Exploring the Conformational Transitions of Biomolecular Systems Using a Simple Two-State Anisotropic Network Model

Biomolecular conformational transitions are essential to biological functions. Most experimental methods report on the long-lived functional states of biomolecules, but information about the transition pathways between these stable states is generally scarce. Such transitions involve short-lived conformational states that are difficult to detect experimentally. For this reason, computational methods are needed to produce plausible hypothetical transition pathways that can then be probed experimentally. Here we propose a simple and computationally efficient method, called ANMPathway, for constructing a physically reasonable pathway between two endpoints of a conformational transition. We adopt a coarse-grained representation of the protein and construct a two-state potential by combining two elastic network models (ENMs) representative of the experimental structures resolved for the endpoints. The two-state potential has a cusp hypersurface in the configuration space where the energies from both the ENMs are equal. We first search for the minimum energy structure on the cusp hypersurface and then treat it as the transition state. The continuous pathway is subsequently constructed by following the steepest descent energy minimization trajectories starting from the transition state on each side of the cusp hypersurface. Application to several systems of broad biological interest such as adenylate kinase, ATP-driven calcium pump SERCA, leucine transporter and glutamate transporter shows that ANMPathway yields results in good agreement with those from other similar methods and with data obtained from all-atom molecular dynamics simulations, in support of the utility of this simple and efficient approach. Notably the method provides experimentally testable predictions, including the formation of non-native contacts during the transition which we were able to detect in two of the systems we studied. An open-access web server has been created to deliver ANMPathway results.     

Functional Roles of Slow Enzyme Conformational Changes in Network Dynamics

Extensive studies from different fields reveal that many macromolecules, especially enzymes, show slow transitions among different conformations. This phenomenon is named such things as dynamic disorder, heterogeneity, hysteretic or mnemonic enzymes across these different fields, and has been directly demonstrated by single molecule enzymology and NMR studies recently. We analyzed enzyme slow conformational changes in the context of regulatory networks. A single enzymatic reaction with slow conformational changes can filter upstream network noises, and can either resonantly respond to the system stimulus at certain frequencies or respond adaptively for sustained input signals of the network fluctuations. It thus can serve as a basic functional motif with properties that are normally for larger intermolecular networks in the field of systems biology. We further analyzed examples including enzymes functioning against pH fluctuations, metabolic state change of Artemia embryos, and kinetic insulation of fluctuations in metabolic networks. The study also suggests that hysteretic enzymes may be building blocks of synthetic networks with various properties such as narrow-banded filtering. The work fills the missing gap between studies on enzyme biophysics and network level dynamics, and reveals that the coupling between the two is functionally important; it also suggests that the conformational dynamics of some enzymes may be evolutionally selected.     

A probabilistic network model for structural transitions in biomolecules

Biological macromolecules often undergo large conformational rearrangements during a functional cycle. To simulate these structural transitions with full atomic detail typically demands extensive computational resources. Moreover, it is unclear how to incorporate, in a principled way, additional experimental information that could guide the structural transition. This article develops a probabilistic model for conformational transitions in biomolecules. The model can be viewed as a network of anharmonic springs that break, if the experimental data support the rupture of bonds. Hamiltonian Monte Carlo in internal coordinates is used to infer structural transitions from experimental data, thereby sampling large conformational transitions without distorting the structure. The model is benchmarked on a large set of conformational transitions. Moreover, we demonstrate the use of the probabilistic network model for integrative modeling of macromolecular complexes based on data from crosslinking followed by mass spectrometry.     

Protein conformational transitions explored by mixed elastic network models

We develop a mixed elastic network model (MENM) to study large-scale conformational transitions of proteins between two (or more) known structures. Elastic network potentials for the beginning and end states of a transition are combined, in effect, by adding their respective partition functions. The resulting effective MENM energy function smoothly interpolates between the original surfaces, and retains the beginning and end structures as local minima. Saddle points, transition paths, potentials of mean force, and partition functions can be found efficiently by largely analytic methods. To characterize the protein motions during a conformational transition, we follow "transition paths" on the MENM surface that connect the beginning and end structures and are invariant to parameterizations of the model and the mathematical form of the mixing scheme. As illustrations of the general formalism, we study large-scale conformation changes of the motor proteins KIF1A kinesin and myosin II. We generate possible transition paths for these two proteins that reveal details of their conformational motions. The MENM formalism is computationally efficient and generally applicable even for large protein systems that undergo highly collective structural changes.     

