Theoretical Studies On The Ca²⁺ Transfer Mechanisms In The Skeletal Muscle Sarcoplasmic Reticulum Ca²⁺-ATPase

In skeletal muscle,the calcium ions transport against a concentration gradient from the cytoplasm into the sarcoplasmic reticulum by Ca²⁺pump and Ca²⁺-channel, which can control the muscles' contraction and the heat production.In addition,the activity of the Ca²⁺conductivity can signal the metabolism of various cells efficiently. Thus the maladjustment of the Ca²⁺pump would result in many diseases and the corresponding work must be done as soon as possible.By now,the mechanism of the Ca²⁺pump and Ca²⁺-channel remains ambiguous.Thus,in the present doctoral dissertation,the relative studies on the geometrical changes,energetic transmission, and the coupling mechanisms between Ca²⁺ions and the main active sites of Ca²⁺ pump have been systematically and extensively investigated employing the theoretical chemistry menthods.Additionally,the specificity and selectivity of Ca²⁺have also be studied to explore the functions and interactive essence of the Ca²⁺pump and Ca²⁺-channel.Besides,the environmental factors,such as the peripheral amino acid and solvent effects,have also been investigated.Upon these studies,the corresponding mechanical models and thermodynamics parameters to describe the Ca²⁺transport have been established elaborately.As a result,some significant progresses have been made,which can be described as follows.(?)Coupling Character Between the Acidic Amino Acid Residues and Ca²⁺and the Corresponding Biological Implicaitons Among the amino acid residues in the sarcoplasmic reticulum(SR)Ca²⁺-ATPase,glutamic acid has played the important roles on the process of the Ca²⁺transmembrane conductivity.On one hand,it paricipates the Ca²⁺coupling in the high-affinity sites;and on the other hand,it is likely to be able to "sense" if siteâ…¡is occupied by Ca²⁺.So,glutamic acid could be part of the Ca²⁺channel.In the present doctoral dissertation,we have investigated the biological relevant glutamic acid-Ca²⁺bonding with density functional theory calculations.Sixteen chelating modes,which are divided into three different chelating types,that is,tridentate,bidentate,and monodentate forms,have been found.Among these isomers,the lowest energy structure is a zwitterionic form, corresponding to Ca²⁺interacting with three carbonyl oxygen atoms.Another tridentate form,with a bonding property of the calcium cation interacting with two carbonyl oxygen atoms and one amino nitrogen,is only 2.1 kcal/mol higher in energy. The geometrical character and relative stability of all isomers have been analyzed from the aspects of coupling forms,relative energies,electrostatic interactions, deformation energies,charge distributions,bonding characters,and intramolecular H-bonds.Results indicate that,among three active groups in glutamic acid,the binding ability order is the carbonyl O＞the amino N＞the hydroxyl O,and the main binding character is that Ca²⁺couples with glutamic acid as in the multidentate form as possible.Became of the similarity in geometry and energy,the geometric transformation mechanisms among different structures have been explored.In actual biological processes of Ca²⁺transport,the residues around Ca²⁺have undergone conformational changes,which can be partly explained by our research:when Ca²⁺ binds to the high-affinity binding sites of El conformation of SR Ca²⁺-ATPase,the glutamic acid chelates with Ca²⁺in a stable form like the tri- or bidentate forms;but when Ca²⁺-ATPase changes to the low-affinity conformation,the glutamic acid-Ca²⁺ chelate is in an unstable form,such as the monodentate geometry,thus release the calcium cation easily.Moreover,harmonic vibrational frequencies and their corresponding infrared frequencies have been determined for chelates in the gas-phase employing the B3LYP/6-31+G(d,p)level of theory.The frequency analyses indicate that the biggest vibratioanl intensity peak corresponds to the C=O stretching mode and it is red-shifted after it binds with Ca²⁺.