Biomod/2013/NanoUANL/Background: Difference between revisions

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<html> <head> <title></title> </head> <body>    BACKGROUND   <img alt="" src="http://openwetware.org/images/9/97/UANLBackground1.jpg" style="width: 635px; height: 375px;" />   Reactions in Containers Nanocontainer is a term used for structures with a size within the nanometer range (1-100 nm). The interest in their use stems from their empty inner cavities that can be used for a variety of applications. Among these, one of peculiar interest is the encapsulation of molecules in order to turn the structure into a reaction vessel. Biological systems have always been an inspiration because of their complexity and diversity.  Cell processes take place within constrained spaces and small volumes, and many are not yet fully understood. Advances in nanoscale fabrication have allowed us to mimic some of these spaces and features with other structures. The volumes that are present at this level (atto and zeptoliter) allow molecules to collide more often, as opposed to an “open space”; simulations based on Brownian diffusion have shown that collision frequency between molecules strongly depend on vesicle size. The most widely studied containers are liposomes: self-assembling structures formed by a lipid bilayer, that have been used to encapsulate enzymes for a variety of applications.  However, other biological systems have also been subject of study, such as block copolymer vesicles, proteins like ferritin, and viral capsids.   <img alt="" src="http://openwetware.org/images/6/65/UANLBackground2.jpg" style="width: 463px; height: 383px;" /> Fig 1. Different viral structures, both with and without a viral envelope   Viral capsids have gained the interest of researchers for some of their properties. The mechanical stability that this structure presents is similar to that of other structures, which protects the container’s cargo. Many viral containers have been used as templates for nanoparticle synthesis. The CCMV virus has been the subject of study for nanotechnology for its unique properties, even among viruses. The container can be disassembled and reassembled at will, depending on the environmental conditions and pores allow the entrance or exit of small molecules. To explore more properties, the capsid has been modified in a variety of ways, allowing us to change the N-terminal amino region.   Enzyme (HRP) Horseradish peroxidase (HRP) is a ~44 kDa glycoprotein from the peroxidase family, with a known three-dimensional structure. Peroxidases typically catalyze a reaction in which a wide variety of both organic and inorganic compounds are oxidized. There has been a great deal of scientific interest in HRP because of its commercial uses, primarily as a component of clinical diagnostic kits and for immunostaining. The enzyme is usually conjugated to specific antibodies or streptavidin, which binds to the compound of interest and activity, is detected with substrates like TMB or ABTS, which are then analyzed by a colorimetric assay. Enzymatic reactions inside CCMV have been studied as single-molecule system, using HRP as the catalyst. The researchers showed that the interior of the capsid presented a suitable environment for enzymatic activity. The reaction was examined by fluorescence microscopy using a fluorogenic substrate.   Capsid-assisted Synthesis The biomimetic approach to material synthesis consists in the combination of well-defined structures, macromolecular templates and molecular interactions. Soluble precursors can be transformed into nanoparticles by a variety of mechanisms inside a viral capsid, such as pH changes. Results have suggested as hypothesis that the condensation of certain materials inside containers is electrostatically driven, and the selection of the metal precursor influences this process. An advantage to these processes is the minimization of hazardous substances used and generated by these reactions. Additionally, these substances are often expensive and need special containment, which is problematic. The reduction of metal ions by combinations of biomolecules found in the extracts of certain organisms (e.g., enzymes/proteins, amino acids, polysaccharides, and vitamins) is environmentally friendly, yet chemically complex, making this system fascinating to study. Silver nanoparticle synthesis has been reported in bacteria, fungi and plants.  <img alt="" src="http://openwetware.org/images/7/74/UANLBackground3.jpg" style="width: 350px; height: 349px;" />  Fig. 2 - 3D structure of the complete CCMV capsid As a nanoreactor, the CCMV capsid is more versatile than other viruses, since its reversible pH-dependent disassembly/assembly behavior permits the encapsulation of enzymes and metal nanoparticles. However, it has fewer examples of functionalization because of the lower thermodynamic stability of the structure, compared to other viruses. CCMV has been previously used to form insoluble TiO2 nanoparticles from soluble Ti(IV) salts inside the capsid. A modified CCMV structure with a negative charge has also been used to selectively bind Fe(II) and Fe(III) to the internal surface. Selective mineralization with the TMV capsid has resulted in Au(0) mineralization on the viral surface, and Ag(0) mineralization within its interior. CoPt and FePt nanowires have been fabricated by incorporating specific nucleating peptides on the surface of the M13 virus coat structure.   Silver nanoparticles synthesis from Ag0 atoms The overall evolution of nanoparticles from bulk Ag metallic atoms is described using a kinetic model detailed by van Embden and collaborators. In summary when Ag0 atoms reach supersaturated concentrations S in solution, clusters of n units Cn are formed (as detailed in Fig 1). Thus, the reaction of an atom C with the cluster can be described as: <img alt="" src="http://openwetware.org/images/3/3a/UANLNuc1.PNG" /> With the equilibrium constant: <img alt="" src="http://openwetware.org/images/4/4b/UANLNuc2.PNG" /> <img alt="" src="http://openwetware.org/images/c/c4/UANLNuc3.PNG" /> Figure 1: Evolution of clusters from monomers to critical Cp nucleus via condensation of p units of monomer C.   As shown above in Figure 1, the pathway from monomer atoms to critical clusters involves the formation of dimers, trimmers, tetramers, and so on. Thus, the reaction pathway can be described as:    <img alt="" src="http://openwetware.org/images/e/ee/UANLNuc4.PNG" style="width: 152px; height: 35px;" />    In this expression u stands for the coagulation coefficient, which determines the probability that nucleation proceeds by the addition of a monomer. u decreases as the concentrations and sizes of coagulants are increased, taking values between 0 and 1. As all the reactions are assumed to take place simultaneously, concentration of critical clusters [Cp] is given by:   <img alt="" src="http://openwetware.org/images/e/e6/Nuc5.PNG" style="width: 341px; height: 73px;" />   Where: p : number of monomer units condensed in a critical cluster Cp kB : Boltzmann’s constant T: Temperature [C]∞ : Concentration of monomer with infinitely flat surface                 When n > p, [C]∞ = 0 ΔGvol1,p : volume free energy change for the critical cluster upon the addition of a monomer unit ΔGsurf1,p : surface free energy change for the critical cluster upon the addition of a monomer unit K1,∞ : reciprocal of the monomer concentration in equilibrium with a flat surface [C]∞   Free energy changes are given by:  <img alt="" src="http://openwetware.org/images/7/7d/UANLNuc6.PNG" style="width: 432px; height: 60px;" />  The nucleation rate –which determines the number of moles of critical clusters Cp formed per unit volume per time– can be described as:  <img alt="" src="http://openwetware.org/images/2/22/UANLNuc7.PNG" style="width: 448px; height: 93px;" />  Where: NA: Avogadro’s number rm : Radius of monomer C u :scaling factor/coagulation coefficient | 1/u ≤p                 * It takes values from 0 to 1. rcrit: radius of critical cluster γ: Surface energy ΔGSurf: 4πr2critγ S : Supersaturation ratio, given by:  <img alt="" src="http://openwetware.org/images/5/5e/UANLNuc8.PNG" style="width: 98px; height: 68px;" />  Where [C]b is the concentration of monomers in the bulk solution and is assumed to be equal to [C] </body> </html>

