1 Introduction

Over the past decade, advances in protein structure prediction - most notably deep learning-based models such as AlphaFold2 [1], RosettaFold [2] and ESMFold [3] - have transformed the field of protein design [4]. The ability to predict the fold of (almost any) arbitrary sequence with relatively high accuracy enables researchers to effectively explore the vast protein sequence space and find those satisfying a set of desired structural and functional properties, increasing the potential for breakthroughs in therapeutic design, biosensing, and industrial biocatalysis [4–6]. Building on top of these developments, a new generation of computational protein design frameworks has emerged [7]. While successful, many remain tightly coupled to specific multi-step workflows inherited from the “inverse folding paradigm” [8], developed prior to the advent of accurate deep learning-based protein-folding algorithms.

The inverse folding paradigm follows the philosophy backbone design → sequence painting → folding. In such a workflow, different algorithms (e.g., hallucination [9] or RFDiffusion [10]) are used to determine specific backbone shapes satisfying a given constraint, for example, formation of an interface with a specific epitope on a target protein. Once the fold of these backbones is determined, an inverse-folding algorithm is applied (e.g., the ProteinMPNN-based models [11–13]) to find the sequences most likely to fold into the backbone shapes. Finally, a protein-folding algorithm is used to check if such sequences indeed fold to the correct structure. This last validation step is necessary because, while a candidate sequence obtained as a result of the second step is the most likely to fold into the target backbone, the latter is not necessarily the most stable structure for that sequence. As a result, many designed sequences are rejected and the process is repeated until one is found that successfully folds into the target backbone. Alternatively to the inverse folding paradigm, one can train a single deep generative model on the joint sequence-structure distribution so that, when conditioned on a desired functional tag, it proposes a complete sequence-structure design in a one-shot generation setting [14–16]; the resulting design also being filtered with a folding predictor. This second approach often leads to poorly interpretable pipelines, with most of the design process becoming abstracted away inside a large neural network.

In both of the previous approaches, conditioning the protein generation on specific functional properties of interest is not particularly straightforward, or even possible. For example, preventing hydrophobic patches to be located on the surface, requesting the presence of certain folds, or enforcing a given symmetry cannot be easily and explicitly implemented. As a result, many different candidates must be generated, and subsequently screened downstream for both validated folding, and wanted properties. Recently, the authors of the hallucination-based pipeline BindCraft [7] recognized that re-folding validation is the critical step for obtaining successful designs. BindCraft’s philosophy, therefore, is to maximize the success rate in this validation stage by using AlphaFold2-Multimer as an oracle to co-design sequence-structure pairs directly during backbone generation - rather than following the traditional multi-step pipeline. Such hallucination-based approach, however, requires all the design properties of the system to be fully differentiable, hindering its generalizability to arbitrary design constraints.

To solve these problems, we introduce BAGEL (Biomolecular Algorithm for Guidance in Energy Landscapes), a general-purpose Python package for programmable protein engineering. Our framework enables users to formalize protein design tasks as the optimization of an energy function (a loss) over sequence space. In practice, BAGEL provides a set of tools to seamlessly build arbitrary sampling and optimization problems by combining energy terms derived from any metric extractable from a sequence. For instance, these can be derived from structure and folding metrics computed by a deep learning structure predictor, vector embeddings from a protein language model (PLM), or metrics based on sequence alone. More specifically, these energy functions include geometric constraints, similarity to user-defined templates, physical properties, and custom objectives based on structural or functional hypotheses, as well as bulk and local confidence scores, e.g., local pLDDT, pTM or interface PAE (iPAE). While various energy terms have already been implemented in this initial release, BAGEL’s modular structure also easily allows a user to define any term that could be calculated from knowledge of a (group of) sequence(s). The flexibility of this abstraction allows our framework to support a wide variety of classical protein engineering problems: from templating specific scaffold motifs for de novo enzymes, through building proteins with desired geometry, to designing protein binders. Crucially, to go beyond the capability of current approaches, we also allow to define loss functions that consider multiple states, which is particularly valuable, for example, in engineering proteins that binds to a specific target, while explicitly maintaining a weak interaction with other specific, non-target proteins.

Our package is inspired by - and builds upon - the seminal work of the former FAIR team at Facebook (now Meta), who developed the suite of ESM projects [3,17], and in particular the paper titled A high-level programming language for generative protein design by [18]. In that work, the authors use Monte Carlo (MC) optimization to scan the sequence space in search for optimal sequences solving a prescribed protein engineering problem. In contrast to their work, we change the representation of a protein sequence and its associated loss function by shifting away from a graph-based representation in favour of one based on groups of residues, which we believe allows for a more flexible and user-friendly design interface. Besides this change in representation, among other differences that will be addressed later, our fully modular design framework provides:

• A Multi-State Formalism. Native support to specify multi-state problems, highly relevant for complex design tasks of, among others, selective binding, or binder design over multiple target variants (cross-reactivity).
• Enhanced Energy Formalism. A unified formalism for expressing arbitrary design constraints as energy penalties, following the convention from molecular simulations where total energy is expressed as a sum of simple, fully customizable N-body terms.
• A Unified Approach to Optimization and Generative Problems. By looking at protein design as the exploration of an energy landscape, optimization and candidate generations can be seen as two related variations of the same problem: finding the energy minimum (optimization) as opposed to exploring the sequence space around a certain energy value (generation).
• Multiple Optimization and Sampling Algorithms. An extensive and easy-to-extend sampling and optimization backend supporting different types of advanced MC algorithms to accelerate exploration of the sequence space including simulated tempering, grand-canonical MC, and custom annealing schedules.
• Flexible Oracle Choice. A generalized and modular implementation of an oracle, which is defined as any algorithm that provides useful information for protein engineering tasks. This includes, for example, protein-folding models that return structures, protein language models that generate embeddings, or other algorithms (or combinations thereof) that compute relevant physicochemical properties for one or more proteins.
• Accessibility. A user-friendly interface that can be seamlessly integrated with other Python workflows, including a serverless implementation of deep learning-based protein models (i.e., oracles) through a standalone package, boileroom [19], abstracting away tedious dependency management.

Compared to other, problem-specific end-to-end solutions, BAGEL has been built from scratch with generality and modularity in mind, enabling continuous extension of the package with new minimization strategies beyond MC and new energy terms describing protein engineering objectives. Moreover, the package is fully model-agnostic, enabling us to leverage the continous advances in deep learning on proteins in terms of both quality and speed.

In this report, we describe the functionality and design philosophy of BAGEL through its algorithm formalism and core class abstractions. We illustrate its utility with four examples: i) simple binder design, ii) design of binders targeting intrinsically disordered epitopes, iii) design of selective binders via multi-state optimization, and iv) enzyme variant generation. Fig 1 summarizes the design workflow and the components of the package, including the applications.

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Fig 1. Conceptual schematic of the BAGEL protein design package.

Modular setup of the System includes multiple States, each of which has its own set of EnergyTerms defining a specific design objective. Each State consists of Chains, that include either mutable or immutable Residues. EnergyTerms come in various flavours; affecting residue groups in a 0-body, 1-body, or 2-body fashion, and requiring the ouput of specialized Oracles, such as a FoldingOracle or an EmbeddingOracle. The latter is symbolized with the dashed outline. A Minimizer is used for the case of optimization, shown in this schematic, while another MonteCarloMinimizer is used for generative sampling. In this case, the System’s energy is optimized with the Minimizer through successive sequence perturbations using the MutationProtocol. Given the modularity, the package can be applied to a variety of applications, including the four highlighted in the figure detailed below in the report.

https://doi.org/10.1371/journal.pcbi.1013774.g001

2 Design and implementation

2.1 Algorithm

The energy landscape we aim to explore is defined by a System Ω and its associated energy . Each System itself is composed of a set of States {S}, each with its own associated energy function E_S dependent on the set of Chains {C}_S. A specific Chain C_i, indicated with the subscript i, is a sequence of amino acid residues , i.e., a monomeric protein, of length L_i. In mathematical form,

(1)(2)(3)

where is the amino acid alphabet. We formalize the protein design problem as the sampling of the energy landscape defined by:

(4)

where a State energy function is a weighted sum over N_S individual energy terms specific to each State:

(5)

The energy terms can be chosen from a plethora of options, shown later in Sect 2.4, but effectively impose a constraint on the design task on a particular State S, weighted by w_js; where j indexes over energy terms, and s over States, as the energy terms are specified for each S independently.

Sequences C_i may be shared or unique among different States. Let us make an example. Consider the case we want to design a protein C₀ that binds to both a protein C₁ but also separately to another protein C₂. The System Ω in this case can be composed of two States, let us call them A and B. Chain C₀ is present in both States, while only C₁ is part of State A and only C₂ is part of State B. We can then optimize C₀ by finding a sequence that at the same time would be predicted to form a stable multimer for the two independent States A and State B.

To calculate the energy terms ε, we introduce the general notion of an oracle, a black-box predictive computation (i.e., a function) mapping a set of chains {C}_S to a useful representation y_s. These informative representations y_s are used as inputs to ε, thus ε being a function of y_s or {C}_S interchangeably. Two important but non-exhaustive examples of classes of oracles are folding oracles and embedding oracles. Folding oracles are typically deep learning-based structure predictors,

(6)

where are three-dimensional atomic coordinates and Φ encodes model confidence metrics. Embedding oracles, in contrast, are language models providing learned high-dimensional features capturing biochemical or evolutionary context:

(7)

where is an embedding vector of dimensionality , that is, one embedding vector of dimensionality per residue in State S. Another simpler but general class of an oracle could be a function that maps a (set of) sequence(s) to a single scalar value :

(8)

For instance, such oracle could calculate the number of polar residues in a State, or predict the unfolding temperature of a chain.

With the previous definitions, we can define protein engineering as a sampling problem, where the goal is to discover a tuple of sequences among all possible sets {C} defining the System that samples a region of the energy landscape for which . When this target energy corresponds to the minimum value of the energy function , the sampling problem becomes what one usually refers to as optimization.

