Finite element solution of the steady-state Smoluchowski equation for rate constant calculations

This article describes the development and implementation of algorithms to study diffusion in biomolecular systems using continuum mechanics equations. Specifically, finite element methods have been developed to solve the steady-state Smoluchowski equation to calculate ligand binding rate constants for large biomolecules. The resulting software has been validated and applied to mouse acetylcholinesterase. Rates for inhibitor binding to mAChE were calculated at various ionic strengths with several different reaction criteria. The calculated rates were compared with experimental data and show very good agreement when the correct reaction criterion is used. Additionally, these finite element methods require significantly less computational resources than existing particle-based Brownian dynamics methods.     

Electron paramagnetic resonance reveals altered topography of the active center gorge of acetylcholinesterase after binding of fasciculin to the peripheral site

Fasciculin, a peptidic toxin from snake venom, inhibits mammalian and fish acetylcholinesterases (AChE) by binding to the peripheral site of the enzyme. This site is located at the rim of a narrow, deep gorge which leads to the active center triad, located at its base. The proposed mechanisms for AChE inhibition by fasciculin include allosteric events resulting in altered conformation of the AChE active center gorge. However, a fasciculin-induced altered topography of the active center gorge has not been directly demonstrated. Using electron paramagnetic resonance with the spin-labeled organophosphate 1-oxyl-2,2,6, 6-tetramethyl-4-piperidinylethylphosphorofluoridate (EtOSL) specifically bound to the catalytic serine of mouse AChE (mAChE), we show that bound fasciculin on mAChE slows down, but does not prevent phosphorylation of the active site serine by EtOSL and protects the gorge conformation against thermal denaturation. Most importantly, a restricted freedom of motion of the spin label bound to the fasciculin-associated mAChE, compared to mAChE, is evidenced. Molecular models of mAChE and fasciculin-associated mAChE with tethered EtOSL enantiomers indicate that this restricted motion is due to greater proximity of the S-EtOSL nitroxide radical to the W86 residue in the fasciculin-associated enzyme. Our results demonstrate a topographical alteration indicative of a restricted conformation of the active center gorge of mAChE with bound fasciculin at its rim.     

Acetylcholinesterase: mechanisms of covalent inhibition of H447I mutant determined by computational analyses

The reaction mechanisms of two inhibitor TFK(+) and TFK(0) binding to H447I mutant mouse acetylcholinesterase (mAChE) have been investigated by using a combined ab initio quantum mechanical/molecular mechanical (QM/MM) approach and classical molecular dynamics (MD) simulations. TFK(+) binding to the H447I mutant may proceed with a different reaction mechanism from the wild-type. A water molecule takes over the role of His447 and participates in the bond breaking and forming as a "charge relayer". Unlike in the wild-type mAChE case, Glu334, a conserved residue from the catalytic triad, acts as a catalytic base in the reaction. The calculated energy barrier for this reaction is about 8kcal/mol. These predictions await experimental verification. In the case of the neutral ligand TFK(0), however, multiple MD simulations on the TFK(0)/H447I complex reveal that none of the water molecules can be retained in the active site as a "catalytic" water. Taken together our computational studies confirm that TFK(0) is almost inactive in the H447I mutant, and also provide detailed mechanistic insights into the experimental observations.     

Comparison of properties of native and lytic forms of acetylcholinesterase from Apis mellifera

The properties of purified native soluble AChE (sAChE) from Apis mellifera were compared with those of purified membrane AChE (mAChE), mAChE solubilized with phosphatidylinositol-specific phospholipase C (AChEPI-PLC), glycosyl phosphatidylinositol-specific phospholipase D (AChEGPI-PLD) and trypsin (AChETi), and other soluble derivative forms obtained from mAChE by autolysis (AChELyt) or limited digestions with proteinase K or chymotrypsin. Analysis by non-denaturing electrophoresis showed that the electrophoretic mobilities of all lytic soluble forms were higher than that of sAChE. sAChE had a K_m value of about 90 μM whereas mAChE, AChETi, AChELyt, AChEPI-PLC, and AChEGPI-PLD displayed a lower K_m value of about 20 μM. The sensitivity to organophosphates was lower for sAChE than for mAChE, AChETi, AChEPI-PLC, and AChEGPI-PLD and was due to higher K_d and lower k₂ values observed for sAChE. In Arrhenius plot analysis, mAChE, AChETi, AChEPI-PLC, and AChEGPI-PLD displayed a homogenous behaviour whereas sAChE exhibited a highly reproducible break at 18°C. Thermal stability studies at 52°C revealed that sAChE, AChEPI-PLC, and AChEGPI-PLD displayed the highest thermal stability with inactivation constants of about 0.020 min⁻¹. This high thermal stability contrasted with those of mAChE, AChELyt, and AChETi, which exhibited respective inactivation constants of 0.051, 0.074, and 0.171 min⁻¹. These results suggest that sAChE is not the mere cleavage product of mAChE by endogenous (glycosyl) phosphatidylinositol-specific phospholipase C/D or proteases. Arch. Insect Biochem. Physiol. 34:143–157, 1997. © 1997 Wiley-Liss, Inc.     