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 			<span style="font-family:trebuchet ms,helvetica,sans-serif;"><span style="font-size: 12px;">CCMV has been previously used to form insoluble TiO2 nanoparticles from soluble Ti(IV) salts inside the capsid. A modified CCMV structure with a negative charge has also been used to selectively bind Fe(II) and Fe(III) to the internal surface. Selective mineralization with the TMV capsid has resulted in Au(0) mineralization on the viral surface, and Ag(0) mineralization within its interior. CoPt and FePt nanowires have been fabricated by incorporating specific nucleating peptides on the surface of the M13 virus coat structure.</span></span></p>
 <p>
-<br />
+			&nbsp;</p>
-			<span style="font-size:14px;"><span style="font-family: trebuchet ms,helvetica,sans-serif;"><strong>Nucleation</strong></span></span></p>
+<p>
+			<span style="font-size:14px;"><span style="font-family: trebuchet ms,helvetica,sans-serif;"><strong>Silver nanoparticles synthesis from Ag0 atoms</strong></span></span></p>
 		<p>
-			Silver nanoparticles synthesis from Ag0 atoms The overall evolution of nanoparticles from bulk Ag metallic atoms is described using a kinetic model detailed by van Embden and collaborators. In summary when Ag0 atoms reach supersaturated concentrations S in solution, clusters of n units Cn are formed (as detailed in Fig 1). Thus, the reaction of an atom C with the cluster can be described as: With the equilibrium constant: Figure 1: Evolution of clusters from monomers to critical Cp nucleus via condensation of p units of monomer C. As shown above in Figure 1, the pathway from monomer atoms to critical clusters involves the formation of dimers, trimmers, tetramers, and so on. Thus, the reaction pathway can be described as: In this expression u stands for the coagulation coefficient, which determines the probability that nucleation proceeds by the addition of a monomer. u decreases as the concentrations and sizes of coagulants are increased, taking values between 0 and 1. As all the reactions are assumed to take place simultaneously, concentration of critical clusters [Cp] is given by: Where: p : number of monomer units condensed in a critical cluster Cp kB : Boltzmann&rsquo;s constant T : Temperature [C]&infin; : Concentration of monomer with infinitely flat surface When n &gt; p, [C]&infin; = 0 &Delta;Gvol1,p : volume free energy change for the critical cluster upon the addition of a monomer unit &Delta;Gsurf1,p : surface free energy change for the critical cluster upon the addition of a monomer unit Free energy changes are given by: K1,&infin; : reciprocal of the monomer concentration in equilibrium with a flat surface [C]&infin; The nucleation rate &ndash;which determines the number of moles of critical clusters Cp formed per unit volume per time&ndash; can be described as: Where: NA : Avogadro&rsquo;s number rm : Radius of monomer C u : scaling factor/coagulation coefficient | 1/u &le; p It takes values from 0 to 1. rcrit : radius of critical cluster &gamma;: Surface energy &Delta;GSurf: 4&pi;r2crit&gamma; S : Supersaturation ratio, given by: Where [C]b is the concentration of monomers in the bulk solution and is assumed to be equal to [C]</p>
+			<span style="font-family:trebuchet ms,helvetica,sans-serif;"><span style="font-size: 12px;">The overall evolution of nanoparticles from bulk Ag metallic atoms is described using a kinetic model detailed by van Embden and collaborators. In summary when Ag<sup>0</sup> atoms reach supersaturated concentrations S in solution, clusters of n units Cn are formed (as detailed in Fig 1). Thus, the reaction of an atom C with the cluster can be described as:</span></span></p>
+		<p style="text-align: center;">
+			<span style="font-family:trebuchet ms,helvetica,sans-serif;"><span style="font-size: 12px;"><img alt="" src="http://openwetware.org/images/3/3a/UANLNuc1.PNG" /></span></span></p>
+		<p>
+			<span style="font-family:trebuchet ms,helvetica,sans-serif;"><span style="font-size: 12px;">With the equilibrium constant:</span></span></p>
