基于极大似然准则的生物序列模体的贝叶斯假设检验

针对生物信息学中序列模体的显著性检验问题,提出了一种基于极大似然准则的贝叶斯假设检验方法.将模体的显著性检验转化为多项分布的拟合优度检验问题,选取Dirichlet分布作为多项分布的先验分布并采用Newton-Raphson算法估计Dirichlet分布的超参数,使得数据的预测分布达到最大.应用贝叶斯定理得到贝叶斯因子进行模型选择,用于评价模体检验的统计显著性,这种方法克服了传统多项分布检验中构造检验统计量并计算其在零假设下确切分布的困难.选择JASPAR数据库中107个转录因子结合位点和100组随机模拟数据进行实验,采用皮尔逊积矩相关系数作为评价检验质量的一个标准,发现实验结果好于传统的模体检验的一些方法.     

Theory of ligand binding to heterogeneous receptor populations: Characterization of the free-energy distribution function

We present a method for characterizing the free-energy and affinity distributions of a heterogeneous population of molecules interacting with a homogeneous population of ligands, by driving expressions for the moments as functions of experimental binding curve characteristics, and then constructing the distribution as an expansion over a Gaussian basis set. Although the method provides the complete distribution in principle, in practice it is restricted by experimental noise, inaccuracies in data fitting, and the severity with which the distribution deviates from a Gaussian. Limitations imposed by experimental inaccuracies and the requirement of an appropriate analytic function for data fitting were evaluated by Monte Carlo simulations of binding experiments with various degrees of error in the data. Thus a distribution was assumed, binding curves with random errors were generated, and the technique was applied in order to determine the extent to which the characteristics of the assumed distribution could be recovered. Typical inaccuracies in the first two moments fell within experimental error, whereas inaccuracies in the third and fourth were generally larger than standard deviations in the data. The accuracy of these higher-order moments was invarient for experimental errors ranging from 2 to 10% and may thus be limited, within this range, primarily by the curve fitting procedure. The other aspect of the problem, accurate inference of the distribution, is limited in part by inaccuracies in the moments but more importantly by the extent to which the distribution deviates from a Gaussian. The extensive statistical literature on the problem of inference enables the delineation of specific criteria for estimating the efficiency of construction, as well as for deciding whether certain features of the inferred distribution, such as bimodality, are artifacts of the procedure. In spite of the limitations of the method, the results indicate that the mean and standard deviation are obtainable with greater accuracy than by a Sipsian analysis. This difference is particularly important when the distribution is narrow and width detection is beyond the sensitivity of the Sips plot. The method should be more accurate than the latter as an assay for homogeneity as well as for characterizing the moments, though equally easy to apply.     

Protein denaturant binding polynomials

We show how moments of the denaturant binding distribution function can be extracted from experimental data on the denaturation of a protein as a function of the concentration of denaturant and how in turn these moments can be used to construct the denaturant binding distribution function. This approach is similar to our recent work on using the maximum-entropy method to construct ligand-binding distributions from moments obtained from titration curves for nucleic acids and proteins. As an example we take literature data on the denaturation of ferro- and ferricytochrome c by guanidine hydrochloride and from it construct the denaturant binding polynomial and binding distribution function for the unfolded protein.     

A strategy for efficient characterization of macromolecular heteroassociations via measurement of sedimentation equilibrium.

A method is proposed for the selection of experimental conditions for sedimentation equilibrium experiments that will provide maximal information about the values of equilibrium association constants within a given scheme for heteroassociation of two solute components. A discriminator function is proposed that indicates the sensitivity of the experimentally observed gradient or gradients to alterations in the underlying association constants. The value of this function is plotted or tabulated as a function of the concentrations of the two components, over a broad range of solution compositions. It is suggested that experiments performed with loading compositions corresponding to large absolute values of the discriminator function will yield the most information with respect to determination of the underlying association constants. This method was tested by predicting optimal conditions for three different types of sedimentation equilibrium experiments: (i) measurement of total (natural) solute absorbance; (ii) measurement of individual component gradients via measurement of tracer absorbance; and (iii) global analysis of multiple experiments. Experimental data resulting from sedimentation equilibrium experiments carried out under the specified conditions were simulated by addition of realistic levels of random error to calculated equilibrium gradients. The simulated data were then analyzed exactly as real experimental data, i.e., without prior knowledge of the underlying association constants. It was found that the highest accuracy and precision in determination of heteroassociation constants are obtained by global analysis of multiple experiments performed using significantly different loading compositions, each of which is selected from 'sensitive' regions of the discriminator map.     

