CCK * (Convex Closure K *): A Suite of Algorithms for the De Novo Design of L- and D-peptide Binders

CCK * (Convex Closure K *): A Suite of Algorithms for the De Novo Design of L- and D-peptide Binders | bioRxiv /* */ /* */ <!-- <!-- /*! * yepnope1.5.4 * (c) WTFPL, GPLv2 */ (function(a,b,c){function d(a){return"[object Function]"==o.call(a)}function e(a){return"string"==typeof a}function f(){}function g(a){return!a||"loaded"==a||"complete"==a||"uninitialized"==a}function h(){var a=p.shift();q=1,a?a.t?m(function(){("c"==a.t?B.injectCss:B.injectJs)(a.s,0,a.a,a.x,a.e,1)},0):(a(),h()):q=0}function i(a,c,d,e,f,i,j){function k(b){if(!o&&g(l.readyState)&&(u.r=o=1,!q&&h(),l.onload=l.onreadystatechange=null,b)){"img"!=a&&m(function(){t.removeChild(l)},50);for(var d in y[c])y[c].hasOwnProperty(d)&&y[c][d].onload()}}var j=j||B.errorTimeout,l=b.createElement(a),o=0,r=0,u={t:d,s:c,e:f,a:i,x:j};1===y[c]&&(r=1,y[c]=[]),"object"==a?l.data=c:(l.src=c,l.type=a),l.width=l.height="0",l.onerror=l.onload=l.onreadystatechange=function(){k.call(this,r)},p.splice(e,0,u),"img"!=a&&(r||2===y[c]?(t.insertBefore(l,s?null:n),m(k,j)):y[c].push(l))}function j(a,b,c,d,f){return q=0,b=b||"j",e(a)?i("c"==b?v:u,a,b,this.i++,c,d,f):(p.splice(this.i++,0,a),1==p.length&&h()),this}function k(){var a=B;return a.loader={load:j,i:0},a}var l=b.documentElement,m=a.setTimeout,n=b.getElementsByTagName("script")[0],o={}.toString,p=[],q=0,r="MozAppearance"in l.style,s=r&&!!b.createRange().compareNode,t=s?l:n.parentNode,l=a.opera&&"[object Opera]"==o.call(a.opera),l=!!b.attachEvent&&!l,u=r?"object":l?"script":"img",v=l?"script":u,w=Array.isArray||function(a){return"[object Array]"==o.call(a)},x=[],y={},z={timeout:function(a,b){return b.length&&(a.timeout=b[0]),a}},A,B;B=function(a){function b(a){var a=a.split("!"),b=x.length,c=a.pop(),d=a.length,c={url:c,origUrl:c,prefixes:a},e,f,g;for(f=0;f<d;f++)g=a[f].split("="),(e=z[g.shift()])&&(c=e(c,g));for(f=0;f<b;f++)c=x[f](c);return c}function g(a,e,f,g,h){var i=b(a),j=i.autoCallback;i.url.split(".").pop().split("?").shift(),i.bypass||(e&&(e=d(e)?e:e[a]||e[g]||e[a.split("/").pop().split("?")[0]]),i.instead?i.instead(a,e,f,g,h):(y[i.url]?i.noexec=!0:y[i.url]=1,f.load(i.url,i.forceCSS||!i.forceJS&&"css"==i.url.split(".").pop().split("?").shift()?"c":c,i.noexec,i.attrs,i.timeout),(d(e)||d(j))&&f.load(function(){k(),e&&e(i.origUrl,h,g),j&&j(i.origUrl,h,g),y[i.url]=2})))}function h(a,b){function c(a,c){if(a){if(e(a))c||(j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}),g(a,j,b,0,h);else if(Object(a)===a)for(n in m=function(){var b=0,c;for(c in a)a.hasOwnProperty(c)&&b++;return b}(),a)a.hasOwnProperty(n)&&(!c&&!--m&&(d(j)?j=function(){var a=[].slice.call(arguments);k.apply(this,a),l()}:j[n]=function(a){return function(){var b=[].slice.call(arguments);a&&a.apply(this,b),l()}}(k[n])),g(a[n],j,b,n,h))}else!c&&l()}var h=!!a.test,i=a.load||a.both,j=a.callback||f,k=j,l=a.complete||f,m,n;c(h?a.yep:a.nope,!!i),i&&c(i)}var i,j,l=this.yepnope.loader;if(e(a))g(a,0,l,0);else if(w(a))for(i=0;i (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0];var j=d.createElement(s);var dl=l!='dataLayer'?'&l='+l:'';j.src='//www.googletagmanager.com/gtm.js?id='+i+dl;j.type='text/javascript';j.async=true;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-M677548'); Skip to main content Home About Submit ALERTS / RSS Search for this keyword Advanced Search New Results CCK * (Convex Closure K *): A Suite of Algorithms for the De Novo Design of L- and D-peptide Binders View ORCID Profile Henry Childs , Allen C. McBride , Bruce R. Donald doi: https://doi.org/10.1101/2025.11.21.689740 Henry Childs 1 Department of Chemistry, Duke University , 124 Science Drive, Durham, NC 27708, USA 2 Department of Computer Science, Duke University , 308 Research Drive, Durham, NC 27708, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site ORCID record for Henry Childs Allen C. McBride 2 Department of Computer Science, Duke University , 308 Research Drive, Durham, NC 27708, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site Bruce R. Donald 1 Department of Chemistry, Duke University , 124 Science Drive, Durham, NC 27708, USA 2 Department of Computer Science, Duke University , 308 Research Drive, Durham, NC 27708, USA 3 Department of Biochemistry, Duke University School of Medicine , 307 Research Drive, Durham, NC 22710, USA 4 Department of Mathematics, Duke University , 120 Science Drive, Durham, NC 27708, USA Find this author on Google Scholar Find this author on PubMed Search for this author on this site For correspondence: bioRxiv26{at}cs.duke.edu Abstract Full Text Info/History Metrics Preview PDF Abstract The computational design of L-peptides and their mirror-image counterparts, D-peptides, is a valuable area in drug design. L- and D-peptides offer exceptional structural diversity and high binding specificity, while D-peptides additionally confer critical advantages such as proteolytic resistance. Progress in de novo D-peptide design has been hindered by the absence of evolutionary context and limited structural data, both of which are essential for the deep learning methods that dominate L-peptide design. Consequently, any framework capable of designing both L- and D-peptides must not only be grounded in data-driven inference but also first-principles, physics-based modeling. Here, we introduce a unified computational framework that supports de novo design of both L- and D-peptides, thereby expanding the accessible design space across the full mirrored proteome. Convex Closure K * ( CCK *) is a suite of chiral-invariant algorithms: scope, montage, and arise. scope, using geometry as a proxy for chemical energetics, computes convex hull representations of rotameric states to rapidly generate multi-sequence protein contacts maps. montage employs geometric hashing in conjunction with the K * algorithm to generate and rank backbone scaffolds by their suitability for sequence design. arise is a sequence design algorithm that uses an iterative residue search approach in an undirected graph to discover high-affinity peptide sequences. We apply the full CCK * suite to six de novo design tasks, benchmarking both homochiral and heterochiral binding on chirality-preserving and chirality-inverting designs. 