(?)Effects of the Stepwise Hydration on the Glutamic Acid-Ca²⁺Complexes and the Corresponding Biological Implicaitons In vivo,the complexes exist in the bulk solvent.Considering the effect of water,some different phenomena may take place for the glutamic acid-Ca²⁺complexes.To approach the real biological processes,the stepwise hydration effects on the glutamic acid-Ca²⁺ complexes have been investigated systematically by employing the B3LYP density functional theory method with the 6-31+G(d,p)and 6-311++G(2d,p)basis sets.The thermodynamics parameters for the hydration reactions,the stepwise hydration energies,and accurate geometries have been explored.To elucidate the Ca²⁺-ligand interaction,the charge transfer,bonding analysis,and IR spectroscopic characteristics have also been investigated.The calculated resultes have revealed that the stepwise hydration has caused a series of geometrical changes on the glutamic acid-Ca²⁺ complexes.Influenced by the ion-ligand electrostatic interaction,charge transfer from ligand to ion,electronic orbital effects,ion-ligand and ligand-ligand repulsions,the increase of the water molecules in the first shell has weakened the Ca²⁺-O bond strength,which also results in the decrease of the(C-)O-Ca²⁺-O(-C)bond angles. Notably,in the first-and-second-shell coordination mode,the peripheral hydration has caused the calcium cation to move closer to the first-shell water molecules,but increased the distance between Ca²⁺and the carboxylic oxygen atoms.Additionally, because of the increase of the H-bonds,the stepwise hydration has stabilized the glutamic acid-Ca²⁺complexes.The correlating data have shown that all of the stepwise hydration reactions are enthalpy-driven because of the relatively small value ofâ–³S,but the number of coordinated water molecules in the first shell of Ca²⁺is not limitless.In our study,the optimal coordination number(CN)of Ca²⁺in the first shell is 6 or 7;the former value agrees well with the datum reported in the Protein Data Bank(PDB),and the latter is the reflection of the most frequent Ca²⁺-binding motif, EF-hand,in soluble proteins.Furthermore,the self-consistent reaction field(SCRF) and higher-level MP2 calculations have confirmed our conclusions.Additionally and very importantly,the stepwise hydration in either the first or second coordination shell can weaken the glutamic acid-Ca²⁺interaction gradually till the glutamic acid ligand is replaced by the added water molecules,resulting in the conversion of coordination mode of the glutamic acid to Ca²⁺from the inner-sphere one to a peripheral interaction mode,just like the ligand exchange process in the Ca²⁺release channel existing in the real biological system.Finally,the similarities and discrepancies between our model and the Ca²⁺-channel in vivo have been compared.(?)Essence of the Ion Selectivity and the Influence Factors As reported previously,the SR Ca²⁺-ATPase selectively transports Ca²⁺in the presence of 10³-10⁵=fold higher concentrations of Mg²⁺.However,the selective mechanisms of the Ca²⁺-ATPase to the calcium ions against the magnesium ions remain ambiguous, and much fewer studies on the basis of the physicochemical characteristics have been reported.Thus,we investigated the nature of the different amino acid residues interacting with the biologically active Ca²⁺and Mg²⁺and the selective transportation of Ca²⁺over Mg²⁺at the enzyme-water interface and in the entrance channel of the SR Ca²⁺-ATPase.The calculated results demonstrate that the electronegative protein cavities,composed of either aliphatic or aromatic amino acids,at the enzyme-water interface and in the entrance channel prefer to bind Mg²⁺rather than Ca²⁺due to the stronger electrostatic interactions between Mg²⁺and ligands.Further investigations show that the affinities of amino acids to the hydrated cations depend on the nature of the metal cations and the electronegativity and binding mode(the first- vs second=shell binding;mono-vs bidentate binding)of the amino acid ligands.In detail, relative to Ca²⁺,Mg²⁺has a stronger electrostatic interaction to the same ligands because of its smaller radius and bigger charge density.On the other hand,when the electronegativity of the ligand increases,the ligand exhibits a bigger affinity to Mg²⁺. Simultaneously,discrimination of the ligands between Ca²⁺and Mg²⁺is also enhanced.For the studied cases,the order of the ligand discrimination between Ca²⁺ and Mg²⁺are as follows:Trp-Glu＞Trp-Gln＞Trp-Trp＞Trp.In addition,the ligand binding modes have essential effects on ligand discrimination.In the Trp and Trp-Trp cases reactions with the biggest ion-selectivity are those which exhibit the second-shell indole binding,while for the Trp-Gln and Trp-Glu cases reactions with the biggest ion selectivity are those whose products have the second-shell indole and the first-shell monodentate aliphatic amino acids.More importantly,the calculations supplied feasible mechanisms to explain the size selectivity of Ca²⁺over Mg²⁺. Concretely to say,when these two kinds of hydrated cations move to the vicinity of the SR Ca²⁺-ATPase,the protein pockets at the enzyme-water interface bind Mg²⁺ more tightly than Ca²⁺,resulting in the concentration decrease of Mg²⁺in the local region.Then Ca²⁺transports into the entrance channel of the Ca²⁺=ATPase favorably. As for the few Mg²⁺ions,which may go into the entrance channel accompanying the Ca²⁺current,the big affinity of the ligands to Mg²⁺hampered the transportation of this cation freely,so the incompactly bound Ca²⁺can transport through the transmembrane region of the Ca²⁺-ATPase at a relatively high rate.This phenomenon is consistent with the "sticky-pore" hypothesis reported previously.Other very important factors to distinguish Ca²⁺and Mg²⁺are the size of the cavities formed by the binding sites and the preferred coordination number of these two cations. Additionally,the phenomenon of Ca²⁺selectivity against much higher background concentrations of monovalent Na⁺ and K⁺ can be explainded as follows(take Na⁺ for example):Firstly,Ca²⁺ions have the same charge-neutralizing effect as two Na⁺ ions while occupying less of the limited volume of the filter.Secondly,because the divalent calcium ions are more strongly attracted by the channel they can displace the sodium ions to occupy this region.Once there,Ca²⁺can only be moved by the repulsion from another divalent ion and not by the lower repulsion from Na⁺.Thirdly, the preferred coordination number of Na⁺(6)and the average Na⁺-O bond length (2.40(?))are unmatched to the Ca²⁺channel.(?)Effects of the Ca²⁺-Ï€Nonvalent Interactions on the Ca²⁺Transfer Nonvalent interactions exist in the biological processes extensively.Among them, cation-Ï€interaction has played the important roles in the Ca²⁺-ATPase,K⁺ channels, and quaternary ammonium inhibitors.Thus,we have studied the biologically relevant Ca²⁺-Ï€interactions and aliphatic amino acid coupled Ca²⁺-Ï€interactions by the Moller-Plesset calculations.The calculated results indicated that the delocalizedÏ€characteristics make the aromatic molecules the active ligands to bind Ca²⁺. Furthermore,the participations of the side chains of the aliphatic amino acids enhanced the Ca²⁺-ligands interactions greatly.For the Ca²⁺-Ï€complexes,we have investigated how Ca²⁺bind to one up to three benzene molecules.When Ca²⁺interacts with two benzene rings,the lowest energy structure is a staggered-parallel sandwich (SPS)form;while when Ca²⁺interacts with three benznene molecules,the lowest energy structure corresponds to a caged(C)form.Inevitably,these cases have the smallest ligands repulsions,which can stabilize the systems effectively.The same phenomena occur in the formamide- and acetate-coupled Ca²⁺-Ï€complexes.Notably, when formamide binds the benzene molecule directly,it has few effect on the aromatic characteristics of benzene.In contrast,the binding of acetate to the benzene ring will weaken the aromatic characteristics of benzene,which can be verified by the NBO and orbital analyses.Most importantly,our calculations have revealed that the side chains of the aliphatic amino acids bind Ca²⁺more strongly than those of the aromatic amino acids.Considerably,the weaker affinity of the aromatic iigands to Ca²⁺has resulted in the easier desorption of this cation from the ligands.Thus the aromatic amino acids can play the important roles in the binding-release balance of Ca²⁺in the Ca²⁺-ATPase.In addition,the Ca²⁺binding can reduce the HUMO-LUMO gaps of the protein ligands,resulting in the occurance of the fluorescence,which may be useful for the experimentalists to detect the Ca²⁺binding sites and conductivity processes.