experiment we used a fluence of 2. Room temperature etching of irradiated mica samples in 10% hydrofluoric acid for one hour leads to highly parallel channels with rhombic cross-section. Figure 2. The resulting porosity was determined to be 7. To avoid charging effects the surface of the sheet was sputter coated with a 8 nm thick gold layer.Muscovite sheets (provided by Jahre GmbH) of 5–10 μm thickness were irradiated at the linear accelerator UNILAC of the GSI Helmholzzentrum in Darmstadt15. The mica sheet was mounted on a goniometer that enables an eucentric rotation in five directions16 with a resolution of less than 1 μm for x, y, z and 0.015° in ϑ and 0.005° in φ. These angles get projected on the sample in the following way: α is the angle between the ion beam and the pore direction, ϑ is a rotation perpendicular to the ion beam and φ is a rotation around the ion beam. The thickness of the mica sheet was determined by means of scanning transmission microscopy (STIM) using H+ ions at a kinetic energy of 2.25 MeV. The beam was focused to below 1 μm and completely penetrated the sheet. The corresponding energy loss of the transmitted ions was compared to a SRIM-201314 calculation yielding a sheet thickness of All ion beam transmission measurements were performed at the particle accelerator laboratory LIPSION at Universität Leipzig+, 2 MeV and 4 MeV N2+ ions. The beam flux was between 1.7 × 106 and 0.1 × 106 ions/cm2 s. In order to ensure a parallel beam, these measurements were performed without any focusing lens. The divergence angle of the ion beam is given by the distance and size of the beam defining apertures yielding 0.2 mrad. According to SRIM, the penetration depth of 4 MeV nitrogen ions in mica is 3 μm. For all beams the mica thickness was thus sufficiently large to completely stop the ions. A two axis goniometer was used to vary the angle of the sample surface with respect to the incoming ion beam. The transmitting ions and their energy were recorded by a surface barrier detector that was mounted behind the sheet. In a first step, the length axis of the pores was aligned parallel to the incident ion beam. Perfect alignment of the pores was assumed at the angle where maximum transmission is monitored. For the subsequent measurements, the angle φ was kept constant while the angle ϑ was varied. For every ϑ angle position, the irradiation time was the same and the number of ions passing the sheet was integrated. Figure 2+ after transmission through the capillaries as a function of their energy for various ϑ angles.To investigate the interaction between ions and capillaries at different kinetic energies, the experiments were performed with 800 keV N+ ions. Several hours of ion irradiation with H+, N+ and N2+ ions of different energies showed no degradation and change on the muscovite. The datasets generated and analyzed during the current study are available from the corresponding author on reasonable request.The radiation stability of the mica sheet was checked by inspecting the surface before and after the ion bombardment by SEM. The structure of the sheet was controlled with scanning transmission ion microscopy measurements using 2.25 MeV H


Palliative care expert teams in hospitals have positive effects on the quality of life and satisfaction with care of patients with advanced disease. Involvement of these teams in medical care is also associated with substantial cost savings. In the Netherlands, professional standards state that each hospital should have a palliative care team by 2017. We studied the number of hospitals that have a palliative care team and the characteristics of these teams.In April 2015, questionnaires were mailed to key palliative care professionals in all general, teaching and academic hospitals in the Netherlands. Out of 92 hospitals, 74 responded (80 %).Seventy-seven percent of all participating hospitals had a palliative care team. Other services, such as outpatient clinics (22 %), palliative care inpatient units (7 %), and palliative day care facilities (4 %) were relatively scarce. The mean number of disciplines that were represented in the teams was 6,5. The most common disciplines were nurses (72 %) and nurse practitioners (54 %), physicians specialized in internal medicine (90 %) or anaesthesiology (75 %), and spiritual caregivers (65 %). In most cases, the physicians did not have labeled hours available for their work as palliative care consultant, whereas nurses and nurse practitioners did. Most teams (77 %) were only available during office hours. Twenty-six percent of the teams could not only be consulted by healthcare professionals but also by patients or relatives. The annual number of consultations for inpatients per year ranged from 2 to 680 (median: 77). On average, teams were consulted for 0.6 % of all patients admitted to the hospitals.The number of Dutch hospitals with a palliative care team is rapidly increasing. There are substantial differences between teams regarding the disciplines represented in the teams, the procedures and the number of consultations. The development of quality standards and adequate staffing of the teams could improve the quality and effectiveness of the teams.The online version of this article (doi:10.1186/s12913-016-1770-2) contains supplementary material, which is available to authorized users. In the Netherlands, palliative care is an integral part of regular healthcare. Dutch government policy is based on the idea that palliative care is generalist care and should therefore be provided by any healthcare professionals whenever necessary. As such, palliative care is not a distinct medical specialty as it is in many other countries. Core elements of palliative care, such as basic symptom management and aligning treatment with patients’ goals, should be integrated in care as it is delivered by any healthcare professional. In case of complex problems, such as managing refractory symptoms or negotiating a difficult family meeting, specialist palliative care should be available. Palliative care teams (PCTs) can be consulted by professionals involved in palliative care and can provide such specialist palliative care, either in or outside the hospital. This model of palliative care delivery resembles the model as described by Quill and Abernethy  which diThis development underlines the important role PCTs are expected to play in supporting professional caregivers and in providing specialized palliative care.The aim of this study is to investigate the number of hospitals that currently have a PCT and to study the characteristics of these teams.In April 2015 we performed a cross-sectional study. An online questionnaire was sent to key persons in palliative care in all 92 general, teaching and university hospitals in the Netherlands, including two oncology centers. The key persons were care professionals who are known to have an important role in the development of palliative care in their hospital. In case of non-response, these persons were contacted after several weeks by mail or phone to remind them of the study and to invite them to fill in the questionnaire.n = 43), teaching hospitals (n = 23) university hospitals (n = 7) and one oncology hospital. Non-responding hospitals included both hospitals with and without PCTs.In total, 74 questionnaires were returned (response 80 %); responses came from general hospitals  compared to PCTs that started after 2012 (median 39 consultations). PCTs in university hospitals have more referrals compared to PCTs in general and teaching