bio_forge/ops/

hydro.rs

//! Protonation-aware hydrogen placement for protein and nucleic acid structures.
//!
//! This module inspects residue templates, predicts protonation states from pH or hydrogen
//! bonding networks, relabels residues accordingly, and rebuilds missing hydrogens while
//! respecting polymer termini, nucleic acid priming, and disulfide bridges.

use crate::db;
use crate::model::{
    atom::Atom,
    residue::Residue,
    structure::Structure,
    types::{Element, Point, ResidueCategory, ResiduePosition, StandardResidue},
};
use crate::ops::error::Error;
use nalgebra::{Matrix3, Rotation3, Vector3};
use rand::Rng;
use std::collections::HashSet;

/// Maximum sulfur–sulfur distance (Å) used to detect disulfide bridges.
const DISULFIDE_SG_THRESHOLD: f64 = 2.2;
/// Henderson–Hasselbalch breakpoint for protonated N-termini.
const N_TERM_PKA: f64 = 8.0;
/// Henderson–Hasselbalch breakpoint for protonated C-termini.
const C_TERM_PKA: f64 = 3.1;
/// Henderson–Hasselbalch breakpoint for the second dissociation of terminal phosphate.
const PHOSPHATE_PKA2: f64 = 6.5;

/// Parameters controlling hydrogen addition behavior.
///
/// `HydroConfig` can target a specific solution pH, remove pre-existing hydrogens, and
/// choose how neutral histidine tautomers are assigned.
#[derive(Debug, Clone)]
pub struct HydroConfig {
    /// Optional solvent pH value used for titration decisions.
    pub target_ph: Option<f64>,
    /// Whether to strip all existing hydrogens before reconstruction.
    pub remove_existing_h: bool,
    /// Strategy for setting neutral histidine tautomer labels.
    pub his_strategy: HisStrategy,
}

impl Default for HydroConfig {
    /// Provides biologically reasonable defaults (physiological pH, removal of old hydrogens,
    /// and hydrogen-bond-aware histidine selection).
    fn default() -> Self {
        Self {
            target_ph: None,
            remove_existing_h: true,
            his_strategy: HisStrategy::HbNetwork,
        }
    }
}

/// Strategies for choosing neutral histidine labels.
#[derive(Debug, Clone, Copy, PartialEq, Eq)]
pub enum HisStrategy {
    /// Force all neutral histidines to HID (delta-protonated).
    DirectHID,
    /// Force all neutral histidines to HIE (epsilon-protonated).
    DirectHIE,
    /// Randomly choose between HID and HIE.
    Random,
    /// Analyze hydrogen-bond networks to select the tautomer most likely to bond.
    HbNetwork,
}

/// Adds hydrogens to all standard residues in-place, updating protonation states when needed.
///
/// Disulfide bridges are detected prior to titration and preserved by relabeling cysteines to
/// `CYX`. Residues lacking required anchor atoms will trigger descriptive errors so upstream
/// cleanup steps can correct the issues.
///
/// # Arguments
///
/// * `structure` - Mutable structure whose residues will be protonated and hydrated.
/// * `config` - Hydrogenation configuration, including pH target and histidine strategy.
///
/// # Returns
///
/// `Ok(())` when hydrogenation succeeds.
///
/// # Errors
///
/// Returns [`Error::MissingInternalTemplate`] when no template is found or
/// [`Error::IncompleteResidueForHydro`] when required anchor atoms are missing.
pub fn add_hydrogens(structure: &mut Structure, config: &HydroConfig) -> Result<(), Error> {
    let mut targets = Vec::new();
    for (c_idx, chain) in structure.iter_chains().enumerate() {
        for (r_idx, residue) in chain.iter_residues().enumerate() {
            if residue.category == ResidueCategory::Standard {
                targets.push((c_idx, r_idx));
            }
        }
    }

    mark_disulfide_bridges(structure);

    for (c_idx, r_idx) in targets {
        let new_name = determine_protonation_state(structure, c_idx, r_idx, config);

        let chain = structure.iter_chains_mut().nth(c_idx).unwrap();
        let residue = chain.iter_residues_mut().nth(r_idx).unwrap();

        if let Some(name) = new_name {
            residue.name = name;
        }

        if config.remove_existing_h {
            residue.strip_hydrogens();
        }

        construct_hydrogens_for_residue(residue, config)?;
    }

    Ok(())
}

/// Predicts the protonation-induced residue rename for a given polymer residue.
///
/// Applies residue-specific pKa thresholds, handles histidine tautomer selection, and
/// respects previously tagged disulfide cysteines.
///
/// # Arguments
///
/// * `structure` - Structure providing context for hydrogen-bond analysis.
/// * `c_idx` - Chain index of the residue under evaluation.
/// * `r_idx` - Residue index within the chain.
/// * `config` - Hydrogenation configuration containing pH and histidine options.
///
/// # Returns
///
/// `Some(new_name)` when the residue should be relabeled; otherwise `None`.
fn determine_protonation_state(
    structure: &Structure,
    c_idx: usize,
    r_idx: usize,
    config: &HydroConfig,
) -> Option<String> {
    let chain = structure.iter_chains().nth(c_idx)?;
    let residue = chain.iter_residues().nth(r_idx)?;
    let std = residue.standard_name?;

