Neutron shielding assessment of a16O hadron therapy room by means of Monte Carlo simulations with the PHITS code.

Hadron radiation therapy is of great interest worldwide. Heavy-ion beams provide ideal therapeutic conditions for deep-seated local tumours. At the Heidelberg Ion Beam Therapy Center (HIT, Germany), protons and carbon ions are already integrated into the clinical routine, while16O ions are still used for research only. To ensure the protection of the technical staff and members of the public, it is required to estimate the neutron dose distribution for optimal working conditions and at different locations. The Particle and Heavy Ion Transport Code System (PHITS) is used in this work to evaluate the dose rate distribution of secondary neutrons in a treatment room at HIT where16O ions are used: an equivalent target in soft tissue is considered in the shielding assessment to simulate the interaction of the beam with patients. The angular dependence of neutron fluences and energy spectra around the considered phantom were calculated. Alongside the spatial distribution of the neutron and photon fluence, a map of the effective dose rate was estimated using the ICRP fluence-to-effective dose conversion coefficients, exploiting the PHITS code's built-in capabilities. The capability of the actual shielding design of the studied HIT treatment room was approved.

Ion transport peptide regulates energy intake, expenditure, and metabolic homeostasis in Drosophila.

In mammals, energy homeostasis is regulated by the antagonistic action of hormones insulin and glucagon. However, in contrast to the highly conserved insulin, glucagon is absent in most invertebrates. Although there are several endocrine regulators of energy expenditure and catabolism (such as the adipokinetic hormone), no single invertebrate hormone with all of the functions of glucagon has been described so far. Here, we used genetic gain- and loss-of-function experiments to show that the Drosophila gene Ion transport peptide (ITP) codes for a novel catabolic regulator that increases energy expenditure, lowers fat and glycogen reserves, and increases glucose and trehalose. Intriguingly, Ion transport peptide has additional functions reminiscent of glucagon, such as inhibition of feeding and transit of the meal throughout the digestive tract. Furthermore, Ion transport peptide interacts with the well-known signaling via the Adipokinetic hormone; Ion transport peptide promotes the pathway by stimulating Adipokinetic hormone secretion and transcription of the receptor AkhR. The genetic manipulations of Ion transport peptide on standard and Adipokinetic hormone-deficient backgrounds showed that the Adipokinetic hormone peptide mediates the hyperglycemic and hypertrehalosemic effects of Ion transport peptide, while the other metabolic functions of Ion transport peptide seem to be Adipokinetic hormone independent. In addition, Ion transport peptide is necessary for critical processes such as development, starvation-induced foraging, reproduction, and average lifespan. Altogether, our work describes a novel master regulator of fly physiology with functions closely resembling mammalian glucagon.

Methods of Measuring Mitochondrial Potassium Channels: A Critical Assessment.

In this paper, the techniques used to study the function of mitochondrial potassium channels are critically reviewed. The majority of these techniques have been known for many years as a result of research on plasma membrane ion channels. Hence, in this review, we focus on the critical evaluation of techniques used in the studies of mitochondrial potassium channels, describing their advantages and limitations. Functional analysis of mitochondrial potassium channels in comparison to that of plasmalemmal channels presents additional experimental challenges. The reliability of functional studies of mitochondrial potassium channels is often affected by the need to isolate mitochondria and by functional properties of mitochondria such as respiration, metabolic activity, swelling capacity, or high electrical potential. Three types of techniques are critically evaluated: electrophysiological techniques, potassium flux measurements, and biochemical techniques related to potassium flux measurements. Finally, new possible approaches to the study of the function of mitochondrial potassium channels are presented. We hope that this review will assist researchers in selecting reliable methods for studying, e.g., the effects of drugs on mitochondrial potassium channel function. Additionally, this review should aid in the critical evaluation of the results reported in various articles on mitochondrial potassium channels.

MONTE-CARLO SIMULATION USING PHITS OF SECONDARY NEUTRONS PRODUCED IN-PATIENT DURING 16O ION THERAPY.

