ScanCer - Breast Cancer Medicine Screening

Throughout the project, our team utilized molecular docking technology to screen drugs from a drug library and validated the scientific accuracy of the wet lab screening results. At the same time, we integrated virtual screening with wet lab screening, conducting further analysis on the drugs that performed well. We ultimately proposed structural modifications for the drugs. The modified drugs achieved higher scores in molecular docking.

On this page, we will introduce the virtual screening (molecular docking) technique in detail and present the corresponding mathematical model. We will also describe the process and results of our computer simulation using this technique and illustrate the significance of our study.

Virtual Screening and Molecular Docking

Drug virtual screening is a computational method used to identify potential drug candidates from large libraries of compounds. It involves simulating how small molecules, or ligands, interact with a biological target, such as a protein or enzyme, to predict their binding affinity and potential efficacy. The process typically begins with a target structure, often derived from experimental data or computational models. Virtual screening methods, including molecular docking, molecular dynamics simulations, and quantitative structure-activity relationship (QSAR) models, are employed to evaluate and rank compounds based on their predicted interactions with the target.

By using virtual screening, researchers can efficiently narrow down a vast number of compounds to those most likely to have therapeutic potential, thus accelerating the drug discovery process and reducing the need for extensive experimental testing. This approach facilitates the identification of promising candidates for further experimental validation and optimization.

Molecular docking, a key technique within this broader virtual screening framework, forecasts noncovalent interactions between macromolecules—typically between a macromolecule (receptor) and a smaller molecule (ligand). This process begins with their unbound forms, often derived from molecular dynamics simulations, homology modeling, or other methods, with the goal of determining bound conformations and estimating binding affinity.

The ability to predict how small molecules bind to proteins is especially valuable in drug discovery. It helps in screening virtual libraries of drug-like compounds to identify potential leads for development. Moreover, docking can estimate the bound conformations of known binders when experimental holo structures are not available. Integrating these approaches not only streamlines the identification of promising drug candidates but also enhances our understanding of their binding mechanisms and potential for structural optimization.

Furthermore, molecular docking provides valuable insights into potential modifications of drug candidates. By analyzing the predicted binding modes and interactions of ligands with the target, researchers can pinpoint regions where structural changes might improve binding affinity or selectivity. For example, docking results can indicate how altering certain chemical groups on a ligand could enhance its fit with the target’s binding site or minimize unwanted interactions. This information is crucial for guiding the design of optimized drug candidates with improved efficacy and fewer side effects.

Mathematical and Physical Theories behind Molecular Docking

Before performing virtual screening, we first conducted experimental screening on over 1200 drugs from our drug library and ultimately selected 14 drugs with the best performance (detailed experimental procedures are available in another section of the wiki). To further validate the scientific accuracy of these experimental results and to provide recommendations for drug structure improvement, we proceeded with virtual screening.

For the virtual screening, we utilized AutoDock Vina. AutoDock Vina is a widely used molecular docking software designed to predict the binding modes of small molecules to macromolecular targets. It improves upon its predecessor, AutoDock, by incorporating a more efficient optimization algorithm and a refined scoring function. AutoDock Vina employs a global optimization approach based on Iterated Local Search, which effectively explores the conformational space of both ligands and receptor sites. This method is combined with a hybrid scoring function that evaluates binding affinity through a mix of empirical terms and knowledge-based potentials. The result is a robust and faster docking process that delivers high-quality predictions of protein-ligand interactions, making AutoDock Vina a valuable tool in drug discovery and molecular modeling.

PDBQT

In AutoDock Vina, we use a special format of files, PDBQT format, which contains detailed information about small molecule ligands and large molecule receptors.

The PDBQT file format is an extension of the Protein Data Bank (PDB) format, specifically designed for use with molecular docking tools such as AutoDock and AutoDock Vina. This format builds on the PDB structure but integrates additional fields to accommodate both receptor (macromolecule) and ligand (small molecule) structures, essential for docking simulations.

The PDBQT format retains the core structure of the PDB format, which includes details about atoms and residues. However, it introduces extra fields to represent torsional degrees of freedom and partial charges, which are crucial for accurate docking simulations. Each line in a PDBQT file describes a single atom and includes information on the atom’s type, coordinates, and additional properties necessary for the docking process.

