John J. Kozak

University of Warsaw, Warsaw, Masovian Voivodeship, Poland

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Publications (75)133.75 Total impact

  • [show abstract] [hide abstract]
    ABSTRACT: We present a new approach to visualizing and quantifying the displacement of segments of Pseudomonas aeruginosa azurin in the early stages of denaturation. Our method is based on a geometrical method developed previously by the authors, and elaborated extensively for azurin. In this study, we quantify directional changes in three α-helical regions, two regions having β-strand residues, and three unstructured regions of azurin. Snapshots of these changes as the protein unfolds are displayed and described quantitatively by introducing a scaling diagnostic. In accord with molecular dynamics simulations, we show that the long α-helix in azurin (residues 54-67) is displaced from the polypeptide scaffolding and then pivots first in one direction, and then in the opposite direction as the protein continues to unfold. The two β-strand chains remain essentially intact and, except in the earliest stages, move in tandem. We show that unstructured regions 72-81 and 84-91, hinged by β-strand residues 82-83, pivot oppositely. The region comprising residues 72-91 (40 % hydrophobic and 16 % of the 128 total residues) forms an effectively stationary region that persists as the protein unfolds. This static behavior is a consequence of a dynamic balance between the competing motion of two segments, residues 72-81 and 84-91.
    European Journal of Biochemistry 12/2013; · 3.42 Impact Factor
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    ABSTRACT: An analytic argument is given to show that the application of the Kirkwood superposition approximation to the description of fluid correlation functions precludes the existence of a critical point. The argument holds irrespective of the dimension of the system and the specific form of the interaction potential and settles a long-standing controversy surrounding the nature of the critical behavior predicted within the approximation.
    The Journal of Chemical Physics 10/2013; 139(14):141101. · 3.16 Impact Factor
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    ABSTRACT: The analytic and numerical methods introduced previously to study the phase behavior of hard sphere fluids starting from the Yvon-Born-Green (YBG) equation under the Kirkwood superposition approximation (KSA) are adapted to the square-well fluid. We are able to show conclusively that the YBG equation under the KSA closure when applied to the square-well fluid: (i) predicts the existence of an absolute stability limit corresponding to freezing where undamped oscillations appear in the long-distance behavior of correlations, (ii) in accordance with earlier studies reveals the existence of a liquid-vapor transition by the appearance of a "near-critical region" where monotonically decaying correlations acquire very long range, although the system never loses stability.
    The Journal of Chemical Physics 04/2013; 138(16):164506. · 3.16 Impact Factor
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    ABSTRACT: We investigate the stability to structural perturbation of Pseudomonas aeruginosa azurin using a previously developed geometric model. Our analysis considers Ru(2,2',6',2″-terpyridine)(1,10-phenanthroline)(His83)-labeled wild-type azurin and five variants with mutations to Cu-ligating residues. We find that in the early stages of unfolding, the β-strands exhibit the most structural stability. The conserved residues comprising the hydrophobic core are dislocated only after nearly complete unfolding of the β-barrel. Attachment of the Ru-complex at His83 does not destabilize the protein fold, despite causing some degree of structural rearrangement. Notably, replacing the Cys112 and/or Met121 Cu ligands does not affect the conformational integrity of the protein. Notably, these results are in accord with experimental evidence, as well as molecular dynamics simulations of the denaturation of azurin.
    Molecular Physics 04/2013; 111(7):922-929. · 1.67 Impact Factor
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    ABSTRACT: Supramolecular architectures provide a reproducible template on which surficial processes can be studied. We consider the irreversible reaction A + B → C where B is a stationary reaction center and A is a coreactant diffusing on a finite, discretized d = 2 dimensional surface of a supramolecular assembly. A lattice-statistical model is developed to quantify how the reaction efficiency changes when the template is planar, Euler characteristic Ω = 0, or wrapped on the surface of a d = 3 host, Ω = 2. We find that for aperiodic or regular surfaces of finite spatial extent, dispersed Ω = 2 assemblies better optimize surficial reactions than Ω = 0 planar hosts.
    Chemical Physics Letters 06/2012; 538:86–92. · 2.15 Impact Factor
  • Harry B. Gray, Jay R. Winkler, John J. Kozak
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    ABSTRACT: A comparative study of the early stages of unfolding of five proteins: cyt c, c-b562, cyt c′, azurin, and lysozyme is reported. From crystallographic data, helical regions and intervening non-helical (or ‘turning’) regions are identified in each. Exploiting a previously introduced geometrical model, the paper describes quantitatively the stepwise extension of a polypeptide chain subject to the geometrical constraint that the spatial relationship among the residues of each triplet is fixed by native-state crystallographic data. Despite differences among the above-cited proteins, remarkable universality of behavior is found in the early stages of unfolding. At the very earliest stages, internal residues in each helical region have a common unfolding history; the terminal residues, however, are extraordinarily sensitive to structural perturbations. Residues in non-helical sections of the polypeptide unfold after residues in the internal helical regions, but with increasing steric perturbation playing a dominant role in advancing denaturation.
