B. Borstnik and D. Lukman
National Institute of Chemistry,
Ljubljana, Slovenia

Properties of clusters appearing in the site percolation problem on square and cubic lattices are expressed in a way that emphasizes the thermodynamic analogy. It is shown that the analogue of the specific heat exhibits expected critical behaviour as a function of the analogue of the temperature. The results support the notion that the partition of the specific heat of Ising systems (Borstnik and Lukman, Phys. Rev. E 60 2595(1999) ) into the structural and populational component is a meaningful one. Another cluster property which is taken under the scrutiny is the fractal dimensionality of clusters which also indicates the presence of phase transition.

Self-similar correlations in the many-particle dynamics

S.S. Kharintsev and M.Kh. Salakhov
Physics Department, Kazan State University
Kazan, Russia

In this paper scale-invariant temporal-spatial correlations of many collisions in a non-equilibrium Bolzmann gas are studied. We proposed a new approach to take into account the non-markovian behavior of collisional process for the non-equilibrium system. To investigate these effects we developed the self-similar diffuse model based on the fractal Brownian motion for a free particle and the self-similar mechanism of interference of scalar perturbations for an atomic oscillator. The motion equations describing the time evolution of many particle dynamics with the self-similar memory are irreversible. Within the framework of these we carried out the detailed analysis of the influence of self-similar correlations of gas kinetic collisions on the spectral line shape in a neutral gas, based on the classical Fourier integral theory. It is shown that taking into account temporal-spatial self-similar (fractal) correlations gives rise to the additional Dicke-narrowing of spectral lines [1], and allows one to explain the asymmetry of spectral lines in wings in the Doppler regime provided that the pressure broadening is one order or more than the Doppler-effect [2].The approach of the given paper is based on the Kadomtsev's external noise idea [3] within the framework of which the irreversibility of the dynamics of a gas consisting of classical particles and the possibility of its statistical treatment are due to a tiny interaction of the system with the irreversible surrounding. In that way B.B. Kadomtsev gave the physical interpretation for the molecular chaos hypothesis [3]. We continue to evolve the Kadomtsev's approach provided that the external surrounding represents the scale-invariant averaged microscopic field of particles.
1. Dicke R.H., Phys. Rev. -1953. -V.89, N.2. -P.472-473.
2. Rautian S. G., Sobelman I.I. Usp. Fiz. Nauk -1966. -V.90, N.2. -P.209-236.
3. Kadomtsev B. B., Dynamics and Information, Moscow: Red. UFN, 1997.
 
 Statistical investigations revealing the origin of the universal genetic code.
Ludwig Hofacker
Theoretische Chemie
Technische Universitaet Muenchen
The concept of a metric distance space for amino acid fitness with respect to to function in proteins , created by Borstnik and Hofacker, provides a unique device to track the orgin of the genetic code back to prebiotic RNA - world scenarios. One finds compelling evidence that the evolution of functional peptides must have been carried by both the direct and reverse RNA strands.
 

Informational aspects of the evolution of algorithmic neural processors in the human brain.

Ludwig Hofacker
Theoretische Chemie
Technische Universitaet Muenchen

The capability of abstract (algorithmic) concept formation and concept processing developed in human/hominide evolution within a period of barely 2 mio years. This poses a problem under informational genetic viewpoints as the number and type of neurotropic point mutations can neatly be estimated - and thereby the mayor part of the of the genetic information available to build elementary neural processors; the latter being prerequisit for furthergoing language and learning capabilities. It turns out that the information provided for coding algotithmic primers of human cortical nets is very limited and inferences can be drawn as to the necessarily parsimonious logical architecture of the human brain. This entails the question to which extent even abstract human cognitive processes might be directed (and possibly limited) by neural evolution with selection in an archaic ambiente.
 
