GROUP07_Final_Project.md

title	author	header-includes	geometry	bibliography	csl	link-citations	reference-section-title	nocite
Computational Methods of Protein Folding	Martin Galvan Connie Li Justin Lim	\usepackage{siunitx}	margin=1in	references.bib	nature-genetics.csl	true	References	@*

1. Introduction for Protein Folding
2. Structural Components of Proteins
3. Predicting Protein Structures
4. Template-Based Structure Modeling
5. Protein Threading
6. De novo Protein Structure Prediction
7. Using Machine Learning
8. Comparison of Computational Methods

Introduction to Protein Folding {#sec-01}

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Proteins are involved in nearly every biological process in a living system. So how are these important molecules made? It is known that the 3-dimensional structure of a protein is what determines its function, but proteins are not synthesized as 3-D structures. Rather, proteins are first translated into a linear amino acid chain on the ribosome from mRNA. Then the chain is folded into its native conformation which is the shape of a properly folded protein. Understanding how a chain of amino acids folds into its native conformation is known as the protein folding problem.

In 1972, Dr. Christian Anfinsen received the Nobel Prize in Chemistry for his research of "ribonuclease and the relationship between amino acid sequence and the biologically active conformation". Through his research, Anfinsen showed that a denatured protein can refold into its native conformation after being removed from denaturing conditions and placed in its normal physiological environment, all without the help of any additional molecular species[@anfinsen73]. This implies that all the information necessary for the proper folding of a protein is entirely encoded in its amino acid sequence. Such an observation offers support for the so called "thermodynamic hypothesis" which states that a protein will fold into a conformation that minimizes its Gibbs free energy. The thermodynamic hypothesis is a powerful theory because it is a well-defined model for how proteins fold and lends itself well to computational methods of calculating proteins structures.

Unfortunately, knowing that protein will fold based on energy considerations does not make the protein folding problem easy. The number of possible configurations of an amino acid of 100 residues is on the order of 10^70^ and a random search of all configurations for the one with the lowest Gibbs free energy would take about 10^52^ years[@karplus97]. Obviously, proteins do not take that long to fold suggesting that there are mechanisms that guide the folding of the protein. Understanding the pathway that a protein takes to its final conformation as well as the structure itself are two key pieces of the puzzle.

Structural Components of Proteins {#sec-02}

Though proteins fold to minimize their Gibbs free energy, they are not just jumbled masses of amino acids that happen be in the lowest energy state. There several distinct structural components that are common to all proteins. The highest levels of protein structure are known as primary, secondary, tertiary and quaternary structure.

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Primary Structure

The primary structure is the linear chain of amino acids directly translated from mRNA. In the linear chain, the side chain of each residue and the position of the residue within the chain determines how it folds as it is the interactions between these residues that guide the folding method.

Secondary Structure

There are two types of secondary structures: $\alpha$-helices and $\beta$-sheets. These structures are the result of intramolecular hydrogen bonding by the backbone of the chain which acts to stabilize the shape. The $\alpha$-helix is a spiral shape while $\beta$-sheets are the result of the chain folding over itself.

Tertiary Structure

Interactions of the residue side chains with each other and with the surrounding environment are the primary drivers of folding in the tertiary structure of a protein. There can be domains in the secondary structure that are hydrophobic or hydrophilic and fold accordingly. Disulfide bonds between cysteine residues stabilize the structure. There can even be ionic interactions between the residues.

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Quaternary Structure

When amino acid chains that have folded into their tertiary structures assemble into multi-subunit complex, this is called quaternary structure. Many proteins are actually several subunits composed together and gain new functionality upon assembly.

Predicting Protein Structure {#sec-03}

There are several experimental techniques to study protein structures like X-ray crystallography, NMR spectroscopy and cryo-EM. While these techniques are used extensively in research, we will be focusing on computational methods.

Most computational approaches to protein structure prediction rely on using information from proteins with known structures to guide the process. The solved structures generally come from one of the techniques mentioned above. Because there is a strong relationship between a protein's structure and its function, proteins that share a common function or have similar functional domains very often share structural features as well[@chothia86]. In fact, it has been shown that protein structure has been well conserved in evolution. Homologous proteins are much more structurally similar than would be expected from residue of identities alone, an observation that is leveraged in research [@kaczanowski10].

Computing Accuracy of Predicted Structures

After a protein structure has been predicted, there must be some measure of accuracy. One widely used metric is called the Root Mean Squared Displacement (RMSD). The RMSD calculates the average difference in the coordinates of each atom in the reference protein structure (the one that was solved experimentally) and the corresponding atom in the structure that was solved computationally. The formula for RMSD is as follows: $$RMSD=\sqrt{\frac{1}{n}\sum_{i=1}^{n}{\lVert v_{i}-w_{i} \rVert}^{2}}$$ where $n$ is the number of atoms in one of the proteins (the sequences of the two proteins should be the same), $v_{i}$ is the coordinates of atom $i$ in the the first protein and $w_{i}$ is the coordinates of atom $i$ in the second protein. The protein coordinates must be given according to the same reference origin or the comparison will not be meaningful. The RMSD, which is given in units of angstrom ($\si{\angstrom}$), is an effective way to measure how close a predicted structure is to the real structure.

Template-Based Structure Modeling {#sec-04}

Template-Based Structure Modeling incorporates single template structures with a group of polypeptide sequences and known structure. Templates structures each consist of separate noncontiguous peptide sequences that have a known interaction and structure when put together. This method attempts a simultaneous alignment of all component sequences of the template on the sequence of interest, then attempts to fold the whole sequence of interest according to the conformation of the template. The gaps between each template aligned core segment will bend and act as connectors to the ends of the template strands.

