Practical computational toolkits for dendrimers and dendrons structure design

Dendrimers and dendrons offer an excellent platform for developing novel drug delivery systems and medicines. The rational design and further development of these repetitively branched systems are restricted by difficulties in scalable synthesis and structural determination, which can be overcome by judicious use of molecular modelling and molecular simulations. A major difficulty to utilise in silico studies to design dendrimers lies in the laborious generation of their structures. Current modelling tools utilise automated assembly of simpler dendrimers or the inefficient manual assembly of monomer precursors to generate more complicated dendrimer structures. Herein we describe two novel graphical user interface (GUI) toolkits written in Python that provide an improved degree of automation for rapid assembly of dendrimers and generation of their 2D and 3D structures. Our first toolkit uses the RDkit library, SMILES nomenclature of monomers and SMARTS reaction nomenclature to generate SMILES and mol files of dendrimers without 3D coordinates. These files are used for simple graphical representations and storing their structures in databases. The second toolkit assembles complex topology dendrimers from monomers to construct 3D dendrimer structures to be used as starting points for simulation using existing and widely available software and force fields. Both tools were validated for ease-of-use to prototype dendrimer structure and the second toolkit was especially relevant for dendrimers of high complexity and size.Peer reviewe

The Dynamics of Ca2+ Ions within the Solvation Shell of Calbindin D9k

The encounter of a Ca2+ ion with a protein and its subsequent binding to specific binding sites is an intricate process that cannot be fully elucidated from experimental observations. We have applied Molecular Dynamics to study this process with atomistic details, using Calbindin D9k (CaB) as a model protein. The simulations show that in most of the time the Ca2+ ion spends within the Debye radius of CaB, it is being detained at the 1st and 2nd solvation shells. While being detained near the protein, the diffusion coefficient of the ion is significantly reduced. However, due to the relatively long period of detainment, the ion can scan an appreciable surface of the protein. The enhanced propagation of the ion on the surface has a functional role: significantly increasing the ability of the ion to scan the protein's surface before being dispersed to the bulk. The contribution of this mechanism to Ca2+ binding becomes significant at low ion concentrations, where the intervals between successive encounters with the protein are getting longer. The efficiency of the surface diffusion is affected by the distribution of charges on the protein's surface. Comparison of the Ca2+ binding dynamics in CaB and its E60D mutant reveals that in the wild type (WT) protein the carboxylate of E60 function as a preferred landing-site for the Ca2+ arriving from the bulk, followed by delivering it to the final binding site. Replacement of the glutamate by aspartate significantly reduced the ability to transfer Ca2+ ions from D60 to the final binding site, explaining the observed decrement in the affinity of the mutated protein to Ca2+

On a smoothed penalty-based algorithm for global optimization

This paper presents a coercive smoothed penalty framework for nonsmooth and nonconvex constrained global optimization problems. The properties of the smoothed penalty function are derived. Convergence to an ε -global minimizer is proved. At each iteration k, the framework requires the ε(k) -global minimizer of a subproblem, where ε(k)→ε . We show that the subproblem may be solved by well-known stochastic metaheuristics, as well as by the artificial fish swarm (AFS) algorithm. In the limit, the AFS algorithm convergence to an ε(k) -global minimum of the real-valued smoothed penalty function is guaranteed with probability one, using the limiting behavior of Markov chains. In this context, we show that the transition probability of the Markov chain produced by the AFS algorithm, when generating a population where the best fitness is in the ε(k)-neighborhood of the global minimum, is one when this property holds in the current population, and is strictly bounded from zero when the property does not hold. Preliminary numerical experiments show that the presented penalty algorithm based on the coercive smoothed penalty gives very competitive results when compared with other penalty-based methods.The authors would like to thank two anonymous referees for their valuable comments and suggestions to improve the paper. This work has been supported by COMPETE: POCI-01-0145-FEDER-007043 and FCT - Fundac¸ao para a Ci ˜ encia e Tecnologia within the projects UID/CEC/00319/2013 and ˆ UID/MAT/00013/2013.info:eu-repo/semantics/publishedVersio

Theoretical and practical convergence of a self-adaptive penalty algorithm for constrained global optimization

This paper proposes a self-adaptive penalty function and presents a penalty-based algorithm for solving nonsmooth and nonconvex constrained optimization problems. We prove that the general constrained optimization problem is equivalent to a bound constrained problem in the sense that they have the same global solutions. The global minimizer of the penalty function subject to a set of bound constraints may be obtained by a population-based meta-heuristic. Further, a hybrid self-adaptive penalty firefly algorithm, with a local intensification search, is designed, and its convergence analysis is established. The numerical experiments and a comparison with other penalty-based approaches show the effectiveness of the new self-adaptive penalty algorithm in solving constrained global optimization problems.The authors would like to thank the referees, the Associate Editor and the Editor-in-Chief for their valuable comments and suggestions to improve the paper. This work has been supported by COMPETE: POCI-01-0145-FEDER-007043 and FCT - Funda¸c˜ao para a Ciˆencia e Tecnologia within the projects UID/CEC/00319/2013 and UID/MAT/00013/2013.info:eu-repo/semantics/publishedVersio