1 Introduction Relative to small molecules and biologics, peptide therapeutics display a number of advantages including high specificity, enhanced membrane permeability, and improved bioavailability [ 1 ]. The reflected stereocenters of D-peptides, the mirror image of proteinogenic L-peptides, deter binding to proteases and thus exhibit improved stability [ 2 ], among other benefits. Due to these favorable properties, L- and D-peptides are of interest for drug design. Peptides are a class of molecule that is particular difficult to design in silico ; the discrete optimization problem of rotamer selection is NP-hard [ 3 ]. Artificial Intelligence (AI) methods show promise for L-peptide binder design [ 4 , 5 ] with some noncanonical amino acid substitutions [ 6 ]. However, likely due to the scarcity of experimental structures and absence of evolutionary data, AI approaches fail to predict D-peptide binders [ 7 ]. Thus, a generalizable framework to design L- and D-peptides must operate in a data-sparse regime while rigorously searching over the large sequence and conformation space from first principles. In particular, for an algorithm to design de novo L- and D-peptides, we define four required capabilities: (1) accurate ligand docking to generate reliable starting points, (2) optimized searches over sequence and conformation space to determine the best binders for design, (3) energy-equivariant physics modeling to support mixed chirality, and (4) ensemble representations of unpruned states to accurately and quickly predict binding affinity of bound structures. Herein, we review existing techniques for each specified capability. Previous strategies for mixed-chirality docking typically focus on sampling from experimentally determined structures to generate a scaffold library. Garton et al. [ 8 ] searched a mirror image of the PDB and identified hotspots residues to design D-peptide GLP1R and PTH1R agonists. Our lab previously reported on an algorithm for de novo D-peptide design, DexDesign [ 9 ], that used reflections and geometric hashing to generate a scaffold library. D-peptides produced by DexDesign were predicted to bind disease-associated PDZ domains. Experimental techniques to assess peptide binding typically focus on screening a large phage library [ 10 , 11 ]. Physics-based methods with provable guarantees have a strong track record in sequence and conformation optimization. Methods implementing deterministic search algorithms, such as dead-end elimination [ 12 , 13 ], generate realistic models with provable guarantees on accuracy. These methods have been applied to diverse chemical systems such as HIV-1 V2-apex antibody redesigns [ 14 ] and KRas binder optimization [ 15 ]. Similar approaches have been applied to non-proteinogenic systems [ 9 , 16 ]. Some physics-based methods, such as Rosetta [ 17 , 18 ], incorporate D-amino acid templates for noncanonical design. However, Monte Carlo tree searches stochastically explore parts of a larger search space at the cost of fewer provable guarantees. The thermodynamic calculation of the association constant ( K a ) employs a partition function ( Z ) for the apo protein ( P ), apo ligand ( L ), and protein:ligand complex ( PL ) [ 19 ]: In this formulation, calculation of binding affinity relies on accurate partition functions. These, in turn, depend on conformational ensembles that adequately sample the relevant regions of the energy landscape to capture the entropic contributions that drive protein interactions. Physics methods such as ensemble docking [ 20 ] and deep learning approaches [ 21 ] can generate ensembles. Although these approaches are enticing for enabling broad searches over large-scale conformational changes, they are heuristic or uninterpretable, and therefore do not offer guarantees of low-energy state representation. Because Boltzmann weighting exponentially amplifies contributions from low-energy states, a failure to include energy minima when calculating the partition function compromises the calculation of binding affinity. The K * algorithm and its extensions, as described in [ 22 – 27 ], bound the required partition functions with provable guarantees of free energy approximation. For each species i ∈ {P, L, PL} , we can compute an approximation to the partition function ( Q i ≈ Z i ) by summing over each state ( s ): R and T are the gas constant and temperature, respectively. The minimized energy of a given state, E ( s ), is computed over continuous rotamers [ 23 ] for a given ensemble. The K * energy function enables mixed-chirality design by mimicking the energy equivariance of reflection precisely. Ensemble conformations are searched using the A* algorithm [ 28 ] and are enumerated in a gap-free list ordered by lower bound on the conformation’s energy. By maintaining an upper bound on the partition function, unenumerated conformations are guaranteed to have higher energy (see [ 22 ] for more information). By computing an ε -accurate partition function for each species, K * approximates the true K a : Pruning high-energy conformations from consideration reduces the number of calls to the energy function, resulting in considerable speedups to Q i calculation without sacrificing accuracy. Pruning algorithms offer combinatorial speedups compared to exhaustive enumeration (see multi-sequence Q i bounds in BBK * [ 25 ] and intra-chain pruning using Inverse Alanine Scanning (IAS) [ 9 ]); however, these algorithms exhibit poor scalability to vast sequence spaces. More effective pruning is required for de novo design because the number of possible sequences is exponential in the number of residues. For example, IAS calculates K * binding predictions for optimal point mutations on a polyalanine peptide, which is then used in a combinatorial search to construct full sequences that are predicted to bind a protein target [ 9 ]. In the ideal case, IAS returns ≤ 5 non-clashing residue identities at each backbone position. A 6-residue peptide combinatorial search will need to enumerate 5 6 = 15, 625 sequences of the 20 6 possible sequences. However, in the analogous case on a 12-residue peptide, a combinatorial search must enumerate 5 12 ≈ 244, 000, 000 sequences after the scanning technique. The pruned search space for the 12-residue peptide (5 12 sequences) is greater than the full search space of the 6-residue peptide (20 6 sequences). Thus, the design of de novo peptides necessarily requires more efficient pruning and sequence construction. Here we introduce Convex Closure K * ( CCK *), a suite