To solve this problem, we employ the well-established Markov Chain Monte Carlo (MCMC) method [20]. At each iteration n, a proposal is generated by mutating the sequence of a chain using a mutation operator . The total energy change is thus , leading to an acceptance with the standard Metropolis criterion:

(9)

where is an effective temperature schedule controlling the probability of accepting proposals when . The sampling properties of MCMC guarantee that, for a large number of transitions, the system will relax to an equilibrium distribution that is the solution of the sampling problem. Moreover, if we replace T with an appropriate temperature schedule T_n, e.g., slowly bringing temperature from some finite initial value to zero, the MCMC method becomes an optimization method able to demonstrably find the global minimum of the energy function (although possibly for an extremely large number of steps).

We summarize the algorithm as:

• Setup. Specify the set of States {S} in terms of their energy terms , weights w_js and the subset of the System chains {C}_S belonging to them.
• Input. Initialize the initial collection of chains {C}⁰.
• Sampling loop (MCMC). For iterations :
  1. 1. Propose by mutating one or more chains.
  2. 2. Evaluate .
  3. (a) Obtain oracle representations y_s.
  4. (b) Compute State energies .
  5. (c) Sum over States to get System energy .
  6. 3. Accept the proposal with probability ; otherwise retain {C}ⁿ.
• Output. Return either the State corresponding to the lowest-energy encountered (optimization) or a collection of States (sampling) once the System energy has reached its equilibrium value. In this latter case, equilibrium is obtained when the System’s energy reaches a plateau, and then randomly oscillates around it.

To avoid any confusion, we stress here that within this manuscript a State (with capital S) is always used only and exclusively with this specific definition: it is a set of single-chain proteins, together with its associated set of energy terms to be evaluated given predictions on these very same chains. It is not, therefore, a reference to a conformational State of such chains. By construction, all energy terms are, in a broader mathematical sense, simply scalar potentials bounded by below. In other words, their value depends only on the current state of the system. However, these terms do not need to represent a physical energy in the thermodynamic sense – these physical energies are instead a more stringent subset of our energies. Importantly, as long as all terms are bounded scalar potentials, strong theoretical convergence results apply to Monte Carlo sampling.

2.4 Energy terms

Below we list the implemented EnergyTerms. For clarity, we categorize them into sequence-only terms, structure-based terms, folding-metric terms, and vector-embedding terms. We define a residue group G as a set of residues that contribute to an EnergyTerm. All residues in a group must belong to the same Chain, but they are not required to be contiguous in sequence. Conceptually, we adopt an N-body formalism similar to that used in molecular simulations: zero-body terms apply globally to all residues in a State, single-body terms act on a single residue group, and two-body terms operate on a pair of residue groups. Although this classification is not explicitly enforced in the code, it serves as a helpful abstraction when constructing and reasoning about EnergyTerms. This N-body energy formulation and its modular implementation constitute a key difference compared to the original framework presented in [18], where defining certain energy terms was extremely cumbersome, especially when this definition required specifying a large number of non-contiguous regions along a single chain. More generally, their reliance on a tree graph-based representation of the system made input files increasingly difficult to construct and interpret for large systems.

2.4.1 Sequence terms.

HydrophobicEnergy. Measures the fraction of hydrophobic residues in a residue group G. Optionally, the magnitude of this energy can be scaled by the mean normalized solvent-accessible surface area (SASA) [24], described in detail in SurfaceAreaEnergy in Sect 2.4.3. In this mode, hydrophobic residues that are buried (low SASA) contribute less, while surface-exposed hydrophobes contribute more, effectively focusing the penalty on exposed hydrophobic patches. Therefore, this term can be used to penalize hydrophobicity on the surface, acting more as a structural constraint, though we keep it here for simplicity.

(10)

where N_G is the number of residues in the residue group and is the count of hydrophobic residues in the group. Hydrophobic residues are defined as valine, isoleucine, leucine, phenylalanine, methionine, and tryptophan, which are regarded as the most strongly hydrophobic. Users may, however incorporate mildly hydrophobic residues such as tyrosine, cysteine, alanine, and glycine in their counting or, alternatively, implement custom terms that employ a more continuous hydrophobicity measure.

ChemicalPotentialEnergy. Adds an energy proportional to the deviation of the number of residues from a target size, optionally raised to a power. This mimics a chemical potential term in the free energy, allowing to run an optimization with a freely floating number of residues, i.e., allowing for insertions and deletions, equivalent to sampling within the grand-canonical ensemble.

(11)

where μ is the chemical potential, is the total number of residues in the System, is the target number of residues, and p is an exponent parameter.

2.4.2 Folding metric terms.

PTMEnergy. Penalizes low predicted Template Modeling (pTM) scores, conceived in the original AlphaFold2 paper [1]. pTM reflects the global confidence of the folding model in the predicted structure, thus it is a single scalar value over the entire State. The metric is based on the original TM-score [25]. This is used to achieve global structures the FoldingOracle is confident in.

(12)

PLDDTEnergy. Penalizes low predicted Local Distance Difference Test (pLDDT) scores, which indicate local structural confidence. This confidence metric, originally also proposed in AlphaFold2 [1] is based on the Local Distance Difference Test [26]. The energy is the negative mean pLDDT over the residue group G. This term is used to promote model’s confidence in a local structure.