hospitals. PCTs in university hospitals tend to have started earlier compared to teaching and general hospitals. There are no other differences between different types of hospitals. All PCTs can be consulted for inpatients, but only 28 teams can also be consulted at the outpatient clinic, with a median annual number of consultations for outpatients of 20 (range 2–384). Ten teams were willing to visit patients at home with a median annual number of six home visits (range 1–74). Twenty-four percent of the respondents stated that the number of consultations exceeds their capacity; 47 % stated that the number of consultations is less than their capacity. The annual number of palliative care consultations for inpatients as a percentage of the total annual number of hospital admissions ranged between 0.01 and 2.3 %, with a mean of 0.6 %.The most common disciplines represented in the PCTs are nurses 72 %) and nurse practitioners (54 %), physicians specialized in internal medicine (90 %) or anesthesiology (75 %) and spiritual caregivers (65 %). Both psychologists and social workers participate in 28 % of the teams. In the majority of teams, nurses and nurse practitioners have labeled hours for their work as a palliative care consultant. However, the majority of medical specialists, social workers and spiritual caregivers have no labeled hours. For the minority that does, the mean number of labeled hours varies between 1 and 4 h per week. About one third of the teams include a general practitioner and another third includes a nursing home physician  Table . The meaSixty-five percent of the PCTs have defined quality criteria for providing their advice. The most frequently defined criterion is that the PCT advice is given within 24 h. Ninety-one percent of PCTs has specified some requirements regarding the PCT members’ expertise. However, a broad range of educational programs is mentioned and there is no consensus regarding the required education for each participating discipline.Respondents were asked to mention factors that either supported or impeded the development and implementation of the team. The most frequently mentioned supportive factors were enthusiasm and motivation of the PCT members, including a role as ‘ambassador’ for the team of nurses and nurse practitioners (46 %), aspects regarding functioning of the team  (47 %), receiving  support from the hospital management (22 %) and satisfaction of patients and referring physicians who acknowledge the added value of the team (16 %). Impeding factors for successful development of a PCT are lack of finances (77 %), lack of commitment and/or financial support by the hospital management (19 %), lack of awareness regarding the existence of the PCT (18 %) and a (negative) attitude of some medical specialists and nurses towards the PCT (18 %). Some respondents (5 %) mentioned late referral to the PCT as an impeding factor.The awareness of palliative care in Dutch hospitals is increasing. A vast majority of hospitals has an assignment from the board of directors or medical staff to develop palliative care or a palliative care steering committee. The percentage of hospitals with a PCT has risen from 39 % in 2013 . As posiIn studies that show positive effects of PCTs, these teams are often consulted relatively early in the a patient’s disease trajectory and often in the outpatient clinic , 11, 20.Besides differences in the number of consultations, there are also differences in the working processes of the teams, in disciplines participating in the teams, in the expertise teams require from their members and in the availability of the team and involvement in care for out-patients. Furthermore, there is no consensus regarding the use of measurement instruments. Non-specialized care professionals in hospitals as well as PCTs use a wide variety of measurement instruments. In this survey, most commonly used instrument by both generalists and specialists in palliative care is the Distress Thermometer, an instrument originally validated as a screening tool for psychological distress, that is now also in some places used to screen patients for referral to a PCT , 22.In a 1-day observational study in 14 Belgian hospitals, it was found that 9.4 % of all patients admitted to the hospital are in the palliative phase, which was defined as the phase where a patient is suffering from an incurable, progressive, life-threatening disease, without a prospect of remission, stabilization or improvement . A studyth on the overall score and 2nd on palliative care and healthcare environment, the score on human resources is relatively low (22nd). This means that the availability of specialists in palliative care and healthcare professionals with general knowledge of palliative care is low, as is the availability of appropriate training [Furthermore, the number of labeled hours that members of the PCTs have for their work as an expert palliative care consultant, is very low, especially for physicians. This is in line with a recent report of the Economic Intelligence Unit on the Quality of Death Index. Although the Netherlands are ranked 8training . This isDumanovsky et al. conclude that higher staffing levels  were associated with higher service penetration . In their study, palliative care programs with the highest staffing levels (≥2.7 FTE per 10.000 admissions) reached a service penetration of 6.5 %. Higher service penetration was associated with shorter time to the initial palliative care consultation .This nationwide study demonstrates the increasing number of PCTs in the Netherlands. It demonstrates variations between the number of referrals and working procedures of the teams. The results can have implications for the development of new (models for) PCTs. A strength of this study is the relatively high response rate. Among the non-responders were both hospitals with and without PCTs. Therefore we can conclude that this study gives a good overview of current palliative care practices in Dutch hospitals.A limitation is that our study does not give insight in the quality of palliative care in Dutch hospitals or in the quality of the PCT involvement. From a recent comparison between different countries, using data from 2010, it was found that end-of- life care in the Netherlands is characterized by a relatively low percentage of hospital deaths, a low percentage of intensive care admissions and a low use of chemotherapy in the last 180 days before death . This suPalliative care in Dutch hospitals is often supported by PCTs. The number of these teams has rapidly increased over the last few years, but there are substantial differences between teams regarding the disciplines represented in the teams, the procedures and the number and timing of referrals. The involvement of PCTs in care for incurably ill patients is relatively limited.To stimulate the further development and implementation of PCTs in hospitals, we recommend the development of a formalized quality framework with models for  palliative care team consultation, to improve the quality of palliative care in hospitals. Such a framework, that should be adopted by professional organizations and policymakers, can form the basis for the development of quality criteria and quality assessment of PCTs. The concepts and borders of generalist and specialist palliative care should be discussed and where possible defined, so that criteria can be set regarding the education of all disciplines involved. Furthermore, adequate staffing of the PCTs is necessary to increase the number of PCT consultations.


