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Reliability of pharmacodynamic analysis by logistic regression: a computer simulation study.

BACKGROUND: Many pharmacologic studies record data as binary yes-or-no variables, and analysis is performed using logistic regression. This study investigates the accuracy of estimation of the drug concentration associated with a 50% probability of drug effect (C50) and the term describing the steepness of the concentration-effect relation (gamma). METHODS: The authors developed a technique for simulating pharmacodynamic studies with binary yes-or-no responses. Simulations were conducted assuming either that each data point was derived from the same patient or that data were pooled from multiple patients in a population with log-normal distributions of C50 and gamma. Coefficients of variation were calculated. The authors also determined the percentage of simulations in which the 95% confidence intervals contained the true parameter value. RESULTS: The coefficient of variation of parameter estimates decreased with increasing n and gamma. The 95% confidence intervals for C50 estimation contained the true parameter value in more than 90% of the simulations. However, the 95% confidence intervals of gamma did not contain the true value in a substantial number of simulations of data from multiple patients. CONCLUSION: The coefficient of variation of parameter estimates may be as large as 40-50% for small studies (n < or = 20). The 95% confidence intervals of C50 almost always contain the true value, underscoring the need for always reporting confidence intervals. However, when data from multiple patients is naively pooled, the estimates of gamma may be biased, and the 95% confidence intervals may not contain the true value.

Algorithms↗

Criteria for conduction block based on computer simulation studies of nerve conduction with human data obtained in the forearm segment of the median nerve.

The finding of conduction block (CB) on nerve conduction studies supports the diagnosis of potentially treatable immune-mediated neuropathies. CB in a number of axons may result in reduction of the compound muscle action potential (CMAP) on proximal versus distal stimulation (decrement). Decrement may also result from increased temporal dispersion (TD) as this leads to desynchronization and phase cancellation of the motor unit action potentials (MUAPs) out of which the CMAP is built up; polyphasia of MUAPs possibly yields additional decrement. To prove the occurrence of CB, decrement has to be larger than can be explained by increased TD or increased phase cancellation. This was established previously by simulations using MUAPs recorded in rats assuming maximal TD. Unfortunately, criteria based on human data and criteria for nerves with limited TD are not available. In the present study, criteria for CB were derived using simulations with thenar surface recorded MUAPs affected by collateral reinnervation that were obtained in patients with lower motor neurone disease (LMND). The effect of TD on decrement was determined for a wide range of TDs in the forearm segment of the median nerve and the segment distal to this. Our criteria for CB were based on area decrement because this was less influenced by TD and more by CB than amplitude decrement. The maximal area decrement in the forearm segment increased as TD in the forearm segment increased but decreased as TD in the distal segment increased. This suggests that, when desynchronization and phase cancellation occur in the distal segment due to TD, less phase cancellation and, therefore, less decrement can occur due to TD in the forearm. The finding that duration prolongation on proximal versus distal stimulation reflected TD within the forearm segment and that distal duration reflected TD in the distal segment allowed proposal of a more flexible set of criteria for forearm segments when TD in the forearm segment is limited or TD in the distal segment is pronounced. A separate investigation showed that the maximal TD in chronic inflammatory demyelinating polyneuropathy was within the range of our simulations, indicating that these were realistic. Our criteria were validated retrospectively in patients with multifocal motor neuropathy and patients with LMND. In the forearm segment of the median nerve, our criteria were more sensitive and equally specific for CB as compared with criteria for CB based on the study using rats. Our criteria have to be evaluated prospectively.

Action Potentials↗

Characterization of Ran-driven cargo transport and the RanGTPase system by kinetic measurements and computer simulation.

Here, we analyse the RanGTPase system and its coupling to receptor-mediated nuclear transport. Our simulations predict nuclear RanGTP levels in HeLa cells to be very sensitive towards the cellular energy charge and to exceed the cytoplasmic concentration approximately 1000-fold. The steepness of the RanGTP gradient appears limited by both the cytoplasmic RanGAP concentration and the imperfect retention of nuclear RanGTP by nuclear pore complexes (NPCs), but not by the nucleotide exchange activity of RCC1. Neither RanBP1 nor the NPC localization of RanGAP has a significant direct impact on the RanGTP gradient. NTF2-mediated import of Ran appears to be the bottleneck for maximal capacity of Ran-driven nuclear transport. We show that unidirectional nuclear transport can be faithfully simulated without the assumption of a vectorial NPC passage; transport receptors only need to reversibly cross NPCs and switch their affinity for cargo in response to the RanGTP gradient. A significant RanGTP gradient after nuclear envelope (NE) breakdown can apparently exist only in large cytoplasm. This indicates that RanGTP gradients can provide positional information for mitotic spindle and NE assembly in early embryonic cells, but hardly any in small somatic cells.