Ligand binding distributions in nucleic acids

We illustrate a new method for the determination of the complete binding polynomial for nucleic acids based on experimental titration data with respect to ligand concentration. From the binding polynomial, one can then calculate the distribution function for the number of ligands bound at any ligand concentration. The method is based on the use of a finite set of moments of the binding distribution function, which are obtained from the titration curve. Using the maximum-entropy method, the moments are then used to construct good approximations to the binding distribution function. Given the distribution functions at different ligand concentrations, one can calculate all of the coefficients in the binding polynomial no matter how many binding sites a molecule has. Knowledge of the complete binding polynomial in turn yields the thermodynamics of binding. This method gives all of the information that can be obtained from binding isotherms without the assumption of any specific molecular model for the nature of the binding. Examples are given for the binding of Mn(2+) and Mg(2+) to t-RNA and for the binding of Mg(2+) and I(6) to poly-C using literature data.     

A fast global fitting algorithm for fluorescence lifetime imaging microscopy based on image segmentation

Global fitting algorithms have been shown to improve effectively the accuracy and precision of the analysis of fluorescence lifetime imaging microscopy data. Global analysis performs better than unconstrained data fitting when prior information exists, such as the spatial invariance of the lifetimes of individual fluorescent species. The highly coupled nature of global analysis often results in a significantly slower convergence of the data fitting algorithm as compared with unconstrained analysis. Convergence speed can be greatly accelerated by providing appropriate initial guesses. Realizing that the image morphology often correlates with fluorophore distribution, a global fitting algorithm has been developed to assign initial guesses throughout an image based on a segmentation analysis. This algorithm was tested on both simulated data sets and time-domain lifetime measurements. We have successfully measured fluorophore distribution in fibroblasts stained with Hoechst and calcein. This method further allows second harmonic generation from collagen and elastin autofluorescence to be differentiated in fluorescence lifetime imaging microscopy images of ex vivo human skin. On our experimental measurement, this algorithm increased convergence speed by over two orders of magnitude and achieved significantly better fits.     

Modeling error and stability of endothelial cytoskeletal membrane parameters based on modeling transendothelial impedance as resistor and capacitor in series

Transendothelial impedance across an endothelial monolayer grown on a microelectrode has previously been modeled as a repeating pattern of disks in which the electrical circuit consists of a resistor and capacitor in series. Although this numerical model breaks down barrier function into measurements of cell-cell adhesion, cell-matrix adhesion, and membrane capacitance, such solution parameters can be inaccurate without understanding model stability and error. In this study, we have evaluated modeling stability and error by using a ² evaluation and Levenberg-Marquardt nonlinear least-squares (LM-NLS) method of the real and/or imaginary data in which the experimental measurement is compared with the calculated measurement derived by the model. Modeling stability and error were dependent on current frequency and the type of experimental data modeled. Solution parameters of cell-matrix adhesion were most susceptible to modeling instability. Furthermore, the LM-NLS method displayed frequency-dependent instability of the solution parameters, regardless of whether the real or imaginary data were analyzed. However, the LM-NLS method identified stable and reproducible solution parameters between all types of experimental data when a defined frequency spectrum of the entire data set was selected on the basis of a criterion of minimizing error. The frequency bandwidth that produced stable solution parameters varied greatly among different data types. Thus a numerical model based on characterizing transendothelial impedance as a resistor and capacitor in series and as a repeating pattern of disks is not sufficient to characterize the entire frequency spectrum of experimental transendothelial impedance. cell-cell adhesion; cell-matrix adhesion; cell membrane capacitance; mathematical computation     