    if std == StandardResidue::CYS && residue.name == "CYX" {
        return None;
    }

    if let Some(ph) = config.target_ph {
        return match std {
            StandardResidue::ASP => Some(if ph < 3.9 {
                "ASH".to_string()
            } else {
                "ASP".to_string()
            }),
            StandardResidue::GLU => Some(if ph < 4.2 {
                "GLH".to_string()
            } else {
                "GLU".to_string()
            }),
            StandardResidue::LYS => Some(if ph > 10.5 {
                "LYN".to_string()
            } else {
                "LYS".to_string()
            }),
            StandardResidue::ARG => Some(if ph > 12.5 {
                "ARN".to_string()
            } else {
                "ARG".to_string()
            }),
            StandardResidue::CYS => Some(if ph > 8.3 {
                "CYM".to_string()
            } else {
                "CYS".to_string()
            }),
            StandardResidue::TYR => Some(if ph > 10.0 {
                "TYM".to_string()
            } else {
                "TYR".to_string()
            }),
            StandardResidue::HIS => {
                if ph < 6.0 {
                    Some("HIP".to_string())
                } else {
                    Some(select_neutral_his(structure, residue, &config.his_strategy))
                }
            }
            _ => None,
        };
    }

    if std == StandardResidue::HIS && matches!(residue.name.as_str(), "HIS" | "HID" | "HIE" | "HIP")
    {
        return Some(select_neutral_his(structure, residue, &config.his_strategy));
    }

    None
}

/// Identifies cysteine pairs forming disulfide bonds and renames them to `CYX`.
///
/// # Arguments
///
/// * `structure` - Mutable structure containing residues to scan and relabel.
fn mark_disulfide_bridges(structure: &mut Structure) {
    let mut cys_sulfurs = Vec::new();
    for (c_idx, chain) in structure.iter_chains().enumerate() {
        for (r_idx, residue) in chain.iter_residues().enumerate() {
            if let (true, Some(sg)) = (
                matches!(residue.standard_name, Some(StandardResidue::CYS)),
                residue.atom("SG"),
            ) {
                cys_sulfurs.push((c_idx, r_idx, sg.pos));
            }
        }
    }

    if cys_sulfurs.len() < 2 {
        return;
    }

    let threshold_sq = DISULFIDE_SG_THRESHOLD * DISULFIDE_SG_THRESHOLD;
    let mut disulfide_residues: HashSet<(usize, usize)> = HashSet::new();
    for i in 0..cys_sulfurs.len() {
        for j in (i + 1)..cys_sulfurs.len() {
            let (ci, ri, pos_i) = &cys_sulfurs[i];
            let (cj, rj, pos_j) = &cys_sulfurs[j];
            if (*pos_i - *pos_j).norm_squared() <= threshold_sq {
                disulfide_residues.insert((*ci, *ri));
                disulfide_residues.insert((*cj, *rj));
            }
        }
    }

    if disulfide_residues.is_empty() {
        return;
    }

    for (c_idx, chain) in structure.iter_chains_mut().enumerate() {
        for (r_idx, residue) in chain.iter_residues_mut().enumerate() {
            if disulfide_residues.contains(&(c_idx, r_idx)) && residue.name != "CYX" {
                residue.name = "CYX".to_string();
            }
        }
    }
}

/// Selects a neutral histidine tautomer using the configured strategy.
///
/// # Arguments
///
/// * `structure` - Structure used when hydrogen-bond networks are considered.
/// * `residue` - Histidine residue being relabeled.
/// * `strategy` - Selection strategy from [`HisStrategy`].
///
/// # Returns
///
/// Either `"HID"` or `"HIE"`.
fn select_neutral_his(structure: &Structure, residue: &Residue, strategy: &HisStrategy) -> String {
    match strategy {
        HisStrategy::DirectHID => "HID".to_string(),
        HisStrategy::DirectHIE => "HIE".to_string(),
        HisStrategy::Random => {
            let mut rng = rand::rng();
            if rng.random_bool(0.5) {
                "HID".to_string()
            } else {
                "HIE".to_string()
            }
        }
        HisStrategy::HbNetwork => optimize_his_network(structure, residue),
    }
}

