clonalg-proteins

A sequential Rust implementation of the Clonal Selection Algorithm (Clonalg) for protein folding in the three-dimensional hydrophobic-polar lattice model (3D HP).

Explore the interactive 3D protein-folding visualization

The project models a protein as a sequence of hydrophobic (H) and polar (P) residues and searches for a low-energy, self-avoiding conformation on a cubic lattice. Each non-consecutive pair of adjacent hydrophobic residues contributes -1 to the conformation's energy, so maximizing H-H contacts minimizes energy.

Protein folding problem

Proteins are chains of amino-acid residues whose biological behavior depends strongly on their three-dimensional conformation. Although the amino-acid sequence describes the protein's primary structure, the chain can assume a very large number of spatial arrangements. Protein structure prediction asks which conformation is energetically most favorable for a given sequence.

Experimental structure determination can be expensive, while an exhaustive computational search quickly becomes impractical as the sequence grows. A simulation therefore needs both a simplified physical model and a search method capable of exploring promising conformations without enumerating the complete space.

The 3D HP model

The hydrophobic-polar model reduces the twenty amino acids to two classes:

• Hydrophobic (H) residues tend to avoid water and cluster inside the folded protein.
• Polar (P) residues interact more readily with the surrounding aqueous environment.

A conformation is represented as a walk on a three-dimensional cubic lattice. Every residue occupies one lattice coordinate and each consecutive pair must be one unit apart. Two residues cannot occupy the same coordinate, making valid conformations self-avoiding.

The model assigns one favorable contact for each pair of hydrophobic residues that are adjacent in space but not consecutive in the protein chain:

energy = -(number of non-local H-H contacts)

Consequently, a more negative energy denotes a better fold. This is an abstraction rather than a complete molecular-energy model, but it preserves the hydrophobic effect as the primary force guiding the simulated folding process.

Clonal selection approach

Clonalg is inspired by the adaptive immune system's clonal selection principle: an antibody with high affinity for an antigen is selected, cloned, and mutated to produce related antibodies that may have still greater affinity.

The protein-folding simulation maps these concepts as follows:

Immune-system concept	Protein-folding representation
Antigen	The fixed H/P protein sequence
Antibody	A candidate lattice conformation
Affinity	Number of non-local H-H contacts
Cloning	Copies of candidate conformations
Somatic hypermutation	Position changes controlled by current affinity
Selection	Survival of conformations with more H-H contacts
Repertoire diversity	Unique candidates and random replacements

Lower-affinity candidates receive a larger mutation allowance, encouraging exploration, while high-affinity candidates are changed more conservatively. Hypermacromutation complements this process by perturbing a randomly selected interval of the conformation. Both operators use the first-constructive-mutation rule: mutations are attempted until the first valid self-avoiding conformation is found; if no constructive change is found within the operator's limit, the original candidate is retained.

Simulation cycle

Each independent simulation performs the following steps:

1. Generate a random population of feasible, self-avoiding conformations.
2. Evaluate affinity by counting every non-local H-H contact.
3. Clone each population member according to the configured clone factor.
4. Apply affinity-dependent hypermutation to one clone population.
5. Apply interval hypermacromutation to a second clone population.
6. Combine the parents and both offspring populations.
7. Rank the candidates, remove duplicate conformations, and retain the best.
8. Introduce random feasible candidates to restore population size and diversity.
9. Repeat until the generation limit or an optional contact target is reached.

Because initialization and mutation are stochastic, a single run is not enough to characterize the algorithm. Reproduction experiments use independent seeds and report the mean, sample standard deviation, minimum, maximum, optimum frequency, score distribution, and mean runtime across all runs.

Scientific background

This implementation follows the research developed by Carolina Paula de Almeida in her 2007 master's dissertation, Aplicação de Sistemas Imunológicos Artificiais para a Predição da Estrutura de Proteínas. Her work applied Artificial Immune Systems to protein structure prediction in the 3D HP model and studied Clonalg, immune networks, feasible and penalized infeasible search spaces, aging operators, affinity maturation, fuzzy inference, and Tabu Search. The dissertation found Clonalg-based models more effective than the evaluated immune-network models, with its strongest results combining penalized search, fuzzy aging, and intensive maturation through Tabu Search.

