A class of exact solutions for biomacromolecule diffusion-reaction in live cells

A class of novel explicit analytic solutions for a system of n+1 coupled partial differential equations governing biomolecular mass transfer and reaction in living organisms are proposed, evaluated, and analyzed. The solution process uses Laplace and Hankel transforms and results in a recursive convolution of an exponentially scaled Gaussian with modified Bessel functions. The solution is developed for wide range of biomolecular binding kinetics from pure diffusion to multiple binding reactions. The proposed approach provides solutions for both Dirac and Gaussian laser beam (or fluorescence-labeled biomacromolecule) profiles during the course of a Fluorescence Recovery After Photobleaching (FRAP) experiment. We demonstrate that previous models are simplified forms of our theory for special cases. Model analysis indicates that at the early stages of the transport process, biomolecular dynamics is governed by pure diffusion. At large times, the dominant mass transfer process is effective diffusion. Analysis of the sensitivity equations, derived analytically and verified by finite difference differentiation, indicates that experimental biologists should use full space-time profile (instead of the averaged time series) obtained at the early stages of the fluorescence microscopy experiments to extract meaningful physiological information from the protocol. Such a small time frame requires improved bioinstrumentation relative to that in use today. Our mathematical analysis highlights several limitations of the FRAP protocol and provides strategies to improve it. The proposed model can be used to study biomolecular dynamics in molecular biology, targeted drug delivery in normal and cancerous tissues, motor-driven axonal transport in normal and abnormal nervous systems, kinetics of diffusion-controlled reactions between enzyme and substrate, and to validate numerical simulators of biological mass transport processes in vivo.     

Perspectives on the landscape and flux theory for describing emergent behaviors of the biological systems

We give a review on the landscape theory of the equilibrium biological systems and landscape-flux theory of the nonequilibrium biological systems as the global driving force. The emergences of the behaviors, the associated thermodynamics in terms of the entropy and free energy and dynamics in terms of the rate and paths have been quantitatively demonstrated. The hierarchical organization structures have been discussed. The biological applications ranging from protein folding, biomolecular recognition, specificity, biomolecular evolution and design for equilibrium systems as well as cell cycle, differentiation and development, cancer, neural networks and brain function, and evolution for nonequilibrium systems, cross-scale studies of genome structural dynamics and experimental quantifications/verifications of the landscape and flux are illustrated. Together, this gives an overall global physical and quantitative picture in terms of the landscape and flux for the behaviors, dynamics and functions of biological systems.

     

The role of dynamics in allosteric regulation

The biomolecular conformational changes often associated with allostery are, by definition, dynamic processes. Recent publications have disclosed the role of pre-existing equilibria of conformational substates in this process. In addition, the role of dynamics as an entropic carrier of free energy of allostery has been investigated. Recent work thus shows that dynamics is pivotal to allostery, and that it constitutes much more than just the move from the 'T'-state to the 'R'-state. Emerging computational studies have described the actual pathways of allosteric change.     

Endothelial and cancer cells interact with mesenchymal stem cells via both microparticles and secreted factors

Tightly associated with blood vessels in their perivascular niche, human mesenchymal stem cells (MSCs) closely interact with endothelial cells (ECs). MSCs also home to tumours and interact with cancer cells (CCs). Microparticles (MPs) are cell‐derived vesicles released into the extracellular environment along with secreted factors. MPs are capable of intercellular signalling and, as biomolecular shuttles, transfer proteins and RNA from one cell to another. Here, we characterize interactions among ECs, CCs and MSCs via MPs and secreted factors in vitro. MPs and non‐MP secreted factors (Sup) were isolated from serum‐free medium conditioned by human microvascular ECs (HMEC‐1) or by the CC line HT1080. Fluorescently labelled MPs were prepared from cells treated with membrane dyes, and cytosolic GFP‐containing MPs were isolated from cells transduced with CMV‐GFP lentivirus. MSCs were treated with MPs, Sup, or vehicle controls, and analysed for MP uptake, proliferation, migration, activation of intracellular signalling pathways and cytokine release. Fluorescently labelled MPs fused with MSCs, transferring the fluorescent dyes to the MSC surface. GFP was transferred to and retained in MSCs incubated with GFP‐MPs, but not free GFP. Thus, only MP‐associated cellular proteins were taken up and retained by MSCs, suggesting that MP biomolecules, but not secreted factors, are shuttled to MSCs. MP and Sup treatment significantly increased MSC proliferation, migration, and MMP‐1, MMP‐3, CCL‐2/MCP‐1 and IL‐6 secretion compared with vehicle controls. MSCs treated with Sup and MPs also exhibited activated NF‐κB signalling. Taken together, these results suggest that MPs act to regulate MSC functions through several mechanisms.     