 
 
 

Energy Landscapes and Folding Kinetics for RNA Secondary Structures

Ivo Hofacker
Institut fuer Theoretische Chemie
Universitaet Wien

The ability to fold into a well-defined native conformation is a prerequisite for biological functional biopolymers. In the case of RNA, secondary structures provide a computationally feasible model, in which most thermodynamic quantities of interest such as the ground state and partition function can be computed via dynamic programming. Such equilibrium properties are, however, not sufficient to characterize the folding behavior. To investigate the folding dynamics of an RNA sequence, we consider the energy landscape formed by all possible conformations (secondary structures). By enumerating all conformations within a predefined energy range, we obtain a detailed picture of the energy landscape in the vicinity of the ground state. In particular we are able to identify local minima, as well as measure their basins of attractions and the energy barriers separating them. This analysis of the landscape can be compared to detailed folding simulations using a Monte Carlo technique, as well as experimental data on some biologically relevant sequences. Folding kinetics depend strongly on the highest energy barrier present in the landscape, and barriers high enough to stabilize mis-folded states over biologically relevant times, can occur even for relatively short sequences. Typical sequences exhibit a small number of significant local minima, which can be reached quickly from the unfolded state. Depending on the energy barriers between these local minima re-folding to the ground state may be possible.

ENTROPIC TRAPPING: ITS POSSIBLE ROLE IN RECEPTOR-LIGAND AND OTHER BIOCHEMICAL SYSTEMS

Adolf Miklavc,
National Institute of Chemistry, Hajdrihova 19,  Ljubljana, Slovenia
                     and
Darko Kocjan,
LEK, Pharmaceutical and Chemical Company,  Ljubljana, Slovenia

Entropy-driven binding continues to be found in receptor-ligand
systems, e.g., and other important biochemical systems, e.g.,
but the interpretation thereof is often rather elusive.
Experimental findings in several systems clearly indicate
that the entropic biding mechanisms usually
considered in the literature could not provide a consistent
interpretation of the binding data in a number of cases. Entropic
trapping was therefore proposed in our earlier work as an
alternative mechanism. It is pointed out here that, subsequently the
existence of such a mechanism was firmly established and that
its role is strongly corroborated by the newest data from various
biochemical systems.
 

Dynamics of Confinement Induced Phase Transition in Liquids
Alenka Luzar
School of Pharmacy
University of California

Glauber dynamics Monte Carlo simulations of a lattice gas close
to liquid-gas coexistence and confined between partially drying
surfaces are used to model the effect of water confinement on the
dynamics of surface-induced phase transition. Specifically, we
examine how kinetics of induced evaporation changes as the texture
of hydrophobic surfaces is varied. Our results provide guidelines
for efficient manipulation of surface properties. We find that
evaporation rates can be considerably slowed upon deposition of
relatively small amount of hydrophilic coverage. The distribution
of hydrophilic patches is however crucial, with the regularly spaced
distribution being much more effective in slowing the formation of
vapor tubes that trigger the evaporation process.  To relate simulation
rates to experimental ones, we also perform simulations using
the mass-conserving Kawasaki algorithm. We predict evaporation
time scales that range from hundreds of picoseconds in the case of
mesoscopic surfaces $\sim 10^4$ nm$^2$ to tens of nanoseconds for
smaller surfaces $\sim 40$ nm$^2$, when the two surfaces are
$\sim$ 10 solvent layers apart.  The study demonstrates
that cavitation is kinetically viable in real systems and should be
considered in studies of processes at confined geometry.
Furthermore, we determine the free energy barrier of vapor tube
formation in a metastable liquid confined between hydrophobic walls.
We apply transition state theory and a constrained umbrella sampling
technique, taking as our transition state a vapor pocket in the
middle of the liquid layer. The calculated transmission coefficients
show that the size of a vapor pocket is indeed a reasonable order
parameter to describe the drying transition.  The umbrella sampling
technique, taking as our transition state a vapor pocket in the
middle of the liquid layer. The calculated transmission coefficients
show that the size of a vapor pocket is indeed a reasonable order
parameter to describe the drying transition.  The umbrella sampling
method gives estimates of free energy barrier for vapor tube formation
that are in order-of-magnitude agreement with direct Monte Carlo simulation
runs.  In all the cases studied, the estimated free energy barriers
are much smaller than those predicted by a previous mean-field approach.
 

