@article{goolsby_losey_fakharzadeh_xu_duker_sherman_matteson_moradi_2023, title={Addressing the Embeddability Problem in Transition Rate Estimation}, ISSN={["1520-5215"]}, DOI={10.1021/acs.jpca.3c01367}, abstractNote={Markov State Models (MSM) and related techniques have gained significant traction as a tool for analyzing and guiding molecular dynamics (MD) simulations due to their ability to extract structural, thermodynamic, and kinetic information on proteins using computationally feasible MD simulations. The MSM analysis often relies on spectral decomposition of empirically generated transition matrices. Here, we discuss an alternative approach for extracting the thermodynamic and kinetic information from the so-called rate/generator matrix rather than the transition matrix. Although the rate matrix is itself built from the empirical transition matrix, it provides an alternative approach for estimating both thermodynamic and kinetic quantities, particularly in diffusive processes. We particularly discuss a fundamental issue with this approach, known as the embeddability problem and offer ways to address this issue. We describe six different methods to overcome the embeddability problem. We use a one-dimensional toy model to show the workings of these methods and discuss the robustness of each method in terms of its dependence in lag time and trajectory length.}, journal={JOURNAL OF PHYSICAL CHEMISTRY A}, author={Goolsby, Curtis and Losey, James and Fakharzadeh, Ashkan and Xu, Yuchen and Duker, Marie-Christine and Sherman, Mila Getmansky and Matteson, David S. and Moradi, Mahmoud}, year={2023}, month={Jun} }
 @article{moradi_sagui_roland_2014, title={Investigating rare events with nonequilibrium work measurements. I. Nonequilibrium transition path probabilities (vol 140, 034114, 2014)}, volume={140}, ISSN={["1089-7690"]}, DOI={10.1063/1.4865580}, abstractNote={First Page}, number={6}, journal={JOURNAL OF CHEMICAL PHYSICS}, author={Moradi, Mahmoud and Sagui, Celeste and Roland, Christopher}, year={2014}, month={Feb} }
 @article{moradi_sagui_roland_2014, title={Investigating rare events with nonequilibrium work measurements. II. Transition and reaction rates (vol 140, 034115, 2014)}, volume={140}, ISSN={["1089-7690"]}, DOI={10.1063/1.4865582}, abstractNote={First Page}, number={6}, journal={JOURNAL OF CHEMICAL PHYSICS}, author={Moradi, Mahmoud and Sagui, Celeste and Roland, Christopher}, year={2014}, month={Feb} }
 @article{moradi_babin_roland_sagui_2012, title={Are Long-Range Structural Correlations Behind the Aggregration Phenomena of Polyglutamine Diseases?}, volume={8}, ISSN={["1553-7358"]}, DOI={10.1371/journal.pcbi.1002501}, abstractNote={We have characterized the conformational ensembles of polyglutamine peptides of various lengths (ranging from to ), both with and without the presence of a C-terminal polyproline hexapeptide. For this, we used state-of-the-art molecular dynamics simulations combined with a novel statistical analysis to characterize the various properties of the backbone dihedral angles and secondary structural motifs of the glutamine residues. For (i.e., just above the pathological length for Huntington's disease), the equilibrium conformations of the monomer consist primarily of disordered, compact structures with non-negligible -helical and turn content. We also observed a relatively small population of extended structures suitable for forming aggregates including - and -strands, and - and -hairpins. Most importantly, for we find that there exists a long-range correlation (ranging for at least residues) among the backbone dihedral angles of the Q residues. For polyglutamine peptides below the pathological length, the population of the extended strands and hairpins is considerably smaller, and the correlations are short-range (at most residues apart). Adding a C-terminal hexaproline to suppresses both the population of these rare motifs and the long-range correlation of the dihedral angles. We argue that the long-range correlation of the polyglutamine homopeptide, along with the presence of these rare motifs, could be responsible for its aggregation phenomena.}, number={4}, journal={PLOS COMPUTATIONAL BIOLOGY}, author={Moradi, Mahmoud and Babin, Volodymyr and Roland, Christopher and Sagui, Celeste}, year={2012}, month={Apr} }
 @article{moradi_sagui_roland_2011, title={Calculating relative transition rates with driven nonequilibrium simulations}, volume={518}, ISSN={["1873-4448"]}, DOI={10.1016/j.cplett.2011.10.054}, abstractNote={A formalism is presented for investigating transition pathways and transition probabilities for rare events in complex systems. Specifically, we show how driven simulations may be used to calculate relative reaction rates between stable states by means of nonequilibrium work measurements. Our relation between equilibrium and nonequilibrium rates may further be optimized by means of bidirectional estimators. A simple proline system is used to numerically illustrate the results.}, journal={CHEMICAL PHYSICS LETTERS}, author={Moradi, Mahmoud and Sagui, Celeste and Roland, Christopher}, year={2011}, month={Dec}, pages={109–113} }
