Styliani Consta - theory
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en_CAStar-shaped droplets
http://theory.chem.uwo.ca/?q=node/65
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>Droplets subject to electric fields may obtain spectacular morphologies. Starting from the seminal works of Rayleigh (1882), Zeleny (1917) and G. I. Taylor (1964), the behaviour of droplets in an electric field continues to fascinate scientists due to their numerous applications. Charged droplets are often generated by electrospray ionization methods. We have found by molecular simulations that when a nano-drop comprising a single spherical central ion and dielectric solvent is charged above a well-defined threshold, it acquires a stable star morphology [S. Consta, Journal of Physical Chemistry B v. 114, pp. 5263--5268 (2010); Soft Matter v. 13 , pp. 8781-8795 (2017)] . Currently, we establish the principles of the formation of star-shaped droplets and their extensions to the formation of highly non-convex nano-particles. </p>
<div class="figure">
<img src="sites/default/files/H2OQ18_3Spikes.jpg" /><p>A three-point star comprised water and a macroion</p>
</div>
<div class="figure">
<img src="sites/default/files/H2OQ22_4Spikes.jpg" /><p>A four-point star comprised water and a macroion</p>
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<div class="figure">
<img src="sites/default/files/H2OQ27_6Spikes.jpg" /><p>A six-point star comprised water and macroion</p>
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</div></div></div><div class="field field-name-taxonomy-vocabulary-1 field-type-taxonomy-term-reference field-label-above"><div class="field-label">Topics: </div><div class="field-items"><div class="field-item even"><a href="/?q=taxonomy/term/3">simulations</a></div><div class="field-item odd"><a href="/?q=taxonomy/term/20">theory</a></div><div class="field-item even"><a href="/?q=taxonomy/term/26">droplets</a></div><div class="field-item odd"><a href="/?q=taxonomy/term/6">electrospray</a></div></div></div>Sun, 31 Dec 2017 23:40:43 +0000Styliani Constas65 at http://theory.chem.uwo.caModeling the stability of non-covalent protein complexes and assemblies
http://theory.chem.uwo.ca/?q=node/64
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<embed src="sites/all/libraries/mediaplayer/mediaplayer.swf?file=/sites/default/files/video/new-frag.mp4" width="512" height="452" allowfullscreen="true" autoplay="true" currenttime="1.0" autostart="true" autorewind="true"></embed></div>
<p>Protein-protein interactions (PPIs) play a pivotal role in all biological processes, including signal transduction, enzymatic catalysis as well as the formation of protein quaternary structures. Elucidating the mechanism of protein complexation/dissociation and finding its kinetics and thermodynamics are therefore important to unveil the fundamental principles underlying biochemical pathways in cells. Specific PPIs in solution rest heavily on non-covalent interactions between constituent protomers, including hydrogen bonding and ionic, hydrophobic, van der Waals and $\pi$-$\pi$ interactions. Polar weak interactions have variable strengths as long-range electrostatic interactions depend largely on the distance between two charge sources and their chemical environment. Electrostatic interactions may be enhanced in a vacuum and in non-polar regions away from bulk solution, but they become weak in a dielectric solvent such as water. These interactions are vital for proteins recognizing their partners in a highly crowded environment. </p>
<p>To dissect PPIs in a vast array of non-covalent protein complexes, a combination of different experimental techniques have been used in structural biology, which include native mass spectrometry (MS), X-ray crystallography, NMR spectroscopy, (cryo-)electron microscopy, and methods of bioinformatics. Native MS usually operates by preceding electrospray ionization (ESI), because ESI is a soft ionization method. ESI transfers analytes directly from the parent solution into the gaseous state via intermediate droplets that carry the analytes, solvent, and other ions. During their journey to the mass spectrometer, the droplets reduce in size via solvent evaporation and release of solvated ions. The analytes then emerge from the droplets following a variety of mechanisms. Because of the unknown role of the droplet chemistry in the stability of PPIs or protein-ligand interactions, the question on whether the gas-phase ensemble of the complexes reflects the chemical equilibria of the species in bulk solution has been debated for over twenty years. </p>