Colloidal and Interprotein Forces in Ionic Environments
                               D. Bratko
          College of Chemistry, University of California at Berkeley

  We are concerned with a range of interactions affecting phase behavior
  of colloidal and protein solutions. Computer simulations and integral
  equation theories are employed to study long-ranged interactions among
  screened ionic micelles and globular proteins. Deviations from pair-wise
  additivity of the potentials of mean force are examined and discussed in the
  context of one-component teories for solution thermodynamics. Calculations
  of Coulombic interactions among oppositely charged macroions are exploited
  in interpretation of electrostatic attraction among globally neutral
  macroparticles with nonuniform charge distributions. Mechanisms of short-
  ranged hydrophobic interaction and specific residue-residue forces that
  implicate conformational changes of interacting proteins are briefly
  discussed.
 

Efficient split integration symplectic method
for Hamiltonian systems

         Dusanka Janezic and  Matej Praprotnik
         National Institute of Chemistry  Hajdrihova 19,
         1000 Ljubljana, Slovenia
          e-mail: dusa@kihp5.cmm.ki.si
 
There is growing recognition in the last few  years that the
symplectic integration methods are often the right way
of integrating the equations of motion.
Recent advances in deveopment of the second and the fourth order
split integration symplectic method (SISM) for numerical  solution of the
Hamiltonian system  based on a factorization of the Liouville propagator
are presented.
The technique, derived in terms of the Lie algebraic language,
 is based on the splitting of the total Hamiltonian of the
system into two pieces, each of which can either be solved exactly or more
conveniently than by using standard methods. The individual solutions
are then combined in such a way as to approximate the evolution of the
original equation for a time step, and to minimize errors.

The SISM uses an anlytical treatment of high frequency motions
within a second order generalized leap-frog scheme and within a fourth
order scheme. The computation cost per integration step of SISM
is approximately  the same as that of commonly used algorithms, and
it allows an integration time step up to an order of magnitude larger
than can be used by other methods of the same order and complexity.
The second and the fourth order SISM  have been tested on a variety of examples.
In all cases the SISM posses  long term stability and the ability to take larger time steps.
The results also show that the fourth order SISM benefits for accuracy
for small step sizes, only.

  Statistical Mechanics of Nonlinear Optical Processes in Liquids

S. Bratos and J.-Cl. Leicknam
Laboratoire de Physique
Theorique des Liquides
Universite P. et M. Curie,
Paris, France

If the interaction between the matter and the light is strong enough, the
Kubo linear response theory no longer applies, and new approaches are
required. There are many circumstances in which this situation occurs,
and particularly so in the laser spectroscopy. Two sort of theories
are available and are described in this lecture. In the first of them,
the von Neumann-Liouville equation for the density matrix is solved
perturbatively. New objects appear such as higher order
susceptibilities and multi-time correlation functions. Diagrammatic
expressions are of current use. In spite of difficulties, the theory
can be formulated in a clean and precise way. Combining it with modern
computer simulation techniques, classical or quantum mechanical, is
strongly recommended. In the second technique, the von
Neumann-Liouville equation is solved numerically. This approach is
necessary in the presence of saturation effects. The power of
Statistical Mechanics in this domain is illustrated on two examples
showing how it can be used for a real time detection of atomic motions
in liquid phase chemical reactions.

MIXED QUANTUM-CLASSICAL MOLECULAR DYNAMICS :
SIMULATION OF PROTON TRANSFER PROCESSES
Janez Mavri
National Institute of Chemistry, Hajdrihova 19, Ljubljana, Slovenia
e-mail:janez@kihp2.ki.si}

An overview of the methods that can mix quantum and classical
dynamics will be given.
Classical molecular dynamics simulations can not properly
describe the proton motion. On the other hand, full quantum
dynamical simulations currently can not take into account more than
twelve degrees of freedom.
A density matrix evolution (DME) method (Berendsen and Mavri,
J. Phys. Chem., 97, 13464, 1993) to simulate the dynamics of quantum
system embedded in a classical environment will be presented. The method
is applicable when the quantum-dynamical degrees of freedom can be described
in a Hilbert space of limited dimensionality.
The rate constant for the  proton transfer between
Asp25 and Asp125 at the active site of apoenzyme HIV-1 proteaze
has been determined. The proton hops between the minima on a
nanosecond time scale. The result is discussed in terms of the active site
polarizability and design of novel HIV-1 proteaze inhibitors.
First principle calculations of the vibrational spectra
of strong hydrogen bonded
systems present a special challenge due to high anharmonicity
of the OH stretching and strong coupling to the other degrees of freedom.
We treat the proton motion
quantum dynamically i.e. we include excited vibrational states
while the remaining intramolecular degrees
of freedom and solvent degress of freedom
are  treated by classical mechanics.
The IR spectrum is calculated numerically from the time-dependent
dipole moment using the Fourier Transform techniques.
 

