1. Mapping RNA Folding/Unfolding Pathways via Large Loop Motions
RNAs, just like proteins, have to fold into highly specific tertiary structures in order for them to carry out the proper biological functions. Some of these include protein synthesis in the ribosome, the excision of non-coding sequence in mRNAs group I & II introns, and the regulation of gene expression by riboswitches.
The folding pathway of RNAs have been studied experimentally for several systems. The folding timescale for the group I intron in Tetrahymena is of the order of seconds to a minute. Folding is often punctuated by the molecule being trapped in various misfolded states Because RNAs are often substantially larger than proteins and their structural motifs are rather complex, a molecular-level understanding of RNA folding pathways is challenging. Compounding this problem, computation methods for studying large-scale conformational rearrangement are still lacking.
We have pioneered the development of a new type of Monte Carlo simulations to target large-scale motions in RNAs. The simulations are based on the closure algorithm (a mathematical solution of inverse kinematics), which can be used to reclose large loops along the RNA sequence onto new alternative conformations. The movie to the left shows some of the large loop motions observed in an all-atom unfolding simulation of the Schistosoma hammerhead ribozyme. The last scene shows a summary of the key gateway states in the hammerhead's unfolding process identified by our simulations.
2. Riboswitches Use Conformation Changes to Regulate Gene Expressions
Sequences in the 5' untranslated regions of certain bacterial mRNAs have recently been found to hold regulatory control over gene expression. These remarkable RNA sequences are called riboswitches. Riboswitches are senesitive to the presence of various metabolites, and depending on their concentration levels, riboswitches employ a large-scale conformational change to alter their shapes, and this signals for gene expression downstream to either turn transcription or translation on or off. We are studying these shape-shifting conformational changes and are beginning to decipher how large-scale motions are used in riboregulatory mechanisms. The movie to the left shows an example of these motions in the aptamer domain of xpt guanine riboswitch. These motions have been identified in our calculations to be the sequence of events that occur when the gunnine unbinds, leading to a large-scale unfolding of the structure. The architecture of this molecule has a 3-way junction similar to the hammerhead ribozyme.
3. Nucleic Acid-Ion and Peptide-RNA Interactions
Nucleic acids (DNA and RNA) are highly charged biopolymers. Under physiological conditions, systems involving nucleic acids also contain positively-charged counterions in solution such at Mg2+ and K+. For a long time, these counterions were thought to act merely as the enforcers of charge neutrality. It is now clear that counterions serve a much larger function. Counterions can stabilize the folding of RNA, can mediate the effective attractive interactions of DNAs during packaging and can modulate peptide-DNA and peptide-RNA interactions. The picture to the left shows how Mg2+ ions (yellow) are typically associated with the backbone of a RNA under physiological concentrations.
In conjunction with experiments in Prof. Qin’s group, we are trying to understand the precise nature of nucleic acid-ion interactions and how they influence peptide-RNA binding. Using large-scale computer simulations, we can study how counterions condense onto nucleic acids, how the diffuse counterions cloud renormalizes the backbone-backbone interactions to stabilize the tertiary structure of the nucleic acid, and how the peptide-RNA are mediated by electrostatics of the counterions. To effectively carry out these simulations involving large number of charges, we have developed efficient linear-scaling methods for computing the electrostatic interactions, which is the universal bottleneck in all large-scale computer simulations of highly charged systems.
4. Nanoscale Superfluidity in Helium and Molecular Hydrogen Droplets
Ultracold (< 1K) nanodroplets of helium-4 (4He) and molecular hydrogen (H2) can now be produced routinely in experiments (see research summaries of Profs. Vilesov and Wittig). Under these extreme experimental conditions, 4He and H2, both bosons, exhibit superfluid characteristics that could be detected by inserting a rotating probe molecule into the center of the droplet. Just like superfluid liquid 4He, 4He and H2 nanodroplets at a sufficiently low temperature show essentially zero viscosity and the transition to superfluid behavior is distinctly clear in the rotational spectrum of the probe molecule.
Using large-scale computer simulations called “path integral Monte Carlo”, we are now studying the nature of this nanoscale superfluid transition in conjunction with the experimental efforts of Prof. Vilesov’s group. The simulations allow us to study the exchange structure of the superfluid droplets and determine the transition temperature to superfluid behavior quite accurately. In contrast with the conventional theory of superfluidity in bulk systems, the precise meaning of nanoscale superfluidity remains largely unclear because the probe molecular forms a tightly-coupled complex with the superfluid. Work is currently underway with the Vilesov group to formulate a comprehensive theory to understand nanoscale superfluidity.
In addition to doped nanodroplets, we are also studying mixed quantum clusters with path integral simulations. We have discovered clear evidence that symmetric quantum mixtures can actually demix as they go through the superfluid transition. This negative-entropy demixing effect is purely quantum in origin and is driven by bosonic exchanges.