<p>The goal of our research is to establish the principles that govern the stability of a weak transient protein complex in the droplet environment and in bulk solution. In relation to the droplet enviroment, we provided the first computational evidence of a protein complex dissociation in a droplet [M. In Oh and SC, Physical Chemistry Chemical Physics v. 19, pp. 31965--31981 (2017); Journal of Physical Chemistry Letters v. 8, pp 80-85 (2017); Analytical Chemistry v. 89, pp. 8192--8202 (2017)]. We have made significant advances by introducing computational methodologies that allow us to find (i) the mechanism of complex dissociation in droplets and (ii) the correction to the equilibrium constant due to possible protein complex dissociation in a droplet. Our computational methods are based on a multi-scale computational approach. In our studies we address the challenging problem of the constantly changing acidity of the droplet due to its evaporation. In droplets we have use all-atom modelling of the protein complexes and explicit modelling of the solvent. On the other end, in bulk solution we use coarse grained models and advanced sampling techniques to investigate the mechanisms of protein association and dissociation. </p>
</div></div></div><div class="field field-name-taxonomy-vocabulary-1 field-type-taxonomy-term-reference field-label-above"><div class="field-label">Topics: </div><div class="field-items"><div class="field-item even"><a href="/?q=taxonomy/term/3">simulations</a></div><div class="field-item odd"><a href="/?q=taxonomy/term/20">theory</a></div><div class="field-item even"><a href="/?q=taxonomy/term/25">proteins</a></div></div></div>Sun, 31 Dec 2017 23:37:43 +0000Styliani Constas64 at http://theory.chem.uwo.caManifestations of Charge Induced Instability in Droplets Effected by Charged Macromolecules
http://theory.chem.uwo.ca/?q=node/47
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Phys. Rev. Lett. 109, 148301 (2012)
</p>
<p style="font-weight:bold;font-style:italic;padding:2em">Ion-release processes from droplets that contain excess charge are of central importance in determining the charge-state distributions of macromolecules in electrospray ionization methods. We develop an analytical theory to describe the mechanism of contiguous extrusion of a charged macromolecule from a droplet. We find that the universal parameter determining the system behavior is the ratio of solvation energy per unit length to the square of the ion charge density per unit length. Systems with the same value of the ratio will follow the same path in the course of droplet evaporation. The analytical model is compared with molecular simulations of charged polyethylene glycol macroion in aqueous droplets, and the results are in excellent agreement.</p>
<div>
<p>
We illustrate the mechanism of extrusion and define the parameters critical to a theoretical examination of the mechanism. The parameters of the model contributing to the energy are the solvation energy of the linear macromolecule and its charge. In the considered model we assume that the droplet has spherical shape. As the droplet shape remains spherical the surface energy is constant and the surface tension term does not enter equation \eqref{eq:ener-total}. Based on the above considerations we express the total energy of the system as<br />
\begin{equation}<br />
E_{\mathrm{total}} = E_{\mathrm{elec}} + (L-{\lambda}) v_{0} .<br />
\label{eq:ener-total}<br />
\end{equation}<br />
where $L$ is the length of the macromolecule, $\lambda$ is the length of the extruded segment of the macromolecule and $v_0$ the solvation energy per unit length of the macromolecule. Electrostatic energy of the straight rigid segment in vacuum is set to zero and the corresponding change in the self-interaction energy upon solvation is accounted for by the solvation energy contribution.
</p>
<div class="figure">
<img src="sites/default/files/illustr-01.png" /><p>Illustration of a system consisting of a partially extruded macromolecule (PEG) in a droplet. Model parameters are defined. The droplet radius is $R$ and the length of the extruded segment is $\lambda$. In a conducting droplet the electric charges (denoted by ``+'') are transferred to the isopotential surface of the droplet.</p>
</div>
<p>
We evaluate the electrostatic energy of a conducting sphere and a linear charged macromolecule using macroscopic description of the constituent parts. Using the general formula for the electrostatic energy \cite[see p. 57]{electrostatics}<br />
\begin{equation}<br />
E_{\mathrm{elec}} = \sum \frac{1}{2} \phi'_i q_i<br />
\label{eq:elec-def}<br />
\end{equation}<br />
where $q_i$ are charges and $\phi'_i$ are electrostatic potentials at the positions of the corresponding charges without that of the charge $q_i$.
</p>
<p>
Using the technique of electrostatic images the electrostatic field from charge $q$ at distance $x$ from the conducting droplet is equivalent to field created by the system of three charges $q$, $-\frac{qR}{R+x}$ at distance $\frac{R}{R+x}$ from the center of the sphere and $\frac{qR}{R+x}$ at the center of the sphere.