In general, enzyme activity is estimated from spectrophotometric data, by taking the slope of the linear part of the progress curve describing the rate of change in the substrate or product monitored. As long as the substrate concentrations are sufficiently high to saturate the enzyme and, the velocity of the catalyzed reaction is directly proportional to the enzyme concentration. Under these premises, this velocity can be taken as a measure of the amount of active enzyme present. Estimation of the enzyme activity through linear regression of the data should only be applied when linearity is true, which is often not the case or has not been checked.Malus x domestica Borkh. cv. ‘Jonagold’). The models are based on Michaelis–Menten and first order kinetics, which describe the reaction mechanism catalyzed by the enzymes.In this paper, we propose a more elaborate method, based on a kinetic modelling approach, to estimate the in vitro specific enzyme activity from spectrophotometric assay data. As a case study, kinetic models were developed to estimate the activity of the enzymes pyruvate decarboxylase and alcohol dehydrogenase extracted from ‘Jonagold’ apple  contains supplementary material, which is available to authorized users. The most diverse and largest group of proteins are enzymes, biological catalysts enhancing the rates of metabolic reactions and thereby play an important role in the regulation of metabolic steps within a cell . MichaelMany assays are described to measure enzyme activity in vitro , 4. Genem value , thiamine pyrophosphate, alcohol dehydrogenase (N-morpholino) ethane sulfonic acid (MES) buffer (pH 7.5), 5 mM dithiothreitol and 2.5% (w/v) polyvinylpyrrolidone and 0.02% (w/v) triton X-100. The homogenate was kept below 4 °C for 20 min and stirred continuously. The homogenate was centrifuged at 14,000g for 20 min at 4 °C. In order to achieve 80% efficiency for the extraction, the pellet was extracted once more using the same protocol. The supernatants of both extractions were well mixed and retained as enzyme extract for measuring PDC and ADH activities. The protein concentration of the crude extracts was determined using the Bradford assay  are two unknowns appearing as a single product term, together being responsible for the overall perceived enzyme activity, a single composite replacement term, + , the modelled absorbance Amod is given by:αNADH being the specific absorbance of NADH. To take into account the sample specific matrix effect , the volume of the extract (Vextr), and the total volume of the reaction mixture (V). Hence, Eq. PDC and the concentration of PDC in the extract [PDCextr] into a single measure of the enzyme activity of PDC as extracted from the sample. Therefore, Eq. 0 and [ACA]0 as initial conditions.Like before, the amount of PDC present in the reaction mixture is related to the concentration of enzyme present in the extract  being, on its turn, a combination of a sample specific absorbance of the extract and the constant absorbance by pyruvate, the modelled absorbance Amod is given by:αNADH being the specific absorbance of NADH as determined by Eq. According to Fig. Km,ADH were estimated per sample, but the model parameter kADH was estimated in common over all samples, as the concentration of the enzyme ADH added to the reaction mixture was the same for all of them.The final model for the PDC assay as defined by Eqs. The kinetic model to estimate the enzyme activity of PDC takes into account the entire progress curve, as shown in Fig. The linear regression approach is generally used to estimate enzyme activity. In the next paragraph a comparison is made between the generally accepted linear regression approach and the kinetic modelling approach to estimate enzyme activity. Advantages of the latter method over the classic method are stressed in the text.m value. However, in the case of NADH, to stay within the detection range, the NADH concentration should not exceed 0.2 mM [When optimum conditions are applied in the enzyme assay, i.e., substrate and cofactor saturation, standard pH, temperature and ionic strength, the slope of the linear part of the progress curve can be taken as a measure of the maximum enzyme activity. To correctly compare the activity of different enzymes, it is important to always quantify their activity under the optimum working conditions. Like mentioned in the introduction, to experimentally realize substrate saturation, the substrate is required to be present in a 100-fold surplus of the Kd 0.2 mM . As a reFigure Since two reactions are involved in the PDC assay, it takes a while before the formation and conversion of the intermediate becomes constant, causing an initial lag phase before reaching the linear phase. As can be seen from the simulated model data Fig. b, only oOf course, one should be aware of the limitations of the kinetic model related to the assumptions applied. As the model was focused towards the reaction period where NADH would still be present, the eventual depletion of pyruvate was not incorporated resulting in an everlasting increase of acetaldehyde. In reality, if the reaction would be allowed to continue, pyruvate would effectively be depleted after 100 h or more. From this it can be concluded that the assumption made was acceptable for the current application.Furthermore, the models can help to optimize the assays by systematically studying the effect of the various design parameters like extract volume, substrate concentration and indicator enzyme amount. For instance, it was hypothesized that the initial lag phase in the PDC assay could be prevented by increasing the amount of ADH, in which case the initial amount of acetaldehyde that needs to accumulate before the conversion to ethanol starts would be less. As shown in Fig. While the accuracy of the linear regression approach will benefit from an increased ADH level, the kinetic modelling approach can deal with nonlinear results, not necessarily requiring an increased ADH level. As an additional advantage, costs of the assay can be reduced.Existing enzyme assays to measure the in vitro specific enzyme activity of PDC and ADH were optimized in order to increase the signal to noise ratio. An elaborated kinetic model based method was proposed to estimate the in vitro specific enzyme activity from the spectrophotometric assay data. The kinetic models developed in this study can accurately estimate the enzyme activity of PDC and ADH in the given assays. In contrast to the linear regression approach, the models can be used to estimate the enzyme activity whether or not linearity is achieved since they take into account the complete progress curve. Using the kinetic modelling approach the maximum activity of the enzyme can be estimated through extrapolation even if the saturating substrate conditions were not fully realized in the enzyme assay, making it possible to compare the obtained results between different experiments and between different labs and publications. The developed models can be applied to routinely analyze continuous spectrophotometric enzyme activity data, but like shown in this paper, they can also be used as a tool to optimize the enzyme assays by systematically studying the effect of the various design parameters. Finally, the use of kinetic models to estimate the in vitro specific enzyme activity can be extended to other enzymes as long as the underlying reaction mechanism is known and the reaction dynamics can be monitored in a continuous way. Furthermore, the differential equations of the developed models can be implemented in any software environment that supports estimation of kinetic parameters on ODE based models, e.g. Matlab , Mathematica , Maple  and R , or in online web tools such as ENZO (enzyme kinetics .Additional file 1. ADH_model.Additional file 2. PDC_model.