(13)

where N_G is the number of residues in the group, and is the pLDDT of residue α. To apply a global (0-body) constraint across the entire protein, the user can instead use OverallPLDDTEnergy, which applies the same formulation over all residues in the System.

PAEEnergy. Measures the uncertainty in the predicted distances between two residue groups G₁ and G₂, using the mean Predicted Alignment Error (PAE). This term encourages confident, well-defined relative positioning of residue groups, in practice, encouraging groups of residues to behave as a single rigid body, where all positions are perfectly correlated. This term is used to create protein-protein interfaces, for instance for peptide binders, and is sometimes referred to as interface PAE (iPAE), or cross PAE. It can optionally be used on a single residue group, when the pairs of residues considered are thus with the same group itself.

(14)

where is the error between residues α and β, PAE_max ≈ 30 Å is the maximum predicted alignment error between any two residues, and is the total number of residue pairs considered.

2.4.3 Structural terms.

SurfaceAreaEnergy. Penalizes exposure of a residue group G by computing its residues’ mean solvent-accessible surface area (SASA), normalized by a reference maximum value. This energy encourages buried or compact structures and can be applied globally (0-body) or to specific residue groups (1-body). The SASA is calculated using the Shrake–Rupley “rolling probe” algorithm [24], as implemented in Biotite [27], with an adjustable probe radius.

(15)

where is the computed SASA of atom a, is a normalization constant (by default, the full surface area of a sulfur atom) in Å units, and is the number of atoms in the residue group G considered.

SeparationEnergy. Controls the spatial separation between two residue groups G₁ and G₂ by penalizing the Euclidean distance, in units of Å, between their backbone atoms’ centroids.

(16)

where and are centroids of the two residue groups respectively.

GlobularEnergy. Favors globular structures by minimizing the variance of distances from backbone atoms to the centroid, promoting compact and spherical distributions. It is effectively proportional to the moment of inertia of the structure.

(17)

where is the position of backbone atom a, c is the centroid of all backbone atoms in the residue group G, and represents the standard deviation over all backbone atoms a in residue group G.

TemplateMatchEnergy. Drives the structure of residue group G to match a provided structural template by minimizing the root mean square deviation (RMSD) between corresponding residues. RMSD is computed after optimal superposition. By default we use all the heavy atoms to obtain the alignment and the RMSD, but one can optionally choose to only use backbone atoms.

(18)

where is the position of atom a in residue β , is the corresponding position in the template after optimal alignment, and is the total number of atoms in the group G. The energy can also be computed using pairwise distance matrices (distograms) instead of direct atom positions.

(19)

where and are the pairwise distances between atoms a and c of residue β in the current structure and template, respectively.

SecondaryStructureEnergy. Encourages residues in the specified group to adopt a target secondary structure (alpha-helix, beta-sheet, or coil) by penalizing deviations from the desired assignment. The secondary structure of each residue is determined using the P-SEA algorithm [28] implemented in Biotite [27]. The energy is defined as the fraction of residues whose assigned secondary structure does not match the target.

(20)

where is the assigned secondary structure of residue α (as a categorical label), is the desired type (e.g., alpha-helix), is the indicator function, and N_G is the number of residues in the group.

RingSymmetryEnergy. This energy term enforces N-fold symmetry, where N is the number of independent residue groups G specified as input. Symmetry among residue groups G is encouraged by minimizing the variance in distances between the groups’ centroids - either for all pairs of G or only their direct neighbors. We define direct neighbours as consecutive groups G specified in the residue group list in the input. The first and last element of the list are also considered direct neighbors.

(21)

where is the distance between centroids of the pairs of groups and , computed by backbone atoms only, and represents the standard deviation over all the group pairs considered. Referring back to the N-body notation, notice that this term is an arbitrary N-body term, given its flexibility to include an arbitrary amount of groups G, achieving an arbitrary N-fold symmetry.

2.4.4 Embedding terms.

EmbeddingsSimilarityEnergy. Measures the cosine similarity between learned embeddings of the current sequence and a group of reference embeddings, encouraging functional or structural similarity at the embedding level.

(22)

where is the angle between the high-dimensional embeddings of residue α in the current sequence and reference sequences respectively as and . is then the cosine similarity and N_G is the number of residues in the group. Note that this energy term is defined so that its minimum is exactly zero when all embeddings are equal to the reference values.

3 Results

To illustrate the utility of BAGEL, we present design tasks that serve as reference workflows and starting points for new applications. These examples span common protein engineering use cases and demonstrate various framework features. All are reproducible, modifiable, and provided as ready-to-run templates in the GitHub repository. Optimization details, along with an input file, are included in the S1 Text. While not experimentally validated, these designs are valid under the assumption that ESMFold and ESM-2 yield accurate predictions. Specifically, one can monitor the expected success of these designs by referring to the evolution of the confidence metrics, e.g., pLDDT, iPAE, or pTM, during optimization. As extensively shown (see [30,31]) by comparison between predictions and experiments, low values of the predicted confidence metrics strongly correlate to lower RMSD values between the predicted and experimentally determined structure, at least in the case of single-chain predictions for natural proteins. While a large-scale assessment of the translational accuracy of these metrics remains to be done for the case of designed proteins, the current available data show that high confidence metrics are indeed correlated to more successful designs, especially for the relevant case of protein binders. Nevertheless, to obtain an orthogonal validation of the stability of the designed sequences, as in [32,33], we perform molecular dynamics trajectories, showing the structures are at least stable on the simulated timescales (details of all simulations are provided in S3 Text).