+		<p style="text-align: center;">
+			<span style="font-family:trebuchet ms,helvetica,sans-serif;"><span style="font-size: 12px;"><img alt="" src="http://openwetware.org/images/4/4b/UANLNuc2.PNG" /></span></span></p>
+		<p>
+			<span style="font-family:trebuchet ms,helvetica,sans-serif;"><span style="font-size: 12px;"><img alt="" src="http://openwetware.org/images/c/c4/UANLNuc3.PNG" /></span></span></p>
+		<p>
+			<span style="font-family:trebuchet ms,helvetica,sans-serif;"><span style="font-size: 12px;">Figure 1: Evolution of clusters from monomers to critical <em>C<sub>p</sub> </em>nucleus via condensation of <em>p </em>units of monomer <em>C</em>.</span></span></p>
+		<p>
+			&nbsp;</p>
+		<p>
+			<span style="font-family:trebuchet ms,helvetica,sans-serif;"><span style="font-size: 12px;">As shown above in Figure 1, the pathway from monomer atoms to critical clusters involves the formation of dimers, trimmers, tetramers, and so on. Thus, the reaction pathway can be described as:</span></span></p>
+		<p style="text-align: center;">
+			<span _fck_bookmark="1" style="display: none;">&nbsp;</span><span _fck_bookmark="1" style="display: none;">&nbsp;</span><span _fck_bookmark="1" style="display: none;">&nbsp;</span><span style="font-family:trebuchet ms,helvetica,sans-serif;"><span style="font-size: 12px;"><img alt="" src="http://openwetware.org/images/e/ee/UANLNuc4.PNG" style="width: 152px; height: 35px;" /><span _fck_bookmark="1" style="display: none;">&nbsp;</span><span _fck_bookmark="1" style="display: none;">&nbsp;</span><span _fck_bookmark="1" style="display: none;">&nbsp;</span></span></span></p>
+		<p>
+			<span style="font-family:trebuchet ms,helvetica,sans-serif;"><span style="font-size: 12px;">In this expression <em>u </em>stands for the coagulation coefficient, which determines the probability that nucleation proceeds by the addition of a monomer. <em>u</em> decreases as the concentrations and sizes of coagulants are increased, taking values between 0 and 1.</span></span></p>
+		<p>
+			<span style="font-family:trebuchet ms,helvetica,sans-serif;"><span style="font-size: 12px;">As all the reactions are assumed to take place simultaneously, concentration of critical clusters [<em>C<sub>p</sub></em>] is given by:</span></span></p>
+		<p style="text-align: center;">
+			<span _fck_bookmark="1" style="display: none;">&nbsp;</span><span _fck_bookmark="1" style="display: none;">&nbsp;</span><span style="font-family:trebuchet ms,helvetica,sans-serif;"><span style="font-size: 12px;"><img alt="" src="http://openwetware.org/images/e/e6/Nuc5.PNG" style="width: 341px; height: 73px;" /><span _fck_bookmark="1" style="display: none;">&nbsp;</span><span _fck_bookmark="1" style="display: none;">&nbsp;</span></span></span></p>
+		<p>
+			<span style="font-family:trebuchet ms,helvetica,sans-serif;"><span style="font-size: 12px;">Where:</span></span></p>
+		<p>
+			<span style="font-family:trebuchet ms,helvetica,sans-serif;"><span style="font-size: 12px;"><em>p </em>: number of monomer units condensed in a critical cluster <em>C<sub>p</sub></em></span></span></p>
+		<p>
+			<span style="font-family:trebuchet ms,helvetica,sans-serif;"><span style="font-size: 12px;"><em>k<sub>B</sub> </em>: Boltzmann&rsquo;s constant</span></span></p>
+		<p>
+			<span style="font-family:trebuchet ms,helvetica,sans-serif;"><span style="font-size: 12px;"><em>T</em>: Temperature</span></span></p>
+		<p>
+			<span style="font-family:trebuchet ms,helvetica,sans-serif;"><span style="font-size: 12px;">[<em>C</em>]<sub>&infin;</sub> : Concentration of monomer with infinitely flat surface</span></span></p>
+		<p>
+			<span style="font-family:trebuchet ms,helvetica,sans-serif;"><span style="font-size: 12px;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; When <em>n &gt; p</em>, [<em>C</em>]<sub>&infin;</sub> = 0</span></span></p>
+		<p>
+			<span style="font-family:trebuchet ms,helvetica,sans-serif;"><span style="font-size: 12px;">&Delta;<em>G</em><sup>vol</sup><sub>1,p</sub> : volume free energy change for the critical cluster upon the addition of a monomer unit</span></span></p>
