One of the most important applications of microarray data is the class prediction of biological samples. For this purpose, statistical tests have often been applied to identify the differentially expressed genes (DEGs), followed by the employment of the state-of-the-art learning machines including the Support Vector Machines (SVM) in particular. The SVM is a typical sample-based classifier whose performance comes down to how discriminant samples are. However, DEGs identified by statistical tests are not guaranteed to result in a training dataset composed of discriminant samples. To tackle this problem, a novel gene ranking method namely the Kernel Matrix Gene Selection (KMGS) is proposed. The rationale of the method, which roots in the fundamental ideas of the SVM algorithm, is described. The notion of ''the separability of a sample'' which is estimated by performing  Microarray data has been applied to the class prediction of different samples, from which the disease diagnosis and prognosis can benefit. A microarray dataset usually contains thousand of genes and a relatively much smaller number of samples  Empirically, wrappers and embedded methods have been observed to be more accurate than filters Meanwhile, although the choice of the classifier also presents a wide diversity, SVMs have been widely recognized for its generalization abilities In summary, a widely-accepted scheme for the analysis of microarray data has been ''identification of DEGs by statistical tests followed by sample classification using SVMs''. The justification is that the prediction accuracy of various classifiers including SVMs, depends on how discriminant the features are. However, SVMs belong to the family of sample-based classifiers whose generalization performance comes down to, more precisely, how discriminant the samples are. DEGs identified by statistical tests cannot guaranteed to establish a set of discriminant samples for SVMs. Consequently, it cannot be promised the highest degree of accuracy for sample classification. This problem necessitates the development of gene selection algorithms that are more consistent with the fundamental ideas of SVMs. It is naturally desired that, the proposed methods can bypass the computationally-expensive training procedure of SVMs, which is required by the SVM-RFE algorithm Given a binary classification problem with the training data set of: As depicted in The condition of optimality requires that the vector Each constant For nonlinear problems where the training data are not separable in the input space, a function, denoted as On a test sample According to the sign of the As mentioned previously, each training sample is eventually assigned a Lagrangian multiplier Using 1. Depending on its class label Consider a sample We use the inner product to measure the similarity level between vectors. Denoting the number of the positive training samples as Likewise, denoting the number of the negative training samples as As a result, we can express, mathematically, the expectation that a positive sample bears more resemblance to class ''+'' than to class ''And a negative training sample 2. The class resemblance of a boundary sample to its supposed class is not as striking as those samples with 3. (a) exactly on the hyperplane of (b) in the region between the hyperplanes of (c) in the region between the hyperplanes of A training sample from group (a), is a boundary sample but its class label can be correctly restored by the SVM solution. As with positive samples whose For a training sample from group (b), the SVM classifier would not have been able to correctly restore its class label if it weren't for the introduction of the slack variables. Our interpretation is that, the class resemblance of this sample to its supposed class is so ambiguous that the SVM has difficulties in acknowledging its actual class membership.For a training sample from group (c), the SVM classifier is simply unable to correctly restore its class label. It is very likely that the class resemblance of this sample to its supposed class in fact contradicts its given class label.In mathematical terms, we reckon that a positive training sample of either group (b) or group (c) satisfies: The hidden information for In summary, the resultant value of Luckily, our analysis above implies that that the function of In the SVM algorithm, the vector of We justify the introduction of standard deviations in the denominator by considering two positive training samples in the feature space. The first sample is assumed to have come from a region of denser population than the second one. We reckon that, compared with the second sample, the first sample is more typical a representative of class ''+'' and is believed to be more similar to class ''+''. The positive sample from a denser population is expected to exhibit a lower deviation of the elements The values of Meanwhile, the similarity between each sample and itself is supposed to be Since the separability of each sample has an impact on the the class separability of a problem, we propose to use the sum of each sample's separability score as an estimate of the separability of the problem.A word about the formulation of In the case of linear kernels, take a positive sample In the case of Gaussian RBF kernels, in order to have Since each gene subset introduces a classification problem represented by the set of training samples, the gene subset thus corresponds to an estimate of the separability of the problem. Consequently, DEGs can be identified as those resulting in ''easier problems'' of high separability. This is the essential idea of our kernel matrix induced gene selection methods, which has been illustrated in Given a microarray dataset of Hence the function The An alternative to the KMGS which proceeds in a greedy manner is also developed, which is namely the Kernel Matrix Sequential Forward Selection (KMSFS) algorithm. The algorithm starts with an empty set of selected DEGs. At each iteration, the algorithm identifies a single DEG which is then appended to the set. We now describe how the KMSFS algorithm proceeds between two consecutive iterations.Given a microarray dataset of Each gene from the remaining The pseudo codes for the KMGS and KMSFS algorithms are given respectively in The proposed methods have noticeable merits:Filter methods identify discriminant features, making them suitable for feature-based classifiers whose normal vector is the linear combination of features. However, A majority of wrapper and embedded methods are based on the assumption that most microarray datasets pose linear problems. However, we reckon that, the problem presented by a set of DEGs can hardly be a linear one when the the set size is as small as only one or two.But the generalization to nonlinear cases have been challenging for various wrappers and embedded methods. For example, the SVM-RFE Advantageously, our algorithms can be directly applied to nonlinear cases by opting for Gaussian RBF kernels. The Gaussian RBF 3. The output of The dataset contains, in total, 136 samples of two types which respectively have 77 and 59 cases. Each sample includes expression values of 12600 genes.The dataset contains the expression values of 2000 genes from 62 tissues, of which 22 are normal and 40 are cancerous.The dataset was collected from 72 patients. 47 of them were diagnosed with acute acute lymphoblastic leukemia (ALL) and 25 with acute myeloid leukemia (AML). Expression values of 7129 genes were measured.Both the prostate dataset and the colon dataset were normalized using the following procedure. A microarray dataset with For the leukemia dataset, we applied the pre-processing procedure proposed by Dudoit et al. Various gene selection algorithms are evaluated and compared by the error rate of SVMs. The simplest technique for error estimation is the holdout method which splits the dataset into a training set and a test set. The gene selection algorithm is performed on the training set and sample classification on the test set. However, the holdout method has been highly discouraged for microarray datasets which usually contain a small number of samples. In contrast to researchers who applied gene selection to the entire training set and employed The B.632+ estimator involves resampling, with replacement, of the original dataset. From a dataset of The flow chart for evaluating a gene selection algorithm using the B.632+ technique has been given by For the methods of KMSFS and KMGS, both the linear kernel and the Gaussian RBF kernel were tested. This resulted in altogether four algorithms which are referred to as Gaussian KMSFS, Gaussian KMGS, linear KMSFS and linear KMGS. They were compared with two wrapper methods: the leave-one-out calculation sequential forward selection (LOOSFS) which improved the least-squares bound measure The Leave-One-Out Cross-Validation(LOOCV) error has been generally used for measuring the generalization abilities of SVMs and Least-Squares SVMs (LS-SVMs). The LOOSFS method thus identifies as DEGs those genes which result in a LS-SVM