The later PIBIC work by Luís Guilherme Bergamini Mendes, supervised by Prof. Dr. Myriam Regattieri B. S. Delgado, was presented as Computação Paralela: Suporte para Pesquisas de Computação Natural com Aplicação em Bioinformática. It adapted the Java Clonalg implementation for sequential and MPI-based execution, then evaluated parallel speedup and migration between independently evolving populations. For the 20-residue benchmark, the sequential experiment performed 96 independent runs of 200 generations and reported a mean contact score of 9.79, a standard deviation of 1.21, and a known optimum of 11 contacts (energy -11).

This Rust project focuses exclusively on the sequential Clonalg search. It does not implement MPI, clusters, island populations, or migration.

3D visualization

Open protein-folding-3d.html directly in a modern browser to watch the benchmark protein change conformation until it reaches a valid energy -11 fold.

The viewer is a single offline HTML file with Three.js and OrbitControls embedded. It requires no web server, package installation, build step, or network connection. It provides:

• real-time 3D residue and bond animation;
• hydrophobic, polar, and non-local contact highlighting;
• live generation, energy, contact, and search-state metrics;
• orbit, zoom, play/pause, reset, progress, and speed controls;
• responsive desktop and mobile layouts.

The publication reports aggregate scores and the final optimum, but does not publish the coordinate history of an individual run. The animation is therefore a deterministic Clonalg-inspired reconstruction, not a claim that these were the article's exact intermediate conformations. Its terminal coordinates form a self-avoiding fold produced by this Rust implementation with 11 non-local H-H contacts.

Implemented model

• Six-direction cubic lattice (±X, ±Y, and ±Z)
• Self-avoiding protein conformations
• Non-local hydrophobic-contact energy function
• Random feasible population initialization
• Clonal expansion
• Affinity-dependent hypermutation
• Interval hypermacromutation
• First-constructive-mutation feasibility rule
• Selection across parents and both offspring populations
• Duplicate-conformation removal
• Random replacement to preserve population diversity
• Deterministic seeded runs
• Early stopping at a requested contact target
• Multi-run statistical experiments

The default protein is the 20-residue Tortilla benchmark:

HPHPPHHPHPPHPHHPPHPH

Its known optimum is 11 H-H contacts, corresponding to energy -11.

PIBIC reproduction

The Rust experiment uses the same benchmark shape as the PIBIC sequential evaluation: 96 independent runs, 200 generations, population size 10, clone factor 2, and hypermutation rate 40%.

Run it with:

cargo run --release -- --runs 96 --seed 0 --generations 200

Results measured on the current implementation:

Metric	Rust reproduction	PIBIC article
Independent runs	96	96
Generations per run	200	200
Mean H-H contacts	10.094	9.79
Sample standard deviation	0.834	1.21
Minimum contacts	8	Not reported
Maximum contacts	11	11
Best energy	-11	-11
Runs reaching the optimum	32 (33.33%)	Not reported
Mean runtime per run	67.552 ms	26.49 s

The Rust solver reproduces the known optimum and slightly exceeds the article's reported mean solution quality. Runtime values are not directly comparable: the PIBIC measurements used a Java implementation on 2009-era 2.4 GHz hardware, whereas the Rust measurement was made on current hardware. Furthermore, the publication does not provide its complete seed list, exact replacement count, or all low-level implementation choices.

For seeds 0..=95, the Rust score distribution was:

H-H contacts	Runs
8	6
9	11
10	47
11	32

Usage

Run one fold using the default benchmark and parameters:

cargo run --release

Use a custom HP sequence and reproducible seed:

cargo run --release -- --sequence HHHHPPHH --seed 7 --generations 500

Stop when a known target is reached:

cargo run --release -- --target-contacts 11 --generations 5000

List every command-line option:

cargo run -- --help

A single run prints the best energy, number of H-H contacts, generation and evaluation counts, lattice moves, and coordinates for every residue. A multi-run experiment prints aggregate statistics and the score distribution.

Development

Format, test, and lint the project with:

cargo fmt --check
cargo test
cargo clippy --all-targets -- -D warnings