In hadrontherapy, oxygen ions 16O can be currently considered as an alternative to carbon ions 12C designed specifically for the treatment of deep and radioresistant tumors. Secondary particles, particularly neutrons constitute a serious problem of undesirable additional irradiation to surrounding healthy tissue. The objective of this study is to evaluate, by Monte-Carlo simulation [code Particle and Heavy Ion Transport code System (PHITS)], the contribution in terms of dose of secondary neutrons produced during interaction 16O ion of 300 MeV u-1 in a soft tissue phantom. The dose of 16O ion, secondary particles and neutrons is evaluated, as well as the particle fluence and energy spectra of neutrons. The contribution to the total dose of secondary neutrons in a soft tissue phantom represents 0.1%. This dose, although apparently insignificant, is essential to conduct even more in-depth studies to understand the long-term effects of these secondary neutrons on the patient's body especially in pediatric case.

Track-structure modes in particle and heavy ion transport code system (PHITS): application to radiobiological research.

PURPOSE: In radiation physics, Monte Carlo radiation transport simulations are powerful tools to evaluate the cellular responses after irradiation. When investigating such radiation-induced biological effects, it is essential to perform track structure simulations by explicitly considering each atomic interaction in liquid water at the sub-cellular and DNA scales. The Particle and Heavy-Ion Transport code System (PHITS) is a Monte Carlo code which enables to calculate track structure at DNA scale by employing the track-structure modes for electrons, protons and carbon ions. In this paper, we review the recent development status and future prospects of the track-structure modes in the PHITS code. CONCLUSIONS: To date, the physical features of these modes have been verified using the available experimental data and Monte Carlo simulation results reported in literature. These track-structure modes can be used for calculating microdosimetric distributions to estimate cell survival and for estimating initial DNA damage yields. The use of PHITS track-structure mode is expected not only to clarify the underlying mechanisms of radiation effects but also to predict curative effects in radiation therapy. The results of PHITS simulations coupled with biophysical models will contribute to the radiobiological studies by precisely predicting radiation-induced biological effects based on the Monte Carlo approach.

Implementation of simplified stochastic microdosimetric kinetic models into PHITS for application to radiation treatment planning.

PURPOSE: The stochastic microdosimetric kinetic (SMK) model is one of the most sophisticated and precise models used in the estimation of the relative biological effectiveness of carbon-ion radiotherapy (CRT) and boron neutron capture therapy (BNCT). However, because of its complicated and time-consuming calculation procedures, it is nearly impractical to directly incorporate this model into a radiation treatment-planning system. MATERIALS AND METHODS: Through the introduction of Taylor expansion (TE) or fast Fourier transform (FFT), we developed two simplified SMK models and implemented them into the Particle and Heavy Ion Transport code System (PHITS). To verify the implementation, we calculated the photon isoeffective doses in a cylindrical phantom placed in the radiation fields of passive CRT and accelerator-based BNCT. RESULTS AND DISCUSSION: Our calculation suggested that both TE-based and FFT-based SMK models can reproduce the data obtained from the original SMK model very well for absorbed doses approximately below 5 Gy, whereas the TE-based SMK model overestimates the original data at higher doses. In terms of computational efficiency, the TE-based SMK model is much faster than the FFT-based SMK model. CONCLUSION: This study enables the instantaneous calculation of the photo isoeffective dose for CRT and BNCT, considering their cellular-scale dose heterogeneities. Treatment-planning systems that use the improved PHITS as a dose-calculation engine are under development.

Medical application of particle and heavy ion transport code system PHITS.

The Particle and Heavy Ion Transport code System (PHITS) is a general-purpose Monte Carlo simulation code that has been applied in various areas of medical physics. These include application in different types of radiotherapy, shielding calculations, application to radiation biology, and research and development of medical tools. In this article, the useful features of PHITS are explained by referring to actual examples of various medical applications.

A549 in-silico 1.0: A first computational model to simulate cell cycle dependent ion current modulation in the human lung adenocarcinoma.

Lung cancer is still a leading cause of death worldwide. In recent years, knowledge has been obtained of the mechanisms modulating ion channel kinetics and thus of cell bioelectric properties, which is promising for oncological biomarkers and targets. The complex interplay of channel expression and its consequences on malignant processes, however, is still insufficiently understood. We here introduce the first approach of an in-silico whole-cell ion current model of a cancer cell, in particular of the A549 human lung adenocarcinoma, including the main functionally expressed ion channels in the plasma membrane as so far known. This hidden Markov-based model represents the electrophysiology behind proliferation of the A549 cell, describing its rhythmic oscillation of the membrane potential able to trigger the transition between cell cycle phases, and it predicts membrane potential changes over the cell cycle provoked by targeted ion channel modulation. This first A549 in-silico cell model opens up a deeper insight and understanding of possible ion channel interactions in tumor development and progression, and is a valuable tool for simulating altered ion channel function in lung cancer electrophysiology.