classifier with the minimal Leave-One-Out Cross-Validation(LOOCV) error rate. The beauty of the algorithm consists in the efficient and exact computation of the LOOCV error. To address the ''ties problem'' in which multiple gene subsets achieve the same LOOCV error rate, a further selection criterion is imposed which favors the gene subset with minimal empirical risk.The starting point of the GLGS method is also the employment of the exact formulation of the LOOCV error for LS-SVMs. The method then utilizes the gradient descent algorithm to seek a diagonal matrix which eventually minimizes the LOOCV error. Genes are ranked according to the absolute values of the diagonal elements of the diagonal matrix.With Cho's method and Yang's methods, genes are individually ranked. We use the following notations for their descriptions. Each micorarray dataset with The score, denoted as The between-class variation with respect to gene In order to estimate within-class variations in terms of gene Two metrics for measuring within-class variations, denoted as compactEventually, two score functions which decide the ranking of gene We refer to these two score functions respectively as Yang's method 1 and Yang's method 2.Cho's method and Yang's two methods identify as DEGs those genes whose associated We employed grid search and Friedman rank sum tests combined with Holm correction to tune the parameters for different algorithms.Among the total 10 gene selection algorithm, both Gaussian KMSFS and Gaussian KMGS require the parameter The Friedman rank sum test is a non-parametric alternative to ANOVA with repeated measures. The test statistic for the Friedman test is a Chi-square with We take the algorithm of Gaussian KMSFS as an example to explain how to apply Friedman test for the discovery of optimal values on Friedman rank sum test was used to detect statistical differences among these 77 groups. The test was based on 100 sets of ranks, with each set corresponding to an individual classification problem. The performances of different parameter settings analyzed are ranked separately for each problem. If we rejected the null-hypothesis stating that all the 77 settings led to equal performance in mean ranking, we employed the Holm post-hoc analysis to identify which setting was significantly better than the rest.All the gene selection methods were coded in Matlab. The linear SVM was implemented using LIBSVM Using Friedman tests with Holm correction, optimal settings on GLGS and linear KMSFS shared the optimal setting of With a minimal error rate of As shown by The error rate of linear KMSFS remained noticeably lower than the filter methods when the number of DEGs fell between 10 and 60. When the number of DEGs grew larger, Gaussian KMGS showed better than performance than the four filter methods.The performance of Gaussian KMGS and linear KMSFS remained competitive to those of the filter methods, respectively between the value ranges of These comparisons lead to the conclusion that linear KMSFS and Gaussian KMGS are the two best methods for the prostate dataset.For Gaussian KMGS, Gaussian KMSFS and LOOSFS, the optimal settings on For the other 3 wrapper methods which are respectively linear KMGS, linear KMSFS, GLGS and the 4 filter methods which are respectively Fisher's ratio, Cho's method and the two methods of Yang's, their optimal parameter settings were found to be With a minimal error rate of It is interesting to note that Gaussian KMGS, with only 10 DEGs, reached the lowest B.632+ error rate which was approximately 0.10. Also the lowest B.632+ error rate of LOOSFS, which was 0.11 was lower than that reported in Gaussian KMSFS remained better than the 4 filter methods whose performances were comparable between each other. Meanwhile, the error rates of Gaussian KMGS were also lower than those of the filter methods, particularly for a smaller number of selected DEGs.In conclusion, Gaussian KMSFS and Gaussian KMGS have proved to be the best methods for the colon dataset.For Gaussian KMGS, Gaussian KMSFS and LOOSFS, the optimal setting on the parameter pair of For GLGS, the optimal setting was found to be However, Gaussian KMGS, linear KMGS and linear KMSFS failed to perform as well as LOOSFS. We reckon it might be attributable to the preprocessing procedure which resulted in the removal of over 86% of the original 7029 genes, although this viewpoint has to be confirmed with more experiments.We regarded the LOOSFS and the Gaussian KMSFS as the two best gene selection algorithms for the leukemia dataset.Due to the employment of B.632+ error estimation technique, each gene selection algorithm was applied to the 200 sets of bootstrap samples as well as the original training set. For each of these 201 sample sets, we selected a sequence of 100 DEGs. This resulted in altogether 201 sets each of which contained 100 DEGs.We calculated the frequency with which each of the 2000 genes was selected into the 201 sets of DEGs and drew the heatmaps of 50 DEGs that were selected most frequently. For the algorithms of Gaussian KMGS, Gaussian KMSFS and LOOSFS, the outcome of gene selection procedures is influenced by the value setting on the parameter Heatmaps for the ten gene selection methods, were shown by It can be seen from The second best gene selection algorithm for the colon data is Gaussian KMGS whose selected DEGs have been presented by The above facts suggest that, although filter methods selected genes whose values, in general, differ significantly between opposing classes, our kernel induced algorithms seemed not to hold it as the selection criterion. Instead, our methods endeavored to select genes that could establish a set of ''discriminant samples'' for SVMs. This possibly accounts for their superiority in terms of B.632+ error rates on the colon dataset.For linear KMGS and linear KMSFS, their B.632+ error rates are affected by value settings on Using the prostate dataset and the colon dataset, we employed the Friedman rank sum test with Holm correction to study the sensitivity of sample classification to value settings on We kept We first analyzed the sensitivity of sample selection for Gaussian KMGS. At the row with Since the optimal value setting for For the other rows for which We can conclude that B.632+ error rates are insensitive to choices of At the first row for Gaussian KMSFS, we can see that For the remaining three rows whose Thus, for Gaussian KMSFS, B.632+ error rates are sensitive to choice of Similar analysis can be performed for the colon dataset, whose scores for various Regarding Gaussian KMGS, we can see that B.632+ error rates are insensitive to choices of In terms of Gaussian KMSFS, we can see that sample classification is sensitive to We then kept For Gaussian KMGS, we can see that B.632+ error rates are sensitive to choices of For Gaussian KMSFS, when In term of both linear KMGS and linear KMSFS, B.632+ error rates remain sensitive to Statistical tests select genes whose expression values differ significantly between the two opposing classes, i.e., the discriminant genes. Samples-based learning machines including SVMs favor genes which results in a set of discriminant samples. The discriminant genes can not be guaranteed to result in a set of discriminant samples. We have shown that the genes leading to discriminant training samples can be detected by applying statistical tests to the kernel matrix.In addition to the competitive performance demonstrated on the three public microarray datasets, the proposed kernel matrix induced gene selection algorithms offer extra advantages:Generality. Our methods are considered applicable to any kernel classifiers, not just SVMs.Flexibility. For the implementation of our methods, users can opt for any mercer kernel which can be linear, Gaussian RBF, sigmoid, or polynomials. However, depending on the specific kernel, properly-designed preprocessing steps may be required. For examples, Gaussian RBF kernels require the tuning of the width parameter. For linear kernels, strategies are required to ensure the diagonal elements of the kernel matrix, each of which suggests the similarity between a sample and itself, to be uniformly one.It is also worth attention that microarray datasets have usually been assumed to present linear problems. However, it is unlikely to be true in the case that the number of DEGs is as few as one. Interestingly, linear problems can be solved by SVMs with nonlinear kernels, while nonlinear problems are hardly solvable with SVMs using linear kernels. A potential solution to the nonlinear problem posed by a small number of DEGs could be the application of nonlinear SVM classifiers. But our method suggested a successful alternative which is the use of the nonlinear Gaussian RBF kernel for the identification of DEGs. We reckon that this effort of instilling ''nonlinearity'' into the identification of DEGs has contributed to the better empirical performance of our methods.Additional File S1The three microarray datasets  in MATLAB format which were used in this work.(ZIP)Click here for additional data file.


