Accelerating the Discovery of Multicatalytic Cooperativity

Summary:

Cooperative catalysis, in which multiple catalytic units operate synergistically, underpins a variety of synthetically and mechanistically important organic reactions^1–4. Despite its potential utility in new reactivity contexts, approaches to the discovery of cooperative catalysts have been limited, typically relying on serendipity or on prior knowledge of single-catalyst reactivity^1,5. Systematic searches for unanticipated types of catalyst cooperativity must contend with vast combinatorial complexity and are therefore not undertaken^6–10. Here, we describe a pooling–deconvolution algorithm, inspired by group testing¹¹, that identifies cooperative catalyst behaviors with low experimental cost while accommodating potential inhibitory effects between catalyst candidates. The workflow was validated first on simulated cooperativity data, and then by experimentally identifying previously documented cooperativity between organocatalysts in an enantioselective oxetane-opening reaction. The workflow was then applied in a discovery context to a Pd-catalyzed decarbonylative cross-coupling reaction, enabling the identification of several ligand pairs that promote the target transformation at substantially lower catalyst loading and temperature than previously reported with single ligand systems.

Multicatalysis, which relies on catalytic cooperativity, has proven to be powerful for promoting efficient and selective chemical transformations^1–4. Notably, enzymes are understood to achieve high levels of reactivity and selectivity by incorporating active-site residues that can operate cooperatively^12–15. Despite the enormous potential of multicatalysis, the methods by which it can be discovered remain very limited. For instance, mechanistic studies of single-catalyst reactions have led to unexpected discoveries of multicatalytic “homocooperativity,” where multiple units of the same catalyst perform different but complementary roles (Fig. 1A, left). Those insights ultimately enabled the development of linked-dimer catalyst that display vastly superior reactivity and selectivity relative to their monomeric counterparts^16–21. Multicatalytic “heterocooperativity,” where different catalysts can be tailored to complementary roles, is in principle more broadly applicable but far less likely to be uncovered serendipitously as it requires the intentional combination of multiple catalysts that have been identified to possess known complementary functions^1,5. While this hypothesis-driven approach has enabled several landmark advances in synthetic catalysis (e.g., Fig. 1A, right)^2,3,22–24, it leaves unexplored a potentially enormous reaction space of unanticipated synergistic effects resulting from previously unknown cooperativity pathways.

Fig. 1. Challenges and opportunities for the empirical discovery of catalytic cooperativity.

(A) Seminal synthetic advances enabled by catalytic cooperativity: homocooperativity in the hydrolytic kinetic resolution, heterocooperativity in metallaphotoredox catalysis and diastereodivergent synthesis. (B) Group testing as a conceptual foundation for catalyst pooling and this proposed workflow incorporating pooling and deconvolution steps to accelerate the empirical discovery of catalytic cooperativity.

The primary obstacle to the empirical exploration for multicatalytic heterocooperativity is that it requires combing through a vast combinatorial catalyst space^6–10. For instance, a set of 50 individual candidates entails a search space of 1225 possible pairs and 19600 possible triples. This plethora of combinations could offer broad possibilities for discovering unexpected cooperativity if the combinatorial space can be searched thoroughly and accurately. Conventional screening approaches such as one-factor-at-a-time (OFAT) and design of experiments (DOE) have limited utility because the cooperativity landscape is likely to be highly discontinuous²⁵. While human/machine model-based approaches are potentially more adaptable to discontinuous response surfaces, they require large sets of positive and negative training data as well as meaningful featurization and representation of cooperative effects^26–30, which are not generally available yet for cooperative catalytic systems.

We envisioned a mechanistically agnostic yet efficient strategy for the discovery of multicatalytic heterocooperativity, in which multiple catalyst candidates are pooled and tested together. This strategy was inspired by “group testing,” which is employed in diverse fields when limited diagnostic tests are available and when most individual tests are expected to return negative (Fig. 1B, left)¹¹. For example, group testing was applied widely during the COVID-19 pandemic³¹ to identify positive cases within a large population by testing pools of samples rather than every individual. Group testing has also been used to accelerate reaction condition optimization and discovery^10,32–36, but its application to the discovery of multicatalytic heterocooperativity involves a fundamental difference in that the goal is identifying positive interactions between candidates, rather than assessing individual performance. Thus, a custom “deconvolution” step is required to identify positive cooperative interactions from the reaction performance of pools (Fig. 1B, right), instead of simply separating individuals from a positive pool and testing them. Another key challenge is the possibility of “negative cooperativity,” where antagonistic interactions between candidates mask positive cooperative signals in the same pool, affecting the sensitivity of the workflow to positive cooperativity. A simple strategy for minimizing the effects of negative cooperativity is to evaluate smaller pools, but that approach necessarily comes at experimental expense. However, by constructing specific overlapping pools designed to guarantee that catalysts meet in multiple contexts, positive cooperative interactions can be deconvoluted from the performances of pools in a more efficient manner (see below). The combination of pooling and deconvolution is crucial for approaching the optimal tradeoff between sensitivity (i.e. the likelihood of finding every cooperative system within a set of catalyst candidates) and screening efficiency.