    Molecular Physics 01/2012; · 1.67 Impact Factor
  • G. Nicolis, John J. Kozak, C. Nicolis
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    ABSTRACT: We present a comparative analysis of sequential versus hierarchical mechanisms of self-assembly in supramolecular architectures. The analysis is multifaceted, drawing on and inter-relating insights from a kinetic mean-field analysis and one based on the theory of finite Markov processes, complemented by Monte Carlo calculations. We give explicit results for two reaction pathways that are likely to dominate in early stages of self-assembly, and draw attention to experimental studies to which our results pertain: crystallization of zeolites from the bulk phase and aggregation of surface-supported supramolecular structures. Among the several conclusions that can be drawn from the theory and the simulations is a crossover from one mechanism to another, depending on the values of system parameters.
    Molecular Physics 01/2012; · 1.67 Impact Factor
  • John J. Kozak, Roberto A. Garza-López
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    ABSTRACT: We explore the consequences of metrically decomposing a finite phase space, modeled as a d-dimensional lattice, into disjoint subspaces (lattices). Ergodic flows of a test particle undergoing an unbiased random walk are characterized by implementing the theory of finite Markov processes. Insights drawn from number theory are used to design the sublattices, the roles of lattice symmetry and system dimensionality are separately considered, and new lattice invariance relations are derived to corroborate the numerical accuracy of the calculated results. We find that the reaction efficiency in a finite system is strongly dependent not only on whether the system is compartmentalized, but also on whether the overall reaction space of the microreactor is further partitioned into separable reactors. We find that the reaction efficiency in a finite system is strongly dependent not only on whether the system is compartmentalized, but also on whether the overall reaction space of the microreactor is further partitioned into separable reactors. The sensitivity of kinetic processes in nanoassemblies to the dimensionality of compartmentalized reaction spaces is quantified.
    ISRN Computational Mathematics. 10/2011; 2012.
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    ABSTRACT: We use an analytic criterion for vanishing of exponential damping of correlations developed previously [J. Piasecki et al., J. Chem. Phys. 133, 164507 (2010)] to determine the threshold volume fractions for structural transitions in hard sphere systems in dimensions D = 3, 4, 5, and 6, proceeding from the Yvon-Born-Green hierarchy and using the Kirkwood superposition approximation. We conclude that the theory does predict phase transitions in qualitative agreement with numerical studies. We also derive, within the superposition approximation, the asymptotic form of the analytic condition for occurrence of a structural transition in the D → ∞ limit.
    The Journal of Chemical Physics 08/2011; 135(8):084509. · 3.16 Impact Factor
  • John J Kozak, G Nicolis
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    ABSTRACT: We study the early stages of self-assembly of elementary building blocks of nanophase materials, considering explicitly their structure and the symmetry and the dimensionality of the reaction space. Previous work [Kozak et al., J. Chem. Phys. 134, 154701 (2007)] focused on characterizing self-assembly on small square-planar templates. Here we consider larger lattices of square-planar symmetry having N = 255 sites, and both hexagonal and triangular lattices of N = 256 sites. Furthermore, to assess the consequences of a depletion zone above a basal layer (λ = 1), we study self-assembly on an augmented diffusion space defined by λ = 2 and λ = 5 stacked layers having the same characteristics as the basal plane. The effective decrease in the efficiency of self-assembly of individual nanophase units when the diffusion space is expanded, by increasing the template size and/or by enlarging the depletion zone, is then quantified. The results obtained reinforce our earlier conclusion that the most significant factor influencing the kinetics of formation of a final self-assembled unit is the number of reaction pathways from one or more precursor states. We draw attention to the relevance of these results to zeolite synthesis and reactions within pillared clays.
    The Journal of Chemical Physics 02/2011; 134(6):064701. · 3.16 Impact Factor
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    The Journal of Chemical Physics 02/2011; 134(5):059902. · 3.16 Impact Factor
  • Harry B. Gray, Jay R. Winkler, John J. Kozak