We give a complete explanation of the macroscopic features of the phase diagram using what we call nested fat shocks.The asymmetric exclusion process is an idealised stochastic model of transport, whose exact solution has given important insight into a general theory of nonequilibrium statistical physics. In this work, we consider a totally asymmetric exclusion process with multiple species of particles on a one-dimensional lattice in contact with reservoirs. We derive the exact nonequilibrium phase diagram for the system in the long time limit. We find two new phenomena in certain regions of the phase diagram:  Using this ansatz, various measurable quantities such as the density and current were calculated in the NESS, from which the exact nonequilibrium phase diagram was derived. While many rigorous results are known in one dimension, there are none for higher dimensional exclusion processes in contact with reservoirs.The one-dimensional asymmetric simple exclusion process (ASEP) with open boundaries has been of great importance as a model system towards understanding nonequilibrium phenomena. The matrix ansatz, which has since become an important tool3. Using the integrability of the ASEP, the spectrum of the transition matrix was computed4. The large deviation functional for the density profiles5 and the large deviation function for the current7 was derived using the matrix ansatz. These calculations helped in the formulation of two general principles for driven diffusive systems; the additivity principle8 and the macroscopic fluctuation theory9.The exact calculation of various out-of-equilibrium quantities was also useful in formulating general principles. For example, the diffusion constant was first calculated exactly for the open TASEP10, cell motility12, chemotaxis13, chemical reactions14 and biological transport in ion-channels17. The ASEP with second-class particles was first considered with periodic boundary conditions18. The first model with two species and open boundaries whose NESS was determined exactly was a model where positive and negative charges moved in the lattice under the influence of an electric field19. Much later, a two-species model called the semipermeable TASEP21 was considered, where second-class particles were confined to the lattice. The computation of the NESS was later generalised to the semipermeable ASEP22. The NESS of a version with more general boundary conditions was also determined exactly23. Later on, the phase diagram for a large class of ASEPs with two species and open boundaries was obtained25. More recently, classes of integrable ASEPs with multiple species of particles and open boundaries were determined26.It is natural to extend the ASEP to several species of particles. Multispecies exclusion processes have applications to studies of traffic flowr species of charges called the mASEP introduced recently27. The hopping rates in the bulk are asymmetric and those in the boundary are defined in such a way that there are r + 1 conserved particle numbers. The main results are the following. We obtain the complete (r + 2)-dimensional phase diagram and present formulas for all densities and currents in the thermodynamic limit in all regions of the phase diagram. It will turn out that all the macroscopic features can be explained by a new structure which we call a nested fat shock. To make the presentation self-contained, we review the features for the semipermeable ASEP in Section I of the Supplementary material. We will prove these results in Section II of the Supplementary material by using projections to the semipermeable ASEP.In this work, we study a multispecies exclusion process on a finite one-dimensional lattice with n, where each site is occupied by exactly one particle of type r species of charges, with the total number of particles of charge j being fixed to be n0 of vacancies is also fixed, with r + 1)-tuple of positive integers n in the alphabet j′s and nj for n0.The mASEP is defined on a one-dimensional lattice of size q < 1. On the left and right boundaries, positive charges can only replace and be replaced by their negatively charged partners with rates given byThe dynamics is the effect of a rightward-pointing electric field. In the bulk, we have the asymmetric hopping ruleq, α and β, and γ and r = 1) and 2 for arbitrary n0, this is the semipermeable ASEP22. Furthermore, if 21 . We thus denote the mASEP with r = 2 are given in Fig. The mASEP possesses charge-conjugation symmetry in the following sense: interchanging positively and negatively charged particles as well as the rates 1 and j between 0 and r, let j. We consider the behaviour of the mASEP in the limit j such that the total density of species j particles converges to θj > 0. Define the quantitiesFor each integer entclass1pt{minimar-species mASEP in Fig. r + 1 phases, ρj for Jj for j’s to the right. The mean densities of the j and Jj change continuously across all phase boundaries in Fig. , the system shows phase coexistence with a sharp interface separating intervals of different density for some particle type, as we show by the illustrative density profiles in Fig. r = 2 and Supplementary Fig. r = 1. The proofs of the density profiles in Table The nonequilibrium phase diagram of the entclass1pt{minimaentclass1pt{minimaentclass1pt{minimaentclass1pt{minimar = 2, and two relevant phase-boundaries. The currents can be calculated by mean-field type calculations from the densities in each of the regions. More precisely, We illustrate the density profiles for various regions in the phase diagram for the example of the 2-species mTASEP . Roughly speaking, the fat shock consists of a macroscopic interval of the system, where all the All coarse features of the phase diagram in Fig. j ≥ 0, particles of species The nested fat shock is a macroscopic interval of the system where, for some j on the right and species Particles of species 0 have a nonzero constant density in a subinterval of fixed width inside this interval. Particles of species 1  The top row of Fig. The precise details for each phase are given below.. See the density plot in Fig. Here, only the particles of species 0 participate in the nested fat shock and the width of the shock is larger than the system size. As a result, all densities are constant throughout the system. This explains the densities and currents in region We give details only for region j − 1, which will then move rightwards in the bulk, until they join the subinterval of the nested fat shock occupied by the particles of species j − 1. Once that process is completed, a similar phenomenon will happen with particles of species In region j − 1 are localised in the interior of the system. Each of these species has undergone phase separation, with one region of non-zero density and the remaining of zero density. The precise locations of the region with non-zero density can be calculated from the values of j − 1 are localised away from the boundary. This is somewhat counterintuitive since we have taken the thermodynamic limit and these particles are infinitely far away from the boundary. We call this phenomenon dynamical localisation. Such a phenomenon cannot occur in an equilibrium system. The second new feature is the complete absence of particles of species dynamical expulsion. In the extreme case of the We point out two new nonequilibrium features of this phase which can be seen in the top row of Fig. r = 2 and The picture in the mentclass2pt{minimj − 2 or j − 2’s becomes zero. More and more shock fronts can get pinned until the fat shock containing 0’s touches the boundary, at which point the latest front to get pinned can only get unpinned. We thus end up with an instantaneous profile whose schematic is given in the top row of Fig. a = b.In the j and In this work, we have found the complete phase diagram for a very general multispecies exclusion process, called the mASEP, in contact with reservoirs. We have found two nonequilibrium phenomena, namely dynamical localisation and dynamical exclusion. Just like the fat shock construction explained the gross features of the semipermeable TASEP in all phases, we find a new object called a nested fat shock which explains the features here. Since the widths of the subintervals in