Karl F. Freed

University of Chicago, Chicago, Illinois, United States

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Publications (547)1316.82 Total impact

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    ABSTRACT: In contrast to mixtures of two small molecule fluids, miscible binary polymer blends often exhibit two structural relaxation times and two glass transition temperatures. Qualitative explanations postulate phenomenological models of local concentration enhancements due to chain connectivity in ideal, fully miscible systems. We develop a quantitative theory that explains qualitative trends in the dynamics of real miscible polymer blends which are never ideal mixtures. The theory is a synthesis of the lattice cluster theory of blend thermodynamics, the generalized entropy theory for glass-formation in polymer materials, and the Kirkwood-Buff theory for concentration fluctuations in binary mixtures.
    The Journal of chemical physics. 06/2014; 140(24):244905.
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    ABSTRACT: In contrast to binary mixtures of small molecule fluids, homogeneous polymer blends exhibit relatively large concentration fluctuations that can strongly affect the transport properties of these complex fluids over wide ranges of temperatures and compositions. The spatial scale and intensity of these compositional fluctuations are studied by applying Kirkwood-Buff theory to model blends of linear semiflexible polymer chains with upper critical solution temperatures. The requisite quantities for determining the Kirkwood-Buff integrals are generated from the lattice cluster theory for the thermodynamics of the blend and from the generalization of the random phase approximation to compressible polymer mixtures. We explore how the scale and intensity of composition fluctuations in binary blends vary with the reduced temperature τ ≡ (T - Tc)/T (where Tc is the critical temperature) and with the asymmetry in the rigidities of the components. Knowledge of these variations is crucial for understanding the dynamics of materials fabricated from polymer blends, and evidence supporting these expectations is briefly discussed.
    The Journal of chemical physics. 05/2014; 140(19):194901.
  • Karl F Freed
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    ABSTRACT: Phase field methods are extended to describe the nonequilibrium dynamics of reversible self-assembly systems, an extension that is complicated by the mutual coupling of many non-conserved order parameters into a set of highly nonlinear partial differential equations. Further complications arise because the sum of all non-conserved order parameters equals a conserved order parameter. The theory is developed for the simplest model of reversible self-assembly in which no additional constraints are imposed on the self-assembly process since the extension to treat more complex self-assembly models is straightforward. Specific calculations focus on the time evolution of the cluster size distribution for a free association system that is rapidly dropped from one ordered state to a more ordered state within the one-phase region. The dynamics proceed as expected, thereby providing validation of the theory which is also capable of treating systems with spatial inhomogeneities.
    The Journal of Chemical Physics 10/2013; 139(13):134904. · 3.16 Impact Factor
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    ABSTRACT: Although molecular dynamics simulations can be accelerated by more than an order of magnitude by implicitly describing the influence of the solvent with a continuum model, most currently available implicit solvent simulations cannot robustly simulate the structure and dynamics of nucleic acids. The difficulties become exacerbated especially for RNAs, suggesting the presence of serious physical flaws in the prior continuum models for the influence of the solvent and counter ions on the nucleic acids. We present a novel, to our knowledge, implicit solvent model for simulating nucleic acids by combining the Langevin-Debye model and the Poisson-Boltzmann equation to provide a better estimate of the electrostatic screening of both the water and counter ions. Tests of the model involve comparisons of implicit and explicit solvent simulations for three RNA targets with 20, 29, and 75 nucleotides. The model provides reasonable agreement with explicit solvent simulations, and directions for future improvement are noted.
    Biophysical Journal 09/2013; 105(5):1248-57. · 3.67 Impact Factor
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    ABSTRACT: We demonstrate the ability of simultaneously determining a protein's folding pathway and structure using a properly formulated model without prior knowledge of the native structure. Our model employs a natural coordinate system for describing proteins and a search strategy inspired by the observation that real proteins fold in a sequential fashion by incrementally stabilizing nativelike substructures or "foldons." Comparable folding pathways and structures are obtained for the twelve proteins recently studied using atomistic molecular dynamics simulations [K. Lindorff-Larsen, S. Piana, R. O. Dror, D. E. Shaw, Science 334, 517 (2011)], with our calculations running several orders of magnitude faster. We find that nativelike propensities in the unfolded state do not necessarily determine the order of structure formation, a departure from a major conclusion of the molecular dynamics study. Instead, our results support a more expansive view wherein intrinsic local structural propensities may be enhanced or overridden in the folding process by environmental context. The success of our search strategy validates it as an expedient mechanism for folding both in silico and in vivo.