5. New Algorithms for Large-Scale Computer Simulations of Complex Systems
We continue to engage in the fundamental development of simulation algorithms that would enable chemists and molecular biologists to carry out calculations for large-scale and complex classical and quantum systems. Some of these new algorithms are already deployed in the studies of nanoscale superfluidity and RNA folding. Other projects currently being developed include real-time path integral simulations for condensed-phase quantum dynamics, as well as simulations using the stochastic potential switching (SPS) algorithm to study biological systems and complex fluids. The movie to the right shows an example revealing the intricate particle correlations in 1/4 x 1/4 portion (about 65,000 particles in each frame) of a 1-million particle simulation, studying the melting of a 2-dimensional fluid. This study with more than 4 million particles, carried out back in 2006, still holds the world's record on the largest 2-d melting simulation ever!
Mak, C. H., 2012,
"Ions and RNAs: Free energies of counterion-mediated RNA fold stabilities," J. Chem. Theo. Comput. xx , xxx-xxx.
Mak, C. H., 2011,
"LOOPS MC: A Monte Carlo simulation program for RNA using generalized loop closure," Mol. Simulat. 37 , 537-556.
Mak, C. H., Chung, W.-Y. and Markivskiy, N. D., 2011,
"RNA Conformational sampling: II. Arbitrary-length multi-nucleotide loop closure," J. Chem. Theo. Comput. 7 , 1198-1207.
Sharma, A. K. and Mak, C. H., 2010,
"Protein conformational sampling using generalized loop closure," J. Chem. Theo. Comput. xx , xxx-xxx.
Mak, C. H., 2009,
"The sign problem in real-time path integral simulations: Using the cumulant action to implement multi-level blocking," J. Chem. Phys. 131 , 044125-044125.
Markovsky, N. D. and Mak, C. H., 2009,
"Path integral studies of the rotations of methane and its heavier isotopomers in 4He nanoclusters," J. Phys. Chem. A 113 , 9165-9173.
Mak, C. H., 2008,
"RNA conformational sampling: 1. Single-nucleotide loop closure," J. Comput. Chem. 29 , 926-933.
Mak, C. H. and Sharma, A. K., 2007,
"Reverse Monte Carlo method and its implications for generalized cluster algorithms," Phys. Rev. Lett. 98 , 180602-180602.
Mak, C. H., 2006,
"A large-scale simulation of two-dimensional melting of hard discs," Phys. Rev. E 73 , 065104-065104.
Mak, C. H., 2005,
"Stochastic potential switching algorithm for Monte Carlo simulations of complex systems," J. Chem. Phys. 122 , 214110-214110.
Mak, C. H., Zakharov, S. and Spry, D. B., 2005,
"Superfluidity in CH$_4$-doped H$_2$ nanoclusters," J. Chem. Phys. 122 , 104301-104301.
Mak, C. H. and Zakharov, S., 2004,
"A multigrid algorithm for sampling imaginary-time paths in quantum Monte Carlo simulations," J. Phys. Chem. B 108 , 6760-6766.
Dikovsky, M. V. and Mak, C. H., 2001,
"Analysis of the multilevel blocking approach to the fermion sign problem: Accuracy, errors and practice," Phys. Rev. B 63 , 235105-235105.
Egger, R. and Mak, C. H., 2001,
"Multilevel blocking Monte Carlo simulations for quantum dots," Intl. J. Mod. Phys. B 15 , 1416-1416.
Egger, R., Muhlbacher, L. and Mak, C. H., 2000,
"Path-integral Monte Carlo simulations with the sign problem: Multilevel blocking approach for effective actions," Phys. Rev. E 61 , 5961-5966.
Egger, R. and Mak, C. H., 2000,
"Multilevel blocking Monte Carlo simulations for quantum dots," in: Advances in Quantum Many-Body Theory, Vol. 3 ,
eds. Bishop, R. F., Gernoth, K. A., Walet, N. R., Xian, Y.,
(World Scientific, London), xxx-xxx.
Drovetsky, B. Y., Liu, A. J. and Mak, C. H., 1999,
"Nematic-isotropic interfaces in semiflexible polymer blends," J. Chem. Phys. 111 , 4334-4342.
Stockburger, J. and Mak, C. H., 1999,
"Stochastic Liouvillian algorithm to simulate dissipative quantum dynamics with arbitrary precision," J. Chem. Phys. 110 , 4983-4985.
Egger, R., Hausler, W., Mak, C. H. and Grabert, H., 1999,
"Erratum: Crossover from Fermi liquid to Wigner molecule behavior in quantum dots," Phys. Rev. Lett. 83 , 462-462.