Reversibly bound and covalently attached ligands induce conformational changes in the omega loop, Cys69-Cys96, of mouse acetylcholinesterase

We have used a combination of cysteine substitution mutagenesis and site-specific labeling to characterize the structural dynamics of mouse acetylcholinesterase (mAChE). Six cysteine-substituted sites of mAChE (Leu(76), Glu(81), Glu(84), Tyr(124), Ala(262), and His(287)) were labeled with the environmentally sensitive fluorophore, acrylodan, and the kinetics of substrate hydrolysis and inhibitor association were examined along with spectroscopic characteristics of the acrylodan-conjugated, cysteine-substituted enzymes. Residue 262, being well removed from the active center, appears unaffected by inhibitor binding. Following the binding of ligand, hypsochromic shifts in emission of acrylodan at residues 124 and 287, located near the perimeter of the gorge, reflect the exclusion of solvent and a hydrophobic environment created by the associated ligand. By contrast, the bathochromic shifts upon inhibitor binding seen for acrylodan conjugated to three omega loop (Omega loop) residues 76, 81, and 84 reveal that the acrylodan side chains at these positions are displaced from a hydrophobic environment and become exposed to solvent. The magnitude of fluorescence emission shift is largest at position 84 and smallest at position 76, indicating that a concerted movement of residues on the Omega loop accompanies gorge closure upon ligand binding. Acrylodan modification of substituted cysteine at position 84 reduces ligand binding and steady-state kinetic parameters between 1 and 2 orders of magnitude, but a similar substitution at position 81 only minimally alters the kinetics. Thus, combined kinetic and spectroscopic analyses provide strong evidence that conformational changes of the Omega loop accompany ligand binding.     

A generalized finite difference method for modeling cardiac electrical activation on arbitrary, irregular computational meshes

A generalized finite difference (GFD) method is presented that can be used to solve the bi-domain equations modeling cardiac electrical activity. Classical finite difference methods have been applied by many researchers to the bi-domain equations. However, these methods suffer from the limitation of requiring computational meshes that are structured and orthogonal. Finite element or finite volume methods enable the bi-domain equations to be solved on unstructured meshes, although implementations of such methods do not always cater for meshes with varying element topology. The GFD method solves the bi-domain equations on arbitrary and irregular computational meshes without any need to specify element basis functions. The method is useful as it can be easily applied to activation problems using existing meshes that have originally been created for use by finite element or finite difference methods. In addition, the GFD method employs an innovative approach to enforcing nodal and non-nodal boundary conditions. The GFD method performs effectively for a range of two and three-dimensional test problems and when computing bi-domain electrical activation moving through a fully anisotropic three-dimensional model of canine ventricles.     

Prediction of the binding energy for small molecules,peptides and proteins

A fast and reliable evaluation of the binding energy from a single conformation of a molecular complex is an important practical task. Knowledge‐based scoring schemes may not be sufficiently general and transferable, while molecular dynamics or Monte Carlo calculations with explicit solvent are too computationally expensive for many applications. Recently, several empirical schemes using finite difference Poisson–Boltzmann electrostatics to predict energies for particular types of complexes were proposed. Here, an improved empirical binding energy function has been derived and validated on three different types of complexes: protein–small ligand, protein–peptide and protein–protein. The function uses the boundary element algorithm to evaluate the electrostatic solvation energy. We show that a single set of parameters can predict the relative binding energies of the heterogeneous validation set of complexes with 2.5 kcal/mol accuracy. We also demonstrate that global optimization of the ligand and of the flexible side‐chains of the receptor improves the accuracy of the evaluation. Copyright © 1999 John Wiley & Sons, Ltd.     

Initiation and progression of mechanical damage in the intervertebral disc under cyclic loading using continuum damage mechanics methodology: A finite element study

It is difficult to study the breakdown of disc tissue over several years of exposure to bending and lifting by experimental methods. There is also no finite element model that elucidates the failure mechanism due to repetitive loading of the lumbar motion segment. The aim of this study was to refine an already validated poro-elastic finite element model of lumbar motion segment to investigate the initiation and progression of mechanical damage in the disc under simple and complex cyclic loading conditions. Continuum damage mechanics methodology was incorporated into the finite element model to track the damage accumulation in the annulus in response to the repetitive loading. The analyses showed that the damage initiated at the posterior inner annulus adjacent to the endplates and propagated outwards towards its periphery under all loading conditions simulated. The damage accumulated preferentially in the posterior region of the annulus. The analyses also showed that the disc failure is unlikely to happen with repetitive bending in the absence of compressive load. Compressive cyclic loading with low peak load magnitude also did not create the failure of the disc. The finite element model results were consistent with the experimental and clinical observations in terms of the region of failure, magnitude of applied loads and the number of load cycles survived.     