Each line in a PDBQT file adheres to a specific format. The record starts with either an ATOM or HETATM designation, where ATOM is used for standard atoms and HETATM for heteroatoms or non-standard residues. Following this, the atom serial number provides a unique identifier for the atom within the molecule. The atom name typically combines the element symbol with additional details (e.g., C1, O2), while the residue name specifies the residue to which the atom belongs (e.g., MET for methionine). The chain identifier is a single letter that distinguishes different chains in a multi-chain structure, and the residue sequence number indicates the position of the residue in the sequence. The insertion code, which is optional, is usually left blank.

The spatial coordinates of the atom are given in angstroms as X, Y, and Z values, followed by occupancy, which is typically set to 1.0, indicating the fraction of the atom’s presence in the given position. The temperature factor, often set to 0.0 in docking simulations, reflects the variability of the atom’s position due to thermal motion. Crucially, the partial charge field specifies the atom’s partial charge, which is used in electrostatic calculations and is vital for accurate docking predictions. Additionally, the PDBQT format includes information on torsional degrees of freedom, indicating which atoms are involved in flexible bonds and allowing the exploration of different conformations during the docking process.

For example, a line from a PDBQT file might look like this:

    
    ATOM      1  N   MET A   1      12.345  22.345  34.567  1.00  0.00  -0.300  N

In this example, ATOM specifies the record type, 1 is the atom serial number, and N is the atom name. MET is the residue name, A is the chain identifier, and 1 is the residue sequence number. The coordinates 12.345, 22.345, and 34.567 represent the atom's position in space. The occupancy is 1.00, the temperature factor is 0.00, and the partial charge is -0.300.

The PDBQT file format plays a crucial role in molecular docking simulations by integrating essential fields for modeling molecular interactions. The inclusion of torsional flexibility and partial charges enhances the accuracy of docking predictions, making the PDBQT format indispensable for effective molecular docking analyses.

Global Optimization Algorithm

In the realm of molecular docking, the primary objective is to predict the optimal binding mode of a ligand (such as a drug molecule) to a receptor (such as a protein). Achieving this goal involves navigating a complex and high-dimensional search space to identify the binding conformation that results in the lowest binding energy. Given the vastness and complexity of this search space, global optimization algorithms are crucial for effectively solving these problems.

Molecular docking typically involves dealing with a highly intricate energy landscape with numerous local minima. The key challenge here is to avoid getting trapped in local optima and to ensure that the global optimum is found. This is where global search algorithms come into play. Their role is to explore the solution space comprehensively, overcoming the limitations of local search methods that might only identify nearby local optima.

One prominent global optimization algorithm used in molecular docking is Iterated Local Search (ILS). The ILS algorithm is designed to balance the exploration of new regions of the search space with the exploitation of known good solutions. It achieves this by iteratively applying local search techniques and perturbing the current best solutions to explore new areas of the search space.

The ILS algorithm in molecular docking operates through a sequence of well-defined steps that combine local and global search strategies. The process begins with an initial solution, which is then subjected to local optimization. During local search, the algorithm aims to find the best possible solution within a defined neighborhood of the current solution. Mathematically, this is represented by:

x_{l o c a l} = {argmin}_{x \in N (x)} f (x)

Here, $x$ represents the current solution, $N (x)$ denotes the neighborhood of $x$ , and $f (x)$ is the objective function, typically representing the binding energy. The goal of the local search is to find $x_{l o c a l}$ , which minimizes $f (x)$ within the neighborhood $N (x)$ .

After obtaining the local optimum $x_{l o c a l}$ , the next step involves generating a new candidate solution $x_{n e w}$ . This is achieved by applying a perturbation to $x_{l o c a l}$ . The perturbation can be represented as:

x_{n e w} = x_{l o c a l} + δ

where $δ$ is a perturbation vector, often randomly generated, that introduces variability and enables exploration of new regions in the search space.

The acceptance of the new solution $x_{n e w}$ is governed by an acceptance criterion. This criterion is often inspired by simulated annealing and can be expressed as:

P (accept) = \exp (- \frac{f (x_{n e w}) - f (x_{l o c a l})}{T})

In this equation, $T$ represents a temperature parameter or a control parameter that decreases over time. The probability $P (accept)$ determines whether $x_{n e w}$ will be accepted as the new current solution based on the difference in objective function values $f (x_{n e w}) - f (x_{l o c a l})$ .

The ILS algorithm iterates through these steps—local search, perturbation, and acceptance—until certain stopping conditions are met. These conditions are typically defined in terms of maximum iterations or minimal improvement over a series of iterations, mathematically represented as:

If iteration \geq max_iterations or improvement < ϵ then stop

where $max_iterations$ is the maximum number of iterations allowed, and $ϵ$ is a small threshold indicating minimal improvement.