Whole body potassium as a biomarker for potassium uptake using a mouse model.

Potassium is known for its effect on modifiable chronic diseases like hypertension, cardiac disease, diabetes (type-2), and bone health. In this study, a new method, neutron generator based neutron activation analysis (NAA), was utilized to measure potassium (K) in mouse carcasses. A DD110 neutron generator based NAA assembly was used for irradiation.Thirty-two postmortem mice (n= 16 males and 16 females, average weight [Formula: see text] and [Formula: see text] g) were employed for this study. Soft-tissue equivalent mouse phantoms were prepared for the calibration. All mice were irradiated for 10 minutes, and the gamma spectrum with 42K was collected using a high efficiency, high purity germanium (HPGe) detector. A lead shielding assembly was designed and developed around the HPGe detector to obtain an improved detection limit. Each mouse sample was irradiated and measured twice to reduce uncertainty. The average potassium concentration was found to be significantly higher in males [Formula: see text] compared to females [Formula: see text]. We also observed a significant correlation between potassium concentration and the weight of the mice. The detection limit for potassium quantification with the NAA system was 46 ppm. The radiation dose to the mouse was approximately 56 [Formula: see text] mSv for 10-min irradiation. In conclusion, this method is suitable for estimating individual potassium concentration in small animals. The direct evaluation of total body potassium in small animals provides a new way to estimate potassium uptake in animal models. This method can be adapted later to quantify potassium in the human hand and small animals in vivo. When used in vivo, it is also expected to be a valuable tool for longitudinal assessment, kinetics, and health outcomes.

Pathological conformations of disease mutant Ryanodine Receptors revealed by cryo-EM.

Ryanodine Receptors (RyRs) are massive channels that release Ca2+ from the endoplasmic and sarcoplasmic reticulum. Hundreds of mutations are linked to malignant hyperthermia (MH), myopathies, and arrhythmias. Here, we explore the first MH mutation identified in humans by providing cryo-EM snapshots of the pig homolog, R615C, showing that it affects an interface between three solenoid regions. We also show the impact of apo-calmodulin (apoCaM) and how it can induce opening by bending of the bridging solenoid, mediated by its N-terminal lobe. For R615C RyR1, apoCaM binding abolishes a pathological 'intermediate' conformation, distributing the population to a mixture of open and closed channels, both different from the structure without apoCaM. Comparisons show that the mutation primarily affects the closed state, inducing partial movements linked to channel activation. This shows that disease mutations can cause distinct pathological conformations of the RyR and facilitate channel opening by disrupting interactions between different solenoid regions.

Assessment of Drug Proarrhythmic Potential in Electrically Paced Human Induced Pluripotent Stem Cell-Derived Ventricular Cardiomyocytes Using Multielectrode Array.

Human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) have been widely used for the assessment of drug proarrhythmic potential through multielectrode array (MEA). HiPSC-CM cultures beat spontaneously with a wide range of frequencies, however, which could affect drug-induced changes in repolarization. Pacing hiPSC-CMs at a physiological heart rate more closely resembles the state of in vivo ventricular myocytes and permits the standardization of test conditions to improve consistency. In this study, we systematically investigated the time window of stable ion currents in high-purity hiPSC-derived ventricular cardiomyocytes (hiPSC-vCMs) and confirmed that these cells could be used to correctly predict the proarrhythmic risk of Comprehensive In Vitro Proarrhythmia Assay (CiPA) reference compounds. To evaluate drug proarrhythmic potentials at a physiological beating rate, we used a MEA to electrically pace hiPSC-vCMs, and we recorded regular field potential waveforms in hiPSC-vCMs treated with DMSO and 10 CiPA reference drugs. Prolongation of field potential duration was detected in cells after exposure to high- and intermediate-risk drugs; in addition, drug-induced arrhythmia-like events were observed. The results of this study provide a simple and feasible method to investigate drug proarrhythmic potentials in hiPSC-CMs at a physiological beating rate.

Assessment of Cell Adhesion After Purinoceptor Activation.

