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{% block page_content %}
<div class="row">
<h1>Molecular Dynamic Simulations</h1>
<p>
<h1 class="reveal-on-scroll">Molecular Dynamic Simulations</h1>
<p class="reveal-on-scroll">
Determining the behaviour of a protein or peptide in response to environmental stresses is crucial in
establishing
the efficacy of the peptide in a system. Thus, molecular dynamics simulation can help us subject the peptide to
different conditions that mimic the natural environment that it may exist in, <i>in silico</i>.
</p>
<p>
<p class="reveal-on-scroll">
Multiple tools can be used to perform MDS, such as GROMACS [1][2][3], CHARMM [4], AMBER [5] and Desmond [6].
However, MDS requires high
computational power. Given our limited resources, we partnered with IISER Pune II, to run molecular dynamics
simulations on their supercomputer PARAM. The results were then analysed by us to check for the stability of the
peptide in the given environment.
</p>
<p>
<p class="reveal-on-scroll">
We discovered that a pH of 7.5 and a temperature of 298K are the typical characteristics of an aquaculture system
for consumable fish through our human practices and research. These parameters were applied to a cubic system and
an
......@@ -27,9 +27,9 @@
peptide.
</p>
<h3>RMSD</h3>
<h3 class="reveal-on-scroll">RMSD</h3>
<figure class="figure">
<figure class="figure reveal-on-scroll">
<img src="https://static.igem.wiki/teams/4200/wiki/model/model-rmds.png" class="figure-img img-fluid rounded"
alt="RMS v/s time" width="70%">
<figcaption class="figure-caption text-center">
......@@ -39,23 +39,25 @@
<i></i>
<p>RMSD or root mean squared distance is the numerical representation of the difference between the peptide's
<p class="reveal-on-scroll">RMSD or root mean squared distance is the numerical representation of the difference
between the peptide's
initial
structure and the structure at a given moment in time. Generally, an RMSD variation of less than 2 Angstorms is
supposed to be very close and stable.
\[ \text{RMSD} = \sqrt{\frac{\sum [m_i(x_i-y_i)^2]}{M}} \]
</p>
<p>The RMSD value was seen to increase for the first 50ns, which is a given due to the peptide stabilizing to the
<p class="reveal-on-scroll">The RMSD value was seen to increase for the first 50ns, which is a given due to the
peptide stabilizing to the
given conditions in the system. It was observed that the RMSD values decreased briefly and then stabilized with a
fluctuation of approximately 1 Angstorms, which falls comfortably below the accepted threshold of
2 Angstorms, indicating that our peptide is very stable in the given environment. It also shows that <b>no
conformational changes</b> occur within the first 100 ns of the simulation, which could otherwise hamper its
target interaction.</p>
<h3>RMSF</h3>
<h3 class="reveal-on-scroll">RMSF</h3>
<figure class="figure">
<figure class="figure reveal-on-scroll">
<img src="https://static.igem.wiki/teams/4200/wiki/model/model-rmsf.jpg" class="figure-img img-fluid rounded"
alt="RMS v/s residue" width="70%">
<figcaption class="figure-caption text-center">
......@@ -63,22 +65,24 @@
</figcaption>
</figure>
<p>RMSF or root mean squared fluctuations is a calculation of individual residue flexibility, or how much a
<p class="reveal-on-scroll">RMSF or root mean squared fluctuations is a calculation of individual residue flexibility,
or how much a
particular
residue moves (fluctuates) during a simulation.
\[
\text{RMSF} = {\sqrt{\frac{\sum [m_i(x_i(t_j)-x_{ref})^2]}{T}}}
\]
</p>
<p>The residues at the very beginning and end of our peptide show the highest fluctuations and this indicates that
<p class="reveal-on-scroll">The residues at the very beginning and end of our peptide show the highest fluctuations
and this indicates that
they are less stable than the residues with fewer fluctuations. For example, the amino acid residues between 14 to
24 are much more stable than the residues from 36 to 40, which correspond to loops in the structure of the
peptide.