By combining local optimization with systematic perturbations and acceptance criteria, the ILS algorithm effectively navigates the complex search space of molecular docking problems. It integrates the fine-tuned exploration of local optima with broader global search strategies, thereby improving the likelihood of finding the global optimum solution for ligand-receptor binding configurations. This approach is essential for addressing the challenges posed by the high-dimensional and multi-modal nature of molecular docking problems, ensuring a comprehensive search for the most stable and effective binding conformations.

Local Optimization Algorithm

The BFGS method is specifically employed for local optimization within the molecular docking workflow. It comes into play after global search strategies have generated candidate solutions. While these global methods explore a broad solution space to identify promising candidates, BFGS focuses on refining these solutions by performing a detailed local optimization. It uses gradient information to iteratively adjust the current solution, aiming to achieve energy minimization more precisely.

The necessity of the BFGS method in molecular docking arises from its ability to enhance the accuracy of the docking results and improve optimization efficiency. Global optimization techniques may identify near-optimal solutions, but they do not guarantee that these solutions are the absolute best. BFGS is essential for fine-tuning these solutions, thereby further lowering the energy and refining the docking results. Its efficiency is derived from leveraging gradient information and an approximate Hessian matrix to accelerate the convergence process.

In optimization problems, BFGS methods update an approximation of the inverse Hessian matrix iteratively to approximate the true Hessian matrix. Consider an objective function $f (x)$ with the gradient at the current iteration point $x_{k}$ being $\nabla f (x_{k})$ . The goal is to find the point where $\nabla f (x) = 0$ . We use the updated point $x_{k + 1}$ and the gradient changes to guide the optimization.

Firstly, using Newton’s iteration formula, we update the point as:

x_{k + 1} = x_{k} - H_{k}^{- 1} \nabla f (x_{k})

where the gradient change $y_{k}$ is defined as:

y_{k} = \nabla f (x_{k + 1}) - \nabla f (x_{k})

and the step length $s_{k}$ is given by:

s_{k} = x_{k + 1} - x_{k}

To compute the gradient change, we have:

\nabla f (x_{k + 1}) = \nabla f (x_{k}) + H_{k} (x_{k + 1} - x_{k})

Substituting ( $x_{k + 1} - x_{k}$ ) into the gradient change formula, we get:

\nabla f (x_{k + 1}) = \nabla f (x_{k}) - H_{k} \cdot H_{k}^{- 1} \nabla f (x_{k})

\nabla f (x_{k + 1}) = \nabla f (x_{k}) - \nabla f (x_{k}) + H_{k} \cdot (- H_{k}^{- 1} \nabla f (x_{k}))

\nabla f (x_{k + 1}) = - H_{k} \cdot H_{k}^{- 1} \nabla f (x_{k}) + H_{k} \cdot (- H_{k}^{- 1} \nabla f (x_{k}))

\nabla f (x_{k + 1}) = H_{k} s_{k}

Thus, the gradient change $y_{k}$ can be expressed as:

y_{k} = \nabla f (x_{k + 1}) - \nabla f (x_{k})

y_{k} = H_{k} s_{k}

Next, the BFGS algorithm updates the inverse Hessian matrix $H_{k}^{- 1}$ to $H_{k + 1}^{- 1}$ using the formula:

H_{k + 1}^{- 1} = H_{k}^{- 1} + \frac{y_{k} y_{k}^{T}}{y_{k}^{T} s_{k}} - \frac{H_{k}^{- 1} s_{k} s_{k}^{T} H_{k}^{- 1}}{s_{k}^{T} H_{k}^{- 1} s_{k}}

This update formula ensures the positive definiteness and symmetry of the inverse Hessian matrix, thereby maintaining the effectiveness of the update. Specifically, this formula adjusts the matrix $H_{k}^{- 1}$ to approximate the true inverse Hessian matrix, making the new matrix $H_{k + 1}^{- 1}$ theoretically a better approximation of the true inverse Hessian matrix.