Protocol for MM/PBSA molecular dynamics simulations of proteins

Continuum solvent models have been employed in past years for understanding processes such as protein folding or biomolecular association. In the last decade, several attempts have been made to merge atomic detail molecular dynamics simulations with solvent continuum models. Among continuum models, the Poisson-Boltzmann solvent accessible surface area model is one of the oldest and most fundamental. Notwithstanding its wide usage for simulation of biomolecular electrostatic potential, the Poisson-Boltzmann equation has been very seldom used to obtain solvation forces for molecular dynamics simulation. We propose here a fast and reliable methodology to implement continuum forces in standard molecular mechanics and dynamics algorithms. Results for a totally unrestrained 1 ns molecular dynamics simulation of a small protein are quantitatively similar to results obtained by explicit solvent molecular dynamics simulations.     

An introduction to biomolecular simulations and docking

The biomolecules in and around a living cell – proteins, nucleic acids, lipids and carbohydrates – continuously sample myriad conformational states that are thermally accessible at physiological temperatures. Simultaneously, a given biomolecule also samples (and is sampled by) a rapidly fluctuating local environment comprising other biopolymers, small molecules, water, ions, etc. that diffuse to within a few nanometres, leading to inter-molecular contacts that stitch together large supramolecular assemblies. Indeed, all biological systems can be viewed as dynamic networks of molecular interactions. As a complement to experimentation, molecular simulation offers a uniquely powerful approach to analyse biomolecular structure, mechanism and dynamics; this is possible because the molecular contacts that define a complicated biomolecular system are governed by the same physical principles (forces and energetics) that characterise individual small molecules, and these simpler systems are relatively well-understood. With modern algorithms and computing capabilities, simulations are now an indispensable tool for examining biomolecular assemblies in atomic detail, from the conformational motion in an individual protein to the diffusional dynamics and inter-molecular collisions in the early stages of formation of cellular-scale assemblies such as the ribosome. This text introduces the physicochemical foundations of molecular simulations and docking, largely from the perspective of biomolecular interactions.     

NMR methods for characterizing microsecond to millisecond dynamics in recognition and catalysis

During the past two years, significant advances have been made in the development of NMR methods for studying biomolecular dynamics on the microsecond to millisecond timescale. Applications of these methods to biologically relevant systems have provided compelling evidence that, in many cases, conformational dynamics on these timescales govern the rates of biomolecular recognition and catalysis.     

Characterization of a new maleimido functionalization of gold for surface plasmon resonance spectroscopy

Para‐maleimidophenyl (p‐MP) modified gold surfaces have been prepared by one‐step electrochemical deposition and used in surface plasmon resonance (SPR) studies. Therefore, a FITC mimotope peptide (MP1, 12 aa), a human mucin 1 epitope peptide (MUC, 9 aa) and a protein with their specific antibodies were used as model systems. The peptides were modified with an N‐terminal cysteine for covalent and directed coupling to the maleimido functionalized surface by means of Michael addition. The coupling yield of the peptide, the binding characteristics of antibody and the unspecific adsorption of the analytes were investigated. The results expand the spectrum of biosensors usable with p‐MP by widely used SPR and support its potential to be versatile for several electrochemical and optical biosensors. This allows the combination of an electrochemical and optical read‐out for a broad variety of biomolecular interactions on the same chip. Copyright © 2014 John Wiley & Sons, Ltd.     