Cell adhesion is a characteristic feature of phagocytic myeloid cells, which is important for several inflammatory processes, such as migration, invasion, and proliferation. Purinergic signaling in macrophages plays an important role in cell adhesion of this cell type to different extracellular substrates. This protocol describes the use of two different detection methods to quantify cell adhesion upon P2X7 receptor activation by extracellular ATP.

The effects of soil phosphorus and zinc availability on plant responses to mycorrhizal fungi: a physiological and molecular assessment.

The positive effects of arbuscular mycorrhizal fungi (AMF) have been demonstrated for plant biomass, and zinc (Zn) and phosphorus (P) uptake, under soil nutrient deficiency. Additionally, a number of Zn and P transporter genes are affected by mycorrhizal colonisation or implicated in the mycorrhizal pathway of uptake. However, a comprehensive study of plant physiology and gene expression simultaneously, remains to be undertaken. Medicago truncatula was grown at different soil P and Zn availabilities, with or without inoculation of Rhizophagus irregularis. Measures of biomass, shoot elemental concentrations, mycorrhizal colonisation, and expression of Zn transporter (ZIP) and phosphate transporter (PT) genes in the roots, were taken. Mycorrhizal plants had a greater tolerance of both P and Zn soil deficiency; there was also evidence of AMF protecting plants against excessive Zn accumulation at high soil Zn. The expression of all PT genes was interactive with both P availability and mycorrhizal colonisation. MtZIP5 expression was induced both by AMF and soil Zn deficiency, while MtZIP2 was down-regulated in mycorrhizal plants, and up-regulated with increasing soil Zn concentration. These findings provide the first comprehensive physiological and molecular picture of plant-mycorrhizal fungal symbiosis with regard to soil P and Zn availability. Mycorrhizal fungi conferred tolerance to soil Zn and P deficiency and this could be linked to the induction of the ZIP transporter gene MtZIP5, and the PT gene MtPT4.

Assessment of Silver-Nanoparticles-Induced Erythrocyte Cytotoxicity through Ion Transport Studies.

BACKGROUND/AIMS: Silver nanoparticles (AgNPs) are the most frequently used nanomaterials in industrial and biomedical applications. Their functionalization significantly impacts their properties and potential applications. Despite the need to produce, investigate and apply them, not much is known about the toxicity of silver nanoparticles to and their interaction with blood components, such as erythrocytes. Here, we report on the effect of two negatively charged AgNPs (Creighton, and Lee-Meisel) on ion transport in human red blood cells (HRBCs). METHODS: HRBCs were obtained from blood of adult donors, which was either expired, fresh or refrigerated for variable lengths of time, and from fresh or refrigerated cord blood. Rb+ and K+ ions were measured by atomic emission and absorption spectrophotometry, respectively. Erythrocyte hemoglobin optical density (Hbc OD), was determined at 527 nm to estimate RBC volume in the same tubes in which Rb+ and K+ were measured. Cellular Rb+ uptake and intracellular K+ concentrations, [K]i, were calculated in mmol/L of original cells (LOC) per time. Rubidium, a potassium ion (K+) congener used to measure K+ influx, [K]i, and Hbc ODs were determined in the presence and absence of several concentrations (0-150 µg mL-1) of spherical AgNPs of an average diameter of 10 nm, at different time points (0-60 min). RESULTS: Creighton AgNPs inhibited Rb+ influx and depleted the cells of K+ independently of the source and in a time and dose-dependent manner. In contrast, Lee-Meisel AgNPs caused ~ 50 % Rb+ influx inhibition and ~ 15 % K+ loss with larger interindividual variability than Creighton AgNPs. The loss of K+ from HRBCs was entirely accounted for by an increase in extracellular K+ concentration, [K]o. Enhanced dark field optical microscopy in conjunction with CytoViva® hyperspectral imaging helped visualize AgNPs internalized by HRBCs, thus pointing to a potential cause for their cytotoxic effects. CONCLUSION: These findings indicate that HRBC K+ homeostasis is an early and sensitive biomarker for AgNPs toxicity and is a function of their surface functionalization.

Are sulfate effects in the mayfly Neocloeon triangulifer driven by the cost of ion regulation?