of generalizable algorithms (scope, montage, and arise) for the de novo design of L- and D-peptide binders. These algorithms extend K * to yield broader applicability and collectively exhibit capabilities (1)-(4) described above. We apply these algorithms in a reproducible workflow to 6 biological systems and validate predictions with in silico benchmarks. CCK * generates high-affinity de novo L- and D-peptides spanning antitumor, antimicrobial, and CFTR-modulating drug classes. By presenting CCK *, this article makes the following contributions: A free and open-source implementation of Convex Closure K * ( CCK *) in the OSPREY [ 24 ] software package. CCK * is a suite of chiral-invariant algorithms (scope, montage, and arise) for the de novo design of L- and D-peptide binders. scope (Side Chain Orientation and Position Evaluation): a geometric algorithm for generating multi-sequence protein contact maps, enabling a priori ranking and pruning of conformation and sequence modeling. This significantly reduces the design search space based on low-energy representations of side chains. montage (Motif-Oriented Noncanonical Template Assembly and Generation Engine): a docking and scaffold generation algorithm that uses geometric hashing, the K * algorithm, and sequence modeling to return L- and D-peptide backbones ranked by viability for de novo sequence design. arise (Affinity-driven Rational Iteration for Sequence Engineering): a sequence determination algorithm that leverages greedy sequence assignment in an undirected graph to generate high-affinity peptide sequences. Bounds on time complexity for each algorithm. Under modest assumptions, the algorithms are polynomial time. Benchmarks of the CCK * software suite on six de novo design tasks for both chirality-preserving and chirality-inverting designs of homochiral and heterochiral complexes. 2 Methods 2.1 SCOPE In computational protein design, posing the question—what should the algorithm search over?—can be just as important as the search itself. Calculating an accurate binding affinity ( Eq. 1 ) relies on consideration of all relevant low-energy conformation states. The Boltzmann weighting of these low-energies ( Eq. 2 ) means low-energy states contribute exponentially more to affinity values; each high-energy state is negligible. We therefore search the productive search space for protein design: the states that contribute meaningfully to the partition function. As reviewed below, models commonly implement simplifications and guiding heuristics to determine the productive search space a priori ; this strategy concentrates the search within conformational regions of maximal likely relevance. Rotamer libraries are a popular simplifying assumption to search the productive search space. By extracting the modal dihedral angles from empirical rotamer populations [ 29 ], a discrete set of amino acids can represent the continuous search space for each proteinogenic amino acid. Reflection is an energy-equivariant geometric transformation [ 30 ], so a rotamer library for D-amino acids can be obtained via a reflection operation on L-rotamers [ 9 ]. Molecular voxel theory [ 23 ] applies high-dimensional degrees of freedom bounds to model continuous protein flexibility for these rotamers. These representations are tractable to search over using optimization algorithms [ 13 , 28 ]. Protein contacts maps [ 31 , 32 ] are valuable for understanding the spatial relationship of apo and holo proteins. These methods commonly use evolutionary signals from sequence homologs and probabilistic contact predictions to infer residue contacts, fold, and function, yielding a productive search space. Deep learning methods, such as AlphaFold, use similar matrices for attention mechanisms in the Evoformer module [ 33 ]. Other work has stored contact maps in matrices and used linear programming to quickly prune rotamers for biophysical modeling [ 34 ]. A protein contact map for L- and D-peptide design must operate with no evolutionary priors (homochiral D-peptides are synthetic) and use novel computational strategies to accommodate the large de novo space, extending contact maps beyond the traditional use in single-sequence structure inference. Here, we introduce scope (Side Chain Orientation and Position Evaluation) that extends the methodology of rotamers and protein contact maps to generate multi-sequence protein contact maps of protein complexes for design (see Fig. 1 ). By using geometry as a proxy for chemical energetics, scope rapidly defines the productive search space of all possible sequences while capturing interaction effects of side chain rotamers. This positions scope as a valuable tool for informed drug design: generated contact maps account for both sequence variants (mutants) and multiple side-chain rotameric states (modal images of continuous rotamers) across protein chains. scope does not require any calls to an energy function nor evolutionary priors. Download figure Open in new tab Figure 1. The SCOPE algorithm applied to kCAL01:CALP. (A) Generation of a mutant convex hull. All rotamers for the 20 L (or D) amino acids are aligned and the convex hull is computed. A wildtype hull is similarly computed using only the rotamers corresponding to the wildtype identity. These convex polyhedra represent the configuration space of amino acid side chains on a fixed backbone. (B) Top: Visualization of the L-peptide kCAL01 bound to biological target CALP (PDB ID 6ov7), a validated cystic fibrosis drug target. CALP (chain A) is displayed in green; kCAL01 (chain C) in cyan. Left: the kCAL01:CALP complex represented as mutant and wildtype hulls. Right: The mutant hulls of residues C4 (wildtype Thr) and C2 (wildtype Gln) intersect with an overlap volume of 145.2 Å 3 . C4 has an overlap volume with the wildtype hull of A342 (wildtype Lys) of 13.4 Å 3 ; C2 has an overlap volume of 26.3 Å 3 . (C) A multi-sequence protein contact map generated using scope for kCAL01:CALP. SCOPE calculates the productive search space relative to a fixed backbone and models rotamer states using convex hulls. For a given peptide:target complex, the algorithm constructs a mutant hull and a wildtype hull for the peptide and target, respectively. A mutant hull is defined as the convex polyhedron that encloses all rotamers for all amino acids (see Fig. 1 (A) ). A wildtype hull is defined as the convex polyhedron that