Anomalous Dynamics in Macromolecular Liquids.

Macromolecular liquids display short-time anomalous behaviors in disagreement with conventional single-molecule mean-field theories. In this study, we analyze the behavior of the simplest but most realistic macromolecular system that displays anomalous dynamics, i.e., a melt of short homopolymer chains, starting from molecular dynamics simulation trajectories. Our study sheds some light on the microscopic molecular mechanisms responsible for the observed anomalous behavior. The relevance of the correlation hole, a unique property of polymer liquids, in relation to the observed subdiffusive dynamics, naturally emerges from the analysis of the van Hove distribution functions and other properties.

Dinucleotides as simple models of the base stacking-unstacking component of DNA 'breathing' mechanisms.

Regulatory protein access to the DNA duplex 'interior' depends on local DNA 'breathing' fluctuations, and the most fundamental of these are thermally-driven base stacking-unstacking interactions. The smallest DNA unit that can undergo such transitions is the dinucleotide, whose structural and dynamic properties are dominated by stacking, while the ion condensation, cooperative stacking and inter-base hydrogen-bonding present in duplex DNA are not involved. We use dApdA to study stacking-unstacking at the dinucleotide level because the fluctuations observed are likely to resemble those of larger DNA molecules, but in the absence of constraints introduced by cooperativity are likely to be more pronounced, and thus more accessible to measurement. We study these fluctuations with a combination of Molecular Dynamics simulations on the microsecond timescale and Markov State Model analyses, and validate our results by calculations of circular dichroism (CD) spectra, with results that agree well with the experimental spectra. Our analyses show that the CD spectrum of dApdA is defined by two distinct chiral conformations that correspond, respectively, to a Watson-Crick form and a hybrid form with one base in a Hoogsteen configuration. We find also that ionic structure and water orientation around dApdA play important roles in controlling its breathing fluctuations.

Kinetics analysis of ubiquitin local fluctuations with Markov state modeling of the LE4PD normal modes.

Local fluctuations are important for protein binding and molecular recognition because they provide conformational states that can be trapped through a selection mechanism of binding. Thus, an accurate characterization of local fluctuations may be important for modeling the kinetic mechanism that leads to the biological activity of a protein. In this paper, we study the fluctuation dynamics of the regulatory protein ubiquitin and propose a novel theoretical approach to model its fluctuations. A coarse-grained, diffusive, mode-dependent description of fluctuations is accomplished using the Langevin Equation for Protein Dynamics (LE4PD). This equation decomposes the dynamics of a protein, simulated by molecular dynamics, into dynamical pathways that explore mode-dependent free energy surfaces. We calculate the time scales of the slow, high-amplitude fluctuations by modeling the kinetics of barrier crossing in the two-dimensional free energy surfaces using Markov state modeling. We find that the LE4PD predicts slow fluctuations in three important binding regions in ubiquitin: the C-terminal tail, the Lys11 loop, and the 50 s loop. These results suggest that the LE4PD can provide useful information on the role of fluctuations in the process of molecular recognition regulating the biological activity of ubiquitin.

Coarse-graining simulation approaches for polymer melts: the effect of potential range on computational efficiency.

The integral equation coarse-graining (IECG) approach is a promising high-level coarse-graining (CG) method for polymer melts, with variable resolution from soft spheres to multi CG sites, which preserves the structural and thermodynamical consistencies with the related atomistic simulations. When compared to the atomistic description, the procedure of coarse-graining results in smoother free energy surfaces, longer-ranged potentials, a decrease in the number of interaction sites for a given polymer, and more. Because these changes have competing effects on the computational efficiency of the CG model, care needs to be taken when studying the effect of coarse-graining on the computational speed-up in CG molecular dynamics simulations. For instance, treatment of long-range CG interactions requires the selection of cutoff distances that include the attractive part of the effective CG potential and force. In particular, we show how the complex nature of the range and curvature of the effective CG potential, the selection of a suitable CG timestep, the choice of the cutoff distance, the molecular dynamics algorithms, and the smoothness of the CG free energy surface affect the efficiency of IECG simulations. By direct comparison with the atomistic simulations of relatively short chain polymer melts, we find that the overall computational efficiency is highest for the highest level of CG (soft spheres), with an overall improvement of the computational efficiency being about 106-108 for various CG levels/resolutions. Therefore, the IECG method can have important applications in molecular dynamics simulations of polymeric systems. Finally, making use of the standard spatial decomposition algorithm, the parallel scalability of the IECG simulations for various levels of CG is presented. Optimal parallel scaling is observed for a reasonably large number of processors. Although this study is performed using the IECG approach, its results on the relation between the level of CG and the computational efficiency are general and apply to any properly-constructed CG model.