Elevated major ion concentrations in streams are commonly observed as a consequence of resource extraction, de-icing and other anthropogenic activities. Ecologists report biodiversity losses associated with increasing salinity, with mayflies typically being highly responsive to increases of different major ions. In this study, we evaluated the performance of the mayfly Neocloeon triangulifer reared for its entire larval phase in a gradient of sulfate concentrations. Two natural waters were amended with SO4 as a blend of CaSO4 and MgSO4 and exposures ranged from 5 to 1500 mg l-1 SO4. Survival (per cent successful emergence to the subimago stage) was significantly reduced at the highest SO4 concentration in both waters, while development was significantly delayed at 667 mg l-1 SO4 Final sub-adult body weights were consistent across treatments, except at the highest treatment concentration. Despite evidence for sulfate uptake rates increasing with exposure concentrations and not being saturated at even extremely high SO4 concentrations, total body sulfur changed little in subimagos. Together, these results suggest that elevated SO4 imposes an energetic demand associated with maintaining homeostasis that is manifested primarily as reduced growth rates and associated developmental delays. We identified two genes related to sulfate transport in N. trianguliferThis article is part of the theme issue 'Salt in freshwaters: causes, ecological consequences and future prospects'.

In silico assessment of the conduction mechanism of the Ryanodine Receptor 1 reveals previously unknown exit pathways.

The ryanodine receptor 1 is a large calcium ion channel found in mammalian skeletal muscle. The ion channel gained a lot of attention recently, after multiple independent authors published near-atomic cryo electron microscopy data. Taking advantage of the unprecedented quality of structural data, we performed molecular dynamics simulations on the entire ion channel as well as on a reduced model. We calculated potentials of mean force for Ba2+, Ca2+, Mg2+, K+, Na+ and Cl- ions using umbrella sampling to identify the key residues involved in ion permeation. We found two main binding sites for the cations, whereas the channel is strongly repulsive for chloride ions. Furthermore, the data is consistent with the model that the receptor achieves its ion selectivity by over-affinity for divalent cations in a calcium-block-like fashion. We reproduced the experimental conductance for potassium ions in permeation simulations with applied voltage. The analysis of the permeation paths shows that ions exit the pore via multiple pathways, which we suggest to be related to the experimental observation of different subconducting states.

Assessment of acquired mucociliary clearance defects using micro-optical coherence tomography.

BACKGROUND: Dehydration of airway surface liquid (ASL) disrupts normal mucociliary clearance (MCC) in sinonasal epithelium, which may lead to chronic rhinosinusitis (CRS). Abnormal chloride (Cl- ) transport is one such mechanism that contributes to this disorder and can be acquired secondary to environmental perturbations, such as hypoxia at the tissue surface. The objective of this study was to assess the technological feasibility of the novel micro-optical coherence tomography (µOCT) imaging technique for investigating acquired MCC defects in cultured human sinonasal epithelial (HSNE) cells. METHODS: Primary HSNE cell cultures were subjected to a 1% oxygen environment for 12 hours to induce acquired cystic fibrosis transmembrane conductance regulator (CFTR) dysfunction. Ion transport characteristics were assessed with pharmacologic manipulation in Ussing chambers. ASL, periciliary fluid (PCL), and ciliary beat frequency (CBF) were evaluated using µOCT. RESULTS: Amiloride-sensitive transport (ΔISC ) was greater in cultures exposed to hypoxia (hypoxia: -13.2 ± 0.6 µA/cm2 ; control: -6.5 ± 0.1 µA/cm2 ; p < 0.01), whereas CFTR-mediated anion transport was significantly diminished (hypoxia: 28.6 ± 0.3 µA/cm2 ; control: 36.2 ± 1.6 µA/cm2 ; p < 0.01), consistent with acquired CFTR dysfunction and sodium hyperabsorption. Hypoxia diminished all markers of airway surface function microanatomy as observed with µOCT, including ASL (hypoxia: 5.0 ± 0.4 µm; control: 9.0 ± 0.9 µm; p < 0.01) and PCL depth (hypoxia: 2.5 ± 0.1 µm; control: 4.8 ± 0.3 µm; p < 0.01), and CBF (hypoxia: 8.7 ± 0.3 Hz; control: 10.2 ± 0.3 Hz; p < 0.01). CONCLUSION: Hypoxia-induced defects in epithelial anion transport in HSNE led to predictable effects on markers of MCC measured with novel µOCT imaging. This imaging method represents a technological leap forward and is feasible for assessing acquired defects impacting the airway surface.