</p>
<h3>Radius of Gyration</h3>
<h3 class="reveal-on-scroll">Radius of Gyration</h3>
<figure class="figure">
<figure class="figure reveal-on-scroll">
<img src="https://static.igem.wiki/teams/4200/wiki/model/model-rg.jpg" class="figure-img img-fluid rounded"
alt="Radius of gyration v/s time" width="70%">
<figcaption class="figure-caption text-center">
......@@ -87,35 +91,39 @@
</figure>
<p>The radius of gyration for a given molecule is a measure of the compactness of the molecule or how far apart the
<p class="reveal-on-scroll">The radius of gyration for a given molecule is a measure of the compactness of the
molecule or how far apart the
mass of the object is distributed around its centre of mass.
\[
R_g = \sqrt{\frac{\sum [m_i(x_i-x_c)^2]}{M}}
\]</p>
<p>From the resulting plot of the radius of gyration versus time, we can see that the net radius of gyration remains
<p class="reveal-on-scroll">From the resulting plot of the radius of gyration versus time, we can see that the net
radius of gyration remains
fairly constant and is <b>within the range of 1 Angstorm</b>. This indicates that the peptide does not fold
or
unfold
over time, thereby contributing to no change in the compactness of the peptide. We can also conclude that the
peptide does not undergo any major conformational changes which can result in changes in the folded volume of the
protein, and thereby talks about the <b>stability of the peptide</b>.</p>
<p>MD Simulations on the MAM7-peptide dock would give a lot more information about the interactions present, the
<p class="reveal-on-scroll">MD Simulations on the MAM7-peptide dock would give a lot more information about the
interactions present, the
stability of the complex, interaction energies, compactness and the effect of conformational changes on the
interaction. Parameters such as RMSF would give crucial information regarding the interacting residues present in
the complex. Induced conformational changes upon docking could be analyzed using graphs for RMSD as well as
observing the trajectory file. We planned on performing these simulations to analyze the MAM7-peptide interaction
but were limited by time and resources.</p>
<h1>IC<sub>50</sub></h1>
<p>The <b>optimum dosage values</b> of the peptide is essential for effective prevention of the disease Since both
<h1 class="reveal-on-scroll">IC<sub>50</sub></h1>
<p class="reveal-on-scroll">The <b>optimum dosage values</b> of the peptide is essential for effective prevention of
the disease Since both
the
peptide and fibronectin are in a position to interact with MAM7, we concluded that our peptide would act as a
<b>competitive inhibitor</b> against fibronectin. Therefore, our mathematical model describes the relationship
between the
concentration of peptide required for a given concentration of fibronectin present in the system.
</p>
<ul>
<ul class="reveal-on-scroll">
<li>IC<sub>50</sub> is the concentration of the drug or displacing ligand in a competitive inhibition mechanism
that
reduces or
......@@ -131,92 +139,98 @@
reaction mechanism. We derived an equation for the IC<sub>50</sub> value of our peptide with the following
steps:
<ol>
<ol class="reveal-on-scroll">
<li>
<p>
<p class="reveal-on-scroll">
The reaction mechanism can be considered to be a parallel reaction scheme where MAM7 gets partitioned
between
Fibronectin and our peptide.
<img src="https://static.igem.wiki/teams/4200/wiki/model/model-1.png" alt="M+F=MF" width="30%">
<img src="https://static.igem.wiki/teams/4200/wiki/model/model-2.png" alt="M+P=MP" width="30%">
<img src="https://static.igem.wiki/teams/4200/wiki/model/model-1.png" alt="M+F=MF" width="30%"
class="reveal-on-scroll">
<img src="https://static.igem.wiki/teams/4200/wiki/model/model-2.png" alt="M+P=MP" width="30%"
class="reveal-on-scroll">
</p>
<p>
<p class="reveal-on-scroll">
Equations for the Association and Dissociation constant can be written as follows:
<img src="https://static.igem.wiki/teams/4200/wiki/model/model-3-4.png"
alt="Association and Dissociation Equations" width="30%">
alt="Association and Dissociation Equations" width="30%" class="reveal-on-scroll">
</p>
<p>
<p class="reveal-on-scroll">
<img src="https://static.igem.wiki/teams/4200/wiki/model/model-5-6.png"
alt="Association and Dissociation Constants" width="30%">
alt="Association and Dissociation Constants" width="30%" class="reveal-on-scroll">
</p>
</li>
<li>
<p>Given the total concentration of MAM7 in a system, the MAM7 would be partitioned between the
<p class="reveal-on-scroll">Given the total concentration of MAM7 in a system, the MAM7 would be partitioned
between the
MAM7-Fibronectin
complex, MAM7-peptide complex and free MAM7.
<img src="https://static.igem.wiki/teams/4200/wiki/model/model-7.png" alt="Total M concentration"
width="30%">
width="30%" class="reveal-on-scroll">
</p>
</li>
<li>
<p>
<p class="reveal-on-scroll">
We defined \(\rho\) as the ratio of the concentration of the MAM7-Fibronectin complex to the total MAM7
concentration.