Dynamical network biomarkers for identifying critical transitions and their driving networks of biologic processes

Non-smooth or even abrupt state changes exist during many biological processes, e.g., cell differentiation processes, proliferation processes, or even disease deterioration processes. Such dynamics generally signals the emergence of critical transition phenomena, which result in drastic changes of system states or eventually qualitative changes of phenotypes. Hence, it is of great importance to detect such transitions and further reveal their molecular mechanisms at network level. Here, we review the recent advances on dynamical network biomarkers (DNBs) as well as the related theoretical foundation, which can identify not only early signals of the critical transitions but also their leading networks, which drive the whole system to initiate such transitions. In order to demonstrate the effectiveness of this novel approach, examples of complex diseases are also provided to detect pre-disease stage, for which traditional methods or biomarkers failed.     

Modeling protein conformational transitions by a combination of coarse-grained normal mode analysis and robotics-inspired methods

Background

Obtaining atomic-scale information about large-amplitude conformational transitions in proteins is a challenging problem for both experimental and computational methods. Such information is, however, important for understanding the mechanisms of interaction of many proteins.

Methods

This paper presents a computationally efficient approach, combining methods originating from robotics and computational biophysics, to model protein conformational transitions. The ability of normal mode analysis to predict directions of collective, large-amplitude motions is applied to bias the conformational exploration performed by a motion planning algorithm. To reduce the dimension of the problem, normal modes are computed for a coarse-grained elastic network model built on short fragments of three residues. Nevertheless, the validity of intermediate conformations is checked using the all-atom model, which is accurately reconstructed from the coarse-grained one using closed-form inverse kinematics.

Results

Tests on a set of ten proteins demonstrate the ability of the method to model conformational transitions of proteins within a few hours of computing time on a single processor. These results also show that the computing time scales linearly with the protein size, independently of the protein topology. Further experiments on adenylate kinase show that main features of the transition between the open and closed conformations of this protein are well captured in the computed path.

Conclusions

The proposed method enables the simulation of large-amplitude conformational transitions in proteins using very few computational resources. The resulting paths are a first approximation that can directly provide important information on the molecular mechanisms involved in the conformational transition. This approximation can be subsequently refined and analyzed using state-of-the-art energy models and molecular modeling methods.

     

Molecular network control through boolean canalization

Boolean networks are an important class of computational models for molecular interaction networks. Boolean canalization, a type of hierarchical clustering of the inputs of a Boolean function, has been extensively studied in the context of network modeling where each layer of canalization adds a degree of stability in the dynamics of the network. Recently, dynamic network control approaches have been used for the design of new therapeutic interventions and for other applications such as stem cell reprogramming. This work studies the role of canalization in the control of Boolean molecular networks. It provides a method for identifying the potential edges to control in the wiring diagram of a network for avoiding undesirable state transitions. The method is based on identifying appropriate input-output combinations on undesirable transitions that can be modified using the edges in the wiring diagram of the network. Moreover, a method for estimating the number of changed transitions in the state space of the system as a result of an edge deletion in the wiring diagram is presented. The control methods of this paper were applied to a mutated cell-cycle model and to a p53-mdm2 model to identify potential control targets.     

How well can we understand large-scale protein motions using normal modes of elastic network models?

In this article, we apply a coarse-grained elastic network model (ENM) to study conformational transitions to address the following questions: How well can a conformational change be predicted by the mode motions? Is there a way to improve the model to gain better results? To answer these questions, we use a dataset of 170 pairs having "open" and "closed" structures from Gerstein's protein motion database. Our results show that the conformational transitions fall into three categories: 1), the transitions of these proteins that can be explained well by ENM; 2), the transitions that are not explained well by ENM, but the results are significantly improved after considering the rigidity of some residue clusters and modeling them accordingly; and 3), the intrinsic nature of these transitions, specifically the low degree of collectivity, prevents their conformational changes from being represented well with the low frequency modes of any elastic network models. Our results thus indicate that the applicability of ENM for explaining conformational changes is not limited by the size of the studied protein or even the scale of the conformational change. Instead, it depends strongly on how collective the transition is.     