/// Determines the best histidine tautomer by inspecting nearby hydrogen-bond acceptors.
///
/// # Arguments
///
/// * `structure` - Complete structure used to search for acceptor atoms.
/// * `residue` - Histidine residue being evaluated.
///
/// # Returns
///
/// The histidine label (`"HID"` or `"HIE"`) that maximizes compatibility with neighbors.
fn optimize_his_network(structure: &Structure, residue: &Residue) -> String {
    let nd1 = residue.atom("ND1");
    let ne2 = residue.atom("NE2");

    let has_acceptor_near = |atom: &Atom| -> bool {
        for chain in structure.iter_chains() {
            for other_res in chain.iter_residues() {
                if other_res.id == residue.id && chain.id == "Unknown" {
                    continue;
                }
                if other_res == residue {
                    continue;
                }

                for other_atom in other_res.iter_atoms() {
                    if matches!(other_atom.element, Element::O | Element::N)
                        && atom.distance_squared(other_atom) < 3.5 * 3.5
                    {
                        return true;
                    }
                }
            }
        }
        false
    };

    let nd1_interaction = nd1.map(has_acceptor_near).unwrap_or(false);
    let ne2_interaction = ne2.map(has_acceptor_near).unwrap_or(false);

    match (nd1_interaction, ne2_interaction) {
        (true, false) => "HID".to_string(),
        (false, true) => "HIE".to_string(),
        _ => "HID".to_string(),
    }
}

/// Rebuilds hydrogens for a single residue using template geometry and terminal rules.
///
/// # Arguments
///
/// * `residue` - Residue to augment with hydrogens.
/// * `config` - Hydrogenation configuration influencing terminal protonation.
///
/// # Returns
///
/// `Ok(())` when all hydrogens were added or already present.
///
/// # Errors
///
/// Returns [`Error::MissingInternalTemplate`] or [`Error::IncompleteResidueForHydro`] when
/// required template data or anchor atoms are missing.
fn construct_hydrogens_for_residue(
    residue: &mut Residue,
    config: &HydroConfig,
) -> Result<(), Error> {
    let template_name = residue.name.clone();

    let template_view =
        db::get_template(&template_name).ok_or_else(|| Error::MissingInternalTemplate {
            res_name: template_name.clone(),
        })?;

    let existing_atoms: HashSet<String> = residue.atoms().iter().map(|a| a.name.clone()).collect();

    for (h_name, h_tmpl_pos, anchors_iter) in template_view.hydrogens() {
        if existing_atoms.contains(h_name) {
            continue;
        }

        let anchors: Vec<&str> = anchors_iter.collect();
        if let Ok(pos) = reconstruct_geometry(residue, h_tmpl_pos, &anchors) {
            residue.add_atom(Atom::new(h_name, Element::H, pos));
        } else {
            return Err(Error::incomplete_for_hydro(
                &residue.name,
                residue.id,
                anchors.first().copied().unwrap_or("?"),
            ));
        }
    }

    match residue.position {
        ResiduePosition::NTerminal if residue.standard_name.is_some_and(|s| s.is_protein()) => {
            construct_n_term_hydrogens(residue, n_term_should_be_protonated(config))?;
        }
        ResiduePosition::CTerminal if residue.standard_name.is_some_and(|s| s.is_protein()) => {
            construct_c_term_hydrogen(residue, c_term_should_be_protonated(config))?;
        }
        ResiduePosition::ThreePrime if residue.standard_name.is_some_and(|s| s.is_nucleic()) => {
            construct_3_prime_hydrogen(residue)?;
        }
        ResiduePosition::FivePrime if residue.standard_name.is_some_and(|s| s.is_nucleic()) => {
            if residue.has_atom("P") {
                construct_5_prime_phosphate_hydrogens(residue, config)?;
            } else if residue.has_atom("O5'") {
                construct_5_prime_hydrogen(residue)?;
            }
        }
        _ => {}
    }

    Ok(())
}

/// Evaluates whether an N-terminus should remain protonated under the configured pH.
///
/// # Arguments
///
/// * `config` - Hydrogenation configuration that may provide a target pH.
///
/// # Returns
///
/// `true` when the pH is below the configured threshold or unspecified.
fn n_term_should_be_protonated(config: &HydroConfig) -> bool {
    config.target_ph.map(|ph| ph < N_TERM_PKA).unwrap_or(true)
}

/// Evaluates whether a C-terminus should remain protonated under the configured pH.
///
/// # Arguments
///
/// * `config` - Hydrogenation configuration potentially specifying pH.
///
/// # Returns
///
/// `true` when the pH is below the acidic cutoff; otherwise `false`.
fn c_term_should_be_protonated(config: &HydroConfig) -> bool {
    config.target_ph.map(|ph| ph < C_TERM_PKA).unwrap_or(false)
}

/// Aligns template coordinates to residue anchors to predict a hydrogen position.
///
/// # Arguments
///
/// * `residue` - Residue containing measured anchor atoms.
/// * `target_tmpl_pos` - Target hydrogen position from the template.
/// * `anchor_names` - Atom names used to determine the rigid-body transform.
///
/// # Returns
///
/// `Ok(point)` containing the placed coordinate or `Err(())` if anchors are missing.
fn reconstruct_geometry(
    residue: &Residue,
    target_tmpl_pos: Point,
    anchor_names: &[&str],
) -> Result<Point, ()> {
    let template_view = db::get_template(&residue.name).ok_or(())?;

    let mut residue_pts = Vec::new();
    let mut template_pts = Vec::new();

    for name in anchor_names {
        let r_atom = residue.atom(name).ok_or(())?;
        residue_pts.push(r_atom.pos);

        let t_pos = template_view
            .heavy_atoms()
            .find(|(n, _, _)| n == name)
            .map(|(_, _, p)| p)
            .ok_or(())?;
        template_pts.push(t_pos);
    }

    let (rot, trans) = calculate_transform(&residue_pts, &template_pts).ok_or(())?;