Structure and Behavior of Human α-Thrombin upon Ligand Recognition: Thermodynamic and Molecular Dynamics Studies

Thrombin is a serine proteinase that plays a fundamental role in coagulation. In this study, we address the effects of ligand site recognition by alpha-thrombin on conformation and energetics in solution. Active site occupation induces large changes in secondary structure content in thrombin as shown by circular dichroism. Thrombin-D-Phe-Pro-Arg-chloromethyl ketone (PPACK) exhibits enhanced equilibrium and kinetic stability compared to free thrombin, whose difference is rooted in the unfolding step. Small-angle X-ray scattering (SAXS) measurements in solution reveal an overall similarity in the molecular envelope of thrombin and thrombin-PPACK, which differs from the crystal structure of thrombin. Molecular dynamics simulations performed with thrombin lead to different conformations than the one observed in the crystal structure. These data shed light on the diversity of thrombin conformers not previously observed in crystal structures with distinguished catalytic and conformational behaviors, which might have direct implications on novel strategies to design direct thrombin inhibitors

Construction and in vivo assembly of a catalytically proficient and hyperthermostable de novo enzyme

Although catalytic mechanisms in natural enzymes are well understood, achieving the diverse palette of reaction chemistries in re-engineered native proteins has proved challenging. Wholesale modification of natural enzymes is potentially compromised by their intrinsic complexity, which often obscures the underlying principles governing biocatalytic efficiency. The maquette approach can circumvent this complexity by combining a robust de novo designed chassis with a design process that avoids atomistic mimicry of natural proteins. Here, we apply this method to the construction of a highly efficient, promiscuous, and thermostable artificial enzyme that catalyzes a diverse array of substrate oxidations coupled to the reduction of H2O2. The maquette exhibits kinetics that match and even surpass those of certain natural peroxidases, retains its activity at elevated temperature and in the presence of organic solvents, and provides a simple platform for interrogating catalytic intermediates common to natural heme-containing enzymes

Spontaneous Quaternary and Tertiary T-R Transitions of Human Hemoglobin in Molecular Dynamics Simulation

We present molecular dynamics simulations of unliganded human hemoglobin (Hb) A under physiological conditions, starting from the R, R2, and T state. The simulations were carried out with protonated and deprotonated HC3 histidines His(β)146, and they sum up to a total length of 5.6µs. We observe spontaneous and reproducible T→R quaternary transitions of the Hb tetramer and tertiary transitions of the α and β subunits, as detected from principal component projections, from an RMSD measure, and from rigid body rotation analysis. The simulations reveal a marked asymmetry between the α and β subunits. Using the mutual information as correlation measure, we find that the β subunits are substantially more strongly linked to the quaternary transition than the α subunits. In addition, the tertiary populations of the α and β subunits differ substantially, with the β subunits showing a tendency towards R, and the α subunits showing a tendency towards T. Based on the simulation results, we present a transition pathway for coupled quaternary and tertiary transitions between the R and T conformations of Hb

Elucidation of the ATP7B N-Domain Mg2+-ATP Coordination Site and Its Allosteric Regulation

The diagnostic of orphan genetic disease is often a puzzling task as less attention is paid to the elucidation of the pathophysiology of these rare disorders at the molecular level. We present here a multidisciplinary approach using molecular modeling tools and surface plasmonic resonance to study the function of the ATP7B protein, which is impaired in the Wilson disease. Experimentally validated in silico models allow the elucidation in the Nucleotide binding domain (N-domain) of the Mg2+-ATP coordination site and answer to the controversial role of the Mg2+ ion in the nucleotide binding process. The analysis of protein motions revealed a substantial effect on a long flexible loop branched to the N-domain protein core. We demonstrated the capacity of the loop to disrupt the interaction between Mg2+-ATP complex and the N-domain and propose a role for this loop in the allosteric regulation of the nucleotide binding process

The Impact of Small Molecule Binding on the Energy Landscape of the Intrinsically Disordered Protein C-Myc

Intrinsically disordered proteins are attractive therapeutic targets owing to their prevalence in several diseases. Yet their lack of well-defined structure renders ligand discovery a challenging task. An intriguing example is provided by the oncoprotein c-Myc, a transcription factor that is over expressed in a broad range of cancers. Transcriptional activity of c-Myc is dependent on heterodimerization with partner protein Max. This protein-protein interaction is disrupted by the small molecule 10058-F4 (1), that binds to monomeric and disordered c-Myc. To rationalize the mechanism of inhibition, structural ensembles for the segment of the c-Myc domain that binds to 1 were computed in the absence and presence of the ligand using classical force fields and explicit solvent metadynamics molecular simulations. The accuracy of the computed structural ensembles was assessed by comparison of predicted and measured NMR chemical shifts. The small molecule 1 was found to perturb the composition of the apo equilibrium ensemble and to bind weakly to multiple distinct c-Myc conformations. Comparison of the apo and holo equilibrium ensembles reveals that the c-Myc conformations binding 1 are already partially formed in the apo ensemble, suggesting that 1 binds to c-Myc through an extended conformational selection mechanism. The present results have important implications for rational ligand design efforts targeting intrinsically disordered proteins