the nested shock are fixed because of the conservation of the total number of The proofs of our results have appealed in a fundamental way to the colouring argument. It is natural to ask how general this argument is. We are working on a large class of multispecies exclusion processes by systematically exploiting this argument, and we expect new kinds of dynamical structures to appear.In recent times, multispecies exclusion processes have found applications in physical, chemical and biological systems, as mentioned in the introduction. It would be interesting to see whether experimental realisations can be found for the various phases that we have shown in this work.Two different methods were used to obtain the results in this paper. The first method is a mathematically rigorous analysis, leading to the picture of the phase diagram. The second method uses simulations to justify the physical picture of the nested fat shock explained here.The phase diagram was rigorously obtained by applying a suitable projection on the stochastic process. The details are explained in Section II of the Supplementary material.The simulations were performed using random sequential updates (RSUs) according to the rules of the dynamics. After reaching steady state, we calculate densities by recording fractional occupation numbers at every site, and currents by noting incoming and outgoing species on the left boundary during subsequent sequences of RSUs. All density profiles show densities for each species averaged over such large sequences. Supplementary Videos showing the evolution of the nested fat shock were obtained by keeping track of individual particles during the RSUs.Supplementary Information: The exact phase diagram for a class of open multispecies asymmetric exclusion processesSupplementary Video 1Supplementary Video 2Supplementary Video 3


A=20 mm with high motion frequencies. Motion phase did not affect the CT number distributions for prolonged projection acquisition that included several respiratory cycles. The mathematical model of the CT number distributions of mobile targets in CBCT reproduced well the measured CT number distributions and predicted their dependence on the target size and phantom motion parameters such as speed, amplitude, frequency, and phase. The CT number distributions varied considerably with motion in CBCT. A motion model of CT number distribution for mobile targets has been developed in this work that predicted well the variations in the measured CT number profiles and their dependence on motion parameters. The model corrected the CT number distribution retrospective to CT image reconstruction where it used a first‐order linear relationship between the number of projections collected in the imaging window of a mobile voxel to obtain the cumulative CT number. This model provides quantitative characterization of motion artifacts on CT number distributions in CBCT that is useful to determine the validity of CT numbers and the accuracy of localization and volume measurement of tumors in diagnostic imaging and interventional applications, such as radiotherapy.The purpose of this study was to investigate quantitatively by measurement and modeling the variations in CT number distributions of mobile targets in cone‐beam CT (CBCT) imaging. CBCT images were acquired for three targets manufactured from homogenous water‐equivalent gel that was inserted into a commercial mobile thorax phantom. The phantom moved with a controlled cyclic motion in one‐dimension along the superior–inferior direction to simulate patient respiratory motion. Profiles of the CT number distributions of the static and mobile targets were obtained using CBCT images. A mathematical model was developed that predicted the variations in CT number distributions and their dependence on the motion parameters of targets moving in one‐dimension using CBCT imaging. The measured CT number distributions for the mobile targets varied considerably, depending on the motion parameters. The extension of the CT number distribution increased linearly with motion amplitude where maximum target elongation reached twice the motion amplitude. The CT number levels of the mobile targets were smeared over a longer distribution; for example, the CT number level for the 20 mm target dropped by nearly 30% at motion amplitude (A) equal to 20 mm in comparison with the CT number distribution of stationary targets. Frequency of motion played an important role in spatial and level variations of the CT number distributions. For example, the level of the CT number profile for the medium target (20 mm) decreased evenly by nearly 50% at PACS number: 87.57.C‐ CT imaging plays an essential role in the diagnosis of various diseases, including cancer, where it provides a valuable tool in screening and staging of various cancers.Cone‐beam computed tomographic imaging (CBCT) provides a robust tool for volumetric tomography using high resolution and sensitive flat‐panel detectors.3×1×5 cm3), medium (3×2×5 cm3), and large (3×4×5 cm3), were fabricated from a gel material and inserted in low‐density foam to simulate mobile lung tumors.A thorax phantom system  was assembled with homogenous water‐equivalent targets that were inserted in the middle of lung tissue‐ equivalent medium. The phantom was then mounted on a sinusoidally moving platform, as shown in 2×2 binning mode, where the projections were acquired with a 1024×768 pixels that covered 40×30cm2 effective area with a spatial resolution of nearly 0.39×0.39 mm2 at isocenter, which is located at a distance of 150 cm from the imaging X‐ray source. The OBI was employed to obtain full‐fan and half‐fan CBCT of the mobile phantom system. In full‐fan scans, a small imaging volume of 25 cm diameter and 15 cm thickness are obtained, where projections are acquired over 180° angular range. In full‐fan scans, the imager position is offset to cover a large imaging volume of 50 cm diameter and 17 cm thickness, where projections are acquired over 360° angular range. The imaging parameters used were 2 mm slices thickness, 125 kVp, and 264 mAs for half‐fan CBCT, and 2 mm slice thickness, 100 kVp, and 146 mAs for full‐fan CBCT. The phantom was scanned while it was static and moving, using the previously mentioned cyclic motion patterns. The CT images were subsequently processed with the Eclipse treatment planning system . Coronal image views for all scans with the different motion amplitudes from each of the two imaging modes were reconstructed and used to measure the CT number distributions and levels. To maintain consistency in the measurement of CBCT number distributions, the coronal slice that passed through the centers of all targets was selected, where all targets were set at the same level in the anterior–posterior direction, as shown in The phantom was then imaged using an on‐board imager (OBI) with kV CBCT integrated with a TrueBeam linear accelerator . The OBI consists of a kV X‐ray source with a diagnostic image quality and a flat‐panel imager . The imager was operated in In) measured at pixel n on the imager represents the attenuation of all voxels along a ray of radiation from the source, as follows:Io is the initial intensity produced by the imaging source, μ1 is the linear attenuation coefficient of voxel i with thickness ti, and Sn is the number of voxels in the ray track. All voxels were assumed to have equal thickness, t, and thus ray, n, passes through a total thickness equal to tSn, as shown in μ1 at voxel i. For example, in the filtered back‐projection image reconstruction,ΔCTni to the cumulative CT number value of voxel i considering that the linear attenuation factor of this voxel is the same in all projections. This is an acceptable approximation considering negligible variations in the value of the linear attenuation coefficient for voxel i due to variations in the imaging beam energy. N is the number of projections that are acquired within an imaging window (w) for the stationary phantom; w is defined here as the spatial interval where the projections of voxel i are acquired which is assumed to be equal for all voxels. Thus, in a stationary voxel, the CT number of the stationary voxel, CTsi, is linearly proportional to the number of projections:CTMi) of voxel i in the