Predicting order of conformational changes during protein conformational transitions using an interpolated elastic network model

The decryption of sequence of structural events during protein conformational transitions is essential to a detailed understanding of molecular functions ofvarious biological nanomachines. Coarse‐grained models have proven useful by allowing highly efficient simulations of protein conformational dynamics. By combining two coarse‐grained elastic network models constructed based on the beginning and end conformations of a transition, we have developed an interpolated elastic network model to generate a transition pathway between the two protein conformations. For validation, we have predicted the order of local and global conformational changes during key ATP‐driven transitions in three important biological nanomachines (myosin, F₁ ATPase and chaperonin GroEL). We have found that the local conformational change associated with the closing of active site precedes the global conformational change leading to mechanical motions. Our finding is in good agreement with the distribution of intermediate experimental structures, and it supports the importance of local motions at active site to drive or gate various conformational transitions underlying the workings of a diverse range of biological nanomachines. Proteins 2010. © 2010 Wiley‐Liss, Inc.     

生物分子网络弹性研究进展

弹性是生物分子网络重要且基础的属性之一,一方面弹性赋予生物分子网络抵抗内部噪声与环境干扰并维持其自身基本功能的能力,另一方面,弹性为网络状态的恢复制造了阻力。生物分子网络弹性研究试图回答如下3个问题：a. 生物分子网络弹性的产生机理是什么？b. 弹性影响下生物分子网络的状态如何发生转移？c. 如何预测生物网络状态转换临界点,以防止系统向不理想的状态演化？因此,研究生物分子网络弹性有助于理解生物系统内部运作机理,同时对诸如疾病发生临界点预测、生物系统状态逆转等临床应用具有重要的指导意义。鉴于此,本文主要针对以上生物分子网络弹性领域的3个热点研究问题,在研究方法和生物学应用上进行了系统地综述,并对未来生物分子网络弹性的研究方向进行了展望。     

The impact of individual variation on abrupt collapses in mutualistic networks

Individual variation is central to species involved in complex interactions with others in an ecological system. Such ecological systems could exhibit tipping points in response to changes in the environment, consequently leading to abrupt transitions to alternative, often less desirable states. However, little is known about how individual trait variation could influence the timing and occurrence of abrupt transitions. Using 101 empirical mutualistic networks, I model the eco-evolutionary dynamics of such networks in response to gradual changes in strength of co-evolutionary interactions. Results indicated that individual variation facilitates the timing of transition in such networks, albeit slightly. In addition, individual variation significantly increases the occurrence of large abrupt transitions. Furthermore, topological network features also positively influence the occurrence of such abrupt transitions. These findings argue for understanding tipping points using an eco-evolutionary perspective to better forecast abrupt transitions in ecological systems.     

Mechanism of the conformational transition of melittin.

It is known that, while melittin at micromolar concentrations is unfolded under conditions of low ionic strength at neutral pH, it adopts a tetrameric alpha-helical structure under conditions of high ionic strength, at alkaline pH, or at high peptide concentrations. To understand the mechanism of the conformational transition of melittin, we examined in detail the conformation of melittin under various conditions by far-UV circular dichroism at 20 degrees C. We found that the helical conformation is also stabilized by strong acids such as perchloric acid. The effects of various acids varied largely and were similar to those of the corresponding salts, indicating that the anions are responsible for the salt- or acid-induced transitions. The order of effectiveness of various monovalent anions was consistent with the electroselectivity series of anions toward anion-exchange resins, indicating that the anion binding is responsible for the salt- or acid-induced transitions. From the NaCl-, HCl-, and alkaline pH-induced conformational transitions, we constructed a phase diagram of the anion- and pH-dependent conformational transition. The phase diagram was similar in shape to that of acid-denatured apomyoglobin [Goto, Y., & Fink, A.L. (1990) J. Mol. Biol. 214, 803-805] or that of the amphiphilic Lys, Leu model polypeptide [Goto, Y., & Aimoto, S. (1991) J. Mol. Biol. 218, 387-396], suggesting a common mechanism of the conformational transition. The anion-, pH-, and peptide concentration-dependent conformational transition of melittin was explained on the basis of an equation in which the conformational transition is linked to proton and anion binding to the titratable groups.     