We present the theoretical foundations of a general principle to infer structure ensembles of flexible biomolecules from spatially and temporally averaged data obtained in biophysical experiments. The central idea is to compute the Kullback-Leibler optimal modification of a given prior distribution  Consequently, the conformational heterogeneity present in the posterior distribution reflects the quality and completeness of the experimental data and the prior distributions, but not necessarily any physical fluctuations Typically, structure determination from experimental data proceeds through hybrid energy minimization Early attempts to model ensemble NMR data involved averaging along molecular dynamics trajectories ensembles: the data is explained by a weighed average of During the past two decades there has been an increasing interest in biomolecules that undergo significant conformational fluctuations, such as natively unfolded and partially unfolded proteins Restraining simulations using an average of multiple replicas is a sensible solution, as it was recently shown that multiple replica restrained simulations constitute the least biased method when the number of replicas goes to infinity in the absence of experimental noise In this work, we approach the problem of modeling sparse, spatially and temporally averaged data through the principles of Bayesian statistics and information theory. Unlike the previous Bayesian efforts We outline a number of general, theoretical advances concerning biomolecular structure determination and restrained molecular simulations. To ensure a focused and concise presentation we limited the number of practical examples. However, one example given uses synthetic data of a small idealized peptide GB1 generated using the PROFASI forcefield at high temperature ensemble average of the simulated experimental data Ultimately, our aim is to sample from the conditional probability distribution We clarify the relation between We start by considering the coarse-grained representations of the distribution, Applying the product rule of probability theory to reference ratio methodinduced in the coarse-grained space by the fine-grained prior, The reference ratio method yields the Kullback-Leibler optimal modification of the fine-grained model The model given by if we choose the Dirac delta function link-function, We also observe that In minus To test the presented theory, we use synthetic NOE data, obtained from an ensemble of the GB1 hair-pin simulated at The restraints used here are visualized on a random conformation of the GB1 hairpin in We use the log-normal distribution as an appropriate error-model for pairwise distances derived from NOEs, which is the approach adopted by ISD In the ideal case, an optimal choice for We use The prior distribution used in this study concerns protein structure on a local length scale, and thus does not model long range distances accurately. Consequently, as a reaction coordinate, we chose a representative distance The conformational prior and PROFASI, which was used to generate the averaged data, result in different distance distributions . HoweverA similar pattern is observed for the distribution of the gyration radii In some cases, compensating for the bias introduced by the reference distribution is not critical to obtain good results. As it constitutes an additional obstacle in terms of estimation and simulation time, we evaluate its significance on the obtained results. In the power averaged case we achieved this by chosing the reference distribution If we again consider the gyration radii as providing complementary views of the ensembles, we find that the power-averaged ensemble with uniform To summarize, in the power averaged case, both In conclusion, we present the theoretical foundations of a Bayesian principle to infer ensembles of protein structures from noisy experimental data subject to ensemble and time averaging. We demonstrate the principle constitutes a generalization of ISD and previously proposed maximum entropy restraining approaches. Finally, the principle is successfully evaluated using synthetic experimental data of a small idealized system.Our approach combines a coarse-grained Bayesian model of the data with a fine-grained model of protein conformational space. The combination is accomplished using the reference ratio method X-ray- or neutron scattering, or other NMR experiments. Also, low-resolution data may be combined with more sophisticated physical prior distributions such as those embodied in force fields. The presented method is thus a general method to obtain physically sound ensemble models of solution and endogenous states of biomolecules, given appropriate experimental data. Practical implementation of protocols for other data sources and larger systems clearly is necessary. Possible issues arising with this methodology include insufficient sampling of the conformational space and difficult estimation procedures for reference distributions and scale parameters alike. However, the work presented herein provides the guiding principles for these future developments.The Bayesian model may in principle be applied to denser and/or ambiguous http://www.phaistos.org). We used a Monte Carlo move set previously described A synthetic dataset was created for the GB1 hairpin . The data were generated by simulating the protein at 400K with the PROFASI forcefield To mimic the effect of distance averaging in a dipolar interaction undergoing fast motion compared to the cross-relaxation but slow motion when compared to molecular tumbling, we calculated a power averaged variant of the dataset as This section describes the estimation of the reference distribution In the case of the power-averaged data, the reference distribution The mean We obtain a point estimate of To sample where


This paper examines the multiple atlas random diffeomorphic orbit model in Computational Anatomy (CA) for parameter estimation and segmentation of subcortical and ventricular neuroanatomy in magnetic resonance imagery. We assume that there exist multiple magnetic resonance image (MRI) atlases, each atlas containing a collection of locally-defined charts in the brain generated via manual delineation of the structures of interest. We focus on maximum a posteriori estimation of high dimensional segmentations of MR within the class of generative models representing the observed MRI as a conditionally Gaussian random field, conditioned on the atlas charts and the diffeomorphic change of coordinates of each chart that generates it. The charts and their diffeomorphic correspondences are unknown and viewed as latent or hidden variables. We demonstrate that the expectation-maximization (EM) algorithm arises naturally, yielding the likelihood-fusion equation which the a posteriori estimator of the segmentation labels maximizes. The likelihoods being fused are modeled as conditionally Gaussian random fields with mean fields a function of each atlas chart under its diffeomorphic change of coordinates onto the target. The conditional-mean in the EM algorithm specifies the convex weights with which the chart-specific likelihoods are fused. The multiple atlases with the associated convex weights imply that the posterior distribution is a multi-modal representation of the measured MRI. Segmentation results for subcortical and ventricular structures of subjects, within populations of demented subjects, are demonstrated, including the use of multiple atlases across multiple diseased groups. The advent of high-resolution T1-weighted magnetic resonance (MR) neuroimaging technologies facilitates a detailed exploration into human brain anatomy. Many quantitative studies have demonstrated that morphometric and functional responses of cortical and subcortical brain structures are highly correlated to numerous neuropsychiatric illnesses. There now exists a large research community supported by universally deployed software packages In these deformable template approaches, the solutions inherit the smoothness and the topological properties from the atlas. The problem focused on in this paper is to extend the generative random diffeomorphic orbit model that has been used in single atlas approaches Since the atlases used for interpreting the image are not known, the conditional-mean technology of the expectation-maximization (EM) algorithm local charts linked through diffeomorphic coordinate transformations. The anatomical model constructs the atlas via charts of subcortical and cortical volumes delineated in varying anatomical coordinate systems. In our case, we focus on subcortical structures and the ventricles. The MAP problem labels each voxel of the target image via mixtures of the locally-chart-defined conditional a posteriori probabilities. Since for any voxel, a chart from any of the atlases could be the generator of its mean field and the associated conditional a posteriori probability, the conditional-mean of the latent variables on chart selection is calculated for each voxel in the target image, thus providing locality in the segmentation as part of the global model.A significant extension, developed in this paper, of the random atlas model is to add to the global deformable template the notion of locality which is usually associated to the local approaches from differential geometry The multi-atlas random orbit model used here for segmentation differs from several other approaches in the following ways. First, the proposed method solves for the single set of unknown segmentation variables Also, it is noteworthy that, in the likelihood-fusion approach, we do not generally find that the posterior probability is concentrated as a delta-function supported on one or a small number of the same atlases, which would be equivalent to the generalized likelihood problem in which the atlases and charts are tested separately with the “closest” ones determining the solution via combination as in The method proposed here is a generative model approach, more akin to the approach suggested in In this paper, we investigate the quality of the multi-atlas multi-chart diffeomorphic orbit model for the segmentation of deep gray matter structures, as well as the ventricles, using T1-weighted MR images. We were particularly interested in characterizing brain atrophy, and therefore, we tested our method in elderly and dementia populations. Results from the automated segmentation scheme have been compared with the manual segmentations to examine the accuracy of the method. More specifically, we investigate: 1) the level of accuracy we can achieve using a single-atlas approach; 2) the degree of improvement by incorporating the multi-atlas approach; and 3) the impact of the anatomical variability on accuracy based on a normal elderly and a dementia patient population.We first examine the class of maximum a posteriori problems in which the generalized parameters Scoring the images in The diffeomorphic flows are generated by the set of time-indexed vector fields Model selection plays a fundamental role in the MAP estimation of parameters. We associate the high dimensional parameter set Now we examine MAP estimation in the high-dimensional setting of unknown segmentation fields, We define a hierarchical model between the image and the underlying diffeomorphic change in coordinates of the atlas, so that Locality is introduced into the global representations by defining the atlases to correspond to manually-labeled T1-weighted imagery with empirical mean and standard-deviation parameters obtained over the subcortical structures indexed throughout the volume. The charts are collections of the manually delineated sixteen subcortical and ventricular structures, each