Development of a pooling–deconvolution algorithm

In our approach to identify positive cooperativity from within a set of N catalyst candidates, we set up pools with k candidates such that every subgroup of t catalysts appears in at least one pool^37,38 (Fig. 2A, top left). The problem of assigning candidates to pools is directly related to the mathematical concept of “covering designs.”^39–41 While covering designs generalize to cooperative sets of any size, our discussion here will focus exclusively on pairs.

Fig. 2. Development and simulation-based testing of pooling–deconvolution algorithm.

(A) Covering designs are the mathematical basis for the pooling step. Relevant parameters k, t, and r that serve to define the optimal size and composition of the candidate pools. A cooperativity score Q can be determined for each pool, whereas a deconvolution score D can be calculated for each pair. (B) Abstracted visualization of the computational pipeline to simulate catalytic cooperativity and test the pooling–deconvolution workflow on various landscapes. Steps (2) and (3) are repeated over 50 randomly generated landscapes to afford statistically meaningful average values of sensitivity and efficiency. The process (1)–(6) can be repeated with different user settings that define the prevalence of cooperativity on hypothetical landscapes. (C) Selection of optimal pooling parameters for experimental execution based on simulation results.

A critical challenge presented to a screening-for-cooperativity effort is the problem of catalyst interference, i.e., the likelihood that certain candidates inhibit the performance of other pool members or pairs and thereby lead to missed hits. To accommodate that scenario, we extend covering designs to require that each candidate pair appear in multiple (specifically r, where r ≥ 1) pools. “Redundant” sets of pools can be generated by randomly permuting the catalyst panel and repeating the pooling design (Fig. 2A, top middle)⁴². Thus, effective pool design must balance robustness against experimental efficiency: larger pools increase the risk of inhibitory catalysts masking cooperative pairs, while smaller pools together with designed redundancy require more experiments overall.

To quantify cooperativity between catalyst candidates within a pool, we define a cooperativity score Q derived from the performance of the pooled catalysts relative to that of the individual catalysts. While cooperativity can lead to enhancements in rate and/or in selectivity, we chose rate enhancement as our primary discovery objective. Pooling–deconvolution approaches could be applied in principle to discovery of enantioselectivity enhancement via cooperative mechanisms. However, such effects could only be detected if coupled to rate enhancements as well, since highly selective but poorly active catalyst combinations may be obscured in a pool. For experimental simplicity, we select product yield at low conversion as an approximation for initial rate. The yield of the pool (y_pool) is then compared to the “zero-cooperativity” yield expected if the candidates were not interacting (y_composite), which can be the sum, average, maximum, or some other function of the yields of the individual candidates depending on the experimental scenario. The cooperativity score Q can then be defined for a pool containing j candidates (Eq. 1, see Supporting Information Section 2.1 for a definition that is robust against experimental noise).

$$Q(1,2,\dots ,j)=\frac{y_{\text{pool}}(1,2,\dots ,j)}{y_{\text{composite}}(1,2,\dots ,j)}-1$$ (1)

Based on this definition, Q > 0 constitutes evidence for positive inter-catalyst cooperativity.

Assuming that catalyst cooperativity is relatively rare, a highly cooperative pair of candidates is expected to consistently appear in pools with high Q scores. Therefore, to estimate the performance of any pair, we can define a deconvolution score D for it by taking the average Q of all the pools that contain the pair (Eq. 2 and Fig. 2A, bottom). Formally, for a pair of candidates (i, j), D can be defined (Eq. 2), where P(i, j) is the set of pools that contains that pair.