Combined affinity and rate constant distributions of ligand populations from experimental surface binding kinetics and equilibria

The present article considers the influence of heterogeneity in a mobile analyte or in an immobilized ligand population on the surface binding kinetics and equilibrium isotherms. We describe strategies for solving the inverse problem of calculating two-dimensional distributions of rate and affinity constants from experimental data on surface binding kinetics, such as obtained from optical biosensors. Although the characterization of a heterogeneous population of analytes binding to uniform surface sites may be possible under suitable experimental conditions, computational difficulties currently limit this approach. In contrast, the case of uniform analytes binding to heterogeneous populations of surface sites is computationally feasible, and can be combined with Tikhonov-Phillips and maximum entropy regularization techniques that provide the simplest distribution that is consistent with the data. The properties of this ligand distribution analysis are explored with several experimental and simulated data sets. The resulting two-dimensional rate and affinity constant distributions can describe well experimental kinetic traces measured with optical biosensors. The use of kinetic surface binding data can give significantly higher resolution than affinity distributions from the binding isotherms alone. The shape and the level of detail of the calculated distributions depend on the experimental conditions, such as contact times and the concentration range of the analyte. Despite the flexibility introduced by considering surface site distributions, the impostor application of this model to surface binding data from transport limited binding processes or from analyte distributions can be identified by large residuals, if a sufficient range of analyte concentrations and contact times are used. The distribution analysis can provide a rational interpretation of complex experimental surface binding kinetics, and provides an analytical tool for probing the homogeneity of the populations of immobilized protein.     

Determination of domain structure of proteins from X-ray solution scattering

An ab initio method for building structural models of proteins from x-ray solution scattering data is presented. Simulated annealing is employed to find a chain-compatible spatial distribution of dummy residues which fits the experimental scattering pattern up to a resolution of 0.5 nm. The efficiency of the method is illustrated by the ab initio reconstruction of models of several proteins, with known and unknown crystal structure, from experimental scattering data. The new method substantially improves the resolution and reliability of models derived from scattering data and makes solution scattering a useful technique in large-scale structural characterization of proteins.     

Bayesian statistical analysis of protein side-chain rotamer preferences.

We present a Bayesian statistical analysis of the conformations of side chains in proteins from the Protein Data Bank. This is an extension of the backbone-dependent rotamer library, and includes rotamer populations and average chi angles for a full range of phi, psi values. The Bayesian analysis used here provides a rigorous statistical method for taking account of varying amounts of data. Bayesian statistics requires the assumption of a prior distribution for parameters over their range of possible values. This prior distribution can be derived from previous data or from pooling some of the present data. The prior distribution is combined with the data to form the posterior distribution, which is a compromise between the prior distribution and the data. For the chi 2, chi 3, and chi 4 rotamer prior distributions, we assume that the probability of each rotamer type is dependent only on the previous chi rotamer in the chain. For the backbone-dependence of the chi 1 rotamers, we derive prior distributions from the product of the phi-dependent and psi-dependent probabilities. Molecular mechanics calculations with the CHARMM22 potential show a strong similarity with the experimental distributions, indicating that proteins attain their lowest energy rotamers with respect to local backbone-side-chain interactions. The new library is suitable for use in homology modeling, protein folding simulations, and the refinement of X-ray and NMR structures.     