Gel electrophoresis in studies of protein conformation and folding

Electrophoresis through polyacrylamide gels is a useful method for distinguishing conformational states of proteins and analyzing the thermodynamic and kinetic properties of transitions between conformations. Although the relationship between protein conformation and electrophoretic mobility is quite complex, relative mobilities provide qualitative estimates of compactness. Conformational states which interconvert slowly on the time scale of the electrophoretic separation can often be resolved, and the rates of interconversion can be estimated. If the transitions are more rapid, then the electrophoretic mobility represents the equilibrium distribution of conformations. Protein unfolding transitions induced by urea are readily studied using slab gels containing a gradient of urea concentration perpendicular to the direction of electrophoresis. Protein applied across the top of such a gel migrates in the presence of continuously varying urea concentrations, and a profile of the unfolding transition is generated directly. Transitions induced by other agents could be studied using analogous gradient gels. Electrophoretic methods are especially suited for studying small quantities of protein, and complex mixtures, since the different components can be separated during the electrophoresis.     

A method for the experimental study of DNA conformational transitions in fibers

The method proposed for the study of DNA conformational transitions is based on the proportionality, experimentally observed, between the length of a DNA fiber and the axial rise per nucleotide characterizing the molecular helix. Precise curves for the A-B and B-C transitions as a function of the relative humidity are obtained by using X-ray fiber data and measurements of fiber dimensions. It is thus shown that the A-B transition is a cooperative process between two different states, whereas the B-C transition can be considered as a progressive change of conformation. The present method is applied on two natural DNAs differing in base composition so that the effect of the nucleotide content on the conformational changes can be estimated.     

Analyzing large‐scale structural change in proteins: Comparison of principal component projection and sammon mapping

Effective analysis of large-scale conformational transitions in macromolecules requires transforming them into a lower dimensional representation that captures the dominant motions. Herein, we apply and compare two different dimensionality reduction techniques, namely, principal component analysis (PCA), a linear method, and Sammon mapping, which is nonlinear. The two methods are used to analyze four different protein transition pathways of varying complexity, obtained by using either the conjugate peak refinement method or constrained molecular dynamics. For the return-stroke in myosin, both Sammon mapping and PCA show that the conformational change is dominated by a simple rotation of a rigid body. Also, in the case of the T-->R transition in hemoglobin, both methods are able to identify the two main quaternary transition events. In contrast, in the cases of the unfolding transition of staphylococcal nuclease or the signaling switch of Ras p21, which are both more complex conformational transitions, only Sammon mapping is able to identify the distinct phases of motion.     

Construction,validation, and application of nocturnal pollen transport networks in an agro‐ecosystem: a comparison using light microscopy and DNA metabarcoding

1. Moths are globally relevant as pollinators but nocturnal pollination remains poorly understood. Plant–pollinator interaction networks are traditionally constructed using either flower‐visitor observations or pollen‐transport detection using microscopy. Recent studies have shown the potential of DNA metabarcoding for detecting and identifying pollen‐transport interactions. However, no study has directly compared the realised observations of pollen‐transport networks between DNA metabarcoding and conventional light microscopy. 2. Using matched samples of nocturnal moths, we constructed pollen‐transport networks using two methods: light microscopy and DNA metabarcoding. Focussing on the feeding mouthparts of moths, we developed and provide reproducible methods for merging DNA metabarcoding and ecological network analysis to better understand species interactions. 3. DNA metabarcoding detected pollen on more individual moths, and detected multiple pollen types on more individuals than microscopy, although the average number of pollen types per individual was unchanged. However, after aggregating individuals of each species, metabarcoding detected more interactions per moth species. Pollen‐transport network metrics differed between methods because of variation in the ability of each to detect multiple pollen types per moth and to separate morphologically similar or related pollen. We detected unexpected but plausible moth–plant interactions with metabarcoding, revealing new detail about nocturnal pollination systems. 4. The nocturnal pollination networks observed using metabarcoding and microscopy were similar yet distinct, with implications for network ecologists. Comparisons between networks constructed using metabarcoding and traditional methods should therefore be treated with caution. Nevertheless, the potential applications of metabarcoding for studying plant–pollinator interaction networks are encouraging, especially when investigating understudied pollinators such as moths.     