Mathematically, The workflow of the whole BFGS algorithm can be summarized as follows:

Define initial guesses $𝐱_{0}$ and $𝐁_{0}$ , and set $k = 0$ .
Obtain descent direction $𝐝_{k} = - 𝐁_{k}^{- 1} \nabla f (𝐱_{k})$ .
Let $α_{k} = 1$ .
Calculate the step $𝐬_{k} = α_{k} 𝐝_{k}$ .
Update the design $𝐱_{k + 1} = 𝐱_{k} + 𝐬_{k}$ .
If $| 𝐱_{k + 1} - 𝐱_{k} | < tol$ or $| \nabla f (𝐱_{k + 1}) | < t o l$ , stop.
Obtain the variation in the gradient $𝐲_{k} = \nabla f (𝐱_{k + 1}) - \nabla f (𝐱_{k})$ .
Update the Hessian approximation $𝐁_{k + 1} = 𝐁_{k} + \frac{𝐲_{k} 𝐲_{k}^{T}}{𝐲_{k}^{T} 𝐬_{k}} - \frac{𝐁_{k} 𝐬_{k} 𝐬_{k}^{T} 𝐁_{k}}{𝐬_{k}^{T} 𝐁_{k} 𝐬_{k}}$ .
Increase the iterator, $k = k + 1$ , and return to step 2.

In summary, the BFGS algorithm improves the optimization process by effectively updating the approximation of the inverse Hessian matrix. This method avoids the computation and storage of the full Hessian matrix, thus enhancing the efficiency and practicality of optimization algorithms, especially in handling large-scale optimization problems.

Scoring Functions

AutoDock Vina employs an empirical scoring function to evaluate and rank the binding affinity between a ligand and a receptor during molecular docking simulations. The scoring function aims to estimate the free energy of binding, providing a quantitative measure of how favorably a ligand is predicted to bind to a target protein. AutoDock Vina’s scoring method combines various energy terms, considering both the intermolecular interactions between the ligand and the receptor and the intramolecular interactions within the ligand itself. In detail, AutoDock Vina consists of a van der Waals-like potential, a non-directional hydrogen-bond term, a hydrophobic term, and a conformational entropy penal.

Van Der Waals-like Potential

AutoDock Vina considers both attractive and repulsive forces among atoms by employing a modified Lennard-Jones potential. This approach allows to effectively model van der Waals interactions, providing a comprehensive representation of the intermolecular forces governing ligand-receptor interactions. The modified potential takes into account both attractive forces, which bring atoms together, and repulsive forces, which prevent overlapping and ensure a realistic representation of molecular interactions. This sophisticated approach enables AutoDock Vina to capture the nuances of van der Waals interactions, crucial for accurately predicting the binding affinities and conformations of ligands within the binding site of a target protein.

Van der Waals-like potential is a potential energy function used to describe the interaction between molecules and is mainly used to model the weak interaction between molecules. Its basic form usually consists of the following parts:

Attraction term: describes the attraction between molecules, usually increasing with the distance between molecules.
Repulsive term: describes the repulsive forces between molecules, usually increasing as the distance between molecules decreases.
Total potential energy: The attractive and repulsive terms are combined to form an overall potential energy function. Common expressions are: $V (r) = - \frac{A}{r^{6}} + \frac{B}{r^{12}}$

Mathematically, The attractive term is generated by the dispersive forces, the instantaneous dipolar and induced dipolar interactions.The repulsive force term is generated by the strong repulsive effect caused by the overlapping electron clouds.

Firstly, we consider the attractive term. Suppose we have two molecules that have instantaneous dipoles and induced dipoles, respectively. We can use the theory of dipole interaction in electromagnetism to derive the potential energy between them. The interaction potential energy between dipoles can be given by the following formula:

V (r) = - \frac{1}{4 π ϵ_{0}} \frac{𝐩_{A} \cdot 𝐩_{B} - 3 (𝐩_{A} \cdot \hat{𝐫}) (𝐩_{B} \cdot \hat{𝐫})}{r^{3}}

By substituting the above electric field into the expression for the induced dipole, we can obtain the induced dipole $𝐩_{B}$ :

𝐩_{B} = α \frac{1}{4 π ϵ_{0}} \frac{3 (𝐩_{A} \cdot \hat{𝐫})}{r^{3}}

Then, this induced dipole is taken into the dipole-dipole interaction potential energy formulation:

V (r) = - \frac{1}{4 π ϵ_{0}} \frac{𝐩_{A} \cdot (α \frac{1}{4 π ϵ_{0}} \frac{3 (𝐩_{A} \cdot \hat{𝐫})}{r^{3}}) - 3 (𝐩_{A} \cdot \hat{𝐫}) \cdot (α \frac{1}{4 π ϵ_{0}} \frac{3 (𝐩_{A} \cdot \hat{𝐫})}{r^{3}})}{r^{3}}

The simplification results in:

V (r) = - \frac{α \cdot 3 (𝐩_{A} \cdot \hat{𝐫})^{2}}{4 π ϵ_{0}^{2} r^{6}}

V (r) = - \frac{A}{r^{6}}

Among them, $A$ is a constant, usually related to the strength of the instantaneous dipole and the molecular polarizability.