This definition of D provides an estimate of pairwise cooperativity while compensating for the possibility that negative cooperativity may affect some of the pools. The top-scoring pairs can then be verified experimentally in isolation (Fig. 1D, Step 3).

$$D(i,j)=\frac{1}{\left|{\text{P}}_{ij}\right|}\sum _{k\in \text{P(}i\text{,}j)}{Q}_k$$ (2)

Simulations of the pooling–deconvolution workflow

We next sought to assess how different choices of parameters (k, t, and r) affect the performance of the pooling–deconvolution workflow. Ostensibly, smaller pools with more redundancy lead to fewer confounding effects but a larger number of experiments. Conversely, larger pools with less redundancy could be highly efficient experimentally, but risk missing highly cooperative combinations due to poisoning effects. This tradeoff can be assessed quantitatively (Fig. 2B, top) in terms of sensitivity and efficiency. We define sensitivity (S) as the expected ($\mathbb{E}$) fraction of cooperative pairs identified relative to all the cooperative pairs in the landscape (Eq. 3)⁴³:

$$S=\mathbb{\text{E}}\left[\frac{n(\text{cooperative}\text{pairs}\text{identified)}}{n\left(\text{cooperative}\text{pairs}\text{on}\text{landscape}\right)}\right]$$ (3)

Efficiency ϵ is defined as the fraction of experiments saved compared to exhaustively testing all pairs or combinations (Eq. 4), where n_pools is the number of experiments in the pooling stage and n_verif is the number of experiments in the verification phase, since both contribute non-negligible experimental cost. $\left(\begin{array}{c}N\\ 2\end{array}\right)=\frac{N(N-1)}{2}$ is the number of pairs that can be formed from N candidates.

$$ϵ=\mathbb{\text{E}}\left[1-\frac{n_{\mathit{\text{pools}}}+n_{\mathit{\text{valid}}}}{\left(\begin{array}{c}N\\ 2\end{array}\right)}\right]$$ (4)

To understand how sensitivity and efficiency trade off as the pooling parameters vary, we built an in silico pipeline to model catalytic cooperativity and to simulate pooling–deconvolution on various hypothetical cooperativity landscapes (Fig. 2B, see SI Section 3 for details). With a user-defined number of candidates N and statistical parameters for rate constants and cooperativity matrices, hypothetical cooperativity landscapes can be generated upon which pooling–deconvolution can be simulated with various combinations of (k, t, r).

We selected N = 50 for simulations, reasoning that pairwise testing of a library that size would be beyond reach of routine experimental execution (1225 pairs). Simulations were conducted with 15 scenarios with varying prevalences of positive and negative cooperativity (0.1% to 32%) (see SI Section 3.5). In even highly challenging scenarios, the pooling–deconvolution workflow generated scores that were robust against confounding effects from negative cooperativity, resulting in the successful identification of cooperative interactions across diverse cooperativity landscapes. For instance, when positive cooperativity is rare (0.1%, 1 pair) and negative cooperativity is 100-fold more prevalent (10%, 123 pairs), the workflow performs well with S = 0.63 and ϵ = 0.70, requiring only 365 reactions relative to 1225 possible pairs. When positive cooperativity is more common (1%, 10 pairs) and negative cooperativity is still prevalent (10%, 123 pairs), the same level of performance is maintained with S = 0.60 and ϵ = 0.70.

Based on these simulations, two hyperparameter sets were identified to provide the best starting points for pooling: (k, t, r) = (4, 2, 1) for rapid screening and (k, t, r) = (7, 4, 2) for more thorough pooling in challenging scenarios (see SI Section 3.5.1). Beyond these general recommendations, practitioners can run their own simulations using the pipeline described above (Fig. 2C) to identify optimal parameters (k, t, r) that balance sensitivity and efficiency for their specific number of candidates N.

Experimental validation of the pooling–deconvolution workflow

We next sought to validate the pooling–deconvolution workflow experimentally on a reaction for which cooperativity had previously been documented to enhance the reaction rate. In the catalytic enantioselective opening of 3-phenyloxetane 2a with TMSCl (Fig. 3A)^44–46, prior investigations had revealed that the application of equimolar loadings of achiral thiourea 1a and chiral squaramide 1c led to significant enhancement in rate relative to each catalyst alone while not diminishing the enantioselectivity of the product obtained with only 1c^47,48. In this validation study, we performed the reactions under more challenging and practical conditions: lower catalyst loading (1 mol %) and higher reaction temperature under ambient atmosphere (Fig. 3A). We chose a panel of N = 11 catalyst candidates 1a–1k, drawing representatives from classes of known organocatalysts (Fig. 3A).

Fig. 3. Validation of pooling–deconvolution workflow on a catalytic enantioselective oxetane opening.