</p>
<p>
Using equation \eqref{eq:elec-def} we write the contribution to the electrostatic energy from charges in the droplet (which are distributed on the surface) as<br />
\begin{equation}<br />
E_{\mathrm{elec}} (Q_1) = \frac{1}{2}\frac{1}{4\pi\epsilon_0 R}<br />
\left( Q_1 + Q_c \right) Q_1<br />
\label{eq:ee-surf}<br />
\end{equation}<br />
where $\gamma$ is the charge per unit length of the macromolecule, $Q_1 = \gamma (L - \lambda)$ is the charge inside the droplet and $Q_c$ is the total induced image charge in the center of the droplet given by<br />
\begin{equation}<br />
Q_c = \int\limits_0^{\lambda} \frac{R \gamma d x}{R+x} .<br />
\label{eq:elec-charge-induced}<br />
\end{equation}<br />
Note, that there is no contribution to the electrostatic energy from the pairs of charges $(q, -\frac{qR}{R+x})$ as they compensate each other exactly on the surface of the sphere.
</p>
<p>
Contribution to the electrostatic energy from the charges on the extruded part of the macromolecule is<br />
\begin{equation}<br />
E_{\mathrm{elec}} (Q_2)<br />
= \frac{1}{2}\frac{1}{4\pi\epsilon_0}<br />
\left[ \left( Q_1 + Q_c \right) \int\limits_0^{\lambda} \frac{\gamma<br />
d x}{R+x} - \int\limits_0^{\lambda} \int\limits_0^{\lambda}<br />
\frac{\gamma dx}{ R + x - \frac{R^2}{R+y} } \frac{R \gamma dy}{ R<br />
+ y } \right] .<br />
\label{eq:ee-macr}<br />
\end{equation}
</p>
<p>
Adding energies given by equations \eqref{eq:ee-surf} and \eqref{eq:ee-macr} and after some algebra we arrive at<br />
\begin{equation}<br />
E_{\mathrm{elec}} = \frac{1}{2}\frac{1}{4\pi\epsilon_0} \biggl[<br />
\frac{1}{R} \left( Q_1 + Q_c \right)^2 - \gamma^2 R<br />
\int\limits_0^{\lambda} \int\limits_0^{\lambda} \frac{dx<br />
dy}{(R+x)(R+y)-R^2} \biggr] .<br />
\label{eq:ee-total}<br />
\end{equation}
</p>
<p>
We analyze stability of the system given by equation \eqref{eq:ee-total}. The central property is the location of the minima of the energy as a function of macromolecule extrusion $\lambda$. The locations of the minima are given by the solutions of the following equations<br />
\begin{equation}<br />
0 = - \frac{\partial E_{\mathrm{total}} } {\partial \lambda} = v_{0}<br />
+ \frac{1}{4\pi\epsilon_0}<br />
\biggl[ \frac{Q_1 + Q_c} {R} \frac{\gamma \lambda}{R+{\lambda}}<br />
+ \gamma^2 R \int\limits_0^{\lambda}<br />
\frac{dx}{(R+x)(R+{\lambda})-R^2} \biggr]<br />
\label{eq:minima}<br />
\end{equation}
</p>
<p>
Equation \eqref{eq:minima} can be explicitly evaluated and recast in the following form<br />
\begin{equation}<br />
-\frac{4\pi\epsilon v_0}{\gamma^2} = \biggl[ \frac{L-\lambda}{R} +<br />
\ln{\frac{R+\lambda}{R}} \biggr] \frac{\lambda}{R+{\lambda}} +<br />
\frac{R}{R+{\lambda}} \ln{\frac{2R+\lambda}{R}},<br />
\label{eq:min-simpl}<br />
\end{equation}<br />
with dimensionless parameters on both sides of the equation. The universal parameter $B_{\mathrm{ex}}$<br />
\begin{equation}<br />
B_{\mathrm{ex}} = \frac{4\pi\epsilon v_0}{\gamma^2} =<br />
\biggl[L v_0\biggr] \cdot \biggl[ \frac{Q^2}{4\pi\epsilon L} \biggr]^{-1}<br />
\label{eq:univ}<br />
\end{equation}<br />
determines the position of the minima for a specific system. $B_{\mathrm{ex}}$ is the ratio of the total solvation energy over a measure of electrostatic energy of the macromolecule and could have been obtained from dimensional analysis as the only combination of two characteristic quantities of the system. The systems with the same ratios of solvation energy to the square of the charge density will follow the same path in the course of droplet evaporation on the $(\lambda/R, L/R)$ diagram.
