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 noncoding 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 molecularlevel understanding of RNA folding pathways is challenging. Compounding this problem, computation methods for studying largescale conformational rearrangement are still lacking.
We have pioneered the development of a new type of Monte Carlo simulations to target largescale 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 allatom 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 largescale 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 shapeshifting conformational changes and are beginning to decipher how largescale 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 largescale unfolding of the structure. The architecture of this molecule has a 3way junction similar to the hammerhead ribozyme.
3. Nucleic AcidIon and PeptideRNA Interactions
Nucleic acids (DNA and RNA) are highly charged biopolymers. Under physiological conditions, systems involving nucleic acids also contain positivelycharged 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 peptideDNA and peptideRNA interactions. The picture to the left shows how Mg^{2+} 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 acidion interactions and how they influence peptideRNA binding. Using largescale computer simulations, we can study how counterions condense onto nucleic acids, how the diffuse counterions cloud renormalizes the backbonebackbone interactions to stabilize the tertiary structure of the nucleic acid, and how the peptideRNA are mediated by electrostatics of the counterions. To effectively carry out these simulations involving large number of charges, we have developed efficient linearscaling methods for computing the electrostatic interactions, which is the universal bottleneck in all largescale computer simulations of highly charged systems.
4. Nanoscale Superfluidity in Helium and Molecular Hydrogen Droplets
Ultracold (< 1K) nanodroplets of helium4 (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 largescale 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 tightlycoupled 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 negativeentropy demixing effect is purely quantum in origin and is driven by bosonic exchanges.
5. New Algorithms for LargeScale 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 largescale 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 realtime path integral simulations for condensedphase 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 1million particle simulation, studying the melting of a 2dimensional fluid. This study with more than 4 million particles, carried out back in 2006, still holds the world's record on the largest 2d melting simulation ever!
Selected publications

Mak, C. H., 2012,
"Ions and RNAs: Free energies of counterionmediated RNA fold stabilities," J. Chem. Theo. Comput. xx , xxxxxx.

Mak, C. H., 2011,
"LOOPS MC: A Monte Carlo simulation program for RNA using generalized loop closure," Mol. Simulat. 37 , 537556.

Mak, C. H., Chung, W.Y. and Markivskiy, N. D., 2011,
"RNA Conformational sampling: II. Arbitrarylength multinucleotide loop closure," J. Chem. Theo. Comput. 7 , 11981207.

Sharma, A. K. and Mak, C. H., 2010,
"Protein conformational sampling using generalized loop closure," J. Chem. Theo. Comput. xx , xxxxxx.

Mak, C. H., 2009,
"The sign problem in realtime path integral simulations: Using the cumulant action to implement multilevel blocking," J. Chem. Phys. 131 , 044125044125.

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 , 91659173.

Mak, C. H., 2008,
"RNA conformational sampling: 1. Singlenucleotide loop closure," J. Comput. Chem. 29 , 926933.

Mak, C. H. and Sharma, A. K., 2007,
"Reverse Monte Carlo method and its implications for generalized cluster algorithms," Phys. Rev. Lett. 98 , 180602180602.

Mak, C. H., 2006,
"A largescale simulation of twodimensional melting of hard discs," Phys. Rev. E 73 , 065104065104.

Mak, C. H., 2005,
"Stochastic potential switching algorithm for Monte Carlo simulations of complex systems," J. Chem. Phys. 122 , 214110214110.

Mak, C. H., Zakharov, S. and Spry, D. B., 2005,
"Superfluidity in CH$_4$doped H$_2$ nanoclusters," J. Chem. Phys. 122 , 104301104301.

Mak, C. H. and Zakharov, S., 2004,
"A multigrid algorithm for sampling imaginarytime paths in quantum Monte Carlo simulations," J. Phys. Chem. B 108 , 67606766.

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 , 235105235105.

Egger, R. and Mak, C. H., 2001,
"Multilevel blocking Monte Carlo simulations for quantum dots," Intl. J. Mod. Phys. B 15 , 14161416.

Egger, R., Muhlbacher, L. and Mak, C. H., 2000,
"Pathintegral Monte Carlo simulations with the sign problem: Multilevel blocking approach for effective actions," Phys. Rev. E 61 , 59615966.

Egger, R. and Mak, C. H., 2000,
"Multilevel blocking Monte Carlo simulations for quantum dots," in: Advances in Quantum ManyBody Theory, Vol. 3 ,
eds. Bishop, R. F., Gernoth, K. A., Walet, N. R., Xian, Y.,
(World Scientific, London), xxxxxx.