Active Transport, Cell Nucleus↗

Use of real time leukaemia data to validate model predictions based on analyses and computer simulations.

Predictions arising out of a mathematical model that describes the expansion of leukaemia from a diffusion-orientated perspective are critiqued and validated by employing available real time data. Based on agreements found between model predictions and the data, but mindful of the limitations it presents, it is concluded that the model could be used to describe the dynamics of normal and abnormal cells in leukaemia. It is suggested that further studies of the behaviour of certain normal cell types in contrast to abnormal cells during leukaemic development could engender additional insights into leukaemia and its treatment.

Cell Death↗

[Use of the computer simulation method of complementary amino acids base on a genetic code algorithm for the search for new peptide compounds belonging to tuftsin-like activity].

Methods of k-neighbours and neural networks were used for prediction of pharmacological effects of new compounds wits tuftsin-like activities. The tested compounds were constructed by the complementarity rule of genetic code algorithm. Five of seven substitutions with stereocomplement amino acids in the tuftsin sequence lead to new active compounds. Thus, the use of amino acid complementary code can be a helpful tool for the construction of a new immunomodulating peptide.

Algorithms↗

Specific mode of interaction between components of model pulmonary surfactants using computer simulations.

Atomistic molecular dynamics simulations and structural bioinformatics tools enable the identification of the exact mode of interaction between model pulmonary surfactant components. Two nanosecond long simulations of the N-terminal region of human surfactant protein-B (SP-B(1-25)) in dipalmitoylphosphatidylcholine (DPPC) and dipalmitoylphosphatidylglycerol (DPPG) monolayers of different lipid surface densities reveal the preferential affinity of SP-B(1-25) for anionic phospholipids. In particular, arginine 12 and lysine 24 interact strongly and with high specificity with the phosphate group of the DPPG lipids, stabilizing the position, the orientation, and the secondary structure of the peptide in the monolayer. The peptide lies at an oblique angle to the interfacial plane, ranging between 47 degrees and 62 degrees, increasing with decreasing lipid surface density. In DPPC monolayers the interaction is largely determined by hydrophobic interactions. The non-specific nature of DPPC-SP-B(1-25) interactions allows for significant flexibility in the topology of the peptide in the lipid matrix. Bioinformatics tools are employed to generalize the simulation results to the sequences of SP-B(1-25) in other organisms. The importance of specific residues, and the role of the largely helical and amphiphilic nature of the peptide in the functionality of SP-B(1-25) are established. The synergy of classical mechanics tools with bioinformatics methods greatly enhances the molecular-level interpretation of pulmonary surfactant action and facilitates the development of design rules for synthetic surfactant analogues.

1,2-Dipalmitoylphosphatidylcholine↗

Analysing a magnetic molecule detection system--computer simulation.

The detection of single molecules, e.g. in biology is possible by marking the interesting molecules with magnetic beads and detect the influence of the beads on giant magnetoresistance (GMR)/tunnel magnetoresistance (TMR)/spin valve (SV) sensors. The development of suitable multilayers has been studied experimentally as well as theoretically in order to optimize the sensor parameters. A finite difference (FD) method including the usually used contributions to the total energy [exchange, antiferromagnetically (af) coupling, anisotropy and magnetostatic] is used for the simulation with additional contributions to the local field according to the stray fields of the beads. In this work, we will show the results of micromagnetic calculations of the magnetization behavior of GMR/TMR sensors considering also the interaction between the domains in the magnetic layers of the sensor and the bead area. We can present first calculations where the bead particles (signal source) and the magnetic layers (sensor device) are considered as a whole magnetic ensemble.

Biopolymers↗

High-resolution field-cycling NMR studies of a DNA octamer as a probe of phosphodiester dynamics and comparison with computer simulation.

