Partially Latent Protein Representation

• Partially latent protein representation is a hybrid approach that separates explicit backbone geometry from latent variables capturing side-chain and sequence details.
• It employs flow matching and conditional VAE decoding to generate detailed atomistic structures and enable joint sequence-structure co-design.
• This method delivers scalable protein design with high co-designability and diversity, advancing robust modeling for complex, long-chain proteins.

A partially latent protein representation is a modeling approach that describes proteins using a hybrid of explicit and latent (typically continuous, learned) variables, with the explicit component typically capturing the backbone geometry and the latent component encapsulating side-chain details and/or sequence identity. This paradigm decomposes the full high-dimensional protein representation into structured explicit coordinates and residue-wise latent codes of fixed dimensionality, enabling efficient and scalable generative modeling over fully atomistic protein structures together with their sequences. The concept is exemplified by the La-Proteina framework, which leverages this decomposition to perform robust and scalable atomistic protein generation via flow matching in partially latent space (Geffner et al., 13 Jul 2025).

1. Definition and Mathematical Framework

The partially latent protein representation formalizes proteins as a joint distribution over backbone atom coordinates, sequence, all other atomistic details, and per-residue latent variables. Formally, for a protein of length $L$,

• The explicit coordinates $C$ represent the backbone (typically Cα atoms).
• The sequence and other atomic details—side chains, atom types, etc.—are captured via per-residue latent variables $z$ of fixed dimension.

This joint model is factorized as:

$$p_{\theta, \phi}(C, a, s, z) = p_\theta(C, z) \cdot p_\phi(a, s \mid C, z)$$

where:

• $p_\theta(C, z)$ models the explicit backbone alongside the continuous latent variables, using a generative flow matching model over the composite space,
• $p_\phi(a, s \mid C, z)$ decodes the latent space, in conjunction with backbone geometry, into all remaining atomic coordinates $a$ and the residue sequence $s$ (typically via a conditional VAE decoder).

This scheme circumvents the need to model variable-length, discrete side-chain and sequence information directly alongside continuous atomic positions. Instead, a fixed-size latent vector per residue serves as a “bottleneck” summarizing all such information, allowing scalable, joint generation of sequence and structure.

2. Flow Matching Generative Modeling in Partially Latent Space

La-Proteina uses a conditional flow matching framework to generatively model the joint distribution $p_\theta(C, z)$. Flow matching is a type of continuous normalizing flow, implemented via a learned “velocity field” or score function, which constructs a continuous path (solution to an ODE or SDE) that transports points from a base distribution (typically isotropic Gaussian noise) to target data points in the hybrid $(C, z)$ space.

Key elements:

• Both explicit coordinates $C$ and latent variables $z$ are evolved jointly—but with independent time or integration schedules (i.e., $t_x$ for $C$, $t_z$ for $z$), which is critical for effective learning and sampling.
• During training, the denoiser network $v_\theta(C^{(t_x)}, z^{(t_z)}, t_x, t_z)$ is trained via a joint loss that minimizes discrepancies between predicted velocities and the ground-truth transport vectors,

$$\mathbb{E}\Big[ \|v_\theta^{x}(C^{(t_x)}, z^{(t_z)}, t_x, t_z) - (C - C^{(0)})\|^2 + \|v_\theta^{z}(C^{(t_x)}, z^{(t_z)}, t_x, t_z) - (z - z^{(0)})\|^2 \Big]$$

• Sampling is performed by integrating SDEs or ODEs for $C$ and $z$ from Gaussian noise to realistic protein structures and per-residue latents.

Following flow matching, the VAE decoder $p_\phi(a, s \mid C, z)$ reconstructs the full sequence and side-chain atom coordinates from the backbone and latent variables, ensuring tractable joint generation of sequence and structure.