3.1 Simple peptide binder

A primary application of BAGEL is designing small proteins that can bind a protein target of interest. Fig 2 shows binders to three clinically relevant targets: carbonic anhydrase IV (CA4, UniProt P22748), a protein associated to hypertension and cardiovascular disease [34], epidermal growth-factor receptor (EGFR, UniProt P00533), an important target for cancer therapeutics [35], and the dust-mite allergen Der f 7 (DERF7, UniProt Q26456), studied for the neutralisation and alleviation of allergic reactions [36]. All were designed to minimize SeparationEnergy and PAEEnergy (interface) in respect to the binder and the hotspot on the target. Taken together, these examples highlight BAGEL’s ability to explore helical, beta-rich, and coil-dominated solutions from the same generic energy function.

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Fig 2. Peptide binder design for three protein targets using BAGEL.

a) System energy (dark, left axis) and binder pLDDT (light, right axis) traces during CA4 binder optimization. The optimal sequence emerged within the first ∼2,000 of 20,000 steps. Increases in energy and pLDDT correspond to the high-temperature regime. Solid lines show the best System found; dashed lines, the current System. b) Final binder-target complexes for carbonic anhydrase IV (CA4), epidermal growth factor receptor (EGFR), and dust-mite allergen Der f 7 (DERF7). Binders in blue, targets in red. CA4 minimization yielded beta-sheet-rich binders despite no secondary structure restraints. For EGFR, we model only Cys329–Val506, which includes a known epitope. For DERF7, no hotspot constraints were used; minimization was over the entire target. Though the DERF7 binder appears loosely structured due to its coil-like geometry, equilibrated structures (10 ns of molecular dynamics at 310K) show plausible interfaces mediated by hydrogen bonds (magenta dashed lines, close-up). The binder wraps around the target as minimizing SeparationEnergy without a hotspot often collapses centroids - illustrating a potential failure mode that may require more careful tuning of energy terms and weights. c) PAE matrices for each binder-target pair, normalized to 1. Black dashed lines delineate binder (upper-left blocks) from target. All interfaces show low iPAE values: 0.242, 0.255, and 0.235, respectively.

https://doi.org/10.1371/journal.pcbi.1013774.g002

3.2 Targeting intrinsically disordered epitopes

In our earlier work [37], we showed how BAGEL’s energy functions can lead to peptide binders design that induce order in an otherwise intrinsically disordered region (IDR) of a protein. We designed several such peptides for four clinically relevant targets - α-synuclein (ASYN, UniProt P37840), T-cell co-receptor CD28 (UniProt P10747), tumour suppressor p53 (P53, UniProt P04637) and Small Ubiquitin-like Modifier 1 (SUMO, UniProt P63165). Traditional drug discovery approaches require docking of molecules into rigid pockets, thus having the ability to bind disordered regions opens up plethora of applications for therapeutic modulation in disease [38], ranging from neurodegenerative diseases (ASYN) [39] through immune system regulation (CD28) [40] to cancer (P53, SUMO) [41]. Binding to disordered epitopes is achieved by enforcing high pLDDT values on the IDR with PLDDTEnergy, and optionally also promoting secondary structure with SecondaryStructureEnergy. In our original work, we also validated these designs and their binding affinities with free energy calculations. Fig 3 illustrates the key effect: the presence of the binder sharply increases the pLDDT confidence - either across the full target (ASYN), or locally at the targeted IDRs (CD28, P53, SUMO) - highlighting BAGEL’s ability to stabilize otherwise disordered segments.

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Fig 3. Targeting of intrinsically disordered epitopes with designed binders using BAGEL.

For each of the four targets in the quadrants - α-synuclein (ASYN), CD28, p53 (P53) and SUMO-1 (SUMO) - the left sub-panel shows the predicted apo structure, while the right sub-panel (holo) includes the magenta peptide binder. Backbones are colored by per-residue pLDDT confidence (red → white→ blue corresponds to 0.0 to 1.0 transition). The bar plots beneath each structure display the same pLDDT values averaged over consecutive 5-residue windows, illustrating the local gain in structural confidence upon the presence of the binder targeting the IDR epitopes highlighted in cyan. Note that the horizontal axis is 0-indexed, while the epitope residue numbers in cyan are 1-indexed. ASYN shows a broad increase in pLDDT across the whole target, while P53 shows a significant reduction in pLDDT on the opposite end of the sequence (beyond residue 200) from the targeted epitope. CD28 and SUMO show the expected behavior, with increased pLDDT localized to the epitope region. Figure adapted from [37].