Drovetsky, B. Y., Liu, A. J. and Mak, C. H., 1999,
"Nematicisotropic interfaces in semiflexible polymer blends," J. Chem. Phys. 111 , 43344342.

Stockburger, J. and Mak, C. H., 1999,
"Stochastic Liouvillian algorithm to simulate dissipative quantum dynamics with arbitrary precision," J. Chem. Phys. 110 , 49834985.

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 , 462462.

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 , 33203323.

Chu, J. C. and Mak, C. H., 1999,
"Inter and intrachain attractions in solutions of flexible polyelectrolytes at nonzero concentration," J. Chem. Phys. 110 , 26692680.

Mak, C. H. and Egger, R., 1999,
"A multilevel blocking approach to the sign problem in realtime quantum Monte Carlo simulations," J. Chem. Phys. 110 , 1214.

Mak, C. H. and Egger, R. WeberGottschick H., 1998,
"Multilevel blocking approach to the fermion sign problem in pathintegral Monte Carlo simulations," Phys. Rev. Lett. 81 , 45334536.

Stockburger, J. T. and Mak, C. H., 1998,
"Dynamical simulation of current fluctuations in a dissipative 2state system," Phys. Rev. Lett. 80 , 26572660.

Luck, A., Winterstetter, M., Weiss, U. and Mak, C. H., 1998,
"Quantum Monte Carlo simulations of driven spinboson systems," Phys. Rev. E 58 , 55655573.

Drovetsky, B. Y., Chu, J. C. and Mak, C. H., 1998,
"Computer simulations of selfavoiding polymerized membranes," J. Chem. Phys. 108 , 65546557.

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 , 83978408.

Mak, C. H., 1998,
"Path integral simulations of condensedphase 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 electrontransfer  Crossover from weak to strong electronic coupling," J. Chem. Phys. 105 , 81268135.

Mak, C. H. and Egger, R., 1996,
"Monte Carlo methods for realtime path integration," in: New Methods in Computational Quantum Mechanics, Adv. Chem. Phys., Vol XCIII ,
eds. Pripogine, I., Rice, S. A.,
(Wiley, New York), 3976.

Leung, K., Egger, R. and Mak, C. H., 1995,
"Dynamical simulation of transport in onedimensional quantum wires," Phys. Rev. Lett. 75 , 33443347.

Mak, C. H. and Egger, R., 1995,
"On the mechanism of the primary charge separation in bacterial photosynthesis," Chem. Phys. Lett. 238 , 149155.

Wang, Y. and Mak, C. H., 1995,
"Transferable tightbinding potential for hydrocarbons," Chem. Phys. Lett. 235 , 3746.

Egger, R. and Mak, C. H., 1994,
"Low temperature dynamical simulation of spinboson systems," Phys. Rev. B 50 , 1521015220.

Egger, R. and Mak, C. H., 1994,
"Dissipative threestate system and the primary electron transfer in the bacterial photosynthetic reaction center," J. Phys. Chem. 98 , 99039918.

Egger, R., Mak, C. H. and Weiss, U., 1994,
"Rate concept and retarded master equations for dissipative tightbinding models," Phys. Rev. E 50 , R655R658.

Mak, C. H. and Egger, R., 1994,
"Quantum Monte Carlo study of tunneling diffusion in a dissipative multistate system," Phys. Rev. E 49 , 19972008.

Egger, R. and Mak, C. H. Weiss U., 1994,
"Quantum rates for nonadiabatic electron transfer," J. Chem. Phys. 100 , 26512660.

Egger, R. and Mak, C. H., 1993,
"Dynamical effects pn the calculation of quantum rates for electron transfer reactions," J. Chem. Phys. 99 , 25412549.

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 , 130136.

Mak, C. H., 1992,
"Stochastic method for realtime path integrations," Phys. Rev. Lett. 68 , 899902.

Mak, C. H. and Chandler, D., 1991,
"Coherentincoherent transition and relaxation in condensedphase tunneling systems," Phys. Rev. A 44 , 23522369.

Mak, C. H. and Chandler, D., 1990,
"Solving the sign problem in quantum Monte Carlo dynamics," Phys. Rev. A 41 , 57095712.

Mak, C. H. and Andersen, H. C., 1990,
"Lowtemperature approximations for Feynman path integrals and their applications to quantum equilibrium and dynamical problems," J. Chem. Phys. 92 , 29532965.