Phosphorus-spin longitudinal relaxation rates of the DNA duplex octamer [d(GGAATTCC)](2) have been measured from 0.1 to 17.6 T by means of conventional and new field-cycling NMR methods. The high-resolution field-cycling method is identical to a conventional relaxation experiment, except that after preparation the sample is moved pneumatically from its usual position at the center of the high-resolution magnet upward to a lower field above its normal position and then returned to the center for readout after it has relaxed for the programmed relaxation delay at the low field. This is the first measurement of all longitudinal relaxation rates R(1) of a nuclear species in a macromolecule over virtually the entire accessible magnetic field range. For detailed analysis, three magnetic field regions can be delineated: (i) dipolar relaxation dominates at fields below 2 T, (ii) chemical shift anisotropy (CSA) relaxation is roughly constant from 2 to 6 T, and (iii) a square-law increasing dependence is seen at fields higher than approximately 6 T due to internal motion CSA relaxation. The analysis provides a rotational correlation time (tau(r) = 4.1 +/- 0.3 ns) for the duplex at both 1.5 and 0.25 mM concentrations (of duplex) at 22 degrees C. For comparison, extraction of tau(r) in the conventional way from the ratio of T(1)/T(2) at 14 T yields 3.2 ns. The tau(r) discrepancy disappears when we exclude the contribution of internal motion from the R(1) in the ratio. The low-field dipolar relaxation provides a weighted inverse sixth power sum of the distances from the phosphorus to the protons responsible for relaxation. This average is similar for all phosphates in the octamer and similar to that in previous B-DNA structures (its inverse sixth root is about 2.40 A for two different concentrations of octamer). The CSA relaxation at intermediate field provides an estimate of the order parameter squared, S(c)(2), for each phosphorus. S(c)(2) is about 0.7-1, clearly different for different phosphate linkages in the octamer duplex. The increasing R(1) at high fields reflects CSA relaxation due to internal motions, for which a correlation time, tau(hf), can be approximately extracted with the aid of additional measurements at 14.0 and 17.6 T. We conclude that tau(hf) values are relatively large, in the range of about 150 ps. Insight into the motions leading to this correlation time was gained by a 28 ns molecular dynamics simulation of the molecule. S(2) and tau(s) (corresponding to tau(hf)) predicted by this simulation were in good agreement with the experimental values from the field-cycling data. Both the effect of Mg(2+) on the dynamic parameters extracted from (31)P relaxation rates and the field dependence of relaxation rates for several protons of the octamer were measured. High-resolution field cycling opens up the possibility of monitoring residue-specific dipolar interactions and dynamics for the phosphorus nuclei of diverse oligonucleotides.

Cations, Divalent↗

Computer simulation of noise resulting from random synaptic activities.

Neuronal behavior is dependent on random inputs from a multitude of synaptic contacts on the soma and dendritic tree. Therefore, simulations of different types of noise are often required in the experimental and theoretical investigation of the properties of neurons and neuronal assemblies. The direct simulation of these noise sources by simple difference equations may therefore be quite useful and a general approach is presented in this paper. Initially, a first order model and its time-discretization are analyzed in detail, followed by a generalization to more complex models. The firing patterns of neurons are dependent on the random behaviors of their membrane potentials at the trigger zone. These depend on the propagation of the randomly occurring postsynaptic potentials from specific places on the dendritic tree or soma to the trigger zone. Different models may represent a variety of circumstances in which random membrane potentials arise at the trigger zone. Simulations of different types of noise are often required in the experimental and theoretical investigation of the properties of neurons and neuronal assemblies. The direct simulation of these noise sources by simple difference equations may therefore be quite useful and a general approach is presented in this paper. This paper presents a detailed analysis of the very useful first order model and its time discretization. The criterion used is that the autocovariance sequence of the discrete time model be a sample of the original autocovariance function. Several cases are presented which are of practical interest, including the case of constant output variance independent of the model's time constant. General models are time-discretized by the impulse response invariance method. Two applications are presented, one is related to the modeling of the synaptic currents by the alpha function instead of the delta function and the second deals with analog synaptic noise generation by D/A conversion of computer generated noise sequences.

Action Potentials↗

Heterogeneity in the mouse epidermal cell cycle analysed by computer simulations.

Different sets of cell kinetic data obtained over many years from hairless mouse epidermis have been simulated by a mathematical model including circadian variations. Simulating several independent sets of data with the same mathematical model strengthens the validity of the results obtained. The data simulated in this investigation were all obtained with the experimental system in a state of natural synchrony. The data include cell cycle phase distributions measured by DNA flow cytometry of isolated epidermal basal cells, fractions of tritiated thymidine ([3H]TdR) labelled cells within the cell cycle phases measured by cell sorting at intervals after [3H]TdR pulse labelling, bivariate bromodeoxyuridine (BrdUrd)/DNA data from epidermal basal cells isolated at intervals after pulse labelling with BrdUrd, mitotic rate and per cent labelled mitosis (PLM) data from histologic sections. The following main new findings were made from the simulations: the second PLM peak observed at about 35 h after pulse labelling is hardly influenced by circadian variations; the peak is mainly determined by persisting synchrony of a rapidly cycling population with a G1-duration (TG1) of 20 h to 30 h; and there is a highly significant population of slowly cycling G1-cells (G1 sigma). However, no significant circadian variations were found in the number of these cells.