    Ok(rot * target_tmpl_pos + trans)
}

/// Rebuilds the N-terminal amine hydrogens using tetrahedral geometry.
///
/// # Arguments
///
/// * `residue` - Residue whose terminal hydrogens are being reconstructed.
/// * `protonated` - Whether to place three hydrogens (`true`) or two (`false`).
///
/// # Returns
///
/// `Ok(())` when hydrogens are successfully placed.
///
/// # Errors
///
/// Returns [`Error::IncompleteResidueForHydro`] if the N or CA atoms are missing.
fn construct_n_term_hydrogens(residue: &mut Residue, protonated: bool) -> Result<(), Error> {
    residue.remove_atom("H");
    residue.remove_atom("H1");
    residue.remove_atom("H2");
    residue.remove_atom("H3");

    let n_pos = residue
        .atom("N")
        .ok_or_else(|| Error::incomplete_for_hydro(&residue.name, residue.id, "N"))?
        .pos;
    let ca_pos = residue
        .atom("CA")
        .ok_or_else(|| Error::incomplete_for_hydro(&residue.name, residue.id, "CA"))?
        .pos;

    let v_ca_n = (n_pos - ca_pos).normalize();
    let bond_len = 1.0;
    let angle = 109.5_f64.to_radians();
    let sin_a = angle.sin();
    let cos_a = angle.cos();

    let up = if v_ca_n.x.abs() < 0.9 {
        Vector3::x()
    } else {
        Vector3::y()
    };
    let v_perp = v_ca_n.cross(&up).normalize();
    let base_dir = v_ca_n.scale(cos_a) + v_perp.scale(sin_a);

    let phases = [0.0_f64, 120.0, 240.0];
    let mut candidates: Vec<Vector3<f64>> = phases
        .iter()
        .map(|deg| {
            let rot_axis = Rotation3::from_axis_angle(
                &nalgebra::Unit::new_normalize(v_ca_n),
                deg.to_radians(),
            );
            rot_axis * base_dir
        })
        .collect();

    candidates.sort_by(|a, b| {
        a.dot(&v_ca_n)
            .partial_cmp(&b.dot(&v_ca_n))
            .unwrap_or(std::cmp::Ordering::Equal)
    });

    let target_count = if protonated { 3 } else { 2 };
    let names = ["H1", "H2", "H3"];
    for (idx, dir) in candidates.into_iter().take(target_count).enumerate() {
        residue.add_atom(Atom::new(
            names[idx],
            Element::H,
            n_pos + dir.scale(bond_len),
        ));
    }

    Ok(())
}

/// Rebuilds the carboxylate proton at the C-terminus when protonated.
///
/// # Arguments
///
/// * `residue` - Residue to modify.
/// * `protonated` - Whether the terminus should include the `HOXT` hydrogen.
///
/// # Returns
///
/// `Ok(())` after either removing or adding hydrogens as needed.
///
/// # Errors
///
/// Returns [`Error::IncompleteResidueForHydro`] if the `C` or `OXT` atoms are missing.
fn construct_c_term_hydrogen(residue: &mut Residue, protonated: bool) -> Result<(), Error> {
    if !protonated {
        residue.remove_atom("HOXT");
        residue.remove_atom("HXT");
        return Ok(());
    }

    residue.remove_atom("HXT");
    if residue.has_atom("HOXT") {
        return Ok(());
    }

    let c_pos = residue
        .atom("C")
        .ok_or_else(|| Error::incomplete_for_hydro(&residue.name, residue.id, "C"))?
        .pos;
    let oxt_pos = residue
        .atom("OXT")
        .ok_or_else(|| Error::incomplete_for_hydro(&residue.name, residue.id, "OXT"))?
        .pos;

    let direction = oxt_pos - c_pos;
    if direction.norm_squared() < 1e-6 {
        return Err(Error::incomplete_for_hydro(
            &residue.name,
            residue.id,
            "OXT",
        ));
    }
    let dir = direction.normalize();
    let h_pos = oxt_pos + dir.scale(0.97);

    residue.add_atom(Atom::new("HOXT", Element::H, h_pos));
    Ok(())
}

/// Adds the 3'-terminal hydroxyl hydrogen to nucleic acid residues when absent.
///
/// # Arguments
///
/// * `residue` - Residue representing a nucleic acid terminal unit.
///
/// # Returns
///
/// `Ok(())` when the hydrogen is added or already present.
///
/// # Errors
///
/// Returns [`Error::IncompleteResidueForHydro`] if required sugar atoms are missing.
fn construct_3_prime_hydrogen(residue: &mut Residue) -> Result<(), Error> {
    if residue.has_atom("HO3'") {
        return Ok(());
    }