with means and variances; associated to each chart are the parameters The charts are “open sets” containing each of the subcortical structure so that their unions cover the full volume and are related with each other as depicted in The multi-atlas random orbit model of the observed imagery We introduce the localized indicator functions associated to the atlas field labelling Define the Q-function as the conditional expectation of the complete-data log-likelihood according toThen the sequence of iterates Initialize: Compute optimized mappingsCompute the approximated atlas selectorGenerate new segmentation If either To maximize To maximize The LDDMM variational problem has direct interpretation as a MAP estimator. Associate to The second method we use to compute the distance is to create triangular meshes of the structures and compute the distance between the atlas structures and meshes of the structures in For computational purpose, we remove outlier atlases used in the computation following a robust scoring scheme analogous to that suggested in In this study, sixteen deep gray matter and ventricles structures were manually defined in the atlases images, which cover only a small part of the images. We defined a cuboid region of interest (ROI) encompassing all the structures of interest in all atlases, and modeled the segmentations within this ROI. Voxels inside the ROI not belonging to any of the sixteen manually delineated structures were automatically labeled as white matter, gray matter, or cerebrospinal fluid (CSF) based on a local brain tissue segmentation algorithm rd ventricle, and the 4th ventricle.In this study, we use T1-weighted images from 35 subjects from three groups, as described in To quantitatively evaluate the accuracy of our algorithm, we employed a leave-one-out cross-validation method on the datasets of Group 1 and Group 2. For Group 3, we used datasets from Group 1 and Group 2 as the atlases for segmentation. Manual segmentations were regarded as the gold standard. The segmentation accuracy was measured through the use of the Dice overlap coefficients. The Dice overlap is computed as: All subjects provided written consent for participation in accordance under the oversight of the Johns Hopkins Medicine Institutional Review Board (JHM-IRB). Additionally, for those subjects with dementia, the consent form was co-signed by a family member. The Johns Hopkins Institutional Review Board approved this study.The segmentation accuracy of the proposed method was compared with that of the segmentations obtained from two label-fusion techniques: STAPLE t-test, we applied Fisher's method of randomization. We utilized Monte Carlo simulations to generate 10,000 uniformly distributed random permutations, which gives rise to a collection of t-statistics coming from each permutation. The p-value is then given by the fraction of times that the t-statistic values from the permutations is larger than the value obtained from the true groups.To measure the statistical significance of differences between two groups in comparison, instead of using the student's In the first experiment, we explored the efficacy of adding neighboring tissue labels around the structures of interest  in the atlas. The same likelihood-fusion procedure was applied to the two sets of labels of the same atlas images: 1) the sixteen manually defined structures, and 2) the sixteen manually defined structures and the three generic neighboring tissue segmentations – gray matter, white matter, and CSF. A quantitative comparison between the two sets of automated segmentations based on the two different sets of label definitions, in terms of all the three groups, is shown in rd ventricle, and the 4th ventricle. In addition to the improvements shown via average Dice values, we also observed that adding tissue definitions prevents the mislabeling between ventricles and their neighboring gray matter structure such as hippocampus and amygdala, particularly in the area close to the inferior horn.As shown in It is clear that having multiple atlases increases the computational complexity. We wanted to be able to quantify the advantages of supporting multiple atlas anatomies in the solution. For this we performed multiple experiments. The first compares the performance of segmentation via single-atlas LDDMM using a leave-one-out technique in which a single subject was chosen as a template and all the other subjects in the group were segmented via the LDDMM image mapping procedure. For this purpose, the data in Groups 1 and 2 were combined; one of the 29 subjects was used as the atlas and the other 28 images were segmented. This process was repeated for 29 different atlases implying each subject was segmented 28 times using 28 different atlases. For subjects in Group 3, the single atlases chosen from groups 1 and 2 were used for segmentation to avoid the potential bias of the leave-one-out approach. The mean Dice values and the standard deviations for each set of Dice values for automated segmentations of various structures from single-atlas LDDMM are shown in As demonstrated in To contrast to the single-atlas LDDMM case, we examined the likelihood-fusion via multi-atlas LDDMM approach using a series of leave-one-out tests combining the data from Groups 1 and 2. In the leave-one-out strategy, the remaining MRIs form the atlases. Shown in Shown in The generative probability model which multi-atlas LDDMM is based averages likelihoods generating a single label for each segmentation voxel. It is natural to compare to competitive methods which average segmentation labels via label fusion. For this we compared the multi-atlas LDDMM with two representative label fusion techniques, STAPLE As accurate segmentation is at the center of many neuropsychiatric studies, there have been many methods developed for brain segmentation, which are typically based on local approaches mostly involving multi-compartment appearance and Gaussian mixture modeling, coupled to MAP or maximum-likelihood The conditionally Gaussian random field model used throughout is the generative random orbit model used for “template” estimation In these global deformable template methods, templates which are far in the deformation space are less accurate for representing anatomical features and parameters being estimated. In the context of segmentation, multiple atlas based methods which embed the global solution with more locally accurate properties via label combination have been used extensively Another aspect of the diffeomorphic framework is that since we model human anatomy via the diffeomorphism metric as a complete metric space The proposed method has been tested based on three datasets with different pathologies – normal aging, subjects with Alzheimer's disease, and subjects with dementia. Likelihood-fusion via multi-atlas LDDMM improves the segmentation accuracy obtained from single-atlas LDDMM. Favorable comparison to label-fusion methods is also evident as shown in Compared with other recently published segmentation methods and the reported Dice overlaps, our method demonstrates comparable or favorable levels of segmentation accuracy, with mean Dice overlap results in the range of 0.8 to 0.93. A direct comparison of segmentation accuracy among different programs is difficult as many programs contain internal structural definition with the resultant differences in performance which can simply reflect the way that structures are defined. Given the structure sizes and the intensity ranges, it is generally considered more difficult to automatically segment the hippocampus and amygdala than other deep gray matter structures. Previous publications such as The current work has focused on subcortical and ventricular regions. Our initial investigation into whole brain segmentation setting via likelihood-fusion has been validated in a limited setting in Appendix S1Proof of the monotonicity in the incomplete-data likelihood with the atlas selector.(DOCX)Click here for additional data file.


Wheat is one of the most important crops in Australia, and the identification of young plants is an important step towards developing an automated system for monitoring crop establishment and also for differentiating crop from weeds. In this paper, a framework to differentiate early narrow-leaf wheat from two common weeds from their digital images is developed. A combination of colour, texture and shape features is used. These features are reduced to three descriptors using Principal Component Analysis. The three components provide an effective and significant means for distinguishing the three grasses. Further analysis enables threshold levels to be set for the discrimination of the plant species. The PCA model was evaluated on an independent data set of plants and the results show accuracy of 88% and 85% in the differentiation of ryegrass and brome grass from wheat, respectively. The outcomes of this study can be integrated into new knowledge in developing computer vision systems used in automated weed management. Wheat is the most common agricultural crop in southern Australia and annual ryegrass and brome grass are reportedly the two most common weeds in South Australian wheat fields . These wThe conventional means of manual weed detection is very time consuming, expert-intensive, and costly, even at the early growth stages. On the other hand, early intensive herbicide spraying is not considered an economically and environmentally good option. Therefore, a vision-based and image analysis method was proposed as a cost-effective and site-specific replacement method for weed detection. Digital image analysis has found recent applications in plant biology, plant taxonomy and precision agriculture -16. PereHemming and Rath  developeIn spite of these efforts, there has been little in the way of theoretical advances in developing a robust general method for combining colour, morphological and textural features for crop-weed classification. In particular, most of the shape-based classification approaches have been developed for broadleaf plant classification. This present study focuses on the crop plant (wheat) and two prominent weeds encountered in Australian farming all of which are narrow-leaf plants. Our aim is to fill in the gaps in our knowledge of the use of combinations of visual properties for the differentiation of narrow-leaf plant species.Having said that, vision-based recognition of grass species is still considered a difficult task. The difficulties are less challenging when distinguishing narrow-leaf plants from broadleaf weeds or using spectral characteristics of certain crop and weed species ,19,21-25A vision-based approach to describe a plant involves defining and measuring some specific visual characteristics such as colour , shape  and texture features (e.g. intensity contrast). In this experiment, quantitative analogues of these features are extracted from the images of plant species using image processing techniques, and Principal Component Analysis is employed to extract a descriptor for differentiating between plant species.The images used for this study were of three plant species cultivated in a 1500 mm × 1000 mm box in a greenhouse facility from the School of Natural and Built Environments at the University of South Australia, .Plant seedlings were imaged regularly every three days following first emergence. The images were taken between 11 AM and 1 PM when the light intensity was high and in the range of [8000-12000] lux. A Canon PowerShot A640  with 1/1.8" sensor size and focal length of 7.3 mm was used for imaging. The images were of the size of 3648 × 2736 pixels and taken from the top view of the plant seedlings at a distance of 1000 mm. The