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    ABSTRACT: A geometrical model has been developed to describe the early stages of unfolding of cytochromes c′ and c-b562. Calculations are based on a step-wise extension of the polypeptide chain subject to the constraint that the spatial relationship among the residues of each triplet is fixed by the native-state crystallographic data. The response of each protein to these structural perturbations allows the evolution of each of the four helices in these two proteins to be differentiated. It is found that the two external helices in c′ unfold before its two internal helices, whereas exactly the opposite behaviour is demonstrated by c-b562. Each of these cytochromes has an extended, internal, non-helical (‘turning’) region that initially lags behind the most labile helix but then, at a certain stage (identified for each cytochrome), unravels before any of the four helices present in the native structure. It is believed that these predictions will be useful in guiding future experimental studies on the unfolding of these two cytochromes.
    Molecular Physics 01/2011; 109(6):905-916. · 1.67 Impact Factor
  • Roberto A. Garza-López, John J. Kozak
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    ABSTRACT: Quantum–mechanical studies have predicted, and experimental studies on SrCu2O3 have confirmed, that the propagation of bound pairs on even-chain copper oxide ladders is possible, but not on ladders with an odd number of legs. To study whether this quantum–mechanical lattice parity effect has a classical analog, and to document the consequences of assuming different coupling scenarios between the ladder and adjacent sublattices, we develop a classical Markovian lattice-statistical model to monitor the efficiency of migration on a composite lattice. Regions of parameter space where significant departures from results obtained via a symmetrical random walk are identified.
    Chemical Physics Letters 01/2011; 514(1):88-93. · 2.15 Impact Factor
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    ABSTRACT: We have developed a geometrical model to study the unfolding of iso-1 cytochrome c. The model draws on the crystallographic data reported for this protein. These data were used to calculate the distance between specific residues in the folded state, and in a sequence of extended states defined by n= 3, 5, 7, 9, 11, 13, and 15 residue units. Exact calculations carried out for each of the 103 residues in the polypeptide chain demonstrate that different regions of the chain have different unfolding histories. Regions where there is a persistence of compact structures can be identified, and this geometrical characterization is fully consistent with analyses of time-resolved fluorescence energy-transfer (TrFET) data using dansyl-derivatized cysteine side-chain probes at positions 39, 50, 66, 85, and 99. Our calculations were carried out assuming that different regions of the polypeptide chain unfold synchronously. To test this assumption, we performed lattice Monte Carlo simulations to study systematically the possible importance of asynchronicity. Our calculations show that small departures from synchronous dynamics can arise if displacements of residues in the main body of the chain are much more sluggish than near-terminal residues.
    Molecular Physics 01/2011; 109(2):301-313. · 1.67 Impact Factor
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    ABSTRACT: Starting from the second equilibrium equation in the BBGKY hierarchy under the Kirkwood superposition closure, we implement a new method for studying the asymptotic decay of correlations in the hard disk fluid in the high density regime. From our analysis and complementary numerical studies, we find that exponentially damped oscillations can occur only up to a packing fraction η(∗)∼0.718, a value that is in substantial agreement with the packing fraction, η∼0.723, believed to characterize the transition from the ordered solid phase to a dense fluid phase, as inferred from Mak's Monte Carlo simulations [Phys. Rev. E 73, 065104 (2006)]. Next, we show that the same method of analysis predicts that the exponential damping of oscillations in the hard sphere fluid becomes impossible when λ=4nπσ(3)[1+H(1)]≥34.81, where H(1) is the contact value of the correlation function, n is the number density, and σ is the sphere diameter in exact agreement with the condition, λ≥34.8, which is first reported in a numerical study of the Kirkwood equation by Kirkwood et al. [J. Chem. Phys. 18, 1040 (1950)]. Finally, we show that our method confirms the absence of any structural transition in hard rods for the entire range of densities below close packing.
    The Journal of Chemical Physics 10/2010; 133(16):164507. · 3.16 Impact Factor
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    ABSTRACT: We continue the study of a particle (atom, molecule) undergoing an unbiased random walk on the Sierpinski gasket, and obtain for the gasket and tower the eigenvalue spectrum of the associated stochastic master equation. Analytic expressions for recurrence relations among the eigenvalues are derived. The recurrence relations obtained are compared with those determined for two Euclidean lattices, the closed chain with an absorbing site and a finite chain with an absorbing site at one end. We check and confirm the internal consistency between the smallest eigenvalue and the mean walklength in each of the cases studied. Attention is drawn to the relevance of the results obtained to a problem of electron transfer in proteins.
    Physical Review E 07/2010; 82(1 Pt 1):011137. · 2.31 Impact Factor