    let o3 = residue
        .atom("O3'")
        .ok_or_else(|| Error::incomplete_for_hydro(&residue.name, residue.id, "O3'"))?
        .pos;
    let c3 = residue
        .atom("C3'")
        .ok_or_else(|| Error::incomplete_for_hydro(&residue.name, residue.id, "C3'"))?
        .pos;
    let c4 = residue
        .atom("C4'")
        .or_else(|| residue.atom("C2'"))
        .map(|a| a.pos)
        .unwrap_or_else(|| c3 + Vector3::x());

    let v_c3_o3 = (o3 - c3).normalize();

    let v_c4_c3 = (c3 - c4).normalize();
    let normal = v_c3_o3.cross(&v_c4_c3).normalize();

    let h_dir = (v_c3_o3 + normal).normalize();
    let h_pos = o3 + h_dir.scale(0.96);

    residue.add_atom(Atom::new("HO3'", Element::H, h_pos));
    Ok(())
}

/// Adds the 5'-terminal hydroxyl hydrogen for nucleic acid residues lacking phosphates.
///
/// # Arguments
///
/// * `residue` - Residue whose 5' terminus is being hydrated.
///
/// # Returns
///
/// `Ok(())` when the hydrogen is added or already exists.
///
/// # Errors
///
/// Returns [`Error::IncompleteResidueForHydro`] if sugar anchor atoms are missing.
fn construct_5_prime_hydrogen(residue: &mut Residue) -> Result<(), Error> {
    if residue.has_atom("HO5'") {
        return Ok(());
    }

    let o5 = residue
        .atom("O5'")
        .ok_or_else(|| Error::incomplete_for_hydro(&residue.name, residue.id, "O5'"))?
        .pos;
    let c5 = residue
        .atom("C5'")
        .ok_or_else(|| Error::incomplete_for_hydro(&residue.name, residue.id, "C5'"))?
        .pos;

    let v_c5_o5 = (o5 - c5).normalize();
    let aux = if v_c5_o5.z.abs() < 0.9 {
        Vector3::z()
    } else {
        Vector3::x()
    };
    let perp = v_c5_o5.cross(&aux).normalize();

    let h_dir = (v_c5_o5 + perp).normalize();
    let h_pos = o5 + h_dir.scale(0.96);

    residue.add_atom(Atom::new("HO5'", Element::H, h_pos));
    Ok(())
}

/// Adds hydrogens to 5'-terminal phosphate groups based on pH.
///
/// At physiological pH (≥6.5), the terminal phosphate carries two negative charges and
/// requires no protons. Below this threshold, one proton is added to OP3. The function
/// respects existing hydrogens when `remove_existing_h` is disabled.
///
/// # Arguments
///
/// * `residue` - Nucleic acid residue with a 5'-terminal phosphate.
/// * `config` - Hydrogenation configuration containing pH settings.
///
/// # Returns
///
/// `Ok(())` when hydrogens are appropriately placed or removed.
///
/// # Errors
///
/// Returns [`Error::IncompleteResidueForHydro`] if phosphate atoms are missing.
fn construct_5_prime_phosphate_hydrogens(
    residue: &mut Residue,
    config: &HydroConfig,
) -> Result<(), Error> {
    let ph = config.target_ph.unwrap_or(7.4);

    if ph >= PHOSPHATE_PKA2 {
        residue.remove_atom("HOP3");
        residue.remove_atom("HOP2");
        return Ok(());
    }

    if residue.has_atom("HOP3") {
        return Ok(());
    }

    let op3 = residue
        .atom("OP3")
        .ok_or_else(|| Error::incomplete_for_hydro(&residue.name, residue.id, "OP3"))?
        .pos;
    let p = residue
        .atom("P")
        .ok_or_else(|| Error::incomplete_for_hydro(&residue.name, residue.id, "P"))?
        .pos;

    let direction = (op3 - p).normalize();
    let h_pos = op3 + direction * 0.96;

    residue.add_atom(Atom::new("HOP3", Element::H, h_pos));
    Ok(())
}

/// Computes the optimal rigid transform mapping template anchor points to residue atoms.
///
/// Uses Kabsch alignment with safeguards for one- and two-point configurations.
///
/// # Arguments
///
/// * `r_pts` - Coordinates from the residue.
/// * `t_pts` - Corresponding coordinates from the template.
///
/// # Returns
///
/// `Some((rotation, translation))` when alignment succeeds; otherwise `None`.
fn calculate_transform(r_pts: &[Point], t_pts: &[Point]) -> Option<(Matrix3<f64>, Vector3<f64>)> {
    let n = r_pts.len();
    if n != t_pts.len() || n == 0 {
        return None;
    }

    let r_center = r_pts.iter().map(|p| p.coords).sum::<Vector3<f64>>() / n as f64;
    let t_center = t_pts.iter().map(|p| p.coords).sum::<Vector3<f64>>() / n as f64;