Heme-peptide/protein ions and phosphorous ligands: search for site-specific addition reactions

High-resolution Fourier transform ion cyclotron resonance mass spectrometry is employed to gain thorough kinetics and thermodynamics information on the reaction of free and ligated heme-type ions with selected ligands, with the aim of obtaining an insight into the coordination environment of the prosthetic group in a variety of biomolecular ions. Adopting a stepwise approach towards systems of increasing complexity, we examined the reactivity of free gaseous iron(III) protoporphyrin IX ions, Fe(III)-heme(+), of the charged species from microperoxidase-11 (MP11) (covalently peptide bound heme), and of the multiply charged ions from heme proteins, namely, cytochrome c (cyt c) and myoglobin (examples of noncovalently protein bound hemes). Among an array of test compounds allowed to react with Fe(III)-heme(+), OP(OMe)(3) and P(OMe)(3) proved to be similarly efficient ligands in the first addition step, yet displayed markedly distinct reactivity towards heme iron already engaged in axial coordination. The ease with which P(OMe)(3) acts as a second axial ligand is exploited to probe structural and conformational features of biomolecular ions. In this way, circumstantial evidence is gained of a folded conformation of +2 charge state ions from MP11 and an elongated one for the +3 charge state ions. Similarly, both the general reaction pattern and detailed kinetics and thermodynamics data point to a regiospecific addition reaction of P(OMe)(3) directed at the heme iron within multiply charged ions from cyt c. This unprecedented example of ion-molecule reaction which specifically involves a prosthetic group belonging to protein ions stands in contrast to the multiple, nonspecific interactions established by OP(OMe)(3) molecules with the protonated sites of multiply charged cyt c and apomyoglobin ions. This finding may develop and provide sensitive probes of the structure and bonding features of protein ions in the gas phase.     

Elastic network models for understanding biomolecular machinery: from enzymes to supramolecular assemblies

With advances in structure genomics, it is now recognized that knowledge of structure alone is insufficient to understand and control the mechanisms of biomolecular function. Additional information in the form of dynamics is needed. As demonstrated in a large number of studies, the machinery of proteins and their complexes can be understood to a good approximation by adopting Gaussian (or elastic) network models (GNM) for simplified normal mode analyses. While this approximation lacks chemical details, it provides us with a means for assessing the collective motions of large structures/assemblies and perform a comparative analysis of a series of proteins, thus providing insights into the mechanical aspects of biomolecular dynamics. In this paper, we discuss recent applications of GNM to a series of enzymes as well as large structures such as the HK97 bacteriophage viral capsids. Understanding the dynamics of large protein structures can be computationally challenging. To this end, we introduce a new approach for building a hierarchical, reduced rank representation of the protein topology and consequently the fluctuation dynamics.     

Unconstrained enhanced sampling for free energy calculations of biomolecules: a review

Abstract

Free energy calculations are central to understanding the structure, dynamics and function of biomolecules. Yet insufficient sampling of biomolecular configurations is often regarded as one of the main sources of error. Many enhanced sampling techniques have been developed to address this issue. Notably, enhanced sampling methods based on biasing collective variables (CVs), including the widely used umbrella sampling, adaptive biasing force and metadynamics, have been discussed in a recent excellent review (Abrams and Bussi, Entropy, 2014). Here, we aim to review enhanced sampling methods that do not require predefined system-dependent CVs for biomolecular simulations and as such do not suffer from the hidden energy barrier problem as encountered in the CV-biasing methods. These methods include, but are not limited to, replica exchange/parallel tempering, self-guided molecular/Langevin dynamics, essential energy space random walk and accelerated molecular dynamics. While it is overwhelming to describe all details of each method, we provide a summary of the methods along with the applications and offer our perspectives. We conclude with challenges and prospects of the unconstrained enhanced sampling methods for accurate biomolecular free energy calculations.     

NbIT - A New Information Theory-Based Analysis of Allosteric Mechanisms Reveals Residues that Underlie Function in the Leucine Transporter LeuT

Complex networks of interacting residues and microdomains in the structures of biomolecular systems underlie the reliable propagation of information from an input signal, such as the concentration of a ligand, to sites that generate the appropriate output signal, such as enzymatic activity. This information transduction often carries the signal across relatively large distances at the molecular scale in a form of allostery that is essential for the physiological functions performed by biomolecules. While allosteric behaviors have been documented from experiments and computation, the mechanism of this form of allostery proved difficult to identify at the molecular level. Here, we introduce a novel analysis framework, called N-body Information Theory (NbIT) analysis, which is based on information theory and uses measures of configurational entropy in a biomolecular system to identify microdomains and individual residues that act as (i)-channels for long-distance information sharing between functional sites, and (ii)-coordinators that organize dynamics within functional sites. Application of the new method to molecular dynamics (MD) trajectories of the occluded state of the bacterial leucine transporter LeuT identifies a channel of allosteric coupling between the functionally important intracellular gate and the substrate binding sites known to modulate it. NbIT analysis is shown also to differentiate residues involved primarily in stabilizing the functional sites, from those that contribute to allosteric couplings between sites. NbIT analysis of MD data thus reveals rigorous mechanistic elements of allostery underlying the dynamics of biomolecular systems.     

