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\begin{document}

\title{SIDE CHAIN}



\author[1]{19muirheadj}%
\author[1]{howdhary.shreya}%
\author[1]{ndogar}%
\affil[1]{Affiliation not available}%


\vspace{-1em}



  
  \date{May 05, 2024}


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Acknowledgment

\par\null\par\null

Abstract

\textbf{The protein structure prediction problem is considered one of
the most difficult problems in bioinformatics and one with the most
profound potential medical applications. Its difficulty is largely due
to its complexity, hence the need for a simple model, such as ~the HP
Model, created by Ken Dill in 1985. Despite its usefulness due to its
computational simplicity, the HP Model is in some ways an
oversimplification, which creates ~the need for an extended model that
is more biologically plausible while still retaining computational
simplicity. This project investigated whether or not the Side Chain
Model would fulfill this need. Initial results suggest that where the
chain is composed of clumps of H-nodes or multiple H-nodes separated by
groups of P-nodes, there exists a more optimal folding in the Side Chain
Model. However, in cases where the chain includes a long string of
consecutive H-nodes, the Side Chain Model may not necessarily be better
than the HP model. Despite these cases, preliminary results suggest that
the Side Chain Model is ~an improvement upon the HP model both
energy-wise and from a biological point of view.}

\par\null

Introduction to proteins and backround on the HP model

\textbf{Proteins are large biological macromolecules that perform
various metabolic functions in the human body. They are composed of
amino acids: a carboxyl functional group, an amino functional group, an
alpha carbon, a hydrogen atom, and a sidechain that varies depending on
the amino acid. There are twenty different amino acids, and proteins
consist of as many of 34,350 amino acids.}

\textbf{Proteins have a unique native structure that is perfectly
matched to their function. Understanding how protein folds can yield a
better understanding of diseases like Huntington's and Parkinson's that
result from protein misfolding and aid in drug inhibitor design. The
protein structure prediction (PSP) problem is very difficult with the
number of possibilities for foldings, given the massive length of these
proteins and the twenty different monomers, which all interact
differently. The PSP problem is so difficult that it is considered as an
NP-hard problem, which means that it may be easy to check if a potential
folding is the true native structure of a protein, but it's nearly
impossible to determine the correct potential folding from scratch.}

\par\null

\textbf{\textbf{To deal with the difficulty of the protein folding
problem, Ken Dill developed the HP model in 1985. He separated each of
the 20 amino acids into 2 groups, hydrophobic and hydrophilic.
Hydrophobic amino acids are represented with a red H-node~and
hydrophilic amino acids are represented with a blue P-node. ~He put the
chain of hydrophobic and hydrophilic amino acids on a~two-dimensional
square lattice to fold them. ~He folded them in a way to maximize the
number of contacts in the fold. ~A contact is when two H nodes are one
unit apart on the lattice but are not next to each other on the amino
acid chain. ~The more contacts a~certain folding of an HP chain has, the
lower the energy level is. ~For example, if a given chain of H's and
P's, when folded, had five contacts, it has an energy value of -5. ~A
lower energy level is ideal because proteins tend to fold into a state
of minimal energy. ~Due to these properties,~amino acid chains in the HP
model tend to fold in a pattern that creates a~dense hydrophobic core.
~If a specific chain of H's and P's can only fold in one way such that
it has its maximum number of conacts it has a "unique optimal folding.}}

\par\null

\textbf{\textbf{\textbf{Because the HP model is an extreme
simplification of a protein's folding pattern, there are a lot of
shortcomings in it relating to how accurate it is to real life. ~First
of all, the HP model only takes into account HH interactions, when
realistically there are more than one type of interaction to be
accounted for in an amino acid chain. ~Secondly, the HP model does not
accurately represent the backbone of the protein. ~Another issue with
the HP model is that it heavily restricts the movement of H and P nodes
because they are all directly connected. ~~}}}

\par\null

Side Chain Model~

\textbf{To address the shortcoming in the HP model, we developed the
side chain model. The Side Chain Model is an extension of the HP model
that separates H and P nodes from their respective backbones, thus
resulting in three monomers: H-nodes, P-nodes, and neutral backbone
nodes. This separation increases H-nodes' flexibility and thus the
possibility for more contacts. The rules of an allowed folding in the HP
model and the definition of a contact still hold for the Side Chain
Model. To fold a chain in the Side Chain Model, the backbone is first
folded, and then the H-nodes are placed to maximize the contacts while
the P-nodes are placed wherever they fit, typically on the outside so
that a central dense hydrophobic core can be formed. Each backbone node
must have a P or H node extending perpendicularly off of it. ~This side
chain model allows for intermediary flips of H and P nodes through
3-space, so that H-nodes can be moved to the center, allowing for the
creation of a dense hydrophobic core.}~

\par\null\par\null

Comparison/Analysis

\textbf{Resultant HP and Side Chain Models were ranked primarily based
off their number of contacts. If two unique foldings of the same chain
had the same number of contacts, centricity was used to determine the
optimal fold. With the aforementioned metrics, the Side Chain Model
outperformed the HP Model in the majority of cases. When the Side Chain
Model did not outperform than the HP Model, it matched the HP model in
the number of contacts. For chains with large consecutive stretches of
H-nodes, optimal conformations in the Side Chain Model typically had
more contacts, but had poor centricity values.}

\textbf{Because the Side Chain Model considers both H-nodes and P-nodes
and backbone nodes, a new description of uniqueness is needed: which
monomers are trivial, and which are significant? The backbone nodes and
the H-nodes forming contacts were deemed significant, as per the HP
Model. However, the P-nodes and peripheral H-nodes aren't covered in the
HP Model, thus requiring a new designation under the Side Chain Model.
Peripheral H-nodes were deemed significant because they contribute to
the dense hydrophobic core. P-nodes were deemed trivial because they are
neutral inactive players in protein folding.}

\par\null\par\null

Conclusion~

\textbf{Although this project investigates the use of the Side Chain
Model in lieu of the standard HP Model, only specific scenarios were
tested and as such it does only specific scenarios were tested, meaning
it does not definitively prove one is superior.one model better that the
other. ~Due to the Side Chain Model's extra flexibility, a given
sequence was more oft to conform totypically conforms to a lower energy
state that in the HP Model. However, certain sequences ended up having
more H-H ~contacts in the Side Chain Model but a more dense hydrophobic
core in the HP Model. The Side Chain Model, unlike the HP model,
considers both the number of contacts and the density of the hydrophobic
core in determining the optimality of a fold.In the HP model, the number
of H-H contacts is the only factor considered in determining the
optimality of a fold because it is assumed that more H-H contacts result
in a hydrophobic core. However, the Side Chain Model requires this
assumption to be reexamined. Instead of just looking at contacts, taking
into account centricity of peripheral H-nodes is in certain cases
necessary to find the optimal folding with the Side Chain Model. Another
area this project adds to the wealth of knowledge is with the definition
of uniqueness in simple models. This project offers a revised definition
of uniqueness, taking into account not only the backbone and H-H
contacts, ~but neutral backbones, hydrophobic side chains, hydrophilic
side chains, and centricity as well. Overall, for the majority of test
cases, the Side Chain Model proved itself superior, and in light of
these findings it should be studied further for potential use over the
standard HP Model.}

Citations

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