Integrated Iterative Approach

The proposed model, termed IMPROViSeD, adopts an integrated, multi-step iterative approach, which is well-aligned with the concept of "integrative modelling." This approach mimics the scientific process—collecting experimental data, proposing hypotheses, and refining models in an iterative manner.

The challenges of computing optimal orientations for subunits forming protein complexes, is broken down into well-known mathematical problem of "Graph-embedding in Euclidean space" and "Multiview registration" in computer vision. This not only makes the pipeline robust, but helps us avert the computational overhead of starting with numerous random starting orientations. We lay out the steps involved in the IMPROViSeD pipeline below.

Localization

Using a supporting structure composed of C-alpha atoms, the model identifies plausible alignments while maintaining distance constraints.

One-Shot Registration

The model performs a global alignment of the protein subunits to the supporting structure, reducing computational cost compared to traditional pairwise alignment approaches that accumulate errors.

Flip Refinement

By incorporating a mirror reflection step, the method corrects for potential symmetry-related errors, ensuring biologically valid configurations.

Iterative Conformation Generation

The model generates multiple conformations to account for the dynamic nature of proteins, enhancing the overall robustness of the resulting models.

This multi-cycle process allows for rapid convergence to a solution that fits experimental crosslinking data, resulting in a highly refined model.

Simplified Flowchart for IMPROViSeD. The subunits are oriented in multiple iterations. Each resulting from a subset of crosslinks, followed by localization and registration. The iterations proceed in parallel. The structures without clashes while satisfying the crosslinks gives final results.

Computational Efficiency

The method addresses the common problem of computational cost by breaking the modelling into different cycles and utilizing distance-preserving transformations through rigid body motions.

Optimization on \(\mathbb{SE}(3)\)

The algorithm takes advantage of the mathematical properties of \(\mathbb{SE}(3)\) to efficiently compute rigid body motions, ensuring distance preservation without deformation.

Semi-Definite Programming

A non-linear optimization formulation known as semi-definite programming is used to solve the registration problem, providing an optimal solution with reduced computation.

Parallel Execution

The iterative steps proceed in parallel, allowing the model to generate multiple conformations simultaneously, reducing overall computation time.

Practical Applications and Novelty

Handling Experimental Noise

The model includes the uncertainty inherent in crosslink data, effectively integrating noise into the optimization to create more biologically realistic structures.

Global Alignment for Accuracy

The global alignment of all subunits ensures that the final configuration is accurate and optimally aligned.

Generation of Hypothetical Contact Points

The use of hypothetical supporting structures allows for the exploration of multiple orientations and predictions of new interfaces, which is valuable for artificial drug design.

Experimental Validation and Refinement

The proposed method was validated using experimental data from protein complexes Ribonuclease Inhibitor Complexed with Ribonuclease A (PDB 1DFJ). The model showed that it could reconstruct protein structures in a single alignment step and provided quantitative metrics like RMSD to verify the accuracy of predictions.

Additional energy minimization step ensures the thermodynamic stability of the final model, allowing researchers to obtain reliable, biologically relevant conformations.

Comprehensive Post-Processing

The energy minimization after alignment ensures that the modelled protein structures are not only geometrically accurate but also energetically favorable. This final refinement step makes the model output suitable for downstream applications, such as structure-based drug design or functional analysis.

Key Highlights for the Best Model Award Submission

Unique Iterative Workflow: IMPROViSeD integrates localization, registration, flip refinement, and parallel iteration—ensuring efficient and accurate protein modelling.
Mathematical Rigor and Flexibility: The utilization of \(\mathbb{SE}(3)\) and semi-definite programming not only offers computational efficiency. Additional corrections ensure biological relevance of the structures.
Practical Relevance: The ability to handle experimental uncertainty and generate biologically plausible hypothetical interfaces positions this model as a valuable tool in biomedicine, especially in drug discovery.
Efficiency and Scalability: The parallel processing capability makes it scalable for modelling large protein complexes, setting it apart from traditional modelling methods.

Conclusion

In conclusion, the IMPROViSeD model represents a well-balanced approach combining accuracy, efficiency, and practical relevance, making it a competitive choice for the iGEM 2024 Best Model Award. Its ability to handle the complexities of protein structure determination with an efficient computational design provides a clear advantage, especially in scenarios involving large datasets or where computational resources are limited.