And then we have repulsive term. Consider two nonpolar molecules approaching each other. The repulsive interaction between them primarily arises from the overlap of their electronic clouds. To understand this interaction, we start by modeling the electronic clouds of the molecules as spherical distributions.

Assume that the electronic clouds of molecules A and B are described by Gaussian distributions centered at their respective molecular centers. The electronic density functions for these clouds can be approximated by:

ρ_{A} (r) \propto e^{- \frac{r^{2}}{2 σ_{A}^{2}}}

ρ_{B} (r) \propto e^{- \frac{r^{2}}{2 σ_{B}^{2}}}

Here, $σ_{A}$ and $σ_{B}$ represent the widths of the electronic clouds for molecules A and B, respectively.

The repulsive potential energy, $V_{repulsion}$ , arises from the overlap of these electronic clouds, which causes a significant repulsive force due to the mutual repulsion of electrons. The repulsive force between two electrons is given by:

V_{ee} (r) = \frac{e^{2}}{4 π ϵ_{0} r}

where $e$ is the charge of an electron, and $ϵ_{0}$ is the vacuum permittivity.

To obtain the total repulsive potential energy between the two molecules, we need to integrate the repulsive interactions over the volume where the electronic clouds overlap. The overlap area $A_{overlap} (r)$ for molecules A and B can be approximated by:

A_{overlap} (r) \approx \int_{overlap} ρ_{A} (\vec{r}) ρ_{B} (\vec{r}) d V

Given that the volume of overlap decreases rapidly with increasing distance $r$ , this integral can be approximated by a power-law function. The result of this approximation leads to a repulsive potential energy term:

V_{repulsion} (r) \approx \frac{B}{r^{12}}

where $B$ is a constant that represents the strength of the repulsive interaction.

The exponent 12 in the $\frac{B}{r^{12}}$ term is chosen to match the specific form of the repulsive interaction observed in practical scenarios. This form effectively captures the rapid increase in repulsion as the molecules come closer, which is consistent with the behavior of electron clouds in actual systems.

Finally, we add the result $V (r) = - \frac{A}{r^{6}}$ for the attraction term and $\frac{B}{r^{12}}$ for the repulsion term to obtain the final result $V (r) = - \frac{A}{r^{6}} + \frac{B}{r^{12}}$ for the van der Waals potential.

Hydrogen Bonding

Hydrogen bonds play a crucial role in molecular recognition, mediating specific interactions between a ligand and its target receptor. AutoDock Vina acknowledges the importance of both hydrogen bond donors and acceptors in this process. The scoring function within AutoDock Vina assigns favorable scores for hydrogen bond interactions, reflecting the energetically advantageous nature of these bonds in stabilizing ligand-receptor complexes. Conversely, clashes between hydrogen bond donors and acceptors are penalized to ensure that the predicted binding conformations align with the principles of favorable hydrogen bonding geometry.

Hydrophobic

AutoDock Vina assesses the desolvation energy related to the entrapment of non-polar groups within the binding site. It does so by applying a penalty to hydrophobic contacts, which models the energy cost of desolvation. The scoring function includes a hydrophobic term that represents non-polar interactions between hydrophobic groups of both the ligand and the receptor. This term aims to favor the entrapment or isolation of hydrophobic regions, acknowledging that such interactions play a crucial role in the stability and specificity of ligand-receptor binding. In essence, by incorporating the hydrophobic term, AutoDock Vina improves its capacity to predict optimal binding conformations by accounting for the energetic impact of desolvation linked to hydrophobic interactions within the binding site.

Gaussian Terms (gauss 1 and gauss 2)

The use of Gaussian functions is a strategic decision, as they offer a mathematically refined approach to modeling the complex contours of the energy landscape. By employing these functions, AutoDock Vina is able to accurately define the spatial interactions between atoms, highlighting areas of favorable overlap that enhance the energetic favorability of ligand-receptor binding.

Weighting Factors

The assigned weights (w) for each term within the scoring function of AutoDock Vina serve as adjustable parameters. These weights play a pivotal role in determining the relative significance of individual components within the overall scoring process. The adjustment of these weights is a customizable aspect that can influence the performance of AutoDock Vina, especially when fine-tuning the parameter for specific receptor-ligand systems.