Protein Threading {#sec-05}

In attempt to solve cases where Protein Data Banks give no viable solved structure, Protein Threading aims to thread multiple template structures simultaneously. There are cases in protein structure modeling where there can be more than one template suitable for a single peptide sequence. Protein threading will accurately align multiple templates to the sequence of interest. This method is able to consolidate the multiple aligned template-based structures into a single protein structure.

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De novo (Free Modeling) Protein Structure Prediction {#sec-06}

Though use of a protein template to predict new structures is a powerful technique, there are some limitations. Two of the biggest challenges for this method are a lack of homologs in the set of solved protein structures and the difficulty of accurately identifying homologs[@friedberg04]. Thus, there has been much research into de novo methods of protein structure prediction, in which a template protein is not used. One popular method of de novo protein structure prediction is Rosetta, which is a suite of software tools designed for computational modeling and analysis of protein structures.

As a brief aside, Rosetta is part of a neat initiative that allows anyone with a computer to donate idle computer to time to various projects using a third-party program. The project, which is called Rosetta@home, gives researchers access to computing resources that would otherwise be impossible to obtain. More information can be found at the project website.

The model of protein folding adopted by Rosetta is that when folding begins, small protein fragments in the single chain simultaneously sample from the space of available conformations. The fragments attempt to fold into local structures according to the thermodynamics of the local sequence. Then the local structures begin folding according to non-local interactions, driven by the desire to minimize free energy. The main types of non-local interactions considered by the program are hydrophobic burial (hydrophobic sections move to the center of the fold), electrostatics, disulfide bonding and main chain hydrogen bonding. It is assumed that the non-local interactions can be accurately modeled at levels above atomic resolution.

In the original Rosetta program, the local structures were predicted by using protein fragments with known structures and the distribution of structures from the database for a given sequence fragment was used as the distribution of local structures that the program would sample from. Thus, many protein-like structures could be generated with a Monte Carlo procedure and then clustered and the centers of the largest clusters were chosen as the predicted models. The fragment library can generated by doing a BLAST or PSI-BLAST search which finds sequences similar to the target sequence[@bonneau02;@bonneau01;@simons99;@simons97].

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Using Machine Learning {#sec-07}

Machine learning algorithms use amino acids to build prediction models by learning the differences between different protein fold categories and using the learned model to predict protein structures for query proteins. The most popular algorithms include the Support Vector Machines (SVMs), Hidden Markov Model (HMM), and Artificial Neural Network. This section will focus particularly on SVMs.

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Machine learning methods involve the following phases: model training and prediction. In model training, sequences of query proteins are submitted into a pipeline of feature representation. Using feature descriptors, sequences of various lengths are encoded with fixed-feature vectors. In prediction, uncharacterized query proteins are submitted into the same pipeline. The trained prediction model uses the resulting feature vectors to predict the fold class of the proteins. This figure below describes the framework of these methods.

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A Support Vector Machine (SVM) is a machine learning algorithm that determines an optimal hyperplane in a multidimensional space in order to classify data points into separate classes. In this algorithm, each data point is plotted as a point in n-dimensional space, where n is the number of features, with the value of each feature being the value of a particular coordinate.

The input for SVMs is a set of training samples that are a pair of input values (termed the features) and output values (termed the results). The output for SVMs is a set of weights for each feature. This algorithm optimizes by reducing the number of weights to a few that are designated as the support vectors, or data points that are within the margin of the hyperplane. This algorithm aims to find a plane that maximizes the maximum distance between support vectors, or the margin. SVMs converge fast and lead to high accuracy. The figure below shows how hyperplanes in SVMs are determined based on the support vectors and the margin.

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SVM has been efficient in protein remote homology detection, protein structural classification, and DNA-binding protein prediction. SVM-based methods include Shamim’s method, Damoulas’ method, and TAXFOLD. These methods vary in their feature representation algorithms. Shamim’s method uses secondary structural state and solvent accessibility state frequencies of amino acids and amino acid pairs as feature vectors. The TAXFOLD method uses global and local sequential and structural features.

Comparison of Various Computational Methods {#sec-08}

Computational methods can be categorized into three classes: (1) de novo modeling methods, (2) template-based methods, and (3) template-free methods.

De novo methods were described in detail in the section above. De novo modelling methods are limited because they require long computational time, and they can only be applied to small proteins.

In template-based methods, proteins of known structures are derived from protein structure databases and used as templates for a query protein sequence. Alignment algorithms are used to detect the evolutionary relationship between a target sequence and a protein of known structure. These methods include threading methods, which is described in detail in the section above, and profile-profile alignment methods. Template-based methods are time-consuming. In addition, these methods are limited by the amount of template proteins in protein structure databases. Furthermore, they are hindered by the quality of the profiles of a query and a template.

Template-free methods assume that the number of protein fold classes is limited. This approach is more efficient for large-scale predictions and can examine a large number of candidates for experimental validation.

CASP

Every other year, scientists from across the world come together in a community-wide competition called the Critical Assessment of Techniques for Protein Structure Prediction or CASP. In each session, the competition organizers release protein sequences for which structures are not yet public. The proteins are divided into categories according to criteria like multimeric targets or existence of homologs. Participants then submit their predictions for the structures and independent assessors evaluate the accuracy of each prediction from each group, allowing them to rank the submissions. In the latest iteration of the competition, CASP13, a machine learning company called DeepMind took the overall top spot with a folding algorithm called AlphaFold which used a deep learning approach. The impressive performance of the algorithm demonstrated the promise of deep learning in protein structure prediction.