    Physical Review Letters 07/2013; 111(2):028103. · 7.94 Impact Factor
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    Wen-Sheng Xu, Karl F Freed
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    ABSTRACT: Many glass-forming fluids exhibit a remarkable thermodynamic scaling in which dynamic properties, such as the viscosity, the relaxation time, and the diffusion constant, can be described under different thermodynamic conditions in terms of a unique scaling function of the ratio ρ(γ)∕T, where ρ is the density, T is the temperature, and γ is a material dependent constant. Interest in the scaling is also heightened because the exponent γ enters prominently into considerations of the relative contributions to the dynamics from pressure effects (e.g., activation barriers) vs. volume effects (e.g., free volume). Although this scaling is clearly of great practical use, a molecular understanding of the scaling remains elusive. Providing this molecular understanding would greatly enhance the utility of the empirically observed scaling in assisting the rational design of materials by describing how controllable molecular factors, such as monomer structures, interactions, flexibility, etc., influence the scaling exponent γ and, hence, the dynamics. Given the successes of the generalized entropy theory in elucidating the influence of molecular details on the universal properties of glass-forming polymers, this theory is extended here to investigate the thermodynamic scaling in polymer melts. The predictions of theory are in accord with the appearance of thermodynamic scaling for pressures not in excess of ∼50 MPa. (The failure at higher pressures arises due to inherent limitations of a lattice model.) In line with arguments relating the magnitude of γ to the steepness of the repulsive part of the intermolecular potential, the abrupt, square-well nature of the lattice model interactions lead, as expected, to much larger values of the scaling exponent. Nevertheless, the theory is employed to study how individual molecular parameters affect the scaling exponent in order to extract a molecular understanding of the information content contained in the exponent. The chain rigidity, cohesive energy, chain length, and the side group length are all found to significantly affect the magnitude of the scaling exponent, and the computed trends agree well with available experiments. The variations of γ with these molecular parameters are explained by establishing a correlation between the computed molecular dependence of the scaling exponent and the fragility. Thus, the efficiency of packing the polymers is established as the universal physical mechanism determining both the fragility and the scaling exponent γ.
    The Journal of Chemical Physics 06/2013; 138(23):234501. · 3.16 Impact Factor
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    ABSTRACT: A Flory-Huggins (FH) type lattice theory of self-assembly is generalized to describe the equilibrium solvation of long polymer chains B by small solvent molecules A. Solvation is modeled as a thermally reversible mutual association between the polymer and a relatively low molar mass solvent. The FH Helmholtz free energy F is derived for a mixture composed of the A and B species and the various possible mutual association complexes AiB, and F is then used to generate expressions for basic thermodynamic properties of solvated polymer solutions, including the size distribution of the solvated clusters, the fraction of solvent molecules contained in solvated states (an order parameter for solvation), the specific heat (which exhibits a maximum at the solvation transition), the second and the third osmotic virial coefficients, and the boundaries for phase stability of the mixture. Special attention is devoted to the analysis of the "entropic" contribution χs to the FH interaction parameter χ of polymer solutions, both with and without associative interactions. The entropic χs parameter arises from correlations associated with polymer chain connectivity and disparities in molecular structure between the components of the mixture. Our analysis provides the first explanation of the longstanding enigma of why χs for polymer solutions significantly exceeds χs for binary polymer blends. Our calculations also reveal that χs becomes temperature dependent when interactions are strong, in sharp contrast to models currently being used for fitting thermodynamic data of associating polymer-solvent mixtures, where χs is simply assumed to be an adjustable constant based on experience with solutions of homopolymers in nonassociating solvents.