After Molecular Docking

In the virtual screening, we performed molecular docking between some drug small molecules and four target proteins in the drug library, and finally selected some drugs with high comprehensive scores. Then, we combined the results of experimental screening and virtual screening, and selected two drugs that performed well in both experimental screening and virtual screening, and further studied their structure at the interface with the target protein, based on which some suggestions for improving the structure of drugs were proposed. According to our improved idea, the improved drugs achieved better performance (corresponding to higher scoring function) in molecular docking.

Cross Validation

It is quite reasonable to assume that if the results of the virtual screening of the drug library match, or partially overlap, the results of the experimental screening are accurate and reliable. In other words, through virtual screening, we can further validate the results of the wet experiment. Conversely, if the results from the wet lab experiments deviate significantly from the virtual screening results, it indicates that there may be issues with the wet lab screening. We need to further examine the experimental procedures and operations in the wet lab.

Ultimately, the results of the experimental screening largely overlapped with those of the virtual screening, indicating the scientific validity of the experimental setup, procedures, operations, and outcomes.

Target Protein Modeling

In the virtual screening, we selected four target proteins as target protein: EGFR, CDK4, Brca1, mTor. The reason why we selected these four target proteins is that they are all related to breast cancer or cancer development, and there are some marketed breast cancer drugs that target these four proteins.

The following is an introduction of these four target proteins.

EGFR (epidermal growth factor receptor) is a transmembrane tyrosine kinase receptor that plays a crucial role in regulating cell proliferation, differentiation, and survival. It is composed of an extracellular ligand-binding domain, a transmembrane region, and an intracellular kinase domain. Upon binding of ligands such as EGF or TGF-α, EGFR undergoes dimerization and autophosphorylation, activating downstream signaling pathways, including the Ras-Raf-MAPK and PI3K-Akt pathways, which promote cellular proliferation and survival. In breast cancer, EGFR expression is often elevated, particularly in triple-negative breast cancer, where its aberrant activation contributes to increased tumor aggressiveness and metastatic potential. Additionally, mutations or amplifications of EGFR are associated with treatment resistance, complicating targeted therapies such as monoclonal antibodies and small molecule inhibitors. Therefore, understanding the mechanisms of EGFR is vital for developing new therapeutic strategies and improving outcomes for breast cancer patients.
CDK4 (Cyclin-Dependent Kinase 4) is a key enzyme involved in cell cycle regulation, specifically transitioning from the G1 phase to the S phase. It forms a complex with cyclin D, which activates its kinase activity, leading to the phosphorylation of the retinoblastoma protein (Rb). This phosphorylation promotes the release of E2F transcription factors, driving the expression of genes required for DNA synthesis and cell proliferation. Dysregulation of CDK4, often through mutations or overexpression, is frequently implicated in various cancers, making it a target for therapeutic interventions, such as CDK4/6 inhibitors.
BRCA1 (Breast Cancer 1) is a vital tumor suppressor protein involved in maintaining genomic stability and repairing DNA double-strand breaks through homologous recombination. Mutations in the BRCA1 gene significantly increase the risk of breast and ovarian cancers, with individuals having a 55-85% lifetime risk of breast cancer. Impaired DNA repair due to BRCA1 mutations allows for the accumulation of genetic damage, promoting tumorigenesis. In clinical settings, BRCA1 status is crucial for personalized treatment, as tumors with BRCA1 mutations may respond better to specific therapies, such as PARP inhibitors. Understanding BRCA1's role enhances both risk assessment and therapeutic strategies for affected patients.
mTOR (mechanistic Target of Rapamycin) is a crucial regulator of cell growth, proliferation, and metabolism, integrating signals from nutrients and growth factors. It exists in two complexes, mTORC1 and mTORC2, with mTORC1 primarily promoting protein synthesis and cell growth, while mTORC2 is involved in cell survival. In the context of breast cancer, mTOR signaling is significantly implicated in tumor progression, as it regulates rapid cell proliferation and can be activated by estrogen in hormone receptor-positive cases, potentially leading to resistance to hormonal therapies. Furthermore, mTOR inhibitors, like everolimus, show promise in treating breast cancers, especially HER2-positive and triple-negative types, by targeting metabolic pathways that support cancer cell growth. Overall, understanding mTOR's role in breast cancer can enhance therapeutic strategies and improve patient outcomes.

We modeled these four proteins, and the following is our modeling results.

Figure 1. Modeled Protein Structure of mTOR

Figure 2. Modeled Protein Structure of CDK4/6