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    ABSTRACT: Recent observations of the growth of protein crystals have identified two different growth regimes. At low supersaturation, the surface of the crystal is smooth and increasing in size due to the nucleation of steps at defects and the subsequent growth of the steps. At high supersaturation, nucleation occurs at many places simultaneously, the crystal surface becomes rough, and the growth velocity increases more rapidly with increasing supersaturation than in the smooth regime. Kinetic roughening transitions are typically assumed to be due to the vanishing of the barrier for two-dimension nucleation on the surface of the crystal. We show here, by means of both analytic mean-field models and kinetic Monte Carlo simulations, that a transition between different growth modes reminiscent of kinetic roughening can also arise as a kinetic effect occurring at finite nucleation barriers.
    The Journal of Chemical Physics 01/2010; 132(3):035102. · 3.16 Impact Factor
  • K. Pawełek, John J. Kozak, Z.J. Grzywna
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    ABSTRACT: A recently proposed Markovian model of K+ ion transport through the selectivity filter of the KcsA bacterial channel is generalized. This generalization allows a specific estimate to be made of the current through the channel which is found to be consistent with experimentally determined values [11.0 (+/−) 0.1 pA]. A further aspect of the generalization presented here is the quantification of the difference of synchronous vs. asynchronous motion of the K+ ions and water molecules in the channel. Considering excluded volume effects only, the difference in mean passage time through the channel is in the range 50%–75%; on the basis of calculations reported here, we argue that this difference will be even more pronounced when K+/ K+ Coulombic repulsions and electrostatic attractive interactions between K+ ions and the carbonyl groups lining the channel are taken into account.
    Physica A: Statistical Mechanics and its Applications 01/2010; 389(16):3013-3022. · 1.68 Impact Factor
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    Kristopher G Urie, John J Kozak, E Abad
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    ABSTRACT: We report lattice Monte Carlo calculations to study the efficiency of diffusion-controlled reactive processes involving geminate radical pairs. Whereas our earlier study [J.J. Kozak, C. Nicolis, G. Nicolis, N.J. Turro, J. Phys. Chem. 105 (2001) 10949] focused on factors affecting the reaction efficiency when a pair of coreactants moved synchronously on a surface modeled as a d = 2 dimensional square planar lattice subject to periodic boundary conditions, we document here differences in reaction efficiency when a pair of coreactants can move synchronously or asynchronously on surfaces which are topologically different but characterized by the same number N of sites. As before, the first surface is taken to be a d = 2 square planar lattice; the second surface considered is a Cartesian shell, the bounded surface of a cube. When studied as a function of system size, we find that synchronous dynamics are more efficient than asynchronous dynamics in optimizing diffusion–reaction processes; and, reactions on planar, periodic surfaces are more efficient than on cubic shells. The relevance of these conclusions to experimental studies on two radiation-induced, radical decay reactions [the one cited above and A.J. Frank, M. Grätzel, J.J. Kozak, J. Am. Chem. Soc. 98 (1976) 3317] is noted and discussed.
    Physica A: Statistical Mechanics and its Applications 01/2010; 389:4061-4070. · 1.68 Impact Factor
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    ABSTRACT: We consider 36 planar nets identified by O'Keeffe and Hyde and calculate for each, using the theory of finite Markovian processes, the overall mean walk length n (first passage time) of a reactant diffusing randomly on a finite platelet before being trapped at a reaction center; the results are analyzed in terms of the total number N of lattice sites, the number N(b) of boundary sites, the average valence nu, and the bond orientation function Psi. We establish that crystalline platelets that are members of the same compatible class are characterized by very comparable catalytic efficiencies. The results obtained are also linked to an analysis of the kinetics of docking in postnucleation stages of protein self-assembly and to a recent conjecture on the symmetries of planar nets and the hard disk freezing transition.
    Physical Review E 08/2009; 80(2 Pt 1):021116. · 2.31 Impact Factor

Publication Stats

103 Citations
227 Downloads
133.75 Total Impact Points

Institutions

  • 2010–2013
    • University of Warsaw
      • Institute of Theoretical Physics
      Warsaw, Masovian Voivodeship, Poland
    • Cray
      Seattle, Washington, United States
  • 2006–2013
    • California Institute of Technology
      • Beckman Institute
      Pasadena, CA, United States
  • 2005–2013
    • DePaul University
      • Department of Chemistry
      Chicago, Illinois, United States
  • 2008
    • University of Chicago
      • James Franck Institute
      Chicago, IL, United States
  • 1999–2008
    • Pomona College
      • Department of Chemistry
      Claremont, California, United States
  • 2007
    • Free University of Brussels
      Bruxelles, Brussels Capital Region, Belgium
  • 1994–2006
    • Iowa State University
      • Department of Chemistry
      Ames, IA, United States
  • 2003
    • Université Libre de Bruxelles
      • Faculty of Sciences
      Bruxelles, Brussels Capital Region, Belgium
  • 1990
    • University of Georgia
      • Department of Chemistry
      Athens, GA, United States