field of view was 980 mm × 720 mm and the pixel ground resolution was 0.266 mm/pixel  to display the image and zoom on to each part of the image containing a plant systemically and the image of each individual plant was cropped from the full image manually for further processing. Not all seeds germinated. The successful seeds provided us with the total 286 images of individual plants during their 1-4 leaves growth period. From this number, we obtained 118 images of wheat, 122 of Brome grass and 46 of ryegrass species. Of the 286 images, 57 images (20%) were randomly selected and put aside for testing a method developed using the remaining 229 images (80%).We developed an algorithm in MatlabExamples of images of individual wheat, ryegrass and brome grass seedlings are shown in Figure In order to extract visual characteristics (or features) of plants from the images, the plant regions needed to be separated from the background by a segmentation process. This was accomplished by converting each true colour image to a grayscale hue image first. Grayscale hue images provide high contrast between plant regions and non-plant background, making the segmentation process easier and more accurate. A hue image is the same size as the actual image with each pixel containing a value in the range of 0° to 360°, representing the position of the colour on the hue circle. Pixels with low colour saturation were zeroed out before the segmentation process . From prThe plant image shown in Figure In theory, there are a large number of visual characteristics of plants which can be extracted from their images. However, in this study, an expert-based approach was followed to select the optimum relevant features -31. The i, gi and bi are colour factors normalized by the grayscale intensity of the pixel. Grayscale intensity is the attribute of light that expresses the amount of illumination and is computed as a weighted sum of the R, G, and B components [The three colour components of R, G and B are the intensity values in the range of 0-255 of the colour channels of Red, Green and Blue, respectively. The factors rmponents . NormaliThe ratio of the width (W) over Waddle disk diameter was used for the first time and defined as "Waddle disk ratio" (WDR). To measure the width (W), the plant region in the binary image was eroded from the border pixels inwards iteratively and until the whole region disappeared. The kernel in the morphological operator was selected as a 3 × 3 square which allows the removal of one pixel-wide layer around the plant region per iteration. The width is calculated as twice the number of iterations required to achieve this.The Waddle disk diameter is the diameter of a circle with the same area as the plant region in the binary segmented image. The Waddle disk ratio, then, is a dimensionless parameter which by definition measures the roundness (as opposed to linearity) of the leaf area.In addition to the colour and shape features, texture features of plant regions have also been extracted from their grayscale images -36. A grp(zi) is the proportion of pixels having a given intensity level zi, and L is the number of possible intensity levels [Uniformity is a maximum when all the gray levels are equal and minimum when the histogram has equal proportions. Entropy measures the degree of randomness and it is a maximum when the histogram has equal proportions. In Table y levels .Once the visual features were extracted, Principal Component Analysis was employed to extract a pattern for differentiating between plant species. Principal Component Analysis (PCA) is an algebraic technique (eigen-decomposition) in which combinations of correlated variables are selected as explaining the variability in observations between images. The resulting principal components have greatly reduced  correlation. By this means a smaller set of relatively uncorrelated variables may take the place of a larger set of correlated variables . The coeThe manner in which PCA creates combinations of measured variables has an intuitive appeal, in that the process in a certain way mimics the cognitive process used by the expert to distinguish plants. The parts to the complete computational process are, firstly, creating quantitative analogues to the visual features; secondly, selecting those which display measurable differences between plants; and finally, finding the appropriate combination of these features to distinguish one plant from another.In this study, we used SPSS software package  to conduct PCA and the results were verified using Matlab.i, RBI, EBI, width, Waddle Disk Ratio, and uniformity.The correlation matrix exhibited a number of high positive and negative correlations, which are an indication of redundant information Table . As can The PCA with Varimax rotation was conducted on the correlation matrix to assess the underlying structure of the six features for the plant species differentiation. Varimax is an orthogonal rotation method which is employed to rotate components while keeping them orthogonal and uncorrelated. Varimax attempts to maximize the dispersion of loadings within components. Thus, this method loads highly a smaller number of variables onto each factor resulting in more interpretable clusters of components .Principal components from the model building set of plant images (= 229 samples) were computed from the eigenvectors. Figure The first principal component accounts for 42% of the total standardized variance in the data set. The second component accounts for 26% and the third principal component accounted for 17% of variability between the images  loadings in the second column. The two features RBI and EBI have almost the same loadings in this component but of opposite sign. The third component, which seemed to represent a combination of texture and shape, was composed of the two features with high loadings in the third column of the table. The Waddle Disk Ratio had its highest loading on the third component. The linking of two unrelated features in one single component was unexpected. It seems that there is an intrinsic relationship between these features which differs from plant to plant in a way not obvious to the human eye.The main source of variability between the plant images is the result of some plants having high values of the principal components and some not. Having built the model, we expect that the components will provide the independent explanations of the differences between the plant images.To calculate the component score for each plant image, the factor loadings were multiplied by the values of the visual features obtained from each image of the plant. The calculated component scores were then used as response variables in the procedure Analysis of Variance (ANOVA) with the plant type as the categorical level, and statistically significant differences were found between the three principal components ,42. The The statistical significance of differences between the images of plant species within each principal component was tested with Bonferroni post hoc tests ,43. PostWe were now able to set up a method that can be used to distinguish crop wheat plants from ryegrass and brome grass weed plants. This method used scores for three components as the classifiers and a threshold value for each classifier. The threshold values were calculated from the confidence intervals mentioned in the detailed table of descriptive statistics Table . For insHaving established a system of principal components that discriminates the three plant species from their images it becomes necessary to validate the system on an independent data set. The colour, shape and texture features of the images in the testing dataset = 57 samples) were converted into the principal component scores using the variable loadings presented in Table 7 samplesi and width W (negative), with some contribution from the red-blue contrast feature RBI. PC1 yielded higher values for ryegrass than for wheat. Evidently the process has been able to detect that ryegrass plants have more red and less blue in the colour, and narrower leaves, than wheat plants, in the early growth stages.The first component, which has succeeded in discriminating ryegrass from wheat, has high loadings on normalized red rThe second component, which has distinguished brome grass from wheat, has high loadings on the red-blue contrast feature RBI (negative) and the excess-green feature EGI. PC2 yielded higher values for brome grass than for wheat. The process has been able to detect some subtle differences in the colours of these plants, not easily discerned by the human eye, to do with the green and blue content of the leaf colour.The third component, which has been even more successful in discriminating ryegrass from wheat, has high loadings on the Waddle disk ratio and the uniformity. PC3 yielded larger negative values for ryegrass than for wheat. This indicates that the process has detected that ryegrass plants have a less uniform leaf surface, combined with more linearity in the leaf shape, than wheat plants, at this stage of growth.The differentiation obtained by these three components approaches that achievable by a trained observer. With higher image resolution enabling better quantitative measures of texture and colour the accuracy is likely to improve significantly, leaving only biological variation as the source of error. The image processing and PCA of themselves are essentially error neutral.Early detection of weeds followed by quick and appropriate actions to remove the weeds is an important part of weed management because if the weeds become too well established and widespread their control becomes technically and financially impossible. However, identification of and dealing with narrow leaf weeds in wheat farms can be a frustrating experience particularly during early growth stages, and it would be desirable to have a machine-based method for identifying and dealing with them.The first step in developing such a method is to automate the identification of individual plants. This study demonstrates that it is possible to differentiate greenhouse-grown wheat from ryegrass and brome grass based on their images with identification accuracy of 88% and 85%, respectively. Given the difficulties of identification of these very similar narrow-leaf species up to the four leaf stage, the achieved accuracies in discriminating brome grass and ryegrass from wheat indicate that automatic identification is feasible. These results were obtained using the images of the plant species grown in the greenhouse environment. As future work, we would like to test our method on images taken under field conditions. The ultimate goal, however, will be to develop the machine vision technology so that crop and weeds may be identified in situ, using a process similar to that outlined here, perhaps using pre-determined thresholds for the discriminating components. A simple application would be in the early identification of weed infestation in a recently planted crop. But it is surely not too futuristic to envisage a machine, equipped with a high definition camera, a fast computer, and other appliances, progressing through a crop while identifying and dealing with individual weeds.The authors declare that they have no competing interests.MRG conceived the study, conducted the glasshouse experiment, acquisition and processing of the image data, carried out the preliminary data analysis, and wrote the first draft of manuscript. MRG and RAF cooperated in developing the PCA model, the further data analysis and interpreting the results. RAF assisted in reading, editing, writing and approving the final manuscript. All authors read and approved the final manuscript.