    if n == 1 {
        return Some((Matrix3::identity(), r_center - t_center));
    }

    if n == 2 {
        let v_r = r_pts[1] - r_pts[0];
        let v_t = t_pts[1] - t_pts[0];
        let rot = Rotation3::rotation_between(&v_t, &v_r).unwrap_or_else(Rotation3::identity);
        let trans = r_center - rot * t_center;
        return Some((rot.into_inner(), trans));
    }

    let mut cov = Matrix3::zeros();
    for (p_r, p_t) in r_pts.iter().zip(t_pts.iter()) {
        let v_r = p_r.coords - r_center;
        let v_t = p_t.coords - t_center;
        cov += v_r * v_t.transpose();
    }

    let svd = cov.svd(true, true);
    let u = svd.u?;
    let v_t = svd.v_t?;

    let mut rot = u * v_t;
    if rot.determinant() < 0.0 {
        let mut corr = Matrix3::identity();
        corr[(2, 2)] = -1.0;
        rot = u * corr * v_t;
    }

    let trans = r_center - rot * t_center;
    Some((rot, trans))
}

#[cfg(test)]
mod tests {
    use super::*;
    use crate::model::{
        atom::Atom,
        chain::Chain,
        residue::Residue,
        types::{Element, Point, ResidueCategory, ResiduePosition, StandardResidue},
    };

    fn residue_from_template(name: &str, std: StandardResidue, id: i32) -> Residue {
        let template = db::get_template(name).unwrap_or_else(|| panic!("missing template {name}"));
        let mut residue = Residue::new(id, None, name, Some(std), ResidueCategory::Standard);
        residue.position = ResiduePosition::Internal;
        for (atom_name, element, pos) in template.heavy_atoms() {
            residue.add_atom(Atom::new(atom_name, element, pos));
        }
        residue
    }

    fn structure_with_residue(residue: Residue) -> Structure {
        let mut chain = Chain::new("A");
        chain.add_residue(residue);
        let mut structure = Structure::new();
        structure.add_chain(chain);
        structure
    }

    fn structure_with_residues(residues: Vec<Residue>) -> Structure {
        let mut chain = Chain::new("A");
        for residue in residues {
            chain.add_residue(residue);
        }
        let mut structure = Structure::new();
        structure.add_chain(chain);
        structure
    }

    fn n_terminal_residue(id: i32) -> Residue {
        let mut residue = residue_from_template("ALA", StandardResidue::ALA, id);
        residue.position = ResiduePosition::NTerminal;
        residue
    }

    fn c_terminal_residue(id: i32) -> Residue {
        let mut residue = residue_from_template("ALA", StandardResidue::ALA, id);
        residue.position = ResiduePosition::CTerminal;
        let c_pos = residue.atom("C").expect("C atom").pos;
        let o_pos = residue.atom("O").expect("O atom").pos;
        let offset = c_pos - o_pos;
        let oxt_pos = c_pos + offset;
        residue.add_atom(Atom::new("OXT", Element::O, oxt_pos));
        residue
    }

    fn five_prime_residue_with_phosphate(id: i32) -> Residue {
        let template = db::get_template("DA").unwrap();
        let mut residue = Residue::new(
            id,
            None,
            "DA",
            Some(StandardResidue::DA),
            ResidueCategory::Standard,
        );
        residue.position = ResiduePosition::FivePrime;
        for (atom_name, element, pos) in template.heavy_atoms() {
            residue.add_atom(Atom::new(atom_name, element, pos));
        }
        let p_pos = residue.atom("P").unwrap().pos;
        let op1_pos = residue.atom("OP1").unwrap().pos;
        let op2_pos = residue.atom("OP2").unwrap().pos;
        let o5_pos = residue.atom("O5'").unwrap().pos;
        let centroid = (op1_pos.coords + op2_pos.coords + o5_pos.coords) / 3.0;
        let direction = (p_pos.coords - centroid).normalize();
        let op3_pos = p_pos + direction * 1.48;
        residue.add_atom(Atom::new("OP3", Element::O, op3_pos));
        residue
    }

    fn five_prime_residue_without_phosphate(id: i32) -> Residue {
        let template = db::get_template("DA").unwrap();
        let mut residue = Residue::new(
            id,
            None,
            "DA",
            Some(StandardResidue::DA),
            ResidueCategory::Standard,
        );
        residue.position = ResiduePosition::FivePrime;
        for (atom_name, element, pos) in template.heavy_atoms() {
            if !matches!(atom_name, "P" | "OP1" | "OP2") {
                residue.add_atom(Atom::new(atom_name, element, pos));
            }
        }
        residue
    }

    fn three_prime_residue(id: i32) -> Residue {
        let template = db::get_template("DA").unwrap();
        let mut residue = Residue::new(
            id,
            None,
            "DA",
            Some(StandardResidue::DA),
            ResidueCategory::Standard,
        );
        residue.position = ResiduePosition::ThreePrime;
        for (atom_name, element, pos) in template.heavy_atoms() {
            residue.add_atom(Atom::new(atom_name, element, pos));
        }
        residue
    }