Direct analysis of the kinetic profiles of organophosphate-acetylcholinesterase adducts by MALDI-TOF mass spectrometry

A sensitive matrix-assisted laser desorption/ionization time-of-flight (MALDI-TOF) mass spectrometry procedure has been established for the detection and quantitation of acetylcholinesterase (AChE) inhibition by organophosphate (OP) compounds. Tryptic digests of purified recombinant mouse AChE (mAChE) were fractionally inhibited by paraoxon to form diethyl phosphoryl enzyme. The tryptic peptide of mAChE that contains the active center serine residue resolves to a molecular mass of 4331.0 Da. Phosphorylation of the enzyme by paraoxon results in covalent modification of the active center serine and a corresponding increase in molecular mass of the tryptic peptide by 136 Da. The relative abundance of AChE peptides containing a modified active center serine strongly correlates with the fractional inhibition of the enzyme, achieving a detection range of phosphorylated to nonphosphorylated enzyme of 5-95%. Modifications of AChE by OP compounds resulting in dimethyl, diethyl, and diisopropyl phosphoryl adducts have been monitored with subpicomole amounts of enzyme. The individual phosphorylated adducts of AChE that result from loss of one alkyl group from the inhibited enzyme (the aging reaction) and the reappearance of unmodified AChE (spontaneous reactivation) have been resolved by the kinetic profiles and relative abundance of species. Further, the tryptic peptide containing the active center serine of AChE, isolated from mouse brain by anion-exchange and affinity chromatography, has been monitored by mass spectrometry. Native brain AChE, purified from mice treated with sublethal doses of metrifonate, has demonstrated that enzyme modifications resulting from OP exposure can be detected in a single mouse brain. For dimethyl phosphorylated AChE, OP exposure has been monitored by the ratio of tryptic peptide peaks that correspond to unmodified (uninhibited and/or reactivated), inhibited, and aged enzyme.     

Blunt Liver Injury with Intact Ribs under Impacts on the Abdomen: A Biomechanical Investigation

Abdominal trauma accounts for nearly 20% of all severe traffic injuries and can often result from intentional physical violence, from which blunt liver injury is regarded as the most common result and is associated with a high mortality rate. Liver injury may be caused by a direct impact with a certain velocity and energy on the abdomen, which may result in a lacerated liver by penetration of fractured ribs. However, liver ruptures without rib cage fractures were found in autopsies in a series of cases. All the victims sustained punches on the abdomen by fist. Many studies have been dedicated to determining the mechanism underlying hepatic injury following abdominal trauma, but most have been empirical. The actual process and biomechanism of liver injury induced by blunt impact on the abdomen, especially with intact ribs remained, are still inexhaustive. In order to investigate this, finite element methods and numerical simulation technology were used. A finite element human torso model was developed from high resolution CT data. The model consists of geometrically-detailed liver and rib cage models and simplified models of soft tissues, thoracic and abdominal organs. Then, the torso model was used in simulations in which the right hypochondrium was punched by a fist from the frontal, lateral, and rear directions, and in each direction with several impact velocities. Overall, the results showed that liver rupture was primarily caused by a direct strike of the ribs induced by blunt impact to the abdomen. Among three impact directions, a lateral impact was most likely to cause liver injury with a minimum punch speed of 5 m/s (the momentum was about 2.447 kg.m/s). Liver injuries could occur in isolation and were not accompanied by rib fractures due to different material characteristics and injury tolerance.     

几何形态学方法及其在动物发育与系统进化研究中的应用

简要回顾了几何形态学的发展历史,介绍了30多年来该领域使用的主要方法及其在生物发育与进化研究中的实际应用。除目前应用最为广泛的标点法和轮廓线法外,基于三维数据的表面特征分析和有限元分析也在该领域得到推广。这些方法可运用于分析两性分化、异速生长、种群分化、种上进化以及复杂功能结构的形态集成等科学问题。几何形态学与生物信息学的综合运用还将有利于探讨表型变化与遗传物质变化的相关性。随着生物成像技术和海量数据计算技术的进步,几何形态学将由目前以二维数据为主的研究向三维重建和分析的方向发展。     