Since then it has been the focus of much effort. This is for two reasons: first, the intellectual curiosity of basic science and the desire to understand fundamental phenomena, and second, its vast practical importance. Allostery is at play in all processes in the living cell, and increasingly in drug discovery. Many models have been successfully formulated, and are able to describe allostery even in the absence of a detailed structural mechanism. However, conceptual schemes designed to qualitatively explain allosteric mechanisms usually lack a quantitative mathematical model, and are unable to link its thermodynamic and structural foundations. This hampers insight into oncogenic mutations in cancer progression and biased agonists' actions. Here, we describe how allostery works from three different standpoints: thermodynamics, free energy landscape of population shift, and structure; all with exactly the same allosteric descriptors. This results in a unified view which not only clarifies the elusive allosteric mechanism but also provides structural grasp of agonist-mediated signaling pathways, and guides allosteric drug discovery. Of note, the unified view reasons that allosteric coupling (or communication) does not determine the allosteric efficacy; however, a communication channel is what makes potential binding sites allosteric.The question of  In cell biology the ability to perform a biological function is determined by how populated a macromolecule in its active conformation is. Rather than direct manipulation of the active  site, allostery is capable of altering the active state population by some perturbation away from the active site, such as that elicited by ligand binding, post-translational modifications (PTMs), and more Numerous approaches have been undertaken over the last 50 years in an effort to explain allostery and to study its underpinnings and consequences 2 to tetrameric hemoglobin (Hb). Among the many models formulated to account for this cooperativity, the two-state concerted MWC model The first realization of allostery in biology was the cooperative binding of Othermodynamic view of allostery a major foundation of allostery. In the diverse mathematical equations formulated for this purpose, each species included in the equation is only given one conformational state and the population is specified by its concentration. The limitations of the operational models, due to the omission of the concept of population shift in species responsible for pharmacological response, have been pointed out in a recent review Following the successful allosteric cooperative binding models, many conceptual allosteric schemes ex) 15N backbone amide CPMG (Carr-Purcell-Meiboom-Gill) relaxation dispersion experiments In 1995, Leff presented the simplest two-state model structural view of allostery considers the interactions among a set of residues as responsible for the allosteric coupling between the allosteric and functional sites. It reasons that allosteric communication is specified by allosteric networks (or channels) through which strain energy created at the allosteric site by binding, PTM, or mutations propagates to the functional site and induces a conformational change The At first glimpse, these two—thermodynamic and structural—allosteric views do not overlap much except for the end result of allosteric activation, and neither view requires the other to explain allostery. However, the free energy landscape allows a unified view which emphasizes the complementarity rather than the contradiction. Starting from the simplest allosteric two-state model, we tag the population shift in the free energy landscape with quantitative allosteric couplings which can be derived from an experimental response-concentration curve. To forge a tight link to the thermodynamic view of allostery, we then use the same descriptors for the structural view. Because common descriptors are adopted, the unified framework (1) illuminates how allostery works; (2) helps in accurately classifying agonist types observed in the literature based on quantities of allosteric efficacy determined by experiments; and most importantly, (3) provides the basis for unraveling the structural mechanism of allostery.Below, we first clarify the terminology of orthosteric agonist, which has been defined as a naturally occurring endogenous ligand of G protein–coupled receptors (GPCRs) The functional efficacy of a protein depends on how it populates its active conformation. As a node in the cellular circuit, a protein is expected to be able to switch its functional mode between on/off states. To fulfil its biological role, a protein has been optimized by evolution not only to populate a single active conformation; instead, two or more switchable states including the folded or disordered state need to be populated as well. Each conformation (or state) corresponds to a local free energy minimum at the bottom of the folding funnel. If the triggering event that effectively switches the protein population from one state to the other is far away from the active site of the protein, as for example in the case of substrate binding or covalent modification (PTM) distal to the functional site, it is referred to as allostery and the trigger site is termed an allosteric site. Since allostery plays significant roles in the cell, two distinct but compensatory approaches have been developed to explain how allostery works: one from a thermodynamic viewpoint, the other from a structural standpoint.The thermodynamic view focuses on how to accurately describe allosteric phenomena, such as the classical cooperative oxygen binding to haemoglobin, without involving detailed structural information. The mathematical models below are mainly based on simple thermodynamic principles. On the other hand, the structural view emphasizes that optimized allosteric communication (or coupling) between allosteric and active sites is responsible for the allosteric conformational switch. It envisages that strain energy, created at an allosteric site by a triggering event, will propagate to the active site via an allosteric coupling channel to alter the functional conformation. The sequence-based statistical method for estimating thermodynamic coupling between residues in proteins has successfully visualized allosteric coupling in long-range energetic interactions for three proteins A) will preferentially bind one state over the other. The binding affinities are quantitatively defined by association constants, with The simplest yet practical model for the thermodynamic view is the two-state model α. As indicated in α in the ATSM, however with differing descriptions, binding affinity, and allosteric intrinsic efficacy. Nonetheless, despite the simple yet powerful description, the ATSM is unable to provide a direct connection between structure and function. To link the thermodynamic view with the structural view, we next sketch the relative free energy between the two states in the ATSM.The ATSM offers allosteric ligands a functional classification through the measured allosteric intrinsic efficacy, P versus R can be expressed by Gibbs free energy R is the ideal gas constant and A approaches its saturation concentration  states. The free energy landscape representation incorporates the preferred ligand binding formulation and transforms the conceptual framework of population shift into an amount of energy which is proportional to the stabilization of the active conformation and (or) destabilization of the inactive conformation, in the case of allosteric activation. The integrated view translates these into an important rule for the classical structural view of allostery: by itself, the structural coupling (or the propagation pathway) between the functional (active) and the allosteric sites does not involve allostery; it merely identifies high correlation between the conformations of the two sites. The importance of this rule can be assessed by the number of publications using couplings and propagation pathways to delineate allostery.The how does allostery work in a specific system of interest? To decipher the allosteric mechanism in a given protein one needs three elements: first, the active conformation which is responsible for the specific function. Structures are essential in order to understand how the agonists act as allosteric triggers. This conformation should populate one of the local free energy basins (the “active basin”) at the bottom of the folding funnel. This emphasizes that an allosteric event such as ligand binding does not create a new conformational state; it only shifts the population among existing states. Second, one needs a set of interacting residues which make up the allosteric communication pathway between the active and allosteric sites; this implies that evolution has set the relative populations of the active versus inactive conformations and linked them to critical pathway residues. Mutations of those residues—if not involving both interacting partners—will affect the allosteric propagation and the population of the active conformation. Knowledge of these mutations is useful because they can be explored by methods such as fast ensemble sampling Beyond generalities, an important question is Figure S1The free energy landscape of ATSM. Instead of the case of (TIF)Click here for additional data file.Figure S2Equilibrium cycles for two functional states with a single ligand. Two assumptions have been made for the drawing. First, the population of the two distinct active states are regulated independently by the ligand. Second, the total concentration of (TIF)Click here for additional data file.Figure S3The structural view of allostery for one allosteric site with two independent functional sites. The drawing shows one allosteric site is independently coupled to two functional sites with allosteric efficacies, (TIF)Click here for additional data file.Figure S4The free energy landscape of the extended ATSM. The energy landscape drawing is similar to (TIF)Click here for additional data file.