    The Journal of Chemical Physics 04/2013; 138(16):164901. · 3.16 Impact Factor
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    ABSTRACT: The theory of equilibrium solvation of polymers B by a relatively low molar mass solvent A, developed in the simplest form in Paper I, is used to explore some essential trends in basic thermodynamic properties of solvated polymer solutions, such as the equilibrium concentrations of solvated polymers AiB and free solvent molecules A, the mass distribution φAiB(i) of solvated clusters, the extent of solvation of the polymer Φsolv, the solvation transition lines Tsolv(φB ( o)), the specific heat CV, the osmotic second virial coefficient B2, phase stability boundaries, and the critical temperatures associated with closed loop phase diagrams. We discuss the differences between the basic thermodynamic properties of solvated polymers and those derived previously for hierarchical mutual association processes involving the association of two different species A and B into AB complexes and the subsequent polymerization of these AB complexes into linear polymeric structures. The properties of solvated polymer solutions are also compared to those for solutions of polymers in a self-associating solvent. Closed loop phase diagrams for solvated polymer solutions arise in the theory from the competition between the associative and van der Waals interactions, a behavior also typical for dispersed molecular and nanoparticle species that strongly associate with the host fluid. Our analysis of the temperature dependence of the second osmotic virial coefficient reveals that the theory must be generalized to describe the association of multiple solvent molecules with each chain monomer, and this complex extension of the present model will be developed in subsequent papers aimed at a quantitative rather than qualitative treatment of solvated polymer solutions.
    The Journal of Chemical Physics 04/2013; 138(16):164902. · 3.16 Impact Factor
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    ABSTRACT: Optimized geometries and normal mode frequencies are evaluated for the ground and low lying excited states of {\em cis-}stilbene ($c$S), {\em trans-}stilbene ($t$S), and 4a,4b-di-hydro-phenanthrene (DHP) from calculations performed with the improved virtual orbital complete active space configuration interaction (IVO-CASCI) method. Structural parameters and vibrational frequencies are also provided for the non-planar conformation of {\em trans-} stilbene. The ground and low lying excited state vibrational frequencies of these systems are found to be real, thus confirming the stability of their optimized geometries. The calculations further show that a non-planar conformer of {\em trans-}stilbene is the most stable among these four systems. The calculated ground and low lying excited state geometries and vibrational frequencies agree well with experiment and with prior theoretical estimates where available. Our IVO-CASCI based multi-reference M{\"o}ller-Plesset (MRMP) computations place the $^1$B$_u$ state of {\em trans} stilbene to be $\sim$4.0 eV above the ground X$^1$A$_g$ state, which is in accord with experiment and with earlier theoretical estimates. The 1$^1$B$_u$ state of {\em trans-}stilbene can be represented by the highest occupied molecular orbital (HOMO)$\rightarrow$lowest unoccupied molecular orbital (LUMO) transition (ionic type) from the ground state, whereas its 2$^1$B$_u$ state is dominated by the HOMO$\rightarrow$ LUMO+1 and HOMO-1$\rightarrow$LUMO transitions (covalent type). Likewise, the 1$^1$B and 2$^1$B states of {\em cis-}stilbene and DHP are also found to be ionic and covalent types, respectively. Multi-reference M{\"o}ller- Plesset (MRMP) perturbation method calculations (based on IVO-CASCI reference states) are presented for the torsional potential energy curve connecting the {\em trans}$\rightarrow${\em cis}$\rightarrow$DHP ground state minima.
    The Journal of Physical Chemistry A 03/2013; · 2.77 Impact Factor
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    ABSTRACT: The actin regulatory protein cofilin plays a central role in actin assembly dynamics by severing filaments and increasing the concentration of ends from which subunits add and dissociate. Cofilin binding modifies the average structure and mechanical properties of actin filaments, thereby promoting fragmentation of partially decorated filaments at boundaries of bare and cofilin-decorated segments. Despite extensive evidence for cofilin-dependent changes in filament structure and mechanics, it is unclear how the two processes are linked at the molecular level. Here, we use molecular dynamics simulations and coarse-grained analyses to evaluate the molecular origins of the changes in filament compliance due to cofilin binding. Filament subunits with bound cofilin are less flat and maintain a significantly more open nucleotide cleft than bare filament subunits. Decorated filament segments are less twisted, thinner (considering only actin), and less connected than their bare counterparts, which lowers the filament bending persistence length and torsional stiffness. Using coarse-graining as an analysis method reveals that cofilin binding increases the average distance between the adjacent long-axis filament subunit, thereby weakening their interaction. In contrast, a fraction of lateral filament subunit contacts are closer and presumably stronger with cofilin binding. A cofilactin interface contact identified by cryo-electron microscopy is unstable during simulations carried out at 310K, suggesting that this particular interaction may be short-lived at ambient temperatures. These results reveal the molecular origins of cofilin-dependent changes in actin filament mechanics that may promote filament severing.