(A) A chiral dual-hydrogen-bond-donor-catalyzed opening of 3-phenyloxetane 2a with TMSCl as the validation reaction and a panel of 11 candidates comprising representatives from privileged organocatalyst classes. Percentages shown are yields of 3a determined by NMR analysis. (B) Implementation of pooling–deconvolution for the oxetane opening reaction. (1) Pool design with simulation-identified parameters (k, t, r) = (4,2,1). In each pool (row), filled squares represent the inclusion of a candidate. (2) Deconvolution scores for every candidate pair based on the performance of pools and individuals. (3) Individual verification of four pairs exhibiting the highest deconvolution scores, recapitulating the expected cooperative pair of 1a and 1c.

Pooling–deconvolution was initiated by measuring the yields of individual candidates at low conversion (3 h) (Fig. 3A). Simulations with N = 11 led to the selection of (k, t, r) = (4, 2, 1) as the optimal parameter set (see SI Section 3.5.2). With small N, simulations revealed that redundancy (r > 1) was not required to achieve high sensitivity. This corresponds to a design of 11 pools of four catalysts each, which was then tested experimentally (Fig. 3B, step 1). At the pooling stage, pool 3 (candidates 1a, 1c, 1d, 1g) exhibited the highest cooperativity (Q = 0.9). Upon deconvolution, catalyst pairs (1c, 1d) and (1c, 1g) were found to have substantially lower D scores due to their presence in other low-Q pools (pools 7 and 5 respectively) (Fig. 3B, step 2). The four remaining pairs tied for the top score and were tested separately in the verification phase (Fig. 3B, step 3). The pair (1a, 1c), previously known to be cooperative, emerged as the most cooperative (Q = 2.4), affording product 4 in 60% yield and 87% ee, providing successful validation of the workflow. Under optimized conditions, this catalyst pair was shown to promote the reaction in 74% yield and 95% ee at 1 mol % loading of each catalyst, a substantial improvement in rate over the performance of the chiral catalyst alone (42% yield and 94% ee at 2 mol % 1c).

The pooling–deconvolution process required 15 experiments to identify a cooperative pair in a space of 55 possible pairs, corresponding to an efficiency of 72%. No further hits with high positive cooperativity (Q > 1.1) were found upon enumeration of every pair post facto (see SI Section 4.4), indicating that the workflow was perfectly accurate in this instance. Furthermore, these experiments revealed that 31 of the 55 pairs exhibited weak to moderate negative cooperativity, reflecting the robustness of the pooling–deconvolution process to interference when negative cooperativity is common.

Pooling–deconvolution leads to discovery of new catalytic cooperativity

Next, we sought to apply this workflow in a discovery context, wherein cooperativity was previously unknown. We selected the Pd-catalyzed decarbonylative Suzuki–Miyaura coupling between aroyl chlorides 4 and arylboronic acids 5 towards biaryls 6 (Fig. 4A, top left), a transformation for which a practical solution remains highly desirable due to the abundance of available carboxylic acid derivatives^49,50. Existing catalytic systems require stepwise separation of the decarbonylation and biaryl coupling steps, high temperatures (130–160 °C), as well as high Pd loadings of 10–15 mol %^49,50. The harsh reaction conditions reflect the high kinetic barrier to decarbonylation as well as the inherent difficulty of integrating a challenging decarbonylation step into a Suzuki–Miyaura mechanistic sequence^51–53.

Fig. 4. Deploying the pooling–deconvolution workflow to discover ligand cooperativity in a Pd-catalyzed decarbonylative Suzuki–Miyaura coupling.

(A) State-of-the-art conditions for the target cross-coupling transformation and diversity-oriented selection strategy for phosphine ligand candidate panel. (B) Implementation of pooling–deconvolution. (1) Automated pooling and high-throughput experimentation/analysis workflow based on simulation-selected parameters; (2) Deconvolution scores for every candidate pair based on the performance of pools and individuals; (3) Verification of catalyst pairs by discrete testing. The y-axis, Q(HTE), is the cooperativity of a pair tested discretely relative its constituent ligands in a small-scale, high-throughput setting. The x-axis of the plot is the rank of each pair by deconvolution score D. The purple points are the 48 points with the highest ctalculated D, whereas the yellow points are a negative control group selected randomly from the remaining pairs. (C) Validation of top cooperative hits in batch mode, with the three highest-yielding cooperative pairs shown. Q is calculated relative to the larger yield of the two individual ligands. ^†Yields were determined by quantitative ¹⁹F NMR integration. ^‡Reaction was performed with 8 mol % total phosphorus atom instead of 12 mol % total phosphorus atom.