High performance computing in biology: multimillion atom simulations of nanoscale systems

Computational methods have been used in biology for sequence analysis (bioinformatics), all-atom simulation (molecular dynamics and quantum calculations), and more recently for modeling biological networks (systems biology). Of these three techniques, all-atom simulation is currently the most computationally demanding, in terms of compute load, communication speed, and memory load. Breakthroughs in electrostatic force calculation and dynamic load balancing have enabled molecular dynamics simulations of large biomolecular complexes. Here, we report simulation results for the ribosome, using approximately 2.64 million atoms, the largest all-atom biomolecular simulation published to date. Several other nano-scale systems with different numbers of atoms were studied to measure the performance of the NAMD molecular dynamics simulation program on the Los Alamos National Laboratory Q Machine. We demonstrate that multimillion atom systems represent a 'sweet spot' for the NAMD code on large supercomputers. NAMD displays an unprecedented 85% parallel scaling efficiency for the ribosome system on 1024 CPUs. We also review recent targeted molecular dynamics simulations of the ribosome that prove useful for studying conformational changes of this large biomolecular complex in atomic detail.     

Microplastics alter composition of fungal communities in aquatic ecosystems

Despite increasing concerns about microplastic (MP) pollution in aquatic ecosystems, there is insufficient knowledge on how MP affect fungal communities. In this study, we explored the diversity and community composition of fungi attached to polyethylene (PE) and polystyrene (PS) particles incubated in different aquatic systems in north‐east Germany: the Baltic Sea, the River Warnow and a wastewater treatment plant. Based on next generation 18S rRNA gene sequencing, 347 different operational taxonomic units assigned to 81 fungal taxa were identified on PE and PS. The MP‐associated communities were distinct from fungal communities in the surrounding water and on the natural substrate wood. They also differed significantly among sampling locations, pointing towards a substrate and location specific fungal colonization. Members of Chytridiomycota, Cryptomycota and Ascomycota dominated the fungal assemblages, suggesting that both parasitic and saprophytic fungi thrive in MP biofilms. Thus, considering the worldwide increasing accumulation of plastic particles as well as the substantial vector potential of MP, especially these fungal taxa might benefit from MP pollution in the aquatic environment with yet unknown impacts on their worldwide distribution, as well as biodiversity and food web dynamics at large.     

Probing conformational dynamics in biomolecules via chemical exchange saturation transfer: a primer

Although Chemical Exchange Saturation Transfer (CEST) type NMR experiments have been used to study chemical exchange processes in molecules since the early 1960s, there has been renewed interest in the past several years in using this approach to study biomolecular conformational dynamics. The methodology is particularly powerful for the study of sparsely populated, transiently formed conformers that are recalcitrant to investigation using traditional biophysical tools, and it is complementary to relaxation dispersion and magnetization transfer experiments that have traditionally been used to study chemical exchange processes. Here we discuss the concepts behind the CEST experiment, focusing on practical aspects as well, we review some of the pulse sequences that have been developed to characterize protein and RNA conformational dynamics, and we discuss a number of examples where the CEST methodology has provided important insights into the role of dynamics in biomolecular function.     

Applications of the molecular dynamics flexible fitting method

In recent years, cryo-electron microscopy (cryo-EM) has established itself as a key method in structural biology, permitting the structural characterization of large biomolecular complexes in various functional states. The data obtained through single-particle cryo-EM has recently seen a leap in resolution thanks to landmark advances in experimental and computational techniques, resulting in sub-nanometer resolution structures being obtained routinely. The remaining gap between these data and revealing the mechanisms of molecular function can be closed through hybrid modeling tools that incorporate known atomic structures into the cryo-EM data. One such tool, molecular dynamics flexible fitting (MDFF), uses molecular dynamics simulations to combine structures from X-ray crystallography with cryo-EM density maps to derive atomic models of large biomolecular complexes. The structures furnished by MDFF can be used subsequently in computational investigations aimed at revealing the dynamics of the complexes under study. In the present work, recent applications of MDFF are presented, including the interpretation of cryo-EM data of the ribosome at different stages of translation and the structure of a membrane-curvature-inducing photosynthetic complex.     