mobile target is again linearly proportional to the number of projections (M) that are acquired:If the previous target is now moving, then the number of projections (M) acquired within the imaging window (w) for voxel i that will be used by the image reconstruction algorithm is different from the stationary target because the mobile target is moving in or out of w. The CT number  are acquired by the gantry as it rotates around the target during scanning within an imaging window (w) of voxel i, as shown in M=2) are acquired in each window and the CT number level is obtained from increments ofΔCTni that broaden over a range of distance (5w) which depends on the speed of the mobile target, as shown in N=10) of a target with ten slices (10w) is acquired for the stationary target. As the target moves, the CT numbers broaden over a longer range of slices (19w). The CT numbers of the different slices vary where the number of projections and the corresponding CT number level, as represented by the dashed curve increases, until it reaches a maximum at the tenth slice (N=10). Afterwards, it decreases, reaching zero at 20th slice.Li is the extension of CT number in the mobile target. The CT number of voxel i for the mobile target is then given by the following:VP is the speed of the mobile target and Ti is the time needed to acquire all cone‐beam projections over a distance Li that the target will move to during imaging.Notice that the cumulative value of all the projections and the corresponding CT numbers from all imaging windows for one voxel  can be generalized to obtain the CT number of voxel i at a specific position yi during imaging from the contributions of different voxels of the mobile target, as given by the following:V is the number of voxels that belong to the target, N is the number of projections acquired in CBCT scanning, yio is the position of voxel i in stationary phantom, yi(t)=VP t is the position of voxel i at time t which changes, depending on the speed of the mobile target (VP during imaging). In VP).In the case of a stationary target, the CT number of voxel i is calculated from N projections acquired in w located at ±20 HU between half‐fan and full‐fan CBCT. The position and length of each target and motion parameters, such as motion amplitude, frequency, and phase, were input in the simulation to calculate the CT number distributions. Furthermore, imaging parameters such as slice thickness, gantry speed, imaging view, and detector resolution were input in the MATLAB program to simulate CT numbers. The calculated CT number profiles of the stationary and mobile targets with various motion patterns from simulation were compared with the measured profiles of CT numbers obtained from CBCT imaging.The modeling of CT number distributions was tested using programming with MATLAB . The composition of the three targets was considered to be water‐equivalent tissues and the CT number level was setup to be equal to the CT number level of each stationary target. The surrounding medium was considered lung tissue‐equivalent. The measured CT numbers for the same target varied by >10 mm), the CT number distributions split in the middle where the CT number maxima were located close to the periphery of the distributions. The maximum of the CT numbers was located centrally for the medium target with ROM <10 mm. When the ROM was larger than the length of the target (20 mm), then the CT number distribution split, with the maximum shifted towards the edges of the broadened target. Similar behavior was seen with the large target (40 mm), as shown in ROM=40 mm, in comparison with the CT number distribution of stationary targets. Although the CT numbers broadened over larger volume and the CT number level decreased with the increase in the extension of the CT number distributions, the total cumulative CT number over the broadening range was preserved, as predicted by A=12.5 mm, which is larger than the actual length of the target (10.0 mm) and which resulted from high gradient in the CT number profiles that were generated by splitting the CT number profile due to spread‐out by motion. PRMS for the small target was generally larger than the medium and large targets because of the high gradient in the CT number profiles for the small target. For the medium target, PRMS decreased as A increased until it reached intermediate values before CT number profiles split and produced high‐gradient CT number profiles when the range of motion (2A) became larger than the actual length of the medium target. As A increased, the CT number profiles for the large target became flatter without splitting the CT number profiles and, thus, PRMS decreased.ROM=40 mm. This is because the mobile targets were present more often in the middle of the distribution for high frequencies in comparison with that at the periphery for low frequencies where they stayed longer times turning around with low speeds. The phase of motion did not affect the CT number distributions when the projections were acquired over several motion cycles.VP) increased, the CT number distribution broadened forward along the direction of motion. The elongation of the CT number distributions increased linearly with the speed of the mobile targets, as shown in In this study, a mathematical model was introduced to predict the CT number distributions of mobile targets in CBCT imaging. This model is based on considering a first‐order linear relationship between the number of projections captured in the imaging widow of a mobile voxel and the cumulative CT number obtained from image reconstruction algorithm. It was used to predict the variations of CT number distributions induced by controlled motion patterns retrospective to the image reconstruction process. The model was verified by measurement of the variations in CT number distributions of mobile targets with different controlled motion patterns and imaged using half‐fan and full‐fan CBCT imaging. The variations in the broadening and level of CT number distributions and their dependence on motion parameters were reproduced by the mathematical modeling. One limitation of this model is that the mobile targets have to stay in the cone‐beam imaging view when using the half‐ and full‐fan imaging modes. If a target moves out of the imaging view in certain projections, then the CT number level obtained from CBCT reconstruction is different. Thus the preservation of cumulative CT numbers represented in CBCT is routinely used as interventional tool in IGRT;±20 HU. New CT scanners use multiple array detectors to image large portions of the patient that combine CBCT and helical or axial CT techniques. In these diagnostic CBCT imaging systems, the variations in the CT number distribution and tumor density due to patient motion influence the accuracy of disease diagnosis. The employment of CBCT in radiotherapy will affect the accuracy of the treatment planning, dose calculation and patient setup. The variations in CBCT number distribution and level by patient motion may cause wrong portrayal of tumor volume. The increase in the extension of the CBCT number distributions of the tumor volume will cause outlining of less tumor or inclusion of normal tissue on the CT images used by the treatment planning system.The use of CBCT images is limited by image artifacts induced by scatter radiation,A mathematical model has been developed in this study that predicted the CT number distributions of mobile targets in CBCT imaging. The model considered first‐order linear relationship between the number of projections collected in the imaging widow of a mobile voxel and the cumulative CT number obtained from image reconstruction algorithm. The model predicted well the variations of CT number distributions induced by controlled motion patterns retrospective to the image reconstruction process. The variations in CT number distribution need to be considered in diagnostic CT imaging in order to achieve accurate tumor localization and volume measurement. The motion‐induced artifacts in the CT number distributions have to be accounted for in radiation therapy in order to outline the actual tumor volumes, use accurate CT numbers in treatment planning, and set up patients and localize tumors using IGRT based on CBCT.