encloses all rotamers for a target residue’s wildtype identity (see Fig. 1 (B) ). By representing the chemical interaction space in this manner, scope rapidly determines pairwise residue interactions by polyhedral configuration space (C-space) intersections. The productive search space is defined from the configuration space as all pairs of hulls that have a volumetric overlap. The volume of polyhedral overlap (Å 3 ) provides a geometric heuristic for the significance of a chemical interaction (similar to a cutoff distance [ 35 ]). Non-overlapping hulls can be inferred to have no meaningful chemical contact; this enables combinatorial pruning of evaluated sequences and conformations in the design search. Mutant and wildtype hulls are computed using the penultimate rotamer library [ 29 ] and an implementation of the Quickhull algorithm [ 36 ]. The time complexity of computing a convex hull in ℝ 3 of p points is 𝒪 ( p log p ). This is the most intensive computation; volume overlap operations [ 37 ] are linear in the number of points. Thus, scope has a computational complexity of 𝒪 ( p log p ). In practice, this algorithm has a runtime of minutes. 2.2 MONTAGE A crucial task in protein design is generating backbone structures that are viable candidates for subsequent sequence design (the process of generating an amino acid sequence that optimizes desired properties, such as binding affinity). Previously, our lab used the DexDesign algorithm [ 9 ] to generate a library of D-peptide candidate binders. To accomplish this, DexDesign calls a geometric hashing algorithm, MASTER [ 38 ], as a subroutine. The C α RMSD and wildtype sequence K * score of these backbone scaffolds were computed to rank scaffolds by viability for sequence design; we refer to this property as designability [ 39 ]. DexDesign combined geometric priors (experimentally determined structures) with physics-based calculations (the K * algorithm [ 27 ]) to generate peptides that were predicted to bind L-targets [ 9 ]. However, this algorithm relies on the wildtype sequence of the sampled structure to predict designability, which biases for selection of structures with large side chains that improve binding site packing [ 40 ]. Additionally, scaffold docking was determined by geometric alignment with sparse entropy modeling. This limited the number of conformations used to calculate K * scores, hindering the designability rankings. montage (Motif-Oriented Noncanonical Template Assembly and Generation Engine) is an algorithm for generating L- and D-peptide scaffold libraries for protein targets. This algorithm calls scope as a subroutine to inform the creation of K *-generated structural ensembles. montage mutates all ligand residues to alanine (excluding glycine and proline residues to preserve any sampled cis bonds). This biases the K * algorithm to rank scaffolds based on backbone compatibility as opposed to binding interface packing. Further, because alanine possesses only a single rotameric state, computational resources can be reallocated to model target chain residue or backbone flexibility. Each scaffold is translated and rotated during the K * search to find docking configurations that better satisfy the geometric constraints of the interface. The combination of all-alanine backbones and informed flexibility modeling augments montage with structural guidance aimed at producing more discriminative designability rankings. montage can generate both L- and D-peptide scaffolds. Given an L-peptide:L-protein complex, montage mirrors the L-peptide to D-space and uses this structure as a query to MASTER [ 38 ]. MASTER, using the L-database, returns L-substructures that are similar to the D-peptide query. Performing one final reflection operation yields D-peptide scaffolds that are geometrically similar to the endogenous L-peptide. All D-scaffold residues are mutated to alanine and ranked by K * score. The conformational modeling during the K * score is defined by scope (see Section 2.1 ). For each scaffold, the MASTER C α RMSD is combined with the K * score to rank by designability. See Fig. 2 for a visualization of this methodology. L-peptide scaffolds are similarly generated by omitting reflection operations. Download figure Open in new tab Figure 2. MONTAGE generates and ranks scaffolds by designability for a D-peptide:L-target system. This figure displays results for D-peptide GNSFDDWLASKG (herein referred to as GNS) bound to Streptavidin (PDB ID 5n89). The viability of a scaffold for sequence design is referred to as designability. (A) The montage algorithm. Using the structure of GNS (cyan) bound to Streptavidin (green), GNS is isolated and reflected to L-space. The MASTER [ 38 ] subroutine uses geometric hashing to sample structurally similar L-backbones (multicolor sticks) from a PDB database. Matches are returned by increasing C α RMSD. These L-backbones are reflected back to D-space and aligned into the binding site of the target (Streptavidin), resulting in D-peptides that mimic the endogenous fold. All D-scaffolds are mutated to polyalanine. The K * algorithm [ 22 ] ranks these complexes by computing the binding affinity over conformational ensembles while translating and rotating the ligand in the binding site. Incorporated residue flexibility for K * ensembles is determined by scope (see Section 2.1 ). (B) Overview of sequence and conformation pruning using montage . Using the structure of GNS:Streptavidin, the MASTER subroutine [ 38 ], and the K * algorithm [ 22 ], montage returns scaffolds ranked by designability. Our MASTER database has 119,160 high-resolution ( ≤ 2.5 Å) structures sampled from the PDB. (C) Sequence logo for the top 20 MASTER matches of (reflected) GNS. For a non-disjoint segment with s residues, the time complexity for MASTER is 𝒪 ( s 2 ). MASTER computes over a million superpositions per second [ 38 ], so the empirical runtime is minutes. For a system with p points, residue flexibility for K * ensembles is computed using scope , which has a complexity of 𝒪 ( p log p ) (see Section 2.1 ). The K * algorithm computes binding affinity for the polyalanine scaffolds. By using bounded partition function sizes and sparse residue interaction graphs [ 35 ], we can compute the K * score ( Eq. 3 ) in time . Here, w is branch width, q is the number of rotamers per residue, and c is number of conformations in a partition function. For many problems the branch width w is constant, reducing the complexity to polynomial time. Thus, montage has a computational complexity of . 