Conformational ensemble of a multidomain protein explored by Gd3+ electron paramagnetic resonance

Despite their importance in function, the conformational state of proteins and its changes are often poorly understood, mainly because of the lack of an efficient tool. MurD, a 47-kDa protein enzyme responsible for peptidoglycan biosynthesis, is one of those proteins whose conformational states and changes during their catalytic cycle are not well understood. Although it has been considered that MurD takes a single conformational state in solution as shown by a crystal structure, the solution nuclear magnetic resonance (NMR) study suggested the existence of multiple conformational state of apo MurD in solution. However, the conformational distribution has not been evaluated. In this work, we investigate the conformational states of MurD by the use of electron paramagnetic resonance (EPR), especially intergadolinium distance measurement using double electron-electron resonance (DEER) measurement. The gadolinium ions are fixed on specific positions on MurD via a rigid double-arm paramagnetic lanthanide tag that has been originally developed for paramagnetic NMR. The combined use of NMR and EPR enables accurate interpretation of the DEER distance information to the structural information of MurD. The DEER distance measurement for apo MurD shows a broad distance distribution, whereas the presence of the inhibitor narrows the distance distribution. The results suggest that MurD exists in a wide variety of conformational states in the absence of ligands, whereas binding of the inhibitor eliminates variation in conformational states. The multiple conformational states of MurD were previously implied by NMR experiments, but our DEER data provided structural characterization of the conformational variety of MurD.     

Gene regulatory network reconstruction by Bayesian integration of prior knowledge and/or different experimental conditions

There have been various attempts to improve the reconstruction of gene regulatory networks from microarray data by the systematic integration of biological prior knowledge. Our approach is based on pioneering work by Imoto et al. where the prior knowledge is expressed in terms of energy functions, from which a prior distribution over network structures is obtained in the form of a Gibbs distribution. The hyperparameters of this distribution represent the weights associated with the prior knowledge relative to the data. We have derived and tested a Markov chain Monte Carlo (MCMC) scheme for sampling networks and hyperparameters simultaneously from the posterior distribution, thereby automatically learning how to trade off information from the prior knowledge and the data. We have extended this approach to a Bayesian coupling scheme for learning gene regulatory networks from a combination of related data sets, which were obtained under different experimental conditions and are therefore potentially associated with different active subpathways. The proposed coupling scheme is a compromise between (1) learning networks from the different subsets separately, whereby no information between the different experiments is shared; and (2) learning networks from a monolithic fusion of the individual data sets, which does not provide any mechanism for uncovering differences between the network structures associated with the different experimental conditions. We have assessed the viability of all proposed methods on data related to the Raf signaling pathway, generated both synthetically and in cytometry experiments.     

Variability of estimated binding parameters

The standard deviation is often used as a measure of the accuracy or reliability of estimated binding parameters and this implies that the parameter values are normally distributed. This may not be the case and we show that the unknown distribution of acceptable parameter values associated with a specific model and a particular set of experimental data can be calculated easily. This can be done for any binding model, linear or non-linear, and the method is very robust and accurate. The effect of the magnitude of the experimental error and the distribution of data points on the variability of the parameters is readily investigated. This makes the method useful for the practical design of experiments in terms of the number and range of concentrations (or doses) which need to be studied in order to obtain the desired accuracy.     

The effect of pore-size distribution on the binding of proteins to porous resin beads

The effect of the distribution of pore radii in the resin beads on protein binding was taken into account to analyze the elution profiles of proteins from the polymer-packed column obtained by repetitive injection method. By assuming that the distribution of pore radii in the resin beads is logarithmic Gaussian, the theoretical curves obtained agreed well with the experimental data.     

Possibility of revealing the role of nonresonant energy exchange between electrons and CO molecules at high vibrational levels

An experimental method providing information about the interaction of electrons with excited CO molecules at high vibrational levels is proposed and justified theoretically. The suggested experimental scheme is based on the use of two successive discharge pulses under the conditions prevailing in an electroionization CO laser. The first pulse should ensure a sufficiently high energy input in order for a nonequilibrium vibrational distribution function to form. The second pulse serves to study the effect of the electric current on the vibrational distribution function of excited molecules at high vibrational levels. The theoretical analysis is based on the simultaneous solution of the Boltzmann equation for the electron energy distribution function and the vibrational kinetic equations realistically describing the multiquantum vibrational-vibrational exchange processes. The calculated results show that the sensitivity of the proposed measurement technique promises to be high.     