Detrended fluctuation analysis of time series of a
firing fusimotor neuron
S. Blesic, S. Milosevic, Dj. STRATIMIROVIC, M. Ljubisavljevic
Institute for Medical Research, Laboratory for Neurophysiology,
and
Faculty of Physics, University of Belgrade,
Serbia, Yugoslavia

We study the interspike intervals (ISI) time series of the
spontaneous fusimotor neuron activity by applying the detrended
fluctuation analysis that is a modification of the random walk
model analysis. Thus, we have found evidence for the white
noise characteristics of the ISI time series, which means that
the fusimotor activity does not possess temporal correlations.
We conclude that such an activity represents the requisite noisy
component for occurrence of the stochastic resonance mechanism
in the neural coordination of muscle spindles.
 

POTENTIAL METHODS IN ANALYTIC HYERARCHY PROCESS
Lavoslav Caklovic
PMF, Univ. Zagreb

Some methods in multi criteria ranking problem are based on the matrix
A obtained by pairwaise comparison. If A is reciprocal one can construct
the underlying oriented graph with corresponding flow. The corresponding
consistent potential gives rise to the ranking function. Strong dominance
and row dominance properties are satisfied. The measure of inconsistency
is also given. Self ranking of a group is done via a fix point theorem.
 
 
 

Simulations of the Systems of Biological Interest by Car-Parrinello
Molecular Dynamics

Paolo Carloni
SISSA
34014 Trieste, Italy
 
 
 
 
 

Molecular modeling in chemical engineering: from the prediction of phase behavior to the characterization of complex molecules

                                      Maurizio Fermeglia and Sabrina Pricl

    Department of Chemical, Environmental and Raw Materials Engineering - DICAMP, University of Trieste,
                                      Piazzale Europa 1, 34127 Trieste, Italy

                           mauf@dicamp.univ.trieste.it sabrinap@dicamp.univ.trieste.it

 
 
In the last decade molecular modeling has marked a breakthrough in chemical engineering, as a consequence of more reliable and faster computer codes and hardware, the development of accurate intermolecular potentials and the implementation of new techniques for tackling phenomena of topical interest in process design. One of the most important applications of molecular modeling in chemical engineering undoubtedly is the prediction of phase behavior.
This paper will present some approaches to this problem we have developed so far, with specific attention to pure liquids and their mixtures. The techniques involved encompass almost all principal simulation methods, such as molecular mechanics, molecular quantum mechanics and molecular dynamics. The basic machinery of the approach is based on the a priori calculation of some physically-based parameters of theoretically sound equation of state (EOS). In
particular, we have focused our attention to the new generation of EOSs, based on perturbation theory applied to chain-like molecules, such as the perturbed-hard-sphere-chain theory (PHSCT) EOS and the SAFT EOS, and other equations of state based on the lattice fluid theory for polymers, e.g., the Sanchez-Lacombe EOS.
We will describe in details the thermodynamic models and the computational strategy for calculating the relevant parameters, and show a number of results obtained for the prediction of the phase behavior of pure components and mixtures. In particular, we will discuss the applications of the methodologies to alternative refrigerants, hydrocarbons, supercritical fluids, rubbery polymers and mixtures of polar and non polar fluids.
At the end, in the spirit of the seminar, we will also present a brief overview of molecular modeling and simulation activity we are carrying out at our CAS-Lab, which span from the characterization of complex materials (dendrimers, host-guest compounds, etc.) to transport phenomena in crystalline and amorphous matrices.