 @article{moradi_babin_roland_sagui_2010, title={A classical molecular dynamics investigation of the free energy and structure of short polyproline conformers}, volume={133}, ISSN={["0021-9606"]}, DOI={10.1063/1.3481087}, abstractNote={Folded polyproline peptides can exist as either left-(PPII) or right-handed (PPI) helices, depending on their environment. In this work, we have characterized the conformations and the free energy landscapes of Ace–(Pro)n–Nme, n=2,3,…,9, and 13 peptides both in vacuo and in an implicit solvent environment. In order to enhance the sampling provided by regular molecular dynamics simulations, we have used the recently developed adaptively biased molecular dynamics method—which provides an accurate description of the free energy landscapes in terms of a set of relevant collective variables—combined with Hamiltonian and temperature replica exchange molecular dynamics methods. The collective variables, which are chosen so as to reflect the stable structures and the “slow modes” of the polyproline system, were based primarily on properties of length and of the cis/trans isomerization associated with the prolyl bonds. Results indicate that the space of peptide structures is characterized not just by pure PPII and PPI structures, but rather by a broad distribution of stable minima with similar free energies. These results are in agreement with recent experimental work. In addition, we have used steered molecular dynamics methods in order to quantitatively estimate the free energy difference of PPI and PPII for peptides of the length n=2,…,5 in vacuo and implicit water and qualitatively investigate transition pathways and mechanisms for the PPII to PPI transitions. A zipper-like mechanism, starting from either the center of the peptide or the amidated end, appear to be the most likely mechanisms for the PPII→PPI transition for the longer peptides.}, number={12}, journal={JOURNAL OF CHEMICAL PHYSICS}, author={Moradi, Mahmoud and Babin, Volodymyr and Roland, Christopher and Sagui, Celeste}, year={2010}, month={Sep} }
 @article{moradi_lee_babin_roland_sagui_2010, title={Free energy and structure of polyproline peptides: An ab initio and classical molecular dynamics investigation}, volume={110}, number={15}, journal={International Journal of Quantum Chemistry}, author={Moradi, M. and Lee, J. G. and Babin, V. and Roland, C. and Sagui, C.}, year={2010}, pages={2865–2879} }
 @article{babin_karpusenka_moradi_roland_sagui_2009, title={Adaptively Biased Molecular Dynamics: An Umbrella Sampling Method With a Time-Dependent Potential}, volume={109}, ISSN={["1097-461X"]}, DOI={10.1002/qua.22413}, abstractNote={Abstract}, number={15}, journal={INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY}, author={Babin, Volodymyr and Karpusenka, Vadzim and Moradi, Mahmoud and Roland, Christopher and Sagui, Celeste}, year={2009}, month={Dec}, pages={3666–3678} }
 @article{moradi_babin_roland_darden_sagui_2009, title={Conformations and free energy landscapes of polyproline peptides}, volume={106}, ISSN={["0027-8424"]}, DOI={10.1073/pnas.0906500106}, abstractNote={The structure of the proline amino acid allows folded polyproline peptides to exist as both left- (PPII) and right-handed (PPI) helices. We have characterized the free energy landscapes of hexamer, nanomer, and tridecamer polyproline peptides in gas phase and implicit water as well as explicit hexane and 1-propanol for the nanomer. To enhance the sampling provided by regular molecular dynamics, we used the recently developed adaptively biased molecular dynamics method, which describes Landau free energy maps in terms of relevant collective variables. These maps, as a function of the collective variables of handedness, radius of gyration, and three others based on the peptide torsion angle ω, were used to determine the relative stability of the different structures, along with an estimate of the transition pathways connecting the different minima. Results show the existence of several metastable isomers and therefore provide a complementary view to experimental conclusions based on photo-induced electron transfer experiments with regard to the existence of stable heterogeneous subpopulations in PPII polyproline.}, number={49}, journal={PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA}, author={Moradi, Mahmoud and Babin, Volodymyr and Roland, Christopher and Darden, Thomas A. and Sagui, Celeste}, year={2009}, month={Dec}, pages={20746–20751} }