2.3 ARISE In de novo design, the number of candidate sequences is exponential in the number of residues. This is intractable even for algorithms such as BBK * [ 25 ], which has a runtime that can be sublinear in the number of sequences. Because the sequence search space is exponentially large, the true global optimum cannot, in practice, be calculated by exhaustive enumeration using intensive physics-based methods. Nevertheless, it is possible to systematically obtain sequences that likely lie within a neighborhood of the optimum, thereby ensuring practical near-optimality. Here, we present arise (Affinity-driven Rational Iteration for Sequence Engineering), an algorithm for de novo sequence selection for affinity optimization. Given an input structural template, ARISE constructs the undirected graph G = ( V, E ). In this graph, vertices ( V ) encode residues. There are two types of residues: those corresponding to design chain residues D , and those corresponding to target chain residues T ( V = V D ∪ V T , V D ∩ V T = ∅). Edges ( E ( τ )) represent a potential chemical interaction between vertices in V based on geometry; using SCOPE (see Section 2.1 ), an edge is drawn between two vertices if the convex hulls of those residues have an overlap greater than volume cutoff threshold τ . We assign to each vertex a set of amino acid identities. Let g be the mapping from a vertex to a set of amino acid identities g : V → 𝒫 ( A ), where 𝒫 is the nonempty powerset and A is the amino acid alphabet. In effect, ARISE changes g to restrict the set of amino acids feasible at each design residue in an iterative fashion (described below). Let c be the mapping from a set of amino acid identities to a convex hull c : 𝒫 ( A ) → S , where S is the set of all convex hulls. Thus, the SCOPE subroutine defines E ( τ ) using its hull volume overlap function h : All design chain residues v ∈ V D are initialized to g ( v ) = A and all target chain residues v ∈ V T are initialized to their wildtype identity. Neighboring residues of a pair v i , v j ∈ V D (where ( v i , v j ) ∈ E ( τ ))) are defined: K ∗ (( a p , b q ), M ) is defined as the binding affinity estimate obtained by running the K * algorithm ( Eq. 3 ) with modified subsequence ( a p , b q ) at design chain positions p and q ( p q, a p , b q ∈ A ). Residues in set M are modeled with continuous flexibility [ 23 ]. Therefore, ARISE computes the highest-affinity sequence pair by: Based on Eq. 6 , ARISE updates g such that g ( v i ) = { a ⋆ } and g ( v j ) = { b ⋆ } . The GMEC is used as the structural template for future iterations; that is, assignments are propagated to future K * searches. ARISE calls SCOPE to recompute edges E ( τ ) ( Eq. 4 ) given these new sequence assignments. This search ( Eq. 6 ) iteratively updates g until all design residues are assigned. The K * algorithm has been shown to accurately design these types of side chain interactions in diverse chemical systems [ 14 , 15 , 40 ]. By modeling design chain residues as convex hulls, ARISE obtains an optimistic upper bound on the feasible C-space for unassigned residue identities. Each residue assignment reduces the exponential sequence and conformation space by generating new scope -defined edges ( Eq. 4 ), effectively pruning the graph and reducing the complexity of subsequent assignment calculations ( Eq. 6 ). While exhaustive exploration of the de novo sequence space remains intractable, this framework implements a greedy search algorithm that enumerates the most promising submanifolds of sequence and conformation space. We do not claim global optimality; the method exploits monotone pruning of G to reduce conformational coupling and concentrate sequence enumeration. See Fig. 3 for a visualization of this graph. This methodology is reminiscent of region-based belief propagation in factor graphs [ 41 ], but replaces heuristic region cutoffs in favor of multi-sequence protein contact maps ( scope ). Download figure Open in new tab Figure 3. The ARISE algorithm finds a high-affinity sequence for a D-peptide:L-protein system. This figure uses a montage -generated match (see Section 2.2 ) from a D-peptide:MDM2 complex (PDB ID 3iwy). Left: the 12-residue D-peptide scaffold is shown in gray sticks, while MDM2 (L-protein) is displayed in blue cartoon representation. For the undirected graph generated by arise , the D-peptide residues are shown as grey boxes and MDM2 residues are shown as blue circles. Edges indicate a hull volume overlap ( Eq. 4 ). The identity of a design residue will be updated for each K * search ( Eq. 6 ). Right: the graph and designed peptide structure after amino acid assignment. Assignments constrict design chain hull volumes, effectively pruning the graph and simplifying the productive search space; residue 1 has no hull intersections when assigned to the highest-affinity residue isoleucine. Download figure Open in new tab Figure 4. CCK * predicts peptides for homochiral and heterochiral systems that converge to high-affinity sequences. The first row is chirality-preserving homochiral systems, the second row is chirality-preserving heterochiral systems, and the third row is chirality-inverting designs. The name of the input template used for design is listed on the left in each cell. Bar graphs: K * scores (log 10 , blue), sequence recovery (%, orange), and number of hydrogen bonds (green) in the GMEC structure for each prediction. Chirality-inverting designs (GNS, GDL) were compared to the corresponding experimentally solved complex in the opposite chirality (GDL and GNS, respectively). The consensus sequence (CS) is listed below the bar graph with square brackets denoting selected residue identities at each position. For example, in kCAL01 position 1 has identities W and R, position 2 has identities E, K, and R, etc. Across these six systems, the consensus sequence degeneracy (number of unique amino acid identities for a given residue position) ranged from 1 to 5 with a mode of 2. Line graphs: K * scores (log 10 ) from the arise algorithm as a function of iteration. Scaffold color labels are listed in the respective legends. The K * score of the known binder is represented as a dashed blue line. For all systems and scaffolds (besides GNS), arise selects sequences that are predicted to have a better binding affinity than the known peptide binder. Across all arise iterations, the average change in K * score (log 10 ) is +1.9 (corresponding to ΔΔ G = − 2.6 kcal/mol). The arise algorithm constructs the undirected graph using scope , which has a computational complexity of 𝒪 ( p log p ) (see Section 2.1 ). The iterative search is linear in the number of design residues, using the K * algorithm for sequence selection. As described in Section 2.2 , the computational complexity of this algorithm is . 