Animals↗

Free energy calculations by computer simulation.

A fundamental problem in chemistry and biochemistry is understanding the role of solvation in determining molecular properties. Recent advances in statistical mechanical theory and molecular dynamics methodology can be used to solve this problem with the aid of supercomputers. By using these advances the free energies of solvation of all the chemical classes of amino acid side chains, four nucleic acid bases and other organic molecules can be calculated. The effect of a site-specific mutation on the stability of trypsin is predicted. The results are in good agreement with available experiments.

Amino Acids↗

Towards understanding the mechanisms of molecular recognition by computer simulations of ligand-protein interactions.

The thermodynamic and kinetic aspects of molecular recognition for the methotrexate (MTX)-dihydrofolate reductase (DHFR) ligand-protein system are investigated by the binding energy landscape approach. The impact of 'hot' and 'cold' errors in ligand mutations on the thermodynamic stability of the native MTX-DHFR complex is analyzed, and relationships between the molecular recognition mechanism and the degree of ligand optimization are discussed. The nature and relative stability of intermediates and thermodynamic phases on the ligand-protein association pathway are studied, providing new insights into connections between protein folding and molecular recognition mechanisms, and cooperativity of ligand-protein binding. The results of kinetic docking simulations are rationalized based on the thermodynamic properties determined from equilibrium simulations and the shape of the underlying binding energy landscape. We show how evolutionary ligand selection for a receptor active site can produce well-optimized ligand-protein systems such as MTX-DHFR complex with the thermodynamically stable native structure and a direct transition mechanism of binding from unbound conformations to the unique native structure.

Animals↗

Computer simulation of water in cytochrome c oxidase.

Statistical mechanics and molecular dynamics simulations have been carried out to study the distribution and dynamics of internal water molecules in bovine heart cytochrome c oxidase (CcO). CcO is found to be capable of holding plenty of water, which in subunit I alone amounts to about 165 molecules. The dynamic characterization of these water molecules is carried out. The nascent water molecules produced in the redox reaction at the heme a(3)-CuB binuclear site form an intriguing chain structure. The chain begins at the position of Glu242 at the end of the D channel, and has a fork structure, one branch of which leads to the binuclear center, and the other to the propionate d of heme a(3). The branch that leads to the binuclear center has dynamic access both to the site where the formation of water occurs, and to delta-nitrogen of His291. From the binuclear center, the chain continues to run into the K channel. The stability of this hydrogen bond network is examined dynamically. The catalytic site is located at the hydrophobic region, and the nascent water molecules are produced at the top of the energy hill. The energy gradient is utilized as the mechanism of water removal from the protein. The water exit channels are explored using high-temperature dynamics simulations. Two putative channels for water exit from the catalytic site have been identified. One is leading directly toward Mg(2+) site. However, this channel is only open when His291 is dissociated from CuB. If His291 is bound to CuB, the only channel for water exit is the one that originates at E242 and leads toward the middle of the membrane. This is the same channel that is presumably used for oxygen supply.

Animals↗

Pancreatic islet discrimination of hexose anomers. II. Transient computer simulation.

We have previously modeled pancreatic islet glycolysis under idealized steady-state conditions where the input is a pure hexose anomer and there is no mutarotation and reproduced the known preference for the alpha-anomers of glucose and mannose as substrates. This model is here extended to simulate real experiments, where the hexoses mutarotate and measurements may be taken over time. The behavior of our model system agrees with available experimental data. The hexose diphosphate activators of phosphofructokinase, whose effect was seen as not important in the preceding steady-state analysis, are found here to have a modest (approximately 10-15%) effect on its flux. The previous conclusion that the anomeric preference of the glycolytic pathway follows from that of glucokinase continues to hold in the real experimental situation.

Animals↗

Computer simulations of the OmpF porin from the outer membrane of Escherichia coli.