On the Density Dependence of the Integral Equation Coarse-Graining Effective Potential.

Coarse-graining (CG) procedures provide computationally efficient methods for investigating the corresponding long time- and length-scale processes. In the bottom-up approaches, the effective interactions between the CG sites are obtained using the information from the atomistic simulations, but reliable CG procedures are required to preserve the structure and thermodynamics. In this regard, the integral equation coarse-graining (IECG) method is a promising approach that uses the first-principles Ornstein-Zernike equation in liquid state theory to determine the effective potential between CG sites. In this work, we present the details of the IECG method while treating the density as an intrinsic property and active variable of the CG system. Performing extensive simulations of polymer melts, we show that the IECG theory/simulation and atomistic simulation results are consistent in structural properties such as the pair-correlation functions and form factors, and also thermodynamic properties such as pressure. The atomistic simulations of the liquids show that the structure is largely sensitive to the repulsive part of the potential. Similarly, the IECG simulations of polymeric liquids show that the structure can be determined by the relatively short-range CG repulsive interactions, but the pressure is only accurately determined once the long-range, weak CG attractive interactions are included. This is in agreement with the seminal work by Widom on the influence of the potential on the phase diagram of the liquid [Widom, B. Science 1967 , 157 , 375 - 382 ]. Other aspects of the IECG theory/simulations are also discussed.

Pseudouridine Modification Inhibits Muscleblind-like 1 (MBNL1) Binding to CCUG Repeats and Minimally Structured RNA through Reduced RNA Flexibility.

Myotonic dystrophy type 2 is a genetic neuromuscular disease caused by the expression of expanded CCUG repeat RNAs from the non-coding region of the CCHC-type zinc finger nucleic acid-binding protein (CNBP) gene. These CCUG repeats bind and sequester a family of RNA-binding proteins known as Muscleblind-like 1, 2, and 3 (MBNL1, MBNL2, and MBNL3), and sequestration plays a significant role in pathogenicity. MBNL proteins are alternative splicing regulators that bind to the consensus RNA sequence YGCY (Y = pyrimidine). This consensus sequence is found in the toxic RNAs (CCUG repeats) and in cellular RNA substrates that MBNL proteins have been shown to bind. Replacing the uridine in CCUG repeats with pseudouridine (Ψ) resulted in a modest reduction of MBNL1 binding. Interestingly, Ψ modification of a minimally structured RNA containing YGCY motifs resulted in more robust inhibition of MBNL1 binding. The different levels of inhibition between CCUG repeat and minimally structured RNA binding appear to be due to the ability to modify both pyrimidines in the YGCY motif, which is not possible in the CCUG repeats. Molecular dynamic studies of unmodified and pseudouridylated minimally structured RNAs suggest that reducing the flexibility of the minimally structured RNA leads to reduced binding by MBNL1.

Modifications to toxic CUG RNAs induce structural stability, rescue mis-splicing in a myotonic dystrophy cell model and reduce toxicity in a myotonic dystrophy zebrafish model.