https://doi.org/10.1371/journal.pcbi.1013774.g003

3.3 Multi-state selective peptide binder

A key strength of BAGEL is its ability to optimize a single binder sequence against multiple targets simultaneously. Here, we demonstrate a two-State design in which the binder must engage the mouse Zif268 zinc-finger domain (EGR1, UniProt P08046), while avoiding binding to the closely related human zinc-finger protein ZNF593 (ZNF, UniProt O00488). Species-selective binders like this could be useful in xenograft transplant settings, where tissue-specific or species-selective gene knock-out is desired [42,43]: for example, when humanizing the mouse immune system. We achieve this selective binding by minimizing the interface PAEEnergy for the mouse target (encouraging interaction), while simultaneously maximizing the same metric for the human off-target (discouraging binding). The latter is implemented using a negative weight w_js. Fig 4 summarizes the results. Multi-State optimization in BAGEL can be extended beyond this example - for instance, by designing cross-species (also known as cross-reactive) binders that target both mouse and human variants simultaneously. This flexibility is critical for therapeutic development, where candidates must succeed in both animal models and human trials. BAGEL’s modular framework supports similar multi-functional design problems with ease.

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Fig 4. Selective binder design against targets, avoiding off-targets using BAGEL.

a) Evolution of the mean interface (iPAE) for the binding (orange) and non-binding (violet) States between the binder and the target. Solid lines are the best energies, and dashed lines are the current energies from the MC trajectory. b) Final PAE matrix for the binding (EGR1) and non-binding (ZNF) States; black dashed lines separate binder (upper-left block) from target residues. The final mean iPAE of the binding and non-binding States are 0.23 and 1.0 respectively (normalized units), observable in the PAE matrices. c) Evolution from the MC optimization of the binder’s mean pLDDT in each State, colors are the same as in a). d) Structure of the binding and non-binding complex (dark blue = binder, orange = target, violet = target to avoid). From further visual inspection, only the binding pair shows a well-packed contact surface, while the non-binding State renders an implausible, sterically clashing structure. The pLDDT of the ZNF binder is relative low (0.66 as shown in a)), while the iPAE is relatively high (shown in b)). All of these hint at a low chance of the binder interacting with the off-target ZNF.

https://doi.org/10.1371/journal.pcbi.1013774.g004

3.4 Enzyme variants with conserved active site

We previously introduced a generative algorithm to design enzyme variants while preserving local function in [44], purely relying on sequence embeddings and without any structural information. Given the modular versatility of BAGEL, this method is now also implemented in this package. In the example, we demonstrate this with oxidoreductase (UniProt P0AEG4), where the active site (Cys30 and Cys33) is held immutable in sequence, while the remainder of the protein is allowed to mutate freely. To guide sampling, we use ESM-2 and EmbeddingsSimilarityEnergy, encouraging similarity to the reference protein in embedding space in the active site, while permitting extensive sequence drift elsewhere. In contrast to the previous applications and converging to a single optimum, we use the MonteCarloMinimizer to collect a diverse ensemble of sequences that satisfy the design constraints at constant temperature. Fig 5 summarizes the results of this simulation. Despite large differences in the sequence and mutable structure, the catalytic site is preserved both geometrically and chemically, demonstrating the ability of embedding-guided sampling to produce viable functional diversity. As described in the original work [44], this in silico sampling can effectively seed rounds of directed evolution in the lab, allowing experimentalists to focus experimental screening on useful mutations, and avoiding deleterious mutations that would destabilize or unfold the active site altogether.

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Fig 5. Enzyme (oxidoreductase) variant generation with BAGEL.

a) Energy evolution of the MC trajectory to sample new enzyme variants. We define the first 3,000 steps as the transient region and analyze the subsequent equilibrium sampling from steps 3,000 to 10,000, collecting 1,286 unique variants as a result. b) Probability density of the sequence identity to the original sequence. c) Probability density of pLDDT values comparing the residues within the mutable and immutable groups. Immutable residues, i.e., the active site, show significantly higher pLDDT values. d) Probability density of RMSD to the original sequence. All RMSD values are computed using folded structures with ESMFold, including the original sequence. Mutable residues’ RMSD is computed on the backbone atoms, immutable residues’ RMSD is computed on all the heavy atoms of the active site, i.e., Cys-30 and Cys-33. Structures are superimposed to minimize the RMSD of the active site. Despite the relatively low sequence identity, the RMSD of the active site remains low, and the pLDDT sufficiently high. e) Example of a variant (blue = original, red = variant), including a close-up of residues Cys-30 to Cys-33. For this variant, the RMSD of the immutable and mutable regions are 0.11 Å and 2.7 Å respectively.

https://doi.org/10.1371/journal.pcbi.1013774.g005

4 Availability and future directions

We built BAGEL with the clear goal not only to withstand the test of time, but to actually mature and improve as time passes, as more accurate and faster algorithms evaluating properties of proteins become available, or with advancements in computing hardware. Nevertheless, the molecular community’s skepticism – summarized in the aphorism “garbage in, garbage out” – remains valid, and BAGEL’s prediction can only be as good as the currently available tools allow. In this regard, we recognize several current limitations: some internal - directly stemming from our choices and omissions for this initial release; and some external - dependent on the accuracy of current models, especially when considering truly de novo protein sequences and multimers, and on their ability to provide accurate predictions, e.g., of the binding interactions between different proteins. The ongoing development of BAGEL is envisioned to address these limitations to ensure continuous relevance and adaptability in the field of protein engineering. We note, however, that even with continued development, BAGEL does not constitute a plug-and-play package to any protein design problem, and should be used with a wider set of computationally available tools, such as PESTO [45] to find binding sites, or sequence inpainting models [11–13] to increase protein candidate diversity. In the long-term, on the other hand, all these could in principle be employed within the BAGEL framework, as a part of a broader protein design optimization campaign.