The model reproduces the dependency of experimentally determined kcat and KM values on the cytoplasmic network strength with good quantitative accuracy, implying that it captures the transport mechanism and can provide a framework to understand the structure-function relationships of this class of transporter. The results show that maximum transport occurs when the interaction energies of the cytoplasmic network, matrix network and substrate binding are approximately equal such that the energy barrier is minimized. Consequently, the model predicts that there will be other interactions in addition to those of the cytoplasmic network that stabilise the matrix conformation of the ADP/ATP carrier.The mitochondrial ADP/ATP carrier catalyses the equimolar exchange of adenosine di- and tri-phosphates. It operates by an alternating access mechanism in which a single substrate-binding site is made available either to the mitochondrial matrix or the intermembrane space through conformational changes. These changes are prevented in the absence of substrate by a large energy barrier due to the need for sequential disruption and formation of a matrix and cytoplasmic salt bridge network that are located on either side of the central cavity. In analogy to enzyme catalysis, substrate lowers the energy barrier by binding tighter in the intermediate state. Here we provide an  •A Markov state model of molecular kinetics is developed for the ADP/ATP carrier.•Captures the free energy profile of the conformational changes of transport•Validated against kinetic measurements from a set of mutant carriers•Establishes how structure shapes the free energy profile, which defines function Furthermore, exchange obligates the carrier to act as an energy-transducing protein due to the charge difference between ATPDE]xx[RK] DE]xx[RK] and it has been shown that the charged residues of this motif form an inter-domain salt bridge network on the cytoplasmic side, closing access to the substrate binding site to the intermembrane space when the carrier is in the matrix-facing conformation The odd-numbered transmembrane α-helices  of the carrier each contain the signature motif of the carrier family, Pxxx[YF] present at the cytoplasmic side of the carrier The model clearly predicts that the maximum transport occurs when the interaction energies of the cytoplasmic network, matrix network and substrate binding are approximately equal such that the energy barrier is a minimum. The wild type carrier has a matrix network of three salt bridges braced by a hydrogen bond from a glutamine residue ΔES of ≈ 400 mV which would lower the energy barrier by ≈ 230 mV. Binding of ADP generated a minimum in the free energy landscape ≈ 260 mV below the energy barrier in the absence of substrate A recent paper has attempted to map out the free energy landscape of the carrier conformation change using well-tempered metadynamics Kd of binding one substrate is much lower when the other substrate is already bound, so that the probability of only having one substrate bound is very low. The glutamate carrier has a matrix network of three salt bridges and a cytoplasmic network lacking any salt bridges or hydrogen bonds kcat for homo exchange (0.083 and 0.019 s− 1 for isoform 1 and 2, respectively The mitochondrial carrier family, in which the matrix and cytoplasmic networks are common motifs, include both exchangers and uniporters. The modelling shows that very unequal network strengths can lead to unidirectional uniport activity in the direction from weak to strong network , becauseTransparency documentImage 1


The multidrug transporter AcrB transports a broad range of drugs out of the cell by means of the proton-motive force. The asymmetric crystal structure of trimeric AcrB suggests a functionally rotating mechanism for drug transport. Despite various supportive forms of evidence from biochemical and simulation studies for this mechanism, the link between the functional rotation and proton translocation across the membrane remains elusive. Here, calculating the minimum free energy pathway of the functional rotation for the complete AcrB trimer, we describe the structural and energetic basis behind the coupling between the functional rotation and the proton translocation at atomic resolution. Free energy calculations show that protonation of Asp408 in the transmembrane portion of the drug-bound protomer drives the functional rotation. The conformational pathway identifies vertical shear motions among several transmembrane helices, which regulate alternate access of water in the transmembrane as well as peristaltic motions that pump drugs in the periplasm. Bacterial multidrug resistance (MDR) is an increasing threat to current antibiotic therapy . ResistaEscherichia coli, the AcrA-AcrB-TolC complex is largely responsible for MDR against many lipophilic antibiotics , we identified conformational transition pathways in one step of the functional rotation for the complete AcrB trimers with different protonation states.1-ATPase . The absolute binding free energy in system 2 is plotted in How does the protonation at D408 induce the conformational change in the TM domain? To address this question, we first investigated the impact of the protonation on the minimum free energy state (image 5) of system 1 by alchemically transforming it towards system 2, that is, by protonating D408 of protomer I and deprotonating D408p of protomer II . Electrostatic potential energy maps before and after the transformation of the protonation state reveal that the TM domain of protomer I is destabilized by the protonation because of a strong positive electrostatic potential bias . This biWe examined another possible protonation scheme. Here, D924 and E346, located at the periplasmic side of the TM domain, were selected for the protonation sites according to the pKa calculation by By monitoring the centers-of-mass for the other TM helices along the conformational pathway, we found that downshifts occur not only in TM4 and TM11 but also in TM3, TM5 and TM6 . Based oThe next question is how D408 becomes protonated. Because proton translocation across the TM domain requires the access of water molecules to supply protons, we investigated the distribution of water molecules in protomer 1 . Also, aBy contrast, water distribution at image 15 of system 2 with D408p is completely different due to the vertical shear motion in the TM domain . There iNext, we studied energy transduction from the TM domain to the porter domain. Does D408p in the B state dynamically induce the conformational change of the porter domain? How are the two sites coupled? To quantify the dynamic correlations of residue pairs, we employed the mutual information analysis, which has been successfully used in analyses of allosteric coupling compared with experiments . Mutual Correlated residue pairs of system 2 are visualized in Protomer I also exhibits weak linkage between PN2 and several TM helices. These weak correlations may arise from PN2’s rearrangements relative to PC1 due to the shrinkage of the distal binding pocket see , which iUnlike protomer I, protomer II (E→A) has only a local correlation network between TM5 and TM8 (and weakly with TM10) and PN1 and PC2. This relatively weak correlation is associated with the reverse helix-to-coil transition of TM8, which closes the drug exit gate. Also, weak correlations can be seen in TM1, TM4, and TM10, which are consistent with the scenario described by In the light of our results and those of previous studies , we prop0F1-ATP synthase . We estimated the TM region using TMHMM  with bong TMHMM  and overhttp://www.mu2lib.org) using CHARMM36 for proteins  variable measured with the nonhydrogen atoms of AcrB. The target structure (EAB state) was created by rotating the initial structure by 120 degrees around the z-axis (perpendicular to the membrane plane). As shown by To generate the initial pathways to be used in the string method, targeted MD simulations were performed with MARBLE. Starting from the BEA trimeric state, a targeted MD simulation of 10 ns was conducted towards the EAB state. A force constant per atom of 1.0 kcal/ÅCollective variables for the string method were carefully chosen according to previous simulation studies. We chose Cartesian coordinates of Cα atoms in the porter domain  and selected TM helices  of all protomers see . The cho2. Mean forces were evaluated every 4 ns of simulation and images were updated according to the calculated mean force, then reparameterized to make the images equidistant from each other . In order to eliminate external components (translations and rotations) in the mean forces, the Cα atoms of TM helices in snapshots were fitted to the reference structure (z-axis from BEA) and ABE states (240 degrees rotation), thus resulting in a 3-fold symmetric structure  were kept fixed during the first 36 ns (nine cycles in the string method), and then allowed to move to relax subtle frustrations in the crystal structure that might result from detergent molecules or crystal packing. In order to avoid any drifts of the terminal images along the pathway, tangential components to the pathway were eliminated from the mean force when updating terminal images  in the free-energy profiles were estimated from block averages. For analysis of the converged pathway . The positional harmonic restraints with a rather weak force constant of 0.01 kcal/Å by MBAR  and weig by MBAR  , Langevin dynamics and Nose-Hoover Langevin piston  were use2) as were used for the string method were imposed on the collective variables. No restraints were imposed on minocycline because it was hard to define binding sites for images after the shrinkage of the distal binding site. Free energy differences over the decoupling were evaluated by the exponential averages  on the collective variables of image 5 of system 1 , the protonation states were alchemically transformed to that of system 2 . Because of the restraints on the collective variables, this calculation mainly evaluates the contribution of protonation to the free energy differences. Transformations were carried out in both forward and backward directions, with 36 intermediate λ-states for each direction, resulting in a total simulation length of 58 ns. During the transformation, the total charge of the system was kept neutral. Free energy difference of the alchemical transformation was evaluated by BAR  (https://github.com/elifesciences-publications/mdtoolbox]). Molecular figures were generated with VMD   and MDTrwith VMD .r1 and r2 because they better capture correlated motions involving semi-rigid regions (p(r1) and p are a probability density of r1, and a joint probability density of r1 and r2, respectively. Unlike usual correlation coefficients, the mutual information contains information about both linear and nonlinear dependences. For numerical evaluation of the mutual information, Kraskov’s algorithm (k-nearest neighbor distances (without binning), was used because it is practical for multi-dimensional data sets such as Cartesian coordinate data.While the minimum free-energy path obtained by the string method provides us with the physically most probable pathway in the collective variable space, it is not useful in characterizing the dynamic properties of conformational change at the atomistic level . Here, in order to characterize the dynamic properties of atomistic fluctuations, we generated reactive trajectories from the umbrella sampling data around the minimum free-energy path. The reactive trajectories are defined as the portions of trajectories when, after leaving the initial BEA state, it enters first the final EBA state before returning to the BEA state . For gen regions  than did regions . p(r1) algorithm , based o In the interests of transparency, eLife includes the editorial decision letter and accompanying author responses. A lightly edited version of the letter sent to the authors after peer review is shown, indicating the most substantive concerns; minor comments are not usually included.eLife. Your article has been favorably evaluated by Richard Aldrich (Senior Editor) and two reviewers, one of whom, Yibing Shan (Reviewer #1), is a member of our Board of Reviewing Editors.Thank you for submitting your article "Energetics and Conformational Pathways of Functional Rotation in the Multidrug Transporter AcrB" for consideration by The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.Summary:Aiming to elucidate the detailed structural mechanism of AcrB RND transporter, this study applied the string method for conformational free-energy calculations on a supercomputing platform to identify the minimum free energy pathway of the functional rotation of AcrB. The all-atom simulations follow the conformational change of the transporter including the travel of the drug molecule (minocycline) from the binding pocket through the gate and finally release of the drug molecule, showing that the protonation of Asp408 in a transmembrane helix of the Binding protomer drives the process. This work represents potentially important progress in our understanding of the molecular mechanism of the transport process in AcrB.Major points:eLife, the manuscript should include a brief and high level description of the simulation techniques  in the main text in terms that a reader unfamiliar with molecular dynamics simulations can relate to. What are the basic ideas and premises behind the approach? The manuscript should explain the free energy reported in Given the readership of The specific procedure should also be explained in more detail as is it is difficult to follow. It would also help if the references to the string method in the last paragraph of the Introduction were made in a more structured way – with explanations, rather than the current lumping together of a large number of very diverse papers ranging from mathematical principles all the way to practical applications.This work only attempts to distinguish two possible schemes. In realty the process of the functional rotation is probably more complicated, possibly involving protonation of not only Asp408. For instance, Asp924 is located in a quite hydrophobic local environment and its protonation is conceivable. The proton could even be passed from Asp408 to Asp924 by the single water file connecting them. Ideally some new simulations should be performed to address this. At the very least this possibility should be more carefully discussed.The explanation for the increase in free energy after the minima  invokingWhy is the drug released from the BEA complex in System 1, if the protonation of the original E protomer stabilizes the whole complex, as shown in the The analysis concerning the dynamics coupling of the transmembrane domains and the porter and the funnel domains  is too p Major points:Given the readership of eLife, the manuscript should include a brief and high level description of the simulation techniques  in the main text in terms that a reader unfamiliar with molecular dynamics simulations can relate to. What are the basic ideas and premises behind the approach? The manuscript should explain the free energy reported in The specific procedure should also be explained in more detail as is it is difficult to follow. It would also help if the references to the string method in the last paragraph of the Introduction were made in a more structured way – with explanations, rather than the current lumping together of a large number of very diverse papers ranging from mathematical principles all the way to practical applications.Following the reviewers’ comment, we added the descriptions of the basic ideas behind the simulation techniques and their specific procedures in the Introduction section. The references to the string method are now explained in a more structured way.This work only attempts to distinguish two possible schemes. In realty the process of the functional rotation is probably more complicated, possibly involving protonation of not only Asp408. For instance, Asp924 is located in a quite hydrophobic local environment and its protonation is conceivable. The proton could even be passed from Asp408 to Asp924 by the single water file connecting them. Ideally some new simulations should be performed to address this. At the very least this possibility should be more carefully discussed.The explanation for the increase in free energy after the minima  invokingWe appreciate the reviewers’ comment on this point. We agree with the reviewers that other protonation schemes  should be considered. Actually, proton translocation occurs from the periplasm  bottom iAs for the increase in free energy at the end state (the EAB complex), we would like to point out that the end state of system 2 (the EAB complex with protonated Asp408 in protomer I) is identical to the initial state of system 1 (the BEA complex with protonated Asp408 in protomer II) by a 120° rotation, if we ignore the drug binding/unbinding. Since our free energy calculations already showed that the initial state of system 1 is stable with the bound drug shown in , we consWhy is the drug released from the BEA complex in System 1, if the protonation of the original E protomer stabilizes the whole complex, as shown in the The methods were not clearly explained. Before optimizing the pathway with the string method, we generated the initial guess for the conformational transition pathway using targeted molecular dynamics from the initial structure (the BEA complex) toward the end structure (the EAB complex). During the simulation, the drug was also forced toward the exit gate. In response to the first comment, we briefly explained the procedure also in the main text, including how we created the initial pathway.The analysis concerning the dynamics coupling of the transmembrane domains and the porter and the funnel domains  is too pThe description on the dynamical coupling is presented in We agree with the reviewers that mutual information is not necessarily intuitive compared to other metrics such as linear correlation or distance. However, the protein contains different types of motions, the closing rotational motion of the porter domain and the translational downward motion of the TM helices. It was thus not possible to capture such complicated nonlinear motions with the linear metrics. Mutual information is one of the major metrics to treat nonlinear relations. More or less, other nonlinear metrics are also nonintuitive. Thus, we have tried to improve the readability of the text by changing the way of the presentation instead of changing the analysis method. Since the description of the mutual information given in