CUG repeat expansions in the 3' UTR of dystrophia myotonica protein kinase (DMPK) cause myotonic dystrophy type 1 (DM1). As RNA, these repeats elicit toxicity by sequestering splicing proteins, such as MBNL1, into protein-RNA aggregates. Structural studies demonstrate that CUG repeats can form A-form helices, suggesting that repeat secondary structure could be important in pathogenicity. To evaluate this hypothesis, we utilized structure-stabilizing RNA modifications pseudouridine (Ψ) and 2'-O-methylation to determine if stabilization of CUG helical conformations affected toxicity. CUG repeats modified with Ψ or 2'-O-methyl groups exhibited enhanced structural stability and reduced affinity for MBNL1. Molecular dynamics and X-ray crystallography suggest a potential water-bridging mechanism for Ψ-mediated CUG repeat stabilization. Ψ modification of CUG repeats rescued mis-splicing in a DM1 cell model and prevented CUG repeat toxicity in zebrafish embryos. This study indicates that the structure of toxic RNAs has a significant role in controlling the onset of neuromuscular diseases.

A theory of protein dynamics to predict NMR relaxation.

We present a theoretical, site-specific, approach to predict protein subunit correlation times, as measured by NMR experiments of (1)H-(15)N nuclear Overhauser effect, spin-lattice relaxation, and spin-spin relaxation. Molecular dynamics simulations are input to our equation of motion for protein dynamics, which is solved analytically to produce the eigenvalues and the eigenvectors that specify the NMR parameters. We directly compare our theoretical predictions to experiments and to simulation data for the signal transduction chemotaxis protein Y (CheY), which regulates the swimming response of motile bacteria. Our theoretical results are in good agreement with both simulations and experiments, without recourse to adjustable parameters. The theory is general, since it allows calculations of any dynamical property of interest. As an example, we present theoretical calculations of NMR order parameters and x-ray Debye-Waller temperature factors; both quantities show good agreement with experimental data.

Translational diffusion of fluorescent proteins by molecular fourier imaging correlation spectroscopy.

The ability to noninvasively observe translational diffusion of proteins and protein complexes is important to many biophysical problems. We report high signal/noise (>or=250) measurements of the translational diffusion in viscous solution of the fluorescent protein, DsRed. This is carried out using a new technique: molecular Fourier imaging correlation spectroscopy (M-FICS). M-FICS is an interferometric method that detects a collective Fourier component of the fluctuating density of a small population of fluorescent molecules, and provides information about the distribution of molecular diffusivities. A theoretical analysis is presented that expresses the detected signal fluctuations in terms of the relevant time-correlation functions for molecular translational diffusion. Furthermore, the role played by optical orientational degrees of freedom is established. We report Fickian self-diffusion of the DsRed tetramer at short timescales. The long-time deviation of our data from Fickian behavior is used to determine the variance of the distribution of the protein self-diffusion coefficient. We compare our results to the expected outcomes for 1), a bi-disperse distribution of protein species, and 2), dynamic disorder of the host solvent.

Cytoskeletal-assisted dynamics of the mitochondrial reticulum in living cells.

Subcellular organelle dynamics are strongly influenced by interactions with cytoskeletal filaments and their associated motor proteins, and lead to complex multiexponential relaxations that occur over a wide range of spatial and temporal scales. Here we report spatio-temporal measurements of the fluctuations of the mitochondrial reticulum in osteosarcoma cells by using Fourier imaging correlation spectroscopy, over time and distance scales of 10(-2) to 10(3) s and 0.5-2.5 microm. We show that the method allows a more complete description of mitochondrial dynamics, through the time- and length-scale-dependent collective diffusion coefficient D(k,tau), than available by other means. Addition of either nocodazole to disrupt microtubules or cytochalasin D to disassemble microfilaments simplifies the intermediate scattering function. When both drugs are used, the reticulum morphology of mitochondria is retained even though the cytoskeletal elements have been de-polymerized. The dynamics of the organelle are then primarily diffusive and can be modeled as a collection of friction points interconnected by elastic springs. This study quantitatively characterizes organelle dynamics in terms of collective cytoskeletal interactions in living cells.