Improved Oracle Models. Future versions will integrate additional state-of-the-art FoldingOracles - a non-exhaustive list to benchmark includes RGN2 [46], AlphaFold2/3 [1,47], Chai-1 [48], and Boltz-1/2 [49,50]. In this regard, unifying the inference access with boileroom will enable direct comparison of the models’ accuracy and computational speed. Given the sequential nature of MC, computationally faster models such as MiniFold [51] also need to be considered, even at the expense of marginal inaccuracy. Moreover, one could only calculate the change in mutated embeddings instead of recomputing their value from scratch (an interpolation of a Car-Parrinello-like approach to embeddings [52]), potentially leading to increased inference speed. We also point out that different models excel in different scenarios: for example, RGN2 has been shown to outperform other models for orphan proteins structure prediction [46]. Therefore, one approach is to employ an ensemble of FoldingOracles with a weighted consensus; although it remains unclear whether such consensus improves design outcomes [53]. Once additional FoldingOracles are implemented inside BAGEL, such an approach can be readily implemented within the current codebase. Regarding EmbeddingOracles, we plan to explore models including AMPLIFY [54] and ProtGen [55], as well as protein language models trained explicitly to provide improved descriptions of protein-protein interactions such as the recently released MINT [56]. In general, the modular nature of BAGEL will help us leverage the continuous improvements of models and hardware in the upcoming months and years; and given that we do not rely on gradient-based optimization, the implementation is more flexible to swap out the underlying models, enabling rapid and convenient experimentation with different models.

Expanded Oracle Suite. The modular design philosophy also motivates us to introduce new types of oracles, helping to provide more physically accurate information on interactions and dynamics. For instance, the promise of emerging sequence-to-ensemble predictors, such as BioEmu [57], AlphaFlow [58] or CryoBoltz [59], could be used to compute EnergyTerms over ensembles as opposed to static structures, with the goal of better capturing the true thermodynamic behavior of biomolecules. A more physically-grounded description will come from introducing molecular dynamics (MD)-based Oracles. Simple energy minimization with a physical force field, such as AMBER [60], would filter out unstable, or sterically clashing structures. Furthermore, a short MD simulation measuring the RMSD between the initial and equilibrated structures could be used to estimate the stability of the complex. Finally, the most computationally demanding approach would involve techniques such as free energy perturbation [61] to provide the most correlated relative binding affinity prediction as an EnergyTerm to guide the MC trajectory in search of the optimal design.

Advanced Minimizer Algorithms. Although currently we only implemented different forms of Monte Carlo sampling with point mutations to explore the energy landscape, see Sect 2.1, arbitrary sampling/optimization algorithms can be employed. In the near future, we plan to benchmark genetic algorithms (GAs) and carefully evaluate their potential to improve sequence space exploration efficiently. We expect that this endeavour will require careful consideration of the crossover mutation algorithms used, especially for shorter sequences. Moreover, we plan to leverage the scalability of boileroom and implement parallel tempering, hence truly taking advantage of parallelization, which may help alleviate the inherent limitations of sequential, single-replica MC. Based on benchmarking the accuracy and speed of different FoldingOracles, a low-hanging fruit that could also be rapidly implemented within the existing codebase is a multi-resolution sampling scheme [62,63]. First, a computationally-cheaper model, such as RGN2 or MiniFold, is initially used to generate a long Markov Chain of n steps to move further and more rapidly in the energy landscape. Second, a more computationally-expensive (and, in principle, more accurate) model, such as AlphaFold3, is used to accept or reject the whole chain. This would be especially useful for systems with very long decorrelation times, when many potential iterations of the MC algorithm are wastefully spent sampling very similar candidates corresponding to the same basin of the energy landscape.

New EnergyTerms. Solving different design problems requires the use of EnergyTerms to drive the system in the correct region of sequence space. While in the current implementation of BAGEL we implemented useful terms to tackle various classical protein design tasks such as motif templating and binder design, there is still much work to be done. Two different but complementary directions are the introduction of terms that a) quantitively improve desired correlations for already implemented design objectives, or b) qualitatively widen the range of potential design tasks. In the first group, the highest-priority advancement includes implementation of new EnergyTerms that more directly correlate with the interaction between two groups of residues, possibly calculated using Oracles specialized in reproducing different aspects of protein-protein interactions, such as the previously discussed MINT [56], or PESTO [45]. In the second group, the choice is only limited by our creativity and the design problem we want to solve. For the next iteration of BAGEL, we plan to implement terms that can be used to enforce the positioning of specific amino acids in user-defined positions, e.g., to create addressable protein scaffolds. Combining such terms with excluded volume terms that create void regions, for example, could be used to create pockets to co-localise drugs or catalysts in a specific protein patch, which could be useful to design enzymes for pro-drugs activation [64]. Similarly, EnergyTerms that measure the propensity for a given protein surface to interact with other class of molecules, such as nucleic acids, could be used to design transcription factors with known binding patches. In this endeavour, we make an open call to the community to contribute new EnergyTerms relevant to their research interests, thus increasing the breadth of problems addressable with BAGEL.