    Journal of Molecular Biology 01/2013; · 3.91 Impact Factor
  • Biophysical Journal 01/2013; 104(2):398-. · 3.67 Impact Factor
  • Karl F Freed
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    ABSTRACT: A wide variety of highly cooperative self-assembly processes in biological and synthetic systems involve the assembly of a large number (m) of units into clusters, with m narrowly peaked about a large size m(0) ≫ 1 and with a second peak centered about the m = 1 unassembled monomers. While very specific models have been proposed for the assembly of, for example, viral capsids and core-shell micelles of ß-casein, no available theory describes a thermodynamically general mechanism for this double peaked, highly cooperative equilibrium assembly process. This study provides a general mechanism for these cooperative processes by developing a minimal Flory-Huggins type theory. Beginning from the simplest non-cooperative, free association model in which the equilibrium constant for addition of a monomer to a cluster is independent of cluster size, the new model merely allows more favorable growth for clusters of intermediate sizes. The theory is illustrated by computing the phase diagram for cases of self-assembly on cooling or heating and for the mass distribution of the two phases.
    The Journal of Chemical Physics 11/2012; 137(20):204906. · 3.16 Impact Factor
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    ABSTRACT: Motivated by the relationship between the folding mechanism and the native structure, we develop a unified approach for predicting folding pathways and tertiary structure using only the primary sequence as input. Simulations begin from a realistic unfolded state devoid of secondary structure and use a chain representation lacking explicit side chains, rendering the simulations many orders of magnitude faster than molecular dynamics simulations. The multiple round nature of the algorithm mimics the authentic folding process and tests the effectiveness of sequential stabilization (SS) as a search strategy wherein 2° structural elements add onto existing structures in a process of progressive learning and stabilization of structure found in prior rounds of folding. Because no a priori knowledge is used, we can identify kinetically significant non-native interactions and intermediates, sometimes generated by only two mutations, while the evolution of contact matrices is often consistent with experiments. Moreover, structure prediction improves substantially by incorporating information from prior rounds. The success of our simple, homology-free approach affirms the validity of our description of the primary determinants of folding pathways and structure, and the effectiveness of SS as a search strategy.
    Proceedings of the National Academy of Sciences 10/2012; 109(43):17442-7. · 9.74 Impact Factor
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    ABSTRACT: The loss of conformational entropy is the largest unfavorable quantity affecting a protein's stability. We calculate the reduction in the number of backbone conformations upon folding using the distribution of backbone dihedral angles (ϕ,ψ) obtained from an experimentally validated denatured state model, along with all-atom simulations for both the denatured and native states. The average loss of entropy per residue is TΔS(BB)(U-N) = 0.7, 0.9, or 1.1 kcal·mol(-1) at T = 298 K, depending on the force field used, with a 0.6 kcal·mol(-1) dispersion across the sequence. The average equates to a decrease of a factor of 3-7 in the number of conformations available per residue (f = Ω(Denatured)/Ω(Native)) or to a total of f(tot) = 3(n)-7(n) for an n residue protein. Our value is smaller than most previous estimates where f = 7-20, that is, our computed TΔS(BB)(U-N) is smaller by 10-100 kcal mol(-1) for n = 100. The differences emerge from our use of realistic native and denatured state ensembles as well as from the inclusion of accurate local sequence preferences, neighbor effects, and correlated motions (vibrations), in contrast to some previous studies that invoke gross assumptions about the entropy in either or both states. We find that the loss of entropy primarily depends on the local environment and less on properties of the native state, with the exception of α-helical residues in some force fields.