Egger, R., Hausler, W., Mak, C. H. and Grabert, H., 1999,
"Crossover from Fermi liquid to Wigner molecule behavior in quantum dots," Phys. Rev. Lett. 82 , 3320-3323.
Chu, J. C. and Mak, C. H., 1999,
"Inter- and intra-chain attractions in solutions of flexible polyelectrolytes at nonzero concentration," J. Chem. Phys. 110 , 2669-2680.
Mak, C. H. and Egger, R., 1999,
"A multilevel blocking approach to the sign problem in real-time quantum Monte Carlo simulations," J. Chem. Phys. 110 , 12-14.
Mak, C. H. and Egger, R. Weber-Gottschick H., 1998,
"Multilevel blocking approach to the fermion sign problem in path-integral Monte Carlo simulations," Phys. Rev. Lett. 81 , 4533-4536.
Stockburger, J. T. and Mak, C. H., 1998,
"Dynamical simulation of current fluctuations in a dissipative 2-state system," Phys. Rev. Lett. 80 , 2657-2660.
Luck, A., Winterstetter, M., Weiss, U. and Mak, C. H., 1998,
"Quantum Monte Carlo simulations of driven spin-boson systems," Phys. Rev. E 58 , 5565-5573.
Drovetsky, B. Y., Chu, J. C. and Mak, C. H., 1998,
"Computer simulations of self-avoiding polymerized membranes," J. Chem. Phys. 108 , 6554-6557.
Lucke, A., Mak, C. H., Egger, R., Ankerhold, J., Stockburger, J. and Grabert, H., 1997,
"Is the direct observation of electronic coherence in electron transfer reactions possible?," J. Chem. Phys. 107 , 8397-8408.
Mak, C. H., 1998,
"Path integral simulations of condensed-phase electronic systems," in: Encyclopedia of Computation Chemistry ,
eds. Schleyer, P., Scheafer, H. F.,
(Wiley, New York), ????-????.
Stockburger, J. and Mak, C. H., 1996,
"A dynamical theory of electron-transfer -- Crossover from weak to strong electronic coupling," J. Chem. Phys. 105 , 8126-8135.
Mak, C. H. and Egger, R., 1996,
"Monte Carlo methods for real-time path integration," in: New Methods in Computational Quantum Mechanics, Adv. Chem. Phys., Vol XCIII ,
eds. Pripogine, I., Rice, S. A.,
(Wiley, New York), 39-76.
Leung, K., Egger, R. and Mak, C. H., 1995,
"Dynamical simulation of transport in one-dimensional quantum wires," Phys. Rev. Lett. 75 , 3344-3347.
Mak, C. H. and Egger, R., 1995,
"On the mechanism of the primary charge separation in bacterial photosynthesis," Chem. Phys. Lett. 238 , 149-155.
Wang, Y. and Mak, C. H., 1995,
"Transferable tight-binding potential for hydrocarbons," Chem. Phys. Lett. 235 , 37-46.
Egger, R. and Mak, C. H., 1994,
"Low temperature dynamical simulation of spin-boson systems," Phys. Rev. B 50 , 15210-15220.
Egger, R. and Mak, C. H., 1994,
"Dissipative three-state system and the primary electron transfer in the bacterial photosynthetic reaction center," J. Phys. Chem. 98 , 9903-9918.
Egger, R., Mak, C. H. and Weiss, U., 1994,
"Rate concept and retarded master equations for dissipative tight-binding models," Phys. Rev. E 50 , R655-R658.
Mak, C. H. and Egger, R., 1994,
"Quantum Monte Carlo study of tunneling diffusion in a dissipative multistate system," Phys. Rev. E 49 , 1997-2008.
Egger, R. and Mak, C. H. Weiss U., 1994,
"Quantum rates for nonadiabatic electron transfer," J. Chem. Phys. 100 , 2651-2660.
Egger, R. and Mak, C. H., 1993,
"Dynamical effects pn the calculation of quantum rates for electron transfer reactions," J. Chem. Phys. 99 , 2541-2549.
Mak, C. H. and Gehlen, J. N., 1993,
"A dynamical test of the centroid formulation of quantum transition state theory for electron transfer reactions," Chem. Phys. Lett 206 , 130-136.
Mak, C. H., 1992,
"Stochastic method for real-time path integrations," Phys. Rev. Lett. 68 , 899-902.
Mak, C. H. and Chandler, D., 1991,
"Coherent-incoherent transition and relaxation in condensed-phase tunneling systems," Phys. Rev. A 44 , 2352-2369.
Mak, C. H. and Chandler, D., 1990,
"Solving the sign problem in quantum Monte Carlo dynamics," Phys. Rev. A 41 , 5709-5712.
Mak, C. H. and Andersen, H. C., 1990,
"Low-temperature approximations for Feynman path integrals and their applications to quantum equilibrium and dynamical problems," J. Chem. Phys. 92 , 2953-2965.