Choice of EnergyTerms. A current limitation of BAGEL lies in the need for users to carefully select both the EnergyTerms and their relative weights. While this flexibility enables highly customizable design objectives, it also places the burden of defining a meaningful optimization target on the user. In practice, success often depends on choosing a metric – or an associated energy term – that best captures the desired physical or functional property. For example, when the design objective is to obtain a stable structure, terms such as pLDDT, pTM, or iPAE can serve as practical surrogates for experimental observables like RMSD or binding affinity [31,65,66]. Nevertheless, there remains to be a system-independent confidence metric coming out of these models that would serve as a one-size-fits-all proxy for experimental success [53,67–69]. Model confidence metrics remain informative but imperfect proxies for real-world biophysical accuracy. Consequently, a key future direction for BAGEL will be to incorporate adaptive schemes that automatically identify and weight the most predictive metrics for a given design class – potentially through Bayesian optimization, reinforcement learning, or large language model-based agents – thus improving both user experience and design reliability.

Future of boileroom. Managing dependencies across diverse deep learning models often results in complex and fragile dependency graphs. We introduced boileroom to alleviate the dependency management, running each model in an isolated, containerized environment on Modal. Nevertheless, this introduces internet connection requirements and network latency, which we hope to tackle by providing better support for local execution of these models. We can achieve this by employing similar logic to Modal, where containers are spun up through conda, Docker or Apptainer, and thus run these models in isolated environments. We are also considering integrating with NVIDIA’s BioNemo and NIM frameworks, which are, however, still in their infancy in terms of the breadth of bio-related models provided. Lastly, boileroom’s API should be unified, abstracting a consistent Protein class to ensure consistent and predictable outputs from the interface.

Biomolecular modality. Long-term additions might include the introduction of non-canonical amino acids, e.g., with RareFold [70], or nucleotides, if models supporting nucleic acids (NAs) - such as Boltz-2 and AlphaFold3 - reach a sufficiently translatable accuracy in predicting protein-NA interactions. Non-canonical-based peptides have been growing in popularity thanks to their stability and bioavailability [71], while targeting nucleic acids could lead to novel gene-editing [72] or cell reprogramming tools [73]. This would require a more detailed refactoring of the Chain and Residue logic, however, the overall codebase’s philosophy and components would stay the same. At the same time, we highlight that FoldingOracles or EmbeddingOracles trained for systems made exclusively of DNA or RNA [74] could be directly implemented and used to design nucleotide-based structures within BAGEL with very minimal changes. Although they would probably require implementation of ad hoc EnergyTerms, such an endeavour would immediately expand BAGELs capability to design a new class of systems.

Expert in the loop. Eventually, whether or not a design will work in practice depends on two important aspects: the quality and accuracy of the Oracles used, and whether the design problem is well-described by the loss function provided by the user. Just to make an example, if a functional property of a protein is strongly dependent on its structural fluctuations, an Oracle able to evaluate these effects should be used. Failure to use the right Oracle, or failure to account for these effects in the loss function, will necessarily result in an experimentally unsuccessful design. In this regard, the continuous improvements of the community around different models, i.e., Oracles, as well as better understanding of their use and limitations, will allow users to use BAGEL better. In other words, while BAGEL allows to easily translate any design problem into a loss function, and quickly test the results of its minimization, it does not replace expert knowledge, which should be used as much as possible to pre-condition the design problem to help finding the correct solution.

Community engagement and contribution. We aim to cultivate a vibrant community around BAGEL by encouraging contributions via GitHub pull requests. Specifically, we welcome implementations of new Oracles into boileroom, new Minimizer algorithms or adaptations of existing ones, and detailed benchmarking studies using the suite of available components. Our principal ambition ultimately remains grounded in experimental validation. We thus aim to rigorously test the practical efficacy of BAGEL-designed proteins in laboratory conditions. This will help establish BAGEL not only as a computational tool, but as a reliable platform for practical biological innovation. Accordingly, we extend an open call to experimentalists seeking in silico designed peptides: the provided templates on GitHub may be readily adapted for specific applications, and we welcome direct contact to discuss potential collaborations.

Supporting information

Acknowledgments

We thank Shanil Panara, Dr Daniele Visco, Arnav Cheruku and Harsh Agrawal for fruitful conversations discussing the implementation of the codebase and design pipeline. We acknowledge computational resources and support provided by the Imperial College Research Computing Service (http://doi.org/10.14469/hpc/2232).