3 Results We applied the complete CCK * software suite in a reproducible workflow ( montage → arise , with scope invoked as a subroutine) to six de novo design tasks. We report benchmarks for homochiral (L-peptide:L-protein) and heterochiral (D-peptide:L-protein) binding. Given a structural template, we evaluated CCK * on both chirality-preserving designs (e.g., L-peptide to L-peptide) and chirality-inverting designs (e.g., L-peptide to D-peptide). To validate designed sequences, we investigated predicted binding affinity ( K * score, where a higher score indicates better binding), hydrogen bonding, and sequence recovery. All K * scores are reported on a log 10 scale. All designs were performed across five backbone scaffolds returned by montage . For tractability, arise K * calculations were capped at 24 hours with two flexible target residues (selected by largest hull volume overlap). Based on scaffold geometry (e.g., isolated vertex), some K * runs ( Eq. 6 ) mutated only one residue. Hydrogen bonds were determined via visual inspection of GMEC structure polar contacts in PyMOL [ 42 ]. Sequence similarity was computed using the VectorBuilder sequence alignment tool [ 43 ]. All designs were run on a 24-core, 48-thread Intel Xeon processor with 4 Nvidia Titan V GPUs. For five out of six systems (25 out of 30 scaffolds), sequences designed by CCK * were predicted to have a better binding affinity to the target than the known peptide binders. Additionally, the consensus sequence degeneracy (number of unique amino acid identities for a given reside position) ranged from 1 to 5 (mode of 2); CCK * therefore produces designs with high positional conservation (low degeneracy). The average arise iteration (identity assignment, see Eq. 6 ) produced a change in K * score of +1.9 (ΔΔ G = −2.6 kcal/mol), which corresponds to an ∼80-fold increase in predicted binding affinity. Thus, parameterized on the scope -defined productive search space, arise generates sequences that introduce energetically significant improvements (on the order of a strong buried hydrogen bond or multiple favorable van der Waals contacts). 3.1 Chirality-Preserving Designs 3.1.1 L-peptide:L-protein Systems The L:L systems were kCAL01:CALP (PDB ID 6ov7) and Thanatin:LptA (PDB ID 8gaj), structures solved by our lab using X-ray crystallography. kCAL01 is a 6-residue peptide inhibitor that binds the PDZ domain of the CFTR-associated ligand (CALP) in humans, thereby blocking its interaction with CFTR and preventing its CALP-mediated degradation [ 44 ]. Podisus maculiventris Thanatin is a 19-residue peptide that binds to the N-terminal β -strand of the periplasmic protein LptA, disrupting its oligomerisation and association within the Lpt transport complex, thereby disabling lipopolysaccharide export in Gram-negative bacteria [ 45 ]. kCAL01:CALP For kCAL01:CALP, the MASTER subroutine was queried with the 6-residue kCAL01 ligand (WQVTRV), which adopts a linear motif when bound to CALP [ 9 ]. The backbone RMSD of the top 20 MASTER returns ranged from 0.05 Å to 0.07 Å, with a median of 0.07 Å. The lowest-RMSD match was the endogenous ligand kCAL01 (RMSD 0 Å), and was therefore discarded. The alanine scaffolds produced by montage (see Section 2.2 ) resulted in K * scores ranging from 6.65 (scaffold-4) to 16.42 (scaffold-6), with a median of 15.81. The five highest-affinity alanine scaffolds returned by montage were scaffold-6 (RMSD 0.06 Å, K * 16.42), scaffold-11 (RMSD 0.07 Å, K * 16.37), scaffold-16 (RMSD 0.07 Å, K * 16.22), scaffold-12 (RMSD 0.07 Å, K * 16.14), and scaffold-17 (RMSD 0.07 Å, K * 16.02). The arise algorithm enumerated a total of 2,988 sequences across these five backbones. The number of enumerated sequences ranged from 452 (scaffold-12) to 819 (scaffold-17), with a median of 459. The K * search runtime for all iterations ranged from 21 minutes (scaffold-6) to 1,467 minutes (scaffold-12), with a median runtime of 74 minutes (scaffold-11). Across all arise iterations, the average change in K * score is +3.15. Full-sequence K * scores ranged from 27.19 (scaffold-12) to 31.02 (scaffold-17), with a median score of 28.84 (scaffold-11). Scaffold-17 produced the tightest binder ( K * 31.02) with sequence WERSRN. kCAL01:CALP has a K * score of 26.82; therefore, all designed sequences have a higher predicted binding affinity to CALP than kCAL01. The consensus sequence across the five backbones is [WR][EKR][RK][DS][PR][CN]. The sequence similarity of highest-affinity scaffold-17 (WERSRN) to kCAL01 (WQVTRV) is 66.67%. The sequence similarity ranged from 37.50% (scaffold-11, 12) to 66.67% (scaffold-6, 16, 17), with a median of 66.67%. The consensus sequence degeneracy ranged from 2 to 3 (mode of 2). kCAL01:CALP has 9 H-bonds. The change in number of H-bonds ranges from −1 (scaffold-11, 12, 16) to +4 (scaffold-17), with a median of only one hydrogen bond lost. Thanatin:LptA For Thanatin:LptA, the MASTER subroutine was queried with the 19-residue Thanatin ligand (KKPVPIIYCNRRTGKCQRM), which adopts a β -hairpin motif when bound to LptA [ 45 ]. The backbone RMSD of the top 20 MASTER returns ranged from 0.75 Å to 0.99 Å, with a median of 0.92 Å. The alanine scaffolds produced by montage (see Section 2.2 ) resulted in K * scores ranging from 19.06 (scaffold-5) to 23.42 (scaffold-14), with a median K * score of 22.29. The five highest-affinity alanine scaffolds returned by montage were scaffold-14 (RMSD 0.98 Å, K * 23.42), scaffold-12 (RMSD 0.96 Å, K * 23.05), scaffold-17 (RMSD 0.99 Å, K * 22.87), scaffold-18 (RMSD 0.99 Å, K * 22.79), and scaffold-16 (RMSD 0.98 Å, K * 22.75). Scaffold-12 exhibited a technical failure during preprocessing, preventing arise from completing the design run. To maintain a consistent sample size across backbones, we substituted with the next best backbone (scaffold-20: RMSD 0.99 Å, K * 