Distribution functions, describing the binding of extended ligands with DNA molecules. Possible use for cases of DNA condensation

Due to noncooperative binding of ligands to DNA molecules, DNA molecules are in equilibrium with different numbers of adsorbed ligands. This equilibrium for a given concentration of the free ligand in the solution is characterized by the distribution function, which describes the probability of revealing the DNA molecule with a definite number of adsorbed ligands. If polycations act as ligands, DNA molecules with the number of ligands sufficient for neutralizing the charges on phosphates may undergo a phase transition. One example of this transition is the formation of liquid-crystalline dispersions during the binding of DNA to chitosan. We analyzed the binding of chitosan to DNA on the assumption that this binding is due to equilibrium adsorption. At a definite concentration of chitosan in solution, DNA molecules are in equilibrium with different numbers of adsorbed molecules of chitosan. If the number of adsorbed ligands exceeds some critical value, the DNA molecule covered with chitosan becomes capable of interacting with other DNA molecules. As a result of this interaction (attraction), liquid-crystalline dispersions can form. Equations describing the dependence of the concentration of DNA molecules on the concentration of the ligand in solution were derived. It was shown that, at given parameters of the model, it is possible to describe experimental data characterizing the formation of cholesteric liquid-crystalline dispersions. The analysis of the data makes it possible to reconstitute both the size of the binding site occupied by chitosan on the DNA and the energy of interaction of chitosan with DNA.     

A parameter estimation technique for stochastic self-assembly systems and its application to human papillomavirus self-assembly

Virus capsid assembly has been a key model system for studies of complex self-assembly but it does pose some significant challenges for modeling studies. One important limitation is the difficulty of determining accurate rate parameters. The large size and rapid assembly of typical viruses make it infeasible to directly measure coat protein binding rates or deduce them from the relatively indirect experimental measures available. In this work, we develop a computational strategy to deduce coat-coat binding rate parameters for viral capsid assembly systems by fitting stochastic simulation trajectories to experimental measures of assembly progress. Our method combines quadratic response surface and quasi-gradient descent approximations to deal with the high computational cost of simulations, stochastic noise in simulation trajectories and limitations of the available experimental data. The approach is demonstrated on a light scattering trajectory for a human papillomavirus (HPV) in vitro assembly system, showing that the method can provide rate parameters that produce accurate curve fits and are in good concordance with prior analysis of the data. These fits provide an insight into potential assembly mechanisms of the in vitro system and give a basis for exploring how these mechanisms might vary between in vitro and in vivo assembly conditions.     

Transport effects on the kinetics of protein-surface binding.

A detailed model is presented for protein binding to active surfaces, with application to the binding of avidin molecules to a biotin-functionalized fiber optic sensor in experiments reported by S. Zhao and W. M. Reichert (American Chemical Society Symposium Series 493, 1992). Kinetic data for binding in solution are used to assign an intrinsic catalytic rate coefficient k to the biotin-avidin pair, deconvoluted from transport and electrostatic factors via application of coagulation theory. This intrinsic chemical constant is built into a reaction-diffusion analysis of surface binding where activity is restricted to localized sites (representing immobilized biotin molecules). The analysis leads to an effective catalytic rate coefficient keff characterizing the active surface. Thereafter, solution of the transport problem describing absorption of avidin molecules by the macroscopic sensor surface leads to predictions of the avidin flux, which are found to be in good agreement with the experimental data. The analysis suggests the following conclusions. 1) Translational diffusion limitations are negligible for avidin-biotin binding in solution owing to the small (kinetically limiting) value k = 0.00045 m/s. 2) The sparse distribution of biotin molecules and the presence of a repulsive hydration force produce an effective surface-average catalytic rate coefficient keff of order 10(-7) m/s, much smaller than k. 3) Avidin binding to the fiber optic sensor occurs in an intermediate regime where the rate is influenced by both kinetics and diffusion.