</p>
<div class="figure">
<img src="sites/default/files/phas-diag-il.png" /><p>Regions of the phase diagram in the system of $\xi = \lambda/L$ and $L/R$ coordinates. Contiguous lines correspond to constant values of the interaction parameter $B_{\mathrm{ex}}$. The gray region in all subplots indicates location of the restricted domain (see details in the text). The plot shows an overall view of the minima of the droplet energy. Representative snapshots of simulations of charged PEG in water droplets that correspond to the various regions of the phase diagram are also shown. </p>
</div>
<p>
Following the approach used to describe gas-liquid boundary lines of the van der Waals equation of state we solved the system of equations $\bigl\{ \frac{\partial E_{\mathrm{total}} } {\partial \lambda} = 0 \wedge \frac{\partial^2 E_{\mathrm{total}} } {\partial \lambda^2} = 0 \bigr\}$ and determined that the allowed region of parameters lie on the r.h.s. of the dashed curve shown in \figref{fig:phas-diag} and given by<br />
\begin{equation}<br />
\frac{L}{R} = \frac{\lambda}{R} + \frac{\lambda^2}{R^2} -<br />
\ln\frac{R+\lambda}{2R+\lambda} - \frac{R+\lambda}{2R+\lambda}.<br />
\label{eq:allowed}<br />
\end{equation}
</p>
<p>
Equations \eqref{eq:minima} and \eqref{eq:allowed} are conveniently presented in the ($\xi = \lambda/L$, $L/R$) system of coordinates. The system of equations were solved numerically and the results of calculations are presented in \figref{fig:phas-diag}. On the phase diagram (\figref{fig:phas-diag}) the dashed line delineates the region of $(\xi, L/R)$ values with the solutions corresponding to the maxima of the total energy (equation \ref{eq:ener-total}). In this region the fully solvated chain (corresponding to $\xi = 0$) and an extruded state lying on the boundary of the allowed region are in dynamic equilibrium as illustrated in \figref{fig:phas-diag}a lower insert. On the phase diagram we identified two distinct regions that correspond to different extrusion mechanisms.
</p>
<p style="font-weight:bold">
</p><pre style="font-style:italic">
@article{consta2012manifestations,
title = {Manifestations of Charge Induced Instability in Droplets Effected by Charged Macromolecules},
author = {Consta, Styliani and Malevanets, Anatoly},
journal = {Phys. Rev. Lett.},
volume = {109},
issue = {14},
pages = {148301},
numpages = {5},
year = {2012},
month = {Oct},
doi = {10.1103/PhysRevLett.109.148301},
url = {http://link.aps.org/doi/10.1103/PhysRevLett.109.148301},
publisher = {American Physical Society}
}
</pre>
</div></div></div></div></div><div class="field field-name-taxonomy-vocabulary-1 field-type-taxonomy-term-reference field-label-above"><div class="field-label">Topics: </div><div class="field-items"><div class="field-item even"><a href="/?q=taxonomy/term/5">fragmentation</a></div><div class="field-item odd"><a href="/?q=taxonomy/term/6">electrospray</a></div><div class="field-item even"><a href="/?q=taxonomy/term/20">theory</a></div></div></div>Sat, 22 Dec 2012 22:32:21 +0000Styliani Constas47 at http://theory.chem.uwo.caResearch
http://theory.chem.uwo.ca/?q=node/18
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><div class="figure">
<img src="http://upload.wikimedia.org/wikipedia/commons/2/25/Alchemist_Thomas_Wijck.jpg" /></div>
<p>
<quote>Every attempt to employ mathematical methods in the study of chemical questions must be considered profoundly irrational and contrary to the spirit of chemistry.... if mathematical analysis should ever hold a prominent place in chemistry, an aberration which is happily almost impossible, it would occasion a rapid and widespread degeneration of that science.</quote></p>
<p>Auguste Comte, <em>Cours de philosophie positive</em>, 1830
</p>
<hr /></div></div></div><div class="field field-name-taxonomy-vocabulary-1 field-type-taxonomy-term-reference field-label-above"><div class="field-label">Topics: </div><div class="field-items"><div class="field-item even"><a href="/?q=taxonomy/term/3">simulations</a></div><div class="field-item odd"><a href="/?q=taxonomy/term/6">electrospray</a></div><div class="field-item even"><a href="/?q=taxonomy/term/20">theory</a></div></div></div>Wed, 03 Oct 2007 20:01:44 +0000Styliani Constas18 at http://theory.chem.uwo.ca