<img src="https://static.igem.wiki/teams/4200/wiki/model/model-8.png" alt="Rho derivation" , width="70%">
<img src="https://static.igem.wiki/teams/4200/wiki/model/model-8.png" alt="Rho derivation" , width="70%"
class="reveal-on-scroll">
</p>
</li>
<li>
<p>
<p class="reveal-on-scroll">
We defined \(\rho_{in}\) as the interaction ratio in the absence of our peptide.
<img src="https://static.igem.wiki/teams/4200/wiki/model/model-9.png" alt="Rho in derivation" width="30%">
<img src="https://static.igem.wiki/teams/4200/wiki/model/model-9.png" alt="Rho in derivation" width="30%"
class="reveal-on-scroll">
</p>
</li>
<li>
<p>
<p class="reveal-on-scroll">
The below relation was arrived at from the definition of IC<sub>50</sub>.
<img src="https://static.igem.wiki/teams/4200/wiki/model/model-10.png" alt="IC50 relation" width="50%">
<img src="https://static.igem.wiki/teams/4200/wiki/model/model-10.png" alt="IC50 relation" width="50%"
class="reveal-on-scroll">
</p>
</li>
<li>
<p>
<p class="reveal-on-scroll">
On simplification, the final equation for IC<sub>50</sub> value of our peptide was found.
<img src="https://static.igem.wiki/teams/4200/wiki/model/model-11.png" alt="Final IC50 equation"
width="30%">
<img src="https://static.igem.wiki/teams/4200/wiki/model/model-11.png" alt="Final IC50 equation" width="30%"
class="reveal-on-scroll">
</p>
</li>
</ol>
</li>
<li>
<p>
<p class="reveal-on-scroll">
The dissociation constant values substituted here were predicted using <b>PRODIGY</b>, thereby, giving us a
prediction of
the IC<sub>50</sub> concentration. The actual values of the dissociation constants would be found using
Isothermal
Calorimetric analysis.
</p>
<p>The <b>PRODIGY</b> predicted values are:</p><br>
<p class="reveal-on-scroll">The <b>PRODIGY</b> predicted values are:</p><br>
<img src="https://static.igem.wiki/teams/4200/wiki/model/model-12.png"
alt="Predicted dissociation constant values" width="20%">
alt="Predicted dissociation constant values" width="20%" class="reveal-on-scroll">
</li>
</ul>
<figure class="figure">
<img src="https://static.igem.wiki/teams/4200/wiki/model/model-ic50-2.png" class="figure-img img-fluid rounded"
alt="fibronectin concentrations" width="80%">
<figure class="figure reveal-on-scroll">
<img src="https://static.igem.wiki/teams/4200/wiki/model/model-ic50-2.png"
class="figure-img img-fluid rounded reveal-on-scroll" alt="fibronectin concentrations" width="80%">
<figcaption class="figure-caption text-center">
Fig 4: \(IC_{50}\) values plotted for a range of Fibronectin concentrations
</figcaption>
</figure>
<p>As an example,
<ul>
<p class="reveal-on-scroll">As an example,
<ul class="reveal-on-scroll">
<li>MW of peptide = 4 kDa = 4 kg/mol</li>
<li>Say [F] = 1 nM</li>
<li>IC<sub>50</sub> = 10.67 microM = 42 mg/L</li>
</ul>
</p>
<b>References</b>
<ol>
<b class="reveal-on-scroll">References</b>
<ol class="reveal-on-scroll">
<li>
S. Pronk et al., “GROMACS 4.5: a high-throughput and highly parallel open source molecular simulation toolkit,”
Bioinformatics, vol. 29, no. 7, pp. 845–854, Apr. 2013, doi: 10.1093/BIOINFORMATICS/BTT055.
......@@ -251,7 +265,8 @@
"Scalable Algorithms for Molecular Dynamics Simulations on Commodity Clusters," Proceedings of the ACM/IEEE
Conference on Supercomputing (SC06), Tampa, Florida, 2006, November 11-17
<p>Schrödinger Release 2022-3: Desmond Molecular Dynamics System, D. E. Shaw Research, New York, NY, 2021.
<p class="reveal-on-scroll">Schrödinger Release 2022-3: Desmond Molecular Dynamics System, D. E. Shaw Research,
New York, NY, 2021.
Maestro-Desmond Interoperability Tools, Schrödinger, New York, NY, 2021.</p>
</li>
</ol>
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