3. Decoupling of Backbone and Side-chain/Sequence Modeling

Classical generative models for proteins face challenges arising from the mixed discrete-continuous nature of sequence-structure co-design, and from the variable number and arrangement of side-chain atoms per residue type. The partially latent approach sidesteps these issues by:

• Modeling only the backbone explicitly, which simplifies the explicit geometry to a fixed-size continuous input,
• Jointly generating, for each residue, a fixed-length latent code that captures all variable-length and discrete features (sequence identity, rotamer, atom types).

This design eliminates the need for separate modeling of categorical and variable-sized objects in a unified generative process. The backbone space is well-studied and lower dimensional, and its decoupling allows the use of powerful generative models (e.g., transformers, continuous flows) in a high-throughput regime.

4. Scalability, Performance, and Benchmark Results

This approach offers high scalability due to the linear complexity of the partially latent factorization:

• Only a small number of latent variables ($L \times d_\text{latent}$) are required regardless of protein length $L$, avoiding quadratic or cubic memory bottlenecks.
• La-Proteina demonstrates co-designability and diversity at sequence lengths up to 800 residues, outperforming previous diffusion-based all-atom models that collapse at such scales.
• On atomistic unconditional protein design benchmarks, La-Proteina achieves all-atom co-designability scores around 68% (or higher in variants with triangular update layers), high diversity (measured by clustering in both structure and sequence), and sample novelty relative to PDB and AFDB sets.
• In atomistic motif scaffolding, difficult scenarios where the model must scaffold a motif given only partial or full atomistic details, La-Proteina outperforms all existing baselines, achieving a significantly higher rate of low-RMSD reconstructions.

The fixed-size latent variables per residue and the efficient backbone+latent generative process ensure robustness at large scale—contrasting with methods relying on full explicit all-atom transformer parameterizations, which become infeasible for long chains.

5. Conditional Decoding and Joint Sequence-Structure Generation

Following the flow matching generation step, the per-residue latent variables $z$ are decoded jointly with the generated backbone $C$ to produce all-atom side chain structures and explicit sequence types:

• The VAE decoder $p_\phi(a, s \mid C, z)$ is trained to reconstruct both atomic coordinates and the categorical sequence labels for each residue, accessing all necessary conditioning (including local backbone context).
• Because $z$ is trained to summarize both categorical and continuous features for each residue, decoding remains fixed-dimensional irrespective of side-chain length or chemistry.
• This conditional decoding enables not only unconditional generation but also supports conditioning (e.g., atomistic motif scaffolding), since motif residues and their atomistic detail can be directly enforced via the decoder.

6. Impact on Protein Design and Generative Modeling

The partially latent protein representation, exemplified by La-Proteina, brings several practical advances for atomistic protein generation:

• It facilitates co-designable, fully atomistic sequence-structure generation at scales previously unreachable for explicit methods.
• The joint modeling naturally accommodates both unconditional design tasks and conditional scaffolding of functional motifs at the atomistic level—essential for enzyme and binder design.
• Robust diversity and novelty are achieved across both sequence and structure, supporting exploration of the protein design space unconstrained by discrete-sequence-only or backbone-only limitations.
• By maintaining architectural and computational efficiency, the method opens the door to high-throughput protein design for complex or large targets, including those required in therapeutic and synthetic biology contexts.

7. Mathematical and Algorithmic Summary

Component	Explicitly Modeled	Latent (Per-Residue)	Decoding Procedure
Backbone (Cα coordinates)	Yes	—	Flow matching over coordinates
Sequence type, sidechain geometry	—	8-dimensional vector $z$	VAE decoder $p_\phi(a, s | C, z)$
Flow matching (generation)	$p_\theta(C, z)$ by neural ODE/SDE	—	Simulate ODE/SDE for $(C, z)$
Conditional decoding	Used for all residues	Used for all residues	Generate all-atom coordinates, labels

This hybrid explicit-latent design provides a tractable, expressive, and scalable route toward realistic and novel protein modeling, enabling a broad class of atomistic generation and design tasks previously inaccessible to both discrete- and fully explicit generative models.