+		<p>
+			<span style="font-family:trebuchet ms,helvetica,sans-serif;"><span style="font-size: 12px;">&Delta;<em>G</em><sup>surf</sup><sub>1,p</sub> : surface free energy change for the critical cluster upon the addition of a monomer unit</span></span></p>
+		<p>
+			<span style="font-family:trebuchet ms,helvetica,sans-serif;"><span style="font-size: 12px;"><em>K<sub>1,&infin; </sub></em>: reciprocal of the monomer concentration in equilibrium with a flat surface [<em>C</em>]<sub>&infin;</sub></span></span></p>
+		<p>
+			&nbsp;</p>
+		<p>
+			<span style="font-family:trebuchet ms,helvetica,sans-serif;"><span style="font-size: 12px;">Free energy changes are given by:</span></span></p>
+		<p style="text-align: center;">
+			<span _fck_bookmark="1" style="display: none;">&nbsp;</span><span style="font-family:trebuchet ms,helvetica,sans-serif;"><span style="font-size: 12px;"><img alt="" src="http://openwetware.org/images/7/7d/UANLNuc6.PNG" style="width: 432px; height: 60px;" /><span _fck_bookmark="1" style="display: none;">&nbsp;</span></span></span></p>
+		<p>
+			<span style="font-family:trebuchet ms,helvetica,sans-serif;"><span style="font-size: 12px;">The nucleation rate &ndash;which determines the number of moles of critical clusters <em>Cp</em> formed per unit volume per time&ndash; can be described as:</span></span></p>
+		<p style="text-align: center;">
+			<span _fck_bookmark="1" style="display: none;">&nbsp;</span><span style="font-family:trebuchet ms,helvetica,sans-serif;"><span style="font-size: 12px;"><img alt="" src="http://openwetware.org/images/2/22/UANLNuc7.PNG" style="width: 448px; height: 93px;" /><span _fck_bookmark="1" style="display: none;">&nbsp;</span></span></span></p>
+		<p>
+			<span style="font-family:trebuchet ms,helvetica,sans-serif;"><span style="font-size: 12px;">Where:</span></span></p>
+		<p>
+			<span style="font-family:trebuchet ms,helvetica,sans-serif;"><span style="font-size: 12px;"><em>N<sub>A</sub></em>: Avogadro&rsquo;s number</span></span></p>
+		<p>
+			<span style="font-family:trebuchet ms,helvetica,sans-serif;"><span style="font-size: 12px;">r<sub>m</sub> : Radius of monomer <em>C</em></span></span></p>
+		<p>
+			<span style="font-family:trebuchet ms,helvetica,sans-serif;"><span style="font-size: 12px;"><em>u :</em>scaling factor/coagulation coefficient | 1/<em>u</em> &le;<em>p </em></span></span></p>
+		<p>
+			<span style="font-family:trebuchet ms,helvetica,sans-serif;"><span style="font-size: 12px;">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; * It takes values from 0 to 1.</span></span></p>
+		<p>
+			<span style="font-family:trebuchet ms,helvetica,sans-serif;"><span style="font-size: 12px;"><em>r</em><sub>crit</sub>: radius of critical cluster</span></span></p>
+		<p>
+			<span style="font-family:trebuchet ms,helvetica,sans-serif;"><span style="font-size: 12px;">&gamma;: Surface energy</span></span></p>
+		<p>
+			<span style="font-family:trebuchet ms,helvetica,sans-serif;"><span style="font-size: 12px;">&Delta;<em>G</em><sup>Surf</sup>: 4&pi;<em>r</em><sup>2</sup><sub>crit</sub>&gamma;</span></span></p>
+		<p>
+			<span style="font-family:trebuchet ms,helvetica,sans-serif;"><span style="font-size: 12px;">S : Supersaturation ratio, given by:</span></span></p>
+		<p style="text-align: center;">
+			<span _fck_bookmark="1" style="display: none;">&nbsp;</span><span style="font-family:trebuchet ms,helvetica,sans-serif;"><span style="font-size: 12px;"><img alt="" src="http://openwetware.org/images/5/5e/UANLNuc8.PNG" style="width: 98px; height: 68px;" /><span _fck_bookmark="1" style="display: none;">&nbsp;</span></span></span></p>
+		<p align="center">
+			<span style="font-family:trebuchet ms,helvetica,sans-serif;"><span style="font-size: 12px;">Where [<em>C</em>]<sub>b </sub>is the concentration of monomers in the bulk solution and is assumed to be equal to [<em>C</em>]</span></span></p>
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Biomod/2013/NanoUANL/Background: Difference between revisions

Latest revision as of 19:11, 26 October 2013

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