In this minireview, we survey recent advances in the synthesis, characterization, and modeling of new oligothiophene–oligopeptide hybrids capable of forming nanostructured fibrillar aggregates in solution and on solid substrates. Compounds of this class are promising for applications because their self-assembly and stimuli-responsive properties, provided by the peptide moieties combined with the semiconducting properties of the thiophene blocks, can result in novel opportunities for the design of advanced smart materials. These bio-inspired molecular hybrids are experimentally shown to form stable fibrils as visualized by AFM and TEM. While the experimental evidence alone is not sufficient to reveal the exact molecular organization of the fibrils, theoretical approaches based on quantum chemistry calculations and large-scale atomistic molecular dynamics simulations are attempted in an effort to reveal the structure of the fibrils at the nanoscale. Based on the combined theoretical and experimental analysis, the most likely models of fibril formation and aggregation are suggested. Amyloid and amyloid-like fibrillar aggregates, formed by natural proteins or oligopeptides, have attracted much attention both due to their involvement in medical pathologies  and tDuring the last decade, considerable progress in our understanding of the principles of fibril formation has been made owing to numerous experimental and theoretical studies and, importantly, the resolution of peptide arrangements at the atomistic level by means of X-ray crystallography and solid-state NMR –6. The oIn this area, the approach that is gaining more and more attention is the synthetic conjugation of peptides to other molecular compounds. Conjugates of synthetic and natural macromolecules are of great current interest because of their promising biomedical, microelectronic, and other advanced technological applications –1014–15.10Several reviews –915 summ9A number of hypothesized self-organized morphologies that may be adopted by various polymer bioconjugates are shown in While the chemical structure of the aggregating compounds is almost always known, and the fibrillar morphology at the submicrometer scale is resolved by electron or atomic force microscopy, the structure of the fibrils at the atomistic and nanoscales, including the packing of the single molecules, very often remains beyond the capabilities of experimental measurements to elucidate. In particular cases, it becomes possible to gain insight into the intrinsic structure of the fibrils, e.g., by means of X-ray diffraction when the corresponding microcrystals can be obtained, or when sufficient solid state NMR data is available. However, for the majority of compounds and moreover for polymer-bioconjugates, the available experimental evidence regarding the intermolecular interactions is in most cases limited to spectroscopic analysis  and diffraction patterns  and thus the exact structural arrangement at the nanoscale and its connection to the morphology remains elusive.The molecular simulation methods in this respect become an attractive tool to supplement and interpret the experimental data, because they can fill in the missing gaps in the understanding of the relationship between the structural arrangement and the fibrillar morphology. When 3-D atomistic structures of microcrystals or oligomeric aggregates are available they may be used to construct computational models of the fibrillar aggregates, and through the application of atomistic molecular dynamics (MD) simulations the structural data can be extended into the dynamic domain. Since microcrystals usually only provide the structures of the basic aggregation units, different arrangements of these units into the protofilaments and then fibers may be probed in computer simulations. However, when no initial 3-D structural data is available, the application of computer simulations may be less straightforward. In this case, it is necessary to predict or suggest various trial arrangements, construct the aggregates, and then test their characteristics against available experimental data. The latter approach has a much wider applicability in terms of studied compounds and potential applications for the rational computer-aided design of new macromolecular systems with specific properties.In this minireview, we discuss the recent progress in the design, synthesis and in computer simulations of new oligothiophene–oligopeptide conjugates that can self-assemble to form nanoscale fibrillar aggregates. The main focus is on the experimental and theoretical results obtained in our group.1 ..15 conju6 was prepared analogously to the A–B–A-type hybrid 1 by the reaction of monoethynylated quaterthiophene 8 and protected peptide–PEO15 conjugate 3 Each of the two remaining principal arrangements can be realized in two variants depending on which kind of faces  are in contact. The resulting four arrangements are shown in These structures were constructed as follows. First, the single-layer structure was replicated, turned 180° around the axis of the tape, and then adjusted in the lateral plane, so that the peptide segments of two single-layer fibrils would be approximately in register forming a “steric zipper” in the center of the fibril as seen in microcrystals of amyloidogenic peptides. Any overlap of molecular fragments that occurred  was removed by small adjustments of the involved torsion angles, which would anyway reach their equilibrium values during the relaxation run. Since double-layers are considerably more complicated conformational assemblies, particularly with respect to the organization of the surfaces buried between the two β-sheets and the interaction of the side chains at these surfaces, a 10 ns MD relaxation run was performed for these periodic structures. During this run, a certain rearrangement of the side chain conformations between the β-sheets took place. The relative enthalpies of formation for these structures during the run were monitored, in order to track the system relaxation. The lowest relative enthalpy of formation was observed for structure III. Relative to structure III, structures I, II and IV have an additional enthalpy of formation of 11, 6 and 12 kcal/mol per molecule, respectively. Although this data set was obtained in vacuum simulations and the effect of solvent was neglected, it gives valuable quantitative data for the understanding of the hierarchy of interactions in such systems and is consistent with the supposition that hydrophilic interlayer contacts and an antiparallel arrangement of the β-sheets are the factors that lead to a gain in enthalpy of formation. However, in our case because of the specific geometry of the molecules, the aggregation pattern based on antiparallel β-sheets and hydrophilic interlayer contact  and (III)) were used to construct long fibrils by replicating the periodic cell along the axis of the filament. For the selected systems, planar straight fibrils 80 β-strands in length (approximately 40 nm) were constructed and subjected to 10 ns MD simulations at  package , based oRepresentative snapshots that describe the conformational evolution of different fibrillar arrangements are presented in All the systems demonstrated their stability during the simulation run in the sense that all molecules preserved their relative positions in the aggregates with respect to their neighbors, however, certain conformational rearrangements both at the molecular level and at the nanoscale were observed. In all the cases, the β-sheet organization dominated the structure and remained the main scaffold for the fibril organization. A simulation time of 10 ns appeared to be enough to grasp the main characteristics of the fibril morphology and its evolution. As seen from 3 sequence with the rest of the molecule. Since glycine has no side chain, it does not hinder the rotation around C–N and C–O bonds of the peptide backbone and hence allows the observed flexibility. Meanwhile, the thiophene moieties of the molecules remain in closely packed alignment, thus forming a continuously organized axial structure with a left-handed twist. On the contrary, the single layer fibril based on the antiparallel arrangement of β-strands, which lacks much of the thiophene–thiophene interactions , tends to curl to form a left-handed helical structure  of various simulated fibrillar aggregates and their spatial dimensions ) with the available AFM data  suggestsCombining synthetic and biological building blocks to form various types of biomimetic thiophene-based hybrid compounds offers a means to construct new ordered supramolecular nanostructures and soft materials through self-organization, and such structures may exhibit a rich polymorphism over nanometer length-scales. The design of such hybrid molecules is a unique strategy, which aims to create smart nanomaterials that combine the properties of both the synthetic and biological components. Applying such an approach in the chemistry of conjugated compounds leads to new organizational concepts at nanoscales for these technologically important molecules.This minireview was focused on and limited to a summary of recent advances in the understanding the self-organization processes observed for oligothiophene–oligopeptide conjugates, which are capable of forming long fibrillar aggregates in solution and on substrates. In particular, we reported on the successful synthesis of new bio-substituted organic semiconductor compounds where the rigid quaterthiophene block is either di- or monosubstituted with peptide sequences that display a high propensity to form β-sheets. These molecular hybrids can spontaneously self-assemble into stable fibrillar aggregates as visualized by AFM and TEM. We presented data on both kinked and nonkinked states of the peptide chains and found that the behavior of both symmetric (A–B–A) and asymmetric (A–B) hybrids in relation to the superstructure formation differs deeply, depending on the peptide conformation. These observations lead to the assumption that the mode of self-assembly of the individual molecules in their respective states, kinked and stretched, differs profoundly. Theoretical approaches based on quantum chemistry calculations and atomistic molecular dynamics (MD) simulations were attempted in order to reveal the possible intermolecular arrangements, their characteristic features, and to devise the possible arrangement models. Several models of the aggregation pattern of molecules for the A–B-and A–B–A-type conjugates were presented based on quantum chemical calculations. We have discussed a theoretical approach developed to study possible intermolecular arrangements and their characteristic features at finite temperature. This methodology incorporates available experimental data to suggest different variants of possible fibrillar nanostructures. These structural candidates were studied theoretically and their behavior was then cross-validated against available experimental evidence. Large-scale all-atom MD simulations for several proposed fibrillar models were also performed. They revealed the dependence of the fibrillar morphology on the intrinsic molecular organization of the fibrils. Using combined theoretical and experimental analysis, we have suggested the most likely models of fibril formation.Future work should be aimed towards the development of new ways for the formation of semiconducting fiber-like supramolecular structures with mechanical properties mimicking those of natural materials such as silk or amyloid fibers. The idea is to obtain conductive materials with good mechanical strength and elasticity for various applications. Innovative methods such as computer simulations and combined multidisciplinary partnerships between chemists, physicists, and biochemists are required for the development and optimization of these bioinspired materials to provide fundamental understanding of their structural and charge transport properties.