Molecular dynamics simulations were used to study the structure and dynamics of the Escherichia coli OmpF porin, which is composed of three identical 16-stranded beta-barrels. Simulations of the full trimer in the absence of water and the membrane led to significant contraction of the channel in the interior of each beta-barrel. With very weak harmonic constraints (0.005 kcal/mol A2/atom) applied to the main-chain C alpha atoms of the beta-barrel, the structure was stabilized without alteration of the average fluctuations. The resulting distribution of the fluctuations (small for beta-strands, large for loops and turns) is in good agreement with the x-ray B factors. Dynamic cross-correlation functions showed the importance of coupling between the loop motions and barrel flexibility. This was confirmed by the application of constraints corresponding to the observed temperature factors to the barrel C alpha atoms. With these constraints, the beta-barrel fluctuations were much smaller than the experimental values because of the intrinsic restrictions on the atomic motions, and the loop motions were reduced significantly. This result indicates that considerable care is required in introducing constraints to keep proteins close to the experimental structure during simulations, as has been done in several recent studies. Loop 3, which is thought to be important in gating the pore, undergoes a displacement that shifts it away from the x-ray structure. Analysis shows that this arises from the breakdown of a hydrogen bond network, which appears to result more from the absence of solvent that from the use of standard ionization states for the side chains of certain beta-barrel residues.

Amino Acid Sequence↗

Hydration properties of xylitol: computer simulation.

We present a molecular dynamics simulation of xylitol in SPC/E water using classical Gibbs ensemble molecular dynamics simulation. The simulation is done both with and without periodic charge update, and no qualitative difference in the results obtained by both methods is found. The analysis of the radial and angular distribution functions, the water-water hydrogen bond distributions, and water residence times allow the conclusion that there is a relatively strong hydration of xylitol. This polyol adopts a single linear conformation and, from the point of view of the hydration dynamics, it should be classified as positively hydrated.

Carbohydrate Conformation↗

Unfolding and refolding of the native structure of bovine pancreatic trypsin inhibitor studied by computer simulations.

A new procedure for studying the folding and unfolding of proteins, with an application to bovine pancreatic trypsin inhibitor (BPTI), is reported. The unfolding and refolding of the native structure of the protein are characterized by the dimensions of the protein, expressed in terms of the three principal radii of the structure considered as an ellipsoid. A dynamic equation, describing the variations of the principal radii on the unfolding path, and a numerical procedure to solve this equation are proposed. Expanded and distorted conformations are refolded to the native structure by a dimensional-constraint energy minimization procedure. A unique and reproducible unfolding pathway for an intermediate of BPTI lacking the [30,51] disulfide bond is obtained. The resulting unfolded conformations are extended; they contain near-native local structure, but their longest principal radii are more than 2.5 times greater than that of the native structure. The most interesting finding is that the majority of expanded conformations, generated under various conditions, can be refolded closely to the native structure, as measured by the correct overall chain fold, by the rms deviations from the native structure of only 1.9-3.1 A, and by the energy differences of about 10 kcal/mol from the native structure. Introduction of the [30,51] disulfide bond at this stage, followed by minimization, improves the closeness of the refolded structures to the native structure, reducing the rms deviations to 0.9-2.0 A. The unique refolding of these expanded structures over such a large conformational space implies that the folding is strongly dictated by the interactions in the amino acid sequence of BPTI. The simulations indicate that, under conditions that favor a compact structure as mimicked by the volume constraints in our algorithm, the expanded conformations have a strong tendency to move toward the native structure; therefore, they probably would be favorable folding intermediates. The results presented here support a general model for protein folding, i.e., progressive formation of partially folded structural units, followed by collapse to the compact native structure. The general applicability of the procedure is also discussed.

Animals↗

Comparison of three lithium dosing methods in 950 "subjects" by computer simulation.

This study compared the accuracy of the one-point method (OPM) of Cooper et al., the repeated one-point method (ROPM) using a 12 h initial dosage interval (ROPM-12), and the ROPM using a 24 h initial dosage interval (ROPM-24) for predicting lithium steady-state concentrations after lithium carbonate 600 mg every 12 h. Pharmacokinetic values for elimination rate constant (k), volume of distribution (V), and absorption rate constant (ka) were generated randomly for 950 subjects to produce normally distributed values of the parameters with target means and standard deviations in accordance with values reported in the literature. Errors with a mean of zero and a standard deviation of +/- 5% (SD5%) and +/- 10% (SD10%) were added to the calculated lithium concentrations used in the prediction methods to simulate assay and timing errors. The mean (+/- SD) values generated for k, ka, and V were 0.035 +/- 0.008 (h-1), 0.897 +/- 0.059 (h-1), and 40.97 +/- 5.27 (L), respectively. Prediction errors were smallest with the OPM (SD5%, SD10%) and ROPM-24 (SD5%). There was a significant correlation between k and the prediction error for the OPM (SD5%, SD10%) and the ROPM-24 (SD5%). The OPM was the most accurate of the methods studied; however, it tended to underpredict actual concentrations in subjects with long half-lives.

Computer Simulation↗