22.72). The arise algorithm enumerated a total of 1,690 sequences across these five backbones. All backbones enumerated 338 sequences across all iterations. The K * search runtime for all iterations ranged from 81 minutes (scaffold-16) to 1,809 minutes (scaffold-17), with a median runtime of 235 minutes (scaffold-14). Across all arise iterations, the average change in K * score is +2.30. Full-sequence K * scores ranged from 61.47 (scaffold-18) to 66.15 (scaffold-20), with a median score of 62.65 (scaffold-17). Scaffold-20 produced the tightest binder ( K * 66.15) with sequence RRGQRMRSRHMKRGYKKRM. Thanatin:LptA has a K * score of 7.15; therefore, all designed sequences have a higher predicted binding affinity to LptA than Thanatin. The consensus sequence across the five backbones is [R][RSA][G][QR][R][MI][R][SAM][R][HR][MKQ][KF HY][RMWS][G][YR][KQRLI][KRM][R][MI]. The sequence similarity of highest-affinity scaffold-20 (RRGQR MRSRHMKRGYKKRM) to Thanatin (KKPVPIIYCNRRTGKCQRM) is 18.75%. The sequence similarity ranged from 18.75% (scaffold-17, 20) to 43.48% (scaffold-16,18), with a median of 22.58% (scaffold-14). The consensus sequence degeneracy ranged from 1 to 5 (mode of 1). Thanatin:LptA has 13 H-bonds. The change in number of H-bonds ranges from 0 (scaffold-16, 18) to +3 (scaffold-20), with a median of +1 (scaffold-14, 17). No designs reduced the total number of hydrogens bonds relative to Thanatin:LptA. 3.1.2 D-peptide:L-protein Systems The D:L systems were DP12:MDM2 (PDB ID 3iwy) and DP19:L-19437 (PDB ID 7yh8). DP12 is a rationally designed D-peptide antagonist that targets the p53-binding domain of MDM2, representing a promising class of antitumor agents [ 46 ]. DP19 is a synthetic D-peptide binder selected against the artificial L-protein target L-19437 [ 47 ]. DP12:MDM2 For DP12:MDM2, the MASTER subroutine was queried with the 12-residue DP12 ligand (DWWPLAFEALLR), which adopts an α -helix motif when bound to MDM2. The backbone RMSD of the top 20 MASTER returns ranged from 0.43 Å to 0.49 Å, with a median of 0.46 Å. The alanine scaf-folds produced by montage (see Section 2.2 ) resulted in K * scores ranging from 12.42 (scaffold-5) to 17.55 (scaffold-17), with a median K * score of 15.20. The five highest-affinity alanine scaffolds returned by MON-TAGE were scaffold-17 (RMSD 0.48 Å, K * 17.55), scaffold-20 (RMSD 0.49 Å, K * 17.53), scaffold-12 (RMSD 0.46 Å, K * 16.43), scaffold-15 (RMSD 0.47 Å, K * 16.24), and scaffold-7 (RMSD 0.45 Å, K * 15.83). The arise algorithm enumerated a total of 1,351 sequences across these five backbones. The number of enumerated sequences ranged from 178 (scaffold-17, 20) to 579 (scaffold-12), with a median of 198 (scaffold-7). The K * search runtime for all iterations ranged from 7 minutes (scaffold-15) to 169 minutes (scaffold-12), with a median runtime of 9 minutes (scaffold-7). Across all arise iterations, the average change in K * score is +2.01. Full-sequence K * scores ranged from 35.17 (scaffold-15) to 40.43 (scaffold-7), with a median score of 36.11 (scaffold-17). Scaffold-7 produced the tightest binder ( K * 40.43) with sequence WYGMPYMEEM CT. DP12:MDM2 has a K * score of 29.49; therefore, all designed sequences have a higher predicted binding affinity to MDM2 than DP12. The consensus sequence across the five backbones is [RWI][FYW][SGIC][PMWE][DP][GY][PM][EF][YE FW][YMQ][CLNT][MTEN]. The sequence similarity of highest-affinity scaffold-7 (WYGMPYMEEMCT) to DP12 (DWWPLAFEALLR) is 35.71%. The sequence similarity ranged from 16.67% (scaffold-12) to 35.71% (scaffold-7), with a median of 27.78% (scaffold-15). The consensus sequence degeneracy ranged from 2 to 4 (mode of 4). DP12:MDM2 has 2 H-bonds. The change in number of H-bonds ranges from −2 (scaffold-15) to +1 (scaffold-17, 20), with a median of 0 (scaffold-12). DP19:L-19437 For DP19:L-19437, the MASTER subroutine was queried with the 19-residue DP19 ligand (DEHELLETAARWFYEIAKR), which adopts an α -helix motif when bound to L-19437. The backbone RMSD of the top 20 MASTER returns ranged from 0.18 Å to 0.20 Å, with a median of 0.20 Å. The alanine scaffolds produced by montage (see Section 2.2 ) resulted in K * scores ranging from 15.70 (scaffold-15) to 18.73 (scaffold-9), with a median K * score of 16.72. The five highest-affinity alanine scaffolds returned by montage were scaffold-9 (RMSD 0.20 Å, K * 18.73), scaffold-10 (RMSD 0.20 Å, K * 17.23), scaffold-7 (RMSD 0.19 Å, K * 17.19), scaffold-6 (RMSD 0.19 Å, K * 17.19), and scaffold-11 (RMSD 0.20 Å, K * 17.11). The arise algorithm enumerated a total of 2,152 sequences across these five backbones. The number of enumerated sequences ranged from 358 (scaffold-6, 9, 11) to 719 (scaffold-7), with a median of 358. Across all arise iterations, the average change in K * score is +1.51. The K * search runtime for all iterations ranged from 11 minutes (scaffold-11) to 28 minutes (scaffold-6), with a median runtime of 16 minutes (scaffold-9). Full-sequence K * scores ranged from 39.78 (scaffold-10) to 51.17 (scaffold-9), with a median score of 45.34 (scaffold-6). Scaffold-9 produced the tightest binder ( K * 51.17) with sequence RHEGHTEWAYEMFVK WARR. DP19:L-19437 has a K * score of 21.91; therefore, all designed sequences have a higher predicted binding affinity to L-19437 than DP19. The consensus sequence across the five backbones is [WRGI][YQHWP][DEW][WG][RSHK][QMTIL][DE Q][WITV][A][FYE][YE][YMW][FM][RVIM][WK][KWQR][A][RH][RK]. The sequence similarity of highest-affinity scaffold-9 (RHEGHTEWAYEMFVKWARR) to DP19 (DEHELLETAARWFYEIAKR) is 43.48%. The sequence similarity ranged from 36.00% (scaffold-7) to 59.09% (scaffold-10), with a median of 43.48% (scaffold-9). The consensus sequence degeneracy ranged from 1 to 5 (mode of 2). DP19:L-19437 has 2 H-bonds. The change in number of H-bonds ranges from +1 (scaffold-6, 10) to +5 (scaffold-7), with a median of +2 (scaffold-11). All DP19 designs are predicted to establish at least one additional hydrogen bond with L-19437. 