    #[test]
    fn titratable_templates_exist_in_database() {
        let expected = [
            "ASP", "ASH", "GLU", "GLH", "LYS", "LYN", "ARG", "ARN", "CYS", "CYM", "TYR", "TYM",
            "HID", "HIE", "HIP",
        ];

        for name in expected {
            assert!(
                db::get_template(name).is_some(),
                "template {name} should exist"
            );
        }
    }

    #[test]
    fn determine_protonation_state_tracks_pka_thresholds() {
        let structure =
            structure_with_residue(residue_from_template("ASP", StandardResidue::ASP, 1));
        let mut config = HydroConfig {
            target_ph: Some(2.5),
            ..HydroConfig::default()
        };
        assert_eq!(
            determine_protonation_state(&structure, 0, 0, &config),
            Some("ASH".to_string())
        );

        config.target_ph = Some(5.0);
        assert_eq!(
            determine_protonation_state(&structure, 0, 0, &config),
            Some("ASP".to_string())
        );

        let structure =
            structure_with_residue(residue_from_template("LYS", StandardResidue::LYS, 2));
        config.target_ph = Some(11.0);
        assert_eq!(
            determine_protonation_state(&structure, 0, 0, &config),
            Some("LYN".to_string())
        );

        config.target_ph = Some(7.0);
        assert_eq!(
            determine_protonation_state(&structure, 0, 0, &config),
            Some("LYS".to_string())
        );
    }

    #[test]
    fn determine_protonation_state_respects_his_strategy() {
        let mut residue = residue_from_template("HID", StandardResidue::HIS, 3);
        residue.name = "HIS".to_string();
        let structure = structure_with_residue(residue);

        let config = HydroConfig {
            target_ph: Some(7.0),
            his_strategy: HisStrategy::DirectHIE,
            ..HydroConfig::default()
        };

        assert_eq!(
            determine_protonation_state(&structure, 0, 0, &config),
            Some("HIE".to_string())
        );

        let mut acid_config = HydroConfig::default();
        acid_config.target_ph = Some(5.5);
        assert_eq!(
            determine_protonation_state(&structure, 0, 0, &acid_config),
            Some("HIP".to_string())
        );
    }

    #[test]
    fn n_terminal_defaults_to_protonated_without_ph() {
        let residue = n_terminal_residue(40);
        let mut structure = structure_with_residue(residue);

        add_hydrogens(&mut structure, &HydroConfig::default()).expect("hydrogenation succeeds");

        let residue = structure.find_residue("A", 40, None).unwrap();
        assert!(residue.has_atom("H1"));
        assert!(residue.has_atom("H2"));
        assert!(residue.has_atom("H3"));
    }

    #[test]
    fn n_terminal_deprotonates_above_pka() {
        let residue = n_terminal_residue(41);
        let mut structure = structure_with_residue(residue);
        let mut config = HydroConfig::default();
        config.target_ph = Some(9.0);

        add_hydrogens(&mut structure, &config).expect("hydrogenation succeeds");

        let residue = structure.find_residue("A", 41, None).unwrap();
        assert!(residue.has_atom("H1"));
        assert!(residue.has_atom("H2"));
        assert!(!residue.has_atom("H3"));
    }

    #[test]
    fn c_terminal_protonates_under_acidic_ph() {
        let residue = c_terminal_residue(50);
        let mut structure = structure_with_residue(residue);
        let mut config = HydroConfig::default();
        config.target_ph = Some(2.5);

        add_hydrogens(&mut structure, &config).expect("hydrogenation succeeds");

        let residue = structure.find_residue("A", 50, None).unwrap();
        assert!(residue.has_atom("HOXT"));
    }

    #[test]
    fn c_terminal_remains_deprotonated_at_physiological_ph() {
        let residue = c_terminal_residue(51);
        let mut structure = structure_with_residue(residue);

        add_hydrogens(&mut structure, &HydroConfig::default()).expect("hydrogenation succeeds");

        let residue = structure.find_residue("A", 51, None).unwrap();
        assert!(!residue.has_atom("HOXT"));
    }

    #[test]
    fn determine_protonation_state_skips_already_marked_cyx() {
        let mut residue = residue_from_template("CYS", StandardResidue::CYS, 25);
        residue.name = "CYX".to_string();
        let structure = structure_with_residue(residue);
        let mut config = HydroConfig::default();
        config.target_ph = Some(9.0);

        assert_eq!(determine_protonation_state(&structure, 0, 0, &config), None);
    }

    #[test]
    fn add_hydrogens_populates_internal_lysine_side_chain() {
        let mut residue = residue_from_template("LYS", StandardResidue::LYS, 10);
        residue.add_atom(Atom::new("FAKE", Element::H, Point::origin()));
        let mut structure = structure_with_residue(residue);

        add_hydrogens(&mut structure, &HydroConfig::default()).expect("hydrogenation succeeds");

        let residue = structure.find_residue("A", 10, None).unwrap();
        assert!(residue.has_atom("HZ1"));
        assert!(residue.has_atom("HZ2"));
        assert!(residue.has_atom("HZ3"));
        assert!(!residue.has_atom("FAKE"));
    }