    Journal of the American Chemical Society 08/2012; 134(38):15929-36. · 10.68 Impact Factor
  • Karl F Freed
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    ABSTRACT: The competition between the formation of linear chain clusters and ring structures in an equilibrium self-assembling system is reexamined by developing a new Flory-Huggins type theory that combines an estimate for the loss of configurational entropy ΔS(ring) upon ring formation with the standard treatment of the free energy of a polydisperse solution of linear chains. The excess entropy of ring formation ΔS(ring) is obtained from an analytical fit to exact enumeration data for self-avoiding chains and rings with 30 or fewer steps on a cubic lattice. Illustrative calculations of the spinodal curves and the extent and the average degree of self-assembly highlight the physical conditions for which the cyclic structures impact the thermodynamic characterization of equilibrium self-assembling systems.
    The Journal of Chemical Physics 06/2012; 136(24):244904. · 3.16 Impact Factor
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    ABSTRACT: The lattice cluster theory of strongly interacting, structured polymer fluids is applied to determine the thermodynamic properties of solutions of telechelic polymers that may associate through bifunctional end groups. Hence, this model represents a significant albeit natural extension of a diverse array of prior popular equilibrium polymerization models in which structureless "bead" monomers associate into chain-like clusters under equilibrium conditions. In particular, the thermodynamic description of the self-assembly of linear telechelic chains in small molecule solvents (initiated in Paper II) is systematically extended through calculations of the order parameter Φ and average degree of self-assembly, the self-assembly transition temperature T(p), and the specific heat C(V) of solutions of telechelic molecules. Special focus is placed on examining how molecular and thermodynamic parameters, such as the solution composition φ, temperature T, microscopic interaction energies (ε(s) and ε), and length M of individual telechelic chains, influence the computed thermodynamic quantities that are commonly used to characterize self-assembling systems.
    The Journal of Chemical Physics 05/2012; 136(19):194902. · 3.16 Impact Factor
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    ABSTRACT: The newly developed lattice cluster theory (in Paper I) for the thermodynamics of solutions of telechelic polymers is used to examine the phase behavior of these complex fluids when effective polymer-solvent interactions are unfavorable. The telechelics are modeled as linear, fully flexible, polymer chains with mono-functional stickers at the two chain ends, and these chains are assumed to self-assemble upon cooling. Phase separation is generated through the interplay of self-assembly and polymer/solvent interactions that leads to an upper critical solution temperature phase separation. The variations of the boundaries for phase stability and the critical temperature and composition are analyzed in detail as functions of the number M of united atom groups in a telechelic chain and the microscopic nearest neighbor interaction energy ε(s) driving the self-assembly. The coupling between self-assembly and unfavorable polymer/solvent interactions produces a wide variety of nontrivial patterns of phase behavior, including an enhancement of miscibility accompanying the increase of the molar mass of the telechelics under certain circumstances. Special attention is devoted to understanding this unusual trend in miscibility.
    The Journal of Chemical Physics 05/2012; 136(19):194903. · 3.16 Impact Factor
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    ABSTRACT: Progress in understanding protein folding relies heavily upon an interplay between experiment and theory. In particular, readily interpretable experimental data that can be meaningfully compared to simulations are required. According to standard mutational ϕ analysis, the transition state for Protein L contains only a single hairpin. However, we demonstrate here using ψ analysis with engineered metal ion binding sites that the transition state is extensive, containing the entire four-stranded β sheet. Underreporting of the structural content of the transition state by ϕ analysis also occurs for acyl phosphatase [Pandit, A. D., Jha, A., Freed, K. F. & Sosnick, T. R., (2006). Small proteins fold through transition states with native-like topologies. J. Mol. Biol.361, 755-770], ubiquitin [Sosnick, T. R., Dothager, R. S. & Krantz, B. A., (2004). Differences in the folding transition state of ubiquitin indicated by ϕ and ψ analyses. Proc. Natl Acad. Sci. USA 101, 17377-17382] and BdpA [Baxa, M., Freed, K. F. & Sosnick, T. R., (2008). Quantifying the structural requirements of the folding transition state of protein A and other systems. J. Mol. Biol.381, 1362-1381]. The carboxy-terminal hairpin in the transition state of Protein L is found to be nonnative, a significant result that agrees with our Protein Data Bank-based backbone sampling and all-atom simulations. The nonnative character partially explains the failure of accepted experimental and native-centric computational approaches to adequately describe the transition state. Hence, caution is required even when an apparent agreement exists between experiment and theory, thus highlighting the importance of having alternative methods for characterizing transition states.