3.2 Chirality-Inverting Designs The complex Gdlwqheatwkkq:Streptavidin (PDB ID 5n8t, herein referred to as GDL:Streptavidin) is a 9-residue D-peptide:L-protein complex. The complex GNSFDDWLASKG:Streptavidin (PDB ID 5n89, herein referred to as GNS:Streptavidin) is a 12-residue L-peptide bound to the L-protein Streptavidin. Both of these peptides were designed using a combined stepwise evolution and rational peptide array method [ 48 ]. GDL and GNS bind the same target (Streptavidin) with a similar motif and binding site location (complex C α alignment RMSD of 0.39 Å), albeit with opposite chirality. Because chirality inversion alters the stereochemical frame of reference, the predicted sequences cannot be benchmarked against the original template. Instead, we initialized the design from the PDB in one chiral space and evaluate the resulting structure against the corresponding experimentally solved complex in the opposite chirality. That is, designs generated with GDL are benchmarked against GNS, and vice versa. GDL:Streptavidin The heterochiral system GDL:Streptavidin was used to design L-peptide binders. The MASTER subroutine was queried with the GDL ligand (LWQHEATWK), which adopts an α -helix motif when bound to Streptavidin. The backbone RMSD of the top 20 MASTER returns ranged from 1.21 Å to 1.53 Å, with a median of 1.48 Å. The alanine scaffolds produced by montage (see Section 2.2 ) resulted in K * scores ranging from 4.89 (scaffold-14) to 9.98 (scaffold-20), with a median K * score of 7.63. The five highest-affinity alanine scaffolds returned by montage were scaffold-20 (RMSD 1.53 Å, K * 9.98), scaffold-19 (RMSD 1.52 Å, K * 9.18), scaffold-18 (RMSD 1.52 Å, K * 9.02), scaffold-9 (RMSD 1.48 Å, K * 8.80), and scaffold-6 (RMSD 1.35 Å, K * 8.21). The arise algorithm enumerated a total of 1,026 sequences across these five backbones. The number of enumerated sequences ranged from 118 (scaffold-9, 18) to 519 (scaffold-6), with a median of 133 (scaffold-20). Across all arise iterations, the average change in K * score is +1.30. The K * search runtime for all iterations ranged from 6 minutes (scaffold-9) to 2,165 minutes (scaffold-20), with a median runtime of 11 minutes (scaffold-19). Full-sequence K * scores ranged from 15.64 (scaffold-20) to 20.80 (scaffold-19), with a median score of 19.10 (scaffold-9). Scaffold-19 produced the tightest binder ( K * 20.80) with sequence RM WEYGGYQ. GNS:Streptavidin (corresponding experimental structure) has a K * score of 14.38; therefore, all designed sequences have a higher predicted binding affinity to Streptavidin than GNS. The consensus sequence across the five backbones is [RMY][AGMSN][HWG][DGE][LEYHM][AG][LG][W NYAF][EGQ]. The sequence similarity of highest-affinity scaffold-19 (RMWEYGGYQ) to GNS (GNSFDDW LASKG) is 11.76%. The sequence similarity ranged from 11.76% (scaffold-19) to 46.15% (scaffold-20), with a median of 17.65%. The consensus sequence degeneracy ranged from 2 to 5 (mode of 3). GNS:Streptavidin (corresponding experimental structure) has 6 H-bonds. The change in number of H-bonds ranges from − 5 (scaffold-19) to − 2 (scaffold-18, 20), with a median of − 4 (scaffold-6, 9). GNS:Streptavidin The homochiral system GNS:Streptavidin was used to design D-peptide binders. For GNS:Streptavidin, the MASTER subroutine was queried with GNS (GNSFDDWLASKG), which adopts an α -helix motif when bound to Streptavidin. The backbone RMSD of the top 20 MASTER returns ranged from 1.11 Å to 2.31 Å, with a median of 2.31 Å. The alanine scaffolds produced by montage (see Section 2.2 ) resulted in K * scores ranging from 8.77 (scaffold-2) to 13.90 (scaffold-1), with a median K * score of 9.62. The five highest-affinity alanine scaffolds returned by montage were scaffold-1 (RMSD 1.11 Å, K * 13.90), scaffold-4 (RMSD 2.00 Å, K * 12.07), scaffold-7 (RMSD 2.15 Å, K * 10.79), scaffold-3 (RMSD 1.89 Å, K * 10.48), and scaffold-6 (RMSD 2.12 Å, K * 10.07). The arise algorithm enumerated a total of 1,394 sequences across these five backbones. The number of enumerated sequences ranged from 192 (scaffold-4) to 579 (scaffold-1), with a median of 212 (scaffold-7). Across all arise iterations, the average change in K * score is +1.01. The K * search runtime for all iterations ranged from 56 minutes (scaffold-6) to 1,530 minutes (scaffold-4), with a median runtime of 1,465 minutes (scaffold-7). Full-sequence K * scores ranged from 17.39 (scaffold-3) to 26.99 (scaffold-1), with a median score of 22.88 (scaffold-4). Scaffold-1 produced the tightest binder ( K * 26.99) with sequence APRLMWYL AYWA. GDL:Streptavidin (corresponding experimental structure) has a K * score of 28.43. The consensus sequence across the five backbones is [RAW][LWHP][RKW][MHFWL][ML][LDWG][RWG FY][GCAHL][CMGA][HWEY][DFWG][AG]. The sequence similarity of highest-affinity scaffold-1 (APRLM WYLAYWA) to GDL (LWQHEATWK) is 38.46%. The sequence similarity ranged from 18.75% (scaffold-6) to 41.67% (scaffold-3), with a median of 31.25% (scaffold-7). The consensus sequence degeneracy ranged from 2 to 5 (mode of 4). GDL:Streptavidin (corresponding experimental structure) has 7 H-bonds. The change in number of H-bonds ranges from − 7 (scaffold-7) to − 4 (scaffold-3, 4, 6), with a median of − 4. 4 Conclusions We presented a computational framework for de novo peptide design that operates seamlessly across both chiral spaces. By creating three new protein design algorithms (scope, montage, arise) and implementing a unified workflow ( CCK *), we introduce a principled approach that couples geometric computation with physics-based sequence evaluation. Previous state-of-the-art platforms that support heterochiral design [ 9 ] scaled poorly with combinatorial sequence space. Despite sampling a small portion of the theoretical sequence space, CCK * converges to sequences with strong predicted binding affinities. Thus, CCK * likely concentrates search on the productive search space, effectively reducing the exponential design problem. Because the framework is energy-function agnostic and compatible with any affinity-based search, it can be inserted into existing modeling workflows. Future work includes removing the need for ligand structural inputs to montage by predicting reliable starting folds, enabling binder design with only a target. Additionally, implementing more backbone flexibility [ 13 , 49 ] may improve design accuracy. Acknowledgments We received funding from the NIH grant R35 GM-144042 to BRD. We thank all members of the Donald lab for helpful discussions. Funder Information Declared NIH , R35 GM-144042 Footnotes Source Code Availability CCK * can be found at github.com/donaldlab/OSPREY3. Conflict of Interest BRD is a founder of Ten63 Therapeutics, Inc. HC and ACM have no competing interest to declare. 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