Escaping the Lattice

The next best thing to seeing real atoms is to mimic them in silico: we assign interactions between the atoms and then — pouf –They’re alive!

The number of particles in a visible sample is on the order of Avogadro’s constant, say ~1023, whereas a fairly muscular computer can only follow ~105-107 atoms at a time. To compensate, computational scientists typically replicate their simulation boxes infinitely in space. This creates a quandary for calculating forces across replication boxes. The simplest option, which is to neglect forces beyond a chosen cut-off, suffices for many interactions, is too crude for the particularly long-range interactions that occur between charges. To accurately account for these interactions, it is customary to use a clever 90-year-old (!) technique, called the Ewald sum.(1)

The problem with the Ewald sum is that it requires imposing a long-range periodicity that is inappropriately short for macromolecules.(2) To avoid artifacts, a number of alternatives have been suggested. One intuitive approach, called “force shifting”, smooths the interaction energy and its first derivative (the force) at the chosen cutoff. However, this creates new artifacts (see figure) when particles have very large or varying charges, as in some ionic liquids. Brandeis scientists Seyit Kale and Judith Herzfeld, have found that this problem can be solved by also smoothing the second derivative of the interaction energy (the acceleration).(3)  This approach performs virtually as well as the Ewald sum in a new reactive force field that they have been developing (see figure).

The neighbor frequencies for bulk water calculated with force shifting at a cutoff of 9 Å (red) and 12 Å (magenta) versus with the authors’ new approach at a 9 Å cutoff (blue) and the Ewald sum (black). The blue and black curves are virtually the same while the red and magenta curves contain artifacts. The inset shows a representation of a water molecule from the force field that the authors are developing.

  1. Ewald P (1921) The Berechnung optischer und elektrostatischer Gitterpotentiale. Ann. Phys. 369: 253-287.
  2. Hunenberger PH, McCammon JA (1999) Effect of artificial periodicity in simulations of biomolecules under Ewald boundary conditions: A continuum electrostatics study. Biophys. Chem. 78: 69-88.
  3. Kale S, Herzfeld J (2011) Pairwise Long-range Compensation for Strongly Ionic Systems. J. Chem. Theory Comput. 7: 3620-3624.

Sugars in Old and New Guises

Spontaneously formed sugar polymers have long been recognized as important components of soil (as humins) and cooked foods (as melanoidin products of non-enzymatic browning).  More recently, it has been suggested that they were also important in the advent of life on earth because they form micro-spherules that can encapsulate reactions, potentially acting as precursors of modern cells.  However, the molecular structures of these polymers has been difficult to determine because of their amorphous and insoluble nature.  All that was clear is that they contain aromatic rings that include oxygen (furans) and nitrogen (pyrroles). The further supposition was that these rings were directly linked in chains.  Now, using solid state NMR, Professor Judith Herzfeld, undergraduate Danielle Rand, graduate students Melody Mak-Jurkauskas and Irena Mamajanov, and postdoctoral research associates Yoh Matsuki and Eugenio Daviso, have shown that the polymer is much more complicated, with the aromatic rings cross-linked by variously dehydrated sugar molecules. Their paper, entitled “Molecular Structure of Humin and Melanoidin via Solid State NMR“, appeared online on April 1 in Journal of Physical Chemisty B.

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