X-ray analysis of the kinetics of Escherichia coli lipid and membrane structural transitions

Synchrotron radiation was used to follow the time course of the transitions, induced by temperature jump, in Escherichia coli membranes and their lipid extracts isolated from a fatty acid auxotroph grown with different fatty acids. We measured the relaxation times associated with the phase transitions as well as with the conformational transition of the hydrocarbon chains and observed different behavior as a function of chemical composition. Relaxation times of about 1-2 s were found at a hexagonal to lamellar phase transition and within a lamellar phase whose parameters display important variations with temperature when the conformational transition takes place. On the other hand, no delay was observed for a phase transition where large lipid or water diffusion was not needed. We have shown that phase transitions and conformational transitions are, to a large extent, uncoupled and that the relaxation times corresponding to the latter transition could be related to the size of the ordered domains. In all cases, the order to disorder conformational transition is more rapid than the disorder to order transition. Finally, the relaxation times of the disorder to order transition observed with the membranes and with their lipid extracts were found to be strongly correlated, indicating that the proteins do not play a role in this transition.     

Landscape and kinetic path quantify critical transitions in epithelial-mesenchymal transition

Epithelial-mesenchymal transition (EMT), a basic developmental process that might promote cancer metastasis, has been studied from various perspectives. Recently, the early warning theory has been used to anticipate critical transitions in EMT from mathematical modeling. However, the underlying mechanisms of EMT involving complex molecular networks remain to be clarified. Especially, how to quantify the global stability and stochastic transition dynamics of EMT and what the underlying mechanism for early warning theory in EMT is remain to be fully clarified. To address these issues, we constructed a comprehensive gene regulatory network model for EMT and quantified the corresponding potential landscape. The landscape for EMT displays multiple stable attractors, which correspond to E, M, and some other intermediate states. Based on the path-integral approach, we identified the most probable transition paths of EMT, which are supported by experimental data. Correspondingly, the results of transition actions demonstrated that intermediate states can accelerate EMT, consistent with recent studies. By integrating the landscape and path with early warning concept, we identified the potential barrier height from the landscape as a global and more accurate measure for early warning signals to predict critical transitions in EMT. The landscape results also provide an intuitive and quantitative explanation for the early warning theory. Overall, the landscape and path results advance our mechanistic understanding of dynamical transitions and roles of intermediate states in EMT, and the potential barrier height provides a new, to our knowledge, measure for critical transitions and quantitative explanations for the early warning theory.     

Path Similarity Analysis: A Method for Quantifying Macromolecular Pathways

Diverse classes of proteins function through large-scale conformational changes and various sophisticated computational algorithms have been proposed to enhance sampling of these macromolecular transition paths. Because such paths are curves in a high-dimensional space, it has been difficult to quantitatively compare multiple paths, a necessary prerequisite to, for instance, assess the quality of different algorithms. We introduce a method named Path Similarity Analysis (PSA) that enables us to quantify the similarity between two arbitrary paths and extract the atomic-scale determinants responsible for their differences. PSA utilizes the full information available in 3N-dimensional configuration space trajectories by employing the Hausdorff or Fréchet metrics (adopted from computational geometry) to quantify the degree of similarity between piecewise-linear curves. It thus completely avoids relying on projections into low dimensional spaces, as used in traditional approaches. To elucidate the principles of PSA, we quantified the effect of path roughness induced by thermal fluctuations using a toy model system. Using, as an example, the closed-to-open transitions of the enzyme adenylate kinase (AdK) in its substrate-free form, we compared a range of protein transition path-generating algorithms. Molecular dynamics-based dynamic importance sampling (DIMS) MD and targeted MD (TMD) and the purely geometric FRODA (Framework Rigidity Optimized Dynamics Algorithm) were tested along with seven other methods publicly available on servers, including several based on the popular elastic network model (ENM). PSA with clustering revealed that paths produced by a given method are more similar to each other than to those from another method and, for instance, that the ENM-based methods produced relatively similar paths. PSA applied to ensembles of DIMS MD and FRODA trajectories of the conformational transition of diphtheria toxin, a particularly challenging example, showed that the geometry-based FRODA occasionally sampled the pathway space of force field-based DIMS MD. For the AdK transition, the new concept of a Hausdorff-pair map enabled us to extract the molecular structural determinants responsible for differences in pathways, namely a set of conserved salt bridges whose charge-charge interactions are fully modelled in DIMS MD but not in FRODA. PSA has the potential to enhance our understanding of transition path sampling methods, validate them, and to provide a new approach to analyzing conformational transitions.