Molecular interactions between a plant virus movement protein and RNA: force spectroscopy investigation

RNA-protein interactions are fundamental for different aspects of molecular biology such as gene expression, assembly of biomolecular complexes or macromolecular transport. The 3a movement protein (MP) of a plant virus, Cucumber mosaic virus (CMV), forms ribonucleoprotein (RNP) complexes with viral RNA, capable of trafficking from cell-to-cell throughout the infected plant only in the presence of the CMV capsid protein (CP). However, deletion of the C-terminal 33 amino acid residues of the CMV MP (in the mutant designated 3aDeltaC33 MP) resulted in CP-independent cell-to-cell movement. The biological differences in the behaviour of CMV wild type (wt) 3a MP and 3aDeltaC33 MP could have been a consequence of differences in the RNA-binding properties of the two MPs detected previously using biochemical assays on ensembles of molecules. To investigate the physical mechanisms of MP-RNA interactions at a single molecule level, we applied atomic force microscopy to measure for the first time unbinding forces between these individual binding partners. Minimal unbinding forces determined for individual interaction of the CMV RNA molecule with the CMV wt or truncated MPs were estimated to be approximately 45 pN and approximately 90 pN, respectively, suggesting that the distinct differences in the strength of MP-RNA interactions for the wt MP and truncated MP are attributable to the molecular binding mechanism. We also demonstrated that molecules of both CMV 3a MP and 3aDeltaC33 MP were capable of self-interaction with minimal unbinding forces of approximately 50 pN and approximately 70 pN, respectively, providing a physical basis for the cooperative mechanism of the RNA binding. The significance of intermolecular force measurements for understanding the structural and functional aspects of viral RNP formation and trafficking is discussed.     

Nonlinear dynamics of the distributed biochemical systems functioning in the dissipative structure formation mode

Nonlinear dynamical biomolecular systems can evidently be considered as prototypes of information processing devices at molecular level capable to solve problems of high computational complexity. Keeping in mind this goal the dynamics of biochemical system based on enzymatic oxidation of uric acid was considered. The system was studied in the version of distributed biomolecular structure having predetermined geometry of enzyme distribution on a porous planar medium. Being in the regime of stepwise dissipative structure formation this system demonstrated complicated modes of behaviour.     

Multiple statistical analysis techniques corroborate intratumor heterogeneity in imaging mass spectrometry datasets of myxofibrosarcoma

MALDI mass spectrometry can generate profiles that contain hundreds of biomolecular ions directly from tissue. Spatially-correlated analysis, MALDI imaging MS, can simultaneously reveal how each of these biomolecular ions varies in clinical tissue samples. The use of statistical data analysis tools to identify regions containing correlated mass spectrometry profiles is referred to as imaging MS-based molecular histology because of its ability to annotate tissues solely on the basis of the imaging MS data. Several reports have indicated that imaging MS-based molecular histology may be able to complement established histological and histochemical techniques by distinguishing between pathologies with overlapping/identical morphologies and revealing biomolecular intratumor heterogeneity. A data analysis pipeline that identifies regions of imaging MS datasets with correlated mass spectrometry profiles could lead to the development of novel methods for improved diagnosis (differentiating subgroups within distinct histological groups) and annotating the spatio-chemical makeup of tumors. Here it is demonstrated that highlighting the regions within imaging MS datasets whose mass spectrometry profiles were found to be correlated by five independent multivariate methods provides a consistently accurate summary of the spatio-chemical heterogeneity. The corroboration provided by using multiple multivariate methods, efficiently applied in an automated routine, provides assurance that the identified regions are indeed characterized by distinct mass spectrometry profiles, a crucial requirement for its development as a complementary histological tool. When simultaneously applied to imaging MS datasets from multiple patient samples of intermediate-grade myxofibrosarcoma, a heterogeneous soft tissue sarcoma, nodules with mass spectrometry profiles found to be distinct by five different multivariate methods were detected within morphologically identical regions of all patient tissue samples. To aid the further development of imaging MS based molecular histology as a complementary histological tool the Matlab code of the agreement analysis, instructions and a reduced dataset are included as supporting information.