    Journal of Molecular Biology 04/2012; 420(3):220-34. · 3.91 Impact Factor
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    ABSTRACT: The lattice cluster theory for solutions of telechelic polymer chains, developed in paper I, is applied to determine the enthalpy Δh(p) and entropy Δs(p) of self-assembly of linear telechelics and to evaluate the Flory-Huggins (FH) interaction parameter χ governing the phase behavior of these systems. Particular focus is placed on examining how these interaction variables depend on the composition of the solution, temperature, van der Waals and local "sticky" interaction energies, and the length of the individual telechelic chains. The FH interaction parameter χ is found to exhibit an entropy-enthalpy compensation effect between the "entropic" and "enthalpic" portions as either the composition or mass of the telechelic species is varied, providing unique theoretical insights into this commonly reported, yet, enigmatic phenomenon.
    The Journal of Chemical Physics 02/2012; 136(6):064903. · 3.16 Impact Factor
  • Jacek Dudowicz, Karl F Freed
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    ABSTRACT: The lattice cluster theory (LCT) for the thermodynamics of a wide array of polymer systems has been developed by using an analogy to Mayer's virial expansions for non-ideal gases. However, the high-temperature expansion inherent to the LCT has heretofore precluded its application to systems exhibiting strong, specific "sticky" interactions. The present paper describes a reformulation of the LCT necessary to treat systems with both weak and strong, "sticky" interactions. This initial study concerns solutions of linear telechelic chains (with stickers at the chain ends) as the self-assembling system. The main idea behind this extension of the LCT lies in the extraction of terms associated with the strong interactions from the cluster expansion. The generalized LCT for sticky systems reduces to the quasi-chemical theory of hydrogen bonding of Panyioutou and Sanchez when correlation corrections are neglected in the LCT. A diagrammatic representation is employed to facilitate the evaluation of the corrections to the zeroth-order approximation from short range correlations.
    The Journal of Chemical Physics 02/2012; 136(6):064902. · 3.16 Impact Factor

Publication Stats

6k Citations
1,316.82 Total Impact Points


  • 1970–2014
    • University of Chicago
      • • James Franck Institute
      • • Department of Biochemistry & Molecular Biology
      • • Department of Physics
      • • Department of Chemistry
      Chicago, Illinois, United States
  • 2011
    • Bengal Engineering and Science University
      • Department of Chemistry
      Hāora, Bengal, India
  • 2005–2011
    • Indian Institute of Astrophysics
      Bengalūru, Karnātaka, India
  • 2010
    • Tsinghua University
      • School of Life Sciences
      Beijing, Beijing Shi, China
  • 1983–2010
    • University of Illinois at Chicago
      Chicago, Illinois, United States
  • 1992–2009
    • National Institute of Standards and Technology
      • Polymers Division
      Gaithersburg, MD, United States
  • 2007
    • Massachusetts Institute of Technology
      • Department of Chemistry
      Cambridge, MA, United States
  • 2004
    • University of California, San Francisco
      • Department of Pharmaceutical Chemistry
      San Francisco, CA, United States
  • 1998
    • Yamagata University
      Ямагата, Yamagata, Japan
  • 1981–1984
    • Ben-Gurion University of the Negev
      • Department of Chemistry
      Beersheba, Southern District, Israel
  • 1977–1981
    • University of California, Santa Barbara
      • Department of Chemistry and Biochemistry
      Santa Barbara, CA, United States
  • 1979
    • Texas A&M University
      • Department of Chemistry
      College Station, TX, United States
  • 1978
    • Université Paris-Sud 11
      • Laboratoire de Photophysique Moléculaire
      Orsay, Île-de-France, France
  • 1977–1978
    • Argonne National Laboratory
      Lemont, Illinois, United States
  • 1974
    • University of Rochester
      • Department of Chemistry
      Rochester, New York, United States