Brain mechanics For neurosurgery: modeling issues

 Brain biomechanics has been investigated for more than 30 years. In particular, finite element analyses and other powerful computational methods have long been used to provide quantitative results in the investigation of dynamic processes such as head trauma. Nevertheless, the potential of these methods to simulate and predict the outcome of quasi-static processes such as neurosurgical procedures and neuropathological processes has only recently been explored. Some inherent difficulties in modeling brain tissues, which have impeded progress, are discussed in this work. The behavior of viscoelastic and poroelastic constitutive models is compared in simple 1-D simulations using the ABAQUS finite element platform. In addition, the behaviors of quasi-static brain constitutive models that have recently been proposed are compared. We conclude that a compressible viscoelastic solid model may be the most appropriate for modeling neurosurgical procedures. Received: 19 March 2002 / Accepted: 6 June 2002 Work is supported by a generous grant from the Whitaker Foundation. We would like to also thank Dr. Christos Davatzikos (Johns Hopkins School of Medicine, Baltimore, Maryland) for his help.     

Characterization of DNA sequences that mediate nuclear protein binding to the regulatory region of the Pisum sativum (pea) chlorophyl a/b binding protein gene AB80: identification of a repeated heptamer motif

Two protein factors binding to the regulatory region of the pea chlorophyl a/b binding protein gene AB80 have been identified. One of these factors is found only in green tissue but not in etiolated or root tissue. The second factor (denominated ABF-2) binds to a DNA sequence element that contains a direct heptamer repeat TCTCAAA. It was found that presence of both of the repeats is essential for binding. ABF-2 is present in both green and etiolated tissue and in roots and factors analogous to ABF-2 are present in several plant species. Computer analysis showed that the TCTCAAA motif is present in the regulatory region of several plant genes.     

Determinants of the interaction between the iron-responsive element-binding protein and its binding site in rat L-ferritin mRNA

Ferritin messenger RNA has been shown to be translationally inactivated by the binding of a cytosolic protein to a 28-nucleotide iron-responsive element (IRE) located in the 5'-untranslated region of the mRNA. This interaction has been studied using quantitative receptor-ligand binding methods with gel retardation and nitrocellulose filter binding assays for the separation of bound complex from free RNA. In competition assays the entire 5'-untranslated region and the isolated IRE bound identically. The specificity of the RNA binding was studied using IRE variants. Two IREs from transferrin receptor mRNA and several variants with single base substitutions in the stem or loop had similar affinities. RNAs which could not form a stem-loop structure bound 1000-fold less well. These studies demonstrate the importance of the RNA conformation and the relative insensitivity of binding to much of the primary sequence. Saturation assays with increasing concentrations of 32P-IRE resulted in a binding hyperbola characteristic of mass action binding to a single class of sites with a KD = 0.09 nM. At 37 degrees C the dissociation rate is 0.04 min-1 (t 1/2 = 17 min). This rate is fast enough to account for the shift of ferritin RNA from the ribonucleoprotein pool to polysomes after rats are injected with iron. Determination of the concentration of the repressor requires accounting for three interconverting pools: free active repressor, mRNA-bound protein, and inactive (low affinity) repressor. Rat liver cytosol has a concentration of free active repressor of about 1 pmol/mg protein. Protein bound to endogenous mRNA can be measured by pretreatment with micrococcal nuclease or by separation with DEAE-Sepharose chromatography; it is present at a level similar to that of the free active protein. Inclusion of high levels of thiol reductants in the binding incubations reduces the inactive or low affinity repressor, forming unstably activated protein which has the same KD as the endogenous active protein; this inactive or low affinity protein is 2-4 times more abundant. A mechanism for iron regulation is proposed which accounts for the kinetics, the multiple protein pools, and the characteristics of the protein in these pools.     

Characterization of nuclear factors binding to AT-rich element in the rat p53 promoter

In this study, we identified AT-rich element located at positions -504 to -516 in the rat p53 promoter by DNase I foot printing assay. This region was previously identified as a positive regulatory element in the murine p53 promoter and designated as PBF1 (p53 binding factor 1) binding site. However, the proteins binding to this AT-rich element have not been identified yet. Therefore, we characterized the binding protein by various biochemical methods. First, we confirmed that by the oligonucleotide competition assay, nuclear factors bound to the AT-rich element in a sequence-specific manner. Two binding proteins were identified in southwestern blotting analysis and the molecular masses of the proteins were 60 and 40 kDa, respectively. The proteins were stable to denaturants or ionic strength. Treatment of chelators showed that the binding proteins did not require divalent cation for DNA-binding activity. In addition, the binding proteins were labile to protease treatment. This study showed that 60 and 40 kDa proteins bound to AT-rich element and the physico-chemical properties provided new insights into the binding proteins.