Functional assessment of SLC4A11, an integral membrane protein mutated in corneal dystrophies.

SLC4A11, a member of the SLC4 family of bicarbonate transporters, is a widely expressed integral membrane protein, abundant in kidney and cornea. Mutations of SLC4A11 cause some cases of the blinding corneal dystrophies, congenital hereditary endothelial dystrophy, and Fuchs endothelial corneal dystrophy. These diseases are marked by fluid accumulation in the corneal stroma, secondary to defective fluid reabsorption by the corneal endothelium. The role of SLC4A11 in these corneal dystrophies is not firmly established, as SLC4A11 function remains unclear. To clarify the normal function(s) of SLC4A11, we characterized the protein following expression in the simple, low-background expression system Xenopus laevis oocytes. Since plant and fungal SLC4A11 orthologs transport borate, we measured cell swelling associated with accumulation of solute borate. The plant water/borate transporter NIP5;1 manifested borate transport, whereas human SLC4A11 did not. SLC4A11 supported osmotically driven water accumulation that was electroneutral and Na+ independent. Studies in oocytes and HEK293 cells could not detect Na+-coupled HCO3- transport or Cl-/HCO3- exchange by SLC4A11. SLC4A11 mediated electroneutral NH3 transport in oocytes. Voltage-dependent OH- or H+ movement was not measurable in SLC4A11-expressing oocytes, but SLC4A11-expressing HEK293 cells manifested low-level cytosolic acidification at baseline. In mammalian cells, but not oocytes, OH-/H+ conductance may arise when SLC4A11 activates another protein or itself is activated by another protein. These data argue against a role of human SLC4A11 in bicarbonate or borate transport. This work provides additional support for water and ammonia transport by SLC4A11. When expressed in oocytes, SLC4A11 transported NH3, not NH3/H.

Assessment of epithelial sodium channel variants in nonwhite cystic fibrosis patients with non-diagnostic CFTR genotypes.

PURPOSE: Several lines of evidence suggest a role for the epithelial sodium channel (ENaC) in cystic fibrosis (CF). The purpose of our study was to assess the contribution of genetic variants in the ENaC subunits (α, ß, γ) in nonwhite CF patients in whom CFTR molecular testing has been non-diagnostic. METHODS: Samples were obtained from patients who were nonwhite and whose molecular CFTR testing did not identify two mutations. Sequencing of the SCNN1A, B, and G genes was performed and variants assessed for pathogenicity and association with CF using databases, protein and splice site mutation analysis software, and literature review. RESULTS: We identified four nonsynonymous amino acid variants in SCNN1A, three in SCNN1B and one in SCNN1G. There was no convincing evidence of pathogenicity. Whereas all have been reported in the dbSNP database, only p.Ala334Thr, p.Val573Ile, and p.Thr663Ala in SCNN1A, p.Gly442Val in SCNN1B and p.Gly183Ser in SCNN1G were previously reported in ENaC genetic studies of CF or CF-like patients. Synonymous substitutions were also observed but novel synonymous variants were not detected. CONCLUSION: There is no conclusive association of ENaC genetic variants with CF in nonwhite CF patients.

Simulating the function of sodium/proton antiporters.

The molecular basis of the function of transporters is a problem of significant importance, and the emerging structural information has not yet been converted to a full understanding of the corresponding function. This work explores the molecular origin of the function of the bacterial Na+/H+ antiporter NhaA by evaluating the energetics of the Na+ and H+ movement and then using the resulting landscape in Monte Carlo simulations that examine two transport models and explore which model can reproduce the relevant experimental results. The simulations reproduce the observed transport features by a relatively simple model that relates the protein structure to its transporting function. Focusing on the two key aspartic acid residues of NhaA, D163 and D164, shows that the fully charged state acts as an Na+ trap and that the fully protonated one poses an energetic barrier that blocks the transport of Na+. By alternating between the former and latter states, mediated by the partially protonated protein, protons, and Na+ can be exchanged across the membrane at 2:1 stoichiometry. Our study provides a numerical validation of the need of large conformational changes for effective transport. Furthermore, we also yield a reasonable explanation for the observation that some mammalian transporters have 1:1 stoichiometry. The present coarse-grained model can provide a general way for exploring the function of transporters on a molecular level.