We hypothesized that a multi-ligand approach might be viable whereby each ligand ostensibly facilitates a subset of the elementary steps⁵⁴. Guided by this motivation but without any more specific mechanistic hypothesis, we constructed a panel of 72 commercially available monodentate and bidentate phosphorus ligands by selecting diverse candidates with principal component analysis using previously published molecular descriptors (Fig. 4A, top right)^55,56. The relative number of monodentate (50) and bidentate (22) ligands that ultimately comprises the ligand panel mirrors the relative number of commercially available ligands in each reference database. The cross-coupling between 1-naphthoyl chloride 4a and 4-fluorophenylboronic acid 5a was selected as a model reaction (Fig. 4A, bottom). To present more a stringent challenge for the discovery workflow, the catalyst loading and temperature were reduced to 4 mol % and 80 °C respectively, both substantially lower relative to established protocols (Fig. 4A, bottom).

To select the optimal hyperparameter set for pooling N = 72 candidates, we performed custom simulations with N = 72 in a challenging hypothetical cooperativity scenario, which led to the identification of (k, t, r) = (6, 2, 2) (see SI Section 3.5.3). These parameters correspond to a pooling design that evaluates 2556 possible ligand pairs with 360 pools of six ligands each. While this experimental space could be in principle investigated manually, we opted for an automated, data-rich experimentation approach to maximize time and material efficiency. We employed a high-throughput workflow comprising robotic liquid handling for ligand pool construction, reaction execution in a 96-well format at 10-μmol scale, followed by ultra-high-pressure liquid chromatography (UPLC) for yield quantitation (Fig. 4B, step 1). Defining Q as the enhancement in yield relative to the maximum yield of the six ligands in each pool, the resulting pool yields were deconvoluted into a set of 2556 D scores (Fig. 4B, step 2). The 48 top-scoring pairs, together with 37 control pairs selected randomly from the remaining 2508 pairs, were then tested experimentally. While the D score does not correlate strictly with the degree of cooperativity of the individual pairs, the top-48 group was found to be enriched in highly cooperative pairs (odds ratio = 9.5) relative to the control group (Fig. 4B, step 3, see SI Section 5.4.3)⁵⁷. With 408 experiments performed relative to 2556 ligand pairs, the experimental savings corresponded to 84%.

The top six cooperative pairs were validated successfully in preparative-scale batch reactions. Three of these, when used as ancillary ligand pairs without further optimization, afforded practically useful yields (Fig. 4C) at substantially reduced catalyst loadings and temperature compared to the state of the art (see SI Section 5.4.5). These ligand combinations, which appear unexpected and unlikely to be selected solely based on “expert intuition,” now serve as starting points for ongoing methodology development and mechanistic investigations that will be reported separately. These results suggest that ligand cooperativity in Pd catalysis can be leveraged to expand the functional space of any given set of ligands^58–67, and that the empirical exploration of combinatorial ligand space with pooling–deconvolution is a valuable alternative to rational design or to serendipity^6,8.

Outlook

This work demonstrates that combining combinatorial pooling designs with simple deconvolution steps provides a systematic and experimentally tractable approach to discover catalytic cooperativity in an empirical manner. This discovery strategy is built on the well-established mathematics of covering designs and group testing without requiring any chemical information about the reaction or about each catalyst candidate. We anticipate that this approach will enable the identification of cooperative interactions whose mechanistic underpinnings may be unknown but are likely rich and complex, laying the foundation for further reaction development and mechanistic investigations. Furthermore, we envision expanding this workflow to identify ternary and higher-order cooperativity using diverse catalyst panels, including mixtures of biocatalysts, organic molecules, and transition-metal complexes—where cooperative mechanisms may differ substantially from the examples explored in this study. Overall, we are hopeful that this approach will broadly expand opportunities to discover and leverage catalytic cooperativity, ultimately enabling more efficient chemical processes.

Supplementary Material

Supplementary Information: Supplementary Information is available for this paper.

Methods and data availability:

All data are available in the main text, in the SI, and on Zenodo (https://doi.org/10.5281/zenodo.17316238).

Code availability:

All code is available on Zenodo (https://doi.org/10.5281/zenodo.17316238). In addition to a persistent version on Zenodo, the Python library developed for simulation and execution is maintained on Github under the GPL 3.0 license (https://github.com/mshyi/multicat-data).