The small GTPase Rac is known to be an important regulator of cell polarization, cytoskeletal reorganization, and motility of mammalian cells. In recent microfluidic experiments, HeLa cells endowed with appropriate constructs were subjected to gradients of the small molecule rapamycin leading to synthetic membrane recruitment of a Rac activator and direct graded activation of membrane-associated Rac. Rac activation could thus be triggered independent of upstream signaling mechanisms otherwise responsible for transducing activating gradient signals. The response of the cells to such stimulation depended on exceeding a threshold of activated Rac. Here we develop a minimal reaction-diffusion model for the GTPase network alone and for GTPase-phosphoinositide crosstalk that is consistent with experimental observations for the polarization of the cells. The modeling suggests that mutual inhibition is a more likely mode of cell polarization than positive feedback of Rac onto its own activation. We use a new analytical tool, Local Perturbation Analysis, to approximate the partial differential equations by ordinary differential equations for local and global variables. This method helps to analyze the parameter space and behaviour of the proposed models. The models and experiments suggest that (1) spatially uniform stimulation serves to sensitize a cell to applied gradients. (2) Feedback between phosphoinositides and Rho GTPases sensitizes a cell. (3) Cell lengthening/flattening accompanying polarization can increase the sensitivity of a cell and stabilize an otherwise unstable polarization. Cell polarization is associated with intracellular gradients of signaling proteins such as Rho GTPases that organize the cytoskeleton in cell motility. We previously observed cells in microfluidic channels and studied their polarization and motility in a simplified  geometry. There, precise gradients of chemically-inducible molecular probes were presented to elicit gradients of active Rac, independent of the upstream signaling. Here we develop a set of spatio-temporal mathematical models to account for the observed polarization behaviour of those cells, and their threshold response to induced Rac activity. These reaction-diffusion models for the interactions of signaling proteins  and membrane lipids (phosphoinositides PIP,  Many types of eukaryotic cells undergo directed motion in response to external spatial signals in a process known as chemotaxis. Before starting to move, a given cell polarizes according to directional cues in the environment, forming nascent “front” and “back” regions. At the front, actin cytoskeleton assembly powers protrusion, whereas at the back, actomyosin contracts and pulls up the rear. Orchestrating the localization of actin network regulators and myosin activators are signalling molecules such as Rho-GTPases and phosphoinositides (PIs). The spatio-temporal distribution of such regulatory molecules is thus critical to the correct polarization, motility, and chemotactic response of such cells.Proteins of the family of Rho-GTPases  and the lipid PIs . Thus, experimental data allowed us to reject this candidate pre-existing model. In hindsight, the reason for this is clear. In the original models, traversing the circuit from Rac to Rho to Cdc42 back to Rac encounters only a single negative feedback. Thus a mild stimulus-induced asymmetry in the Rac profile feeds back negatively onto itself. As this feedback is the source of amplification, it overpowers the original signal and leads to polarization in a direction opposing the initial stimulus. In view of the observation that HeLa cells polarize in the correct direction (up the gradient of Rac activator), we discarded these previous full models and decided to reconstruct a new model from the ground up. We use evidence from In the following sequence of models, we first asked whether a single GTPase coupled to PIs (Model 1) could account for major features of the data. We find that a single GTPase module can account for threshold based polarization with and without PI feedback. If PI feedback is added, the polarization capability is enhanced. However it is known that Cdc42 and Rho also participate in polarization. We next discuss Model 2 where Rho is passively coupled to the single GTPase polarization model (Model 1). For reasons discussed previously, we reject Models 1,2 as incomplete. In Model 3, a modification of an existing model in To assemble a new model, we started with the most basic relevant single-GTPase model due to We connected the basic GTPase model to the model for PIs as in To avoid introducing too many features at once, we first consider a situation where Rac is a primary regulator that directs Cdc42 and Rho. An important flaw in this model is that in the absence of PI feedback, Rho cannot influence Rac. While they are not specifically probed in the experiments that motivate these investigations, Rho and Cdc42 are observed to be more than passive regulators enslaved to Rac We adapted Model 2 by revising the number and types of feedback arrows to incorporate mutual Rac-Rho inhibition, as shown in While this model appears to be schematically similar to Model 2, it incorporates an important structural difference. The bistability necessary for wave pinning to occur results from mutual inhibition (two negative feedbacks) as opposed to cooperative positive feedback. This is a natural next step in light of a result long posited by Thomas and recently proved Model 3 exhibits the following minimal required features to account for basic experimental observations on HeLa cells. (1) It has regimes with bistable kinetics needed for polarizability . (2) It exhibits complementary localization of Rac and Rho, known to be related to protrusion and retraction respectively. This allows us to account for both “frontness” and “backness” cell attributes. (3) These behaviours occur both in presence and absence of PI feedback with all other system parameters held fixed, but can be “tuned” by the magnitude of that feedback.In principle, Model 3 would comprise the minimal required model. For completeness, we added Cdc42, as shown in We introduce Cdc42 with four criteria in mind. First, we sought interactions that lead to co-localization of Cdc42 and Rac that are complementary to the Rho profile. Second, we preserved the essential construction of two inhibitory connections of Model 3 to retain its bistable character. Third, we added a minimal number of overall GTPase interactions consistent with biological literature. Fourth, none of the GTPases is enslaved to the others. The model depicted in The GTPase part of this model consisting of Eqs. (1), (8) exhibits the bistability necessary for wave pinning to occur. To see this, consider the case of no PI feedback  of GTPase activity in Region II of Both the signal strength  to obtain polarization. (This prediction was verified with the full PDE system.)Next, we increased this parameter. As expected, an increase in the strength of this positive feedback serves to sensitize the cell, i.e., increases the extent of the ultrasensitive Region III. For example, while for Experimental manipulations in We next investigated the approximation that PIs are slow  variables, as shown in the right panel of To check this prediction, we carried out simulations of the full 9 PDEs under systematic variation of the two parameters Experimental observations in An additional feature seen here is the reduction and subsequent elimination of hysteresis as Consider, first, the following experiment with a resting cell of some fixed length. If Interestingly, in addition to sensitizing the model, increasing length Now consider the same experiment but with a cell capable of length change. Begin with a stable cell in a resting state  signal shape appropriate. Finally, the stimulus bypasses a number of upstream signalling components and directly targets the Rac-GEF, making the input to the model clear and direct. Through these simplifications, we have produced a model that is both a reasonable representation of the system, and numerically and analytically tractable. This allowed for qualitative comparisons between model and experiment.Because of the unique form of stimulation , we could not directly use previously developed GTPase-PI model that had been tuned to stimulus inputs via Cdc42 GEFs. Rather than tinkering with that model we developed the new version from the ground up, proceeding from the simplest bistable GTPase module. A sequence of models involving one, two, or three GTPases with and without PI feedback were developed, allowing us to identify models with the minimal required capabilities. We showed that although the simplest model (with a single GTPase coupled to PIs driving polarization through positive feedback) does reproduce polarization (via “wave-pinning”) it is less suitable than models based on mutual inhibition since it does not incorporate the remaining GTPases, Cdc42 and Rho in the polarization process. In terms of complexity, the final variant (Model 4) consisting of three GTPases is a minimal mutual-inhibition model that mimics the typically observed GTPase localization behaviour, and accounts for the observed response to PI feedback tuning.We investigated the roles of stimulus mean and gradient, feedback, as well as cell geometry using Model 4. Both full simulations of the model PDEs as well as bifurcation analysis of the LPA reduction provided insights. We found that signal mean could affect overall cell sensitivity while signal gradient drives the asymmetries needed to overcome a threshold for polarization. Further temporal buildup of Rac-GEF that results from a prolonged exposure to stimulus can account for bifurcations observed experimentally. This leads to the idea that that cells become increasingly sensitive with sustained stimulus, and is consistent with experiments. As far as the role of feedback between PIs and GTPases, we found that removal or reduction of PI feedback reduces sensitivity of the model cell to applied stimulus gradients. This, along with matching experimental results, supports the idea of feedback between PIs and GTPases (as opposed to PIs acting upstream of GTPases). Finally, we also found a role for changing cell geometry. When the cell lengthens, an increase in its surface area to volume ratio can remove hysteresis. This suggests that such purely geometric effects could stabilize otherwise unstable polarizations.Limitations of the model include the absence of the cytoskeletal network, and possible feedback to and from that layer. In Experiments were performed by methods described in Models were formulated to describe the dynamic behaviour of these cells in several stages, as described in the main text. Detailed equations are provided in the following sections. Bifurcation diagrams were produced using MatCont In general, we consider up to three GTPases: Cdc42, Rac, and Rho, each of which is assumed to have three forms. Rather than writing all 9 PDEs, we here provide the form for a given GTPase, using the notation Based on the 1D experimental geometry and controlled stimulus, it is reasonable to neglect gradients in all but the length direction. Define a 1D projection of the variable We now invoke the assumption that cycling between membrane and cytosol is very fast to make a quasi steady state (QSS) assumption. Then the fractions of the inactive form on the membrane and in the cytosol are, respectively, Let We briefly outline the LPA method first introduced in Now consider a small perturbation that leads to localized high activation of the GTPase (square pulse in The bifurcation diagram in Four distinct parameter regions are found: insensitive (I), polarizable (bistable) (II), ultrasensitive (Turing unstable) (III), and overstimulated (IV). Cells with states represented by Region (I) do not respond to a pulse stimulus, and return to the rest state rather than polarizing. Cells with state in Region (IV) have a uniformly high level of active GTPase throughout, and cannot polarize - they might typically flatten and protrude in all directions, but retain their uniform GTPase distribution. Region III represents cell states wherein polarization can occur spontaneously, or in response to noise of arbitrarily small magnitude. Finally, Region II represents cells that require a heterogeneous stimulus with a sufficiently asymetric profile in order to polarize. That is, the stimulus must be sufficient for part of the cell to breach some threshold.Mathematically, these observations can be inferred from This analysis of the local-global LPA reduction provides insights, but is not fully predictive of the behaviour of the PDE system with finite rates of diffusion. The related collection of ODEs provides an approximation of the PDEs only as long as the perturbation is spatially localized. Once it spreads and a pattern begins to emerge, an asymptotic assumption that the integrated size of the perturbation be small fails and the approximation breaks down. Further, the bifurcation points present in the related ODEs are an approximation, rather than exact match, to full PDE bifurcation points. Thus, numerical simulations are necessary to provide a more complete understanding of the system.