    #[test]
    fn add_hydrogens_relabels_asp_under_acidic_ph() {
        let residue = residue_from_template("ASP", StandardResidue::ASP, 15);
        let mut structure = structure_with_residue(residue);
        let mut config = HydroConfig::default();
        config.target_ph = Some(2.0);

        add_hydrogens(&mut structure, &config).expect("hydrogenation succeeds");

        let residue = structure.find_residue("A", 15, None).unwrap();
        assert_eq!(residue.name, "ASH");
        assert!(residue.has_atom("HD2"));
    }

    #[test]
    fn construct_hydrogens_errors_when_anchor_missing() {
        let template = db::get_template("ALA").expect("template ALA");
        let mut residue = Residue::new(
            20,
            None,
            "ALA",
            Some(StandardResidue::ALA),
            ResidueCategory::Standard,
        );
        residue.position = ResiduePosition::Internal;

        let (name, element, pos) = template.heavy_atoms().next().unwrap();
        residue.add_atom(Atom::new(name, element, pos));

        let err = construct_hydrogens_for_residue(&mut residue, &HydroConfig::default())
            .expect_err("should fail");
        assert!(matches!(err, Error::IncompleteResidueForHydro { .. }));
    }

    #[test]
    fn close_cysteines_are_relabelled_to_cyx_and_skip_hydrogens() {
        let cys1 = residue_from_template("CYS", StandardResidue::CYS, 30);
        let mut cys2 = residue_from_template("CYS", StandardResidue::CYS, 31);

        let sg1 = cys1.atom("SG").expect("SG in cys1").pos;
        let sg2 = cys2.atom("SG").expect("SG in cys2").pos;
        let desired = sg1 + Vector3::new(0.5, 0.0, 0.0);
        let offset = desired - sg2;
        for atom in cys2.iter_atoms_mut() {
            atom.translate_by(&offset);
        }

        let mut structure = structure_with_residues(vec![cys1, cys2]);
        add_hydrogens(&mut structure, &HydroConfig::default()).expect("hydrogenation");

        let res1 = structure.find_residue("A", 30, None).unwrap();
        let res2 = structure.find_residue("A", 31, None).unwrap();
        assert_eq!(res1.name, "CYX");
        assert_eq!(res2.name, "CYX");
        assert!(!res1.has_atom("HG"));
        assert!(!res2.has_atom("HG"));
    }

    #[test]
    fn five_prime_phosphate_deprotonated_at_physiological_ph() {
        let residue = five_prime_residue_with_phosphate(60);
        let mut structure = structure_with_residue(residue);

        add_hydrogens(&mut structure, &HydroConfig::default()).expect("hydrogenation succeeds");

        let residue = structure.find_residue("A", 60, None).unwrap();
        assert!(residue.has_atom("OP3"), "OP3 should remain");
        assert!(
            !residue.has_atom("HOP3"),
            "HOP3 should not exist at neutral pH"
        );
        assert!(
            !residue.has_atom("HOP2"),
            "HOP2 should not exist at neutral pH"
        );
    }

    #[test]
    fn five_prime_phosphate_protonated_below_pka() {
        let residue = five_prime_residue_with_phosphate(61);
        let mut structure = structure_with_residue(residue);
        let mut config = HydroConfig::default();
        config.target_ph = Some(5.5);

        add_hydrogens(&mut structure, &config).expect("hydrogenation succeeds");

        let residue = structure.find_residue("A", 61, None).unwrap();
        assert!(residue.has_atom("OP3"), "OP3 should remain");
        assert!(residue.has_atom("HOP3"), "HOP3 should be added below pKa");
    }

    #[test]
    fn five_prime_without_phosphate_gets_ho5() {
        let residue = five_prime_residue_without_phosphate(62);
        let mut structure = structure_with_residue(residue);

        add_hydrogens(&mut structure, &HydroConfig::default()).expect("hydrogenation succeeds");

        let residue = structure.find_residue("A", 62, None).unwrap();
        assert!(
            residue.has_atom("HO5'"),
            "HO5' should be added for 5'-OH terminus"
        );
        assert!(!residue.has_atom("P"), "phosphorus should not exist");
    }

    #[test]
    fn three_prime_nucleic_gets_ho3() {
        let residue = three_prime_residue(70);
        let mut structure = structure_with_residue(residue);

        add_hydrogens(&mut structure, &HydroConfig::default()).expect("hydrogenation succeeds");

        let residue = structure.find_residue("A", 70, None).unwrap();
        assert!(
            residue.has_atom("HO3'"),
            "HO3' should be added for 3' terminal"
        );
    }
}