AI-guided few-shot inverse design of HDP-mimicking polymers against drug-resistant bacteria

Data preprocessingWe made same data preprocessing to all the antibacterial activity data including MIC values as well as HC10 values. If the end point of bacterial growth had not been arrived during the experiment, the values was estimated to be the current available value. (e.g., for the experimental estimated value HC10 > 400 μg mL−1, it was seen as 400 μg mL−1). Note that natural logarithm transformation was performed to all the estimated results due to the regular values so that all the results were transformed as integers labels for corresponding properties (e.g., “12.5” was recorded as “3”, “400” was recorded as “8”). All models were trained to predict the natural logarithm of all properties.Polymer data augmentationAn important property for cationic-hydrophobic β-amino acid polymers, or more specifically for multi-component polymers is that the machine learning or deep learning model used should follow the permutation invariance of the polymer input, i.e. the results of the model should not be influenced by the order of the components, and it could be formulated as,$$\left\{\begin{array}{l}H={M}_{1}[({p}_{1},\, {r}_{1}),\, ({p}_{2},{r}_{2})]={M}_{1}[({p}_{2},\, {r}_{2}),\, ({p}_{1},\, {r}_{1})],\quad \\ S={M}_{2}[({p}_{1},\, {r}_{1}),\, ({p}_{2},\, {r}_{2})]={M}_{2}[({p}_{2},\, {r}_{2}),\, ({p}_{1},\, {r}_{1})],\quad \\ E={M}_{3}[({p}_{1},\, {r}_{1}),\, ({p}_{2},\, {r}_{2})]={M}_{3}[({p}_{2},\, {r}_{2}),\, ({p}_{1},\, {r}_{1})],\quad \end{array}\right.$$
(1)
where M1, M2, M3 were different map functions from the polymer input to corresponding properties, H, S, E were the value of MICS.aureus, MICE.coli and HC10, respectively, p, r were the polymer unit and its composition information. In the previous work47, it had been proved that by considering the permutation invariance, the model accuracy can be improved. In this way, we reasonably introduced this property as a method for data augmentation, aiming at improving the accuracy of the predictive model. Detailed, we adjusted the order of the input cationic and hydrophobic subunits and the feature orders in all representations were also changed with the same property label, so as to avoid the influence of the input order.Multi-modal random polymer representationTranslating polymers into machine readable vectors was one important problem with ongoing concerns for polymer informatics69. Different from micromolecules with deterministic topology connections of atoms and bonds, it was hard to completely represent random polymers with unregular sequence by general representation methods for micromolecules (e.g., SMILES or graphs) due to the intrinsically stochastic nature of polymers44. Generally considering, the property of a polymer was mainly decided by 1) structures of subunits and 2) subunit sequence connection, while for random polymers, the subunit ratio should be taken into consideration instead of sequence connection. In our work, we proposed a multi-modal polymer representation method from the following three perspectives:Molecular descriptorsMolecular descriptors are mathematical representation of chemicals which are generally used to build predictive models. We used an open-sourced Mordred calculator45, which included 1826 two- and three-dimensional descriptors. For cationic-hydrophobic polymers, descriptors of both the cationic and hydrophobic subunits were calculated and stacked together, totally dimensioned 3654 for candidate descriptor vector with adding composition information r1,r2 of two subunits. Then we applied a two-stage descriptor downselection strategy with a stage of statistical downselection and a stage of machine learning based downselection46. In the first stage, constant or almost constant descriptors were dropped from the initial set (Init., 3654 descriptors), and descriptors with variance larger than 10% of the mean value across the initial set were filtered out as validate set (Var., 1014 descriptors). Next, we evaluated Spearman rank correlations of each descriptor pair, and descriptors with correlation higher than 0.9 as well as correlation with the target property (MICS.aureus, MICE.coli and HC10) lower than 0.05 were filtered out as correlation set (Cor., 182, 171, 174 descriptors for MICS.aureus, MICE.coli and HC10, respectively). In the second stage, a recursive feature elimination (RFE) method70 was introduced on the Cor. descriptors set based on a random forest (RF) model. With RF regression, each descriptor was eliminated recursively according to the importance rankings until the last descriptor. Then, a 15-fold cross-validation was adopted with repeated stratified subsampling descriptors. The principle of choosing the optimized descriptor set was to choose a descriptor which has the lowest mean RMSE. In this way, descriptors with most important information related on the target property were selected. In our work, we chose 40 descriptors as the optimized molecular descriptors (Opt., 40 descriptors for MICS.aureus, MICE.coli and HC10, respectively) for part of the input of the predictive model (Results of selected descriptors are shown in Supplementary Figs. 3–8, and supplied predictive results are shown in Supplementary Fig. 9).Molecular representationsMolecular representations are another popular ways to encode molecules. In recent polymer informatics, BigSMILES is a recently developed structurally-based line notation to reflect the stochastic nature of polymer molecules44. Compared with molecular descriptors, hidden chemical information could be learned from molecular representations via a data-driven pattern. According to the syntax of BigSMILES, we developed two kinds of other rules to completely define cationic-hydrophobic β-amino acid polymers, and also these rules are universal for other random polymers.Sequence representation. Traditional SMILES strings generally consisted of various atom tokens (e.g., “C”, “O”, “[NH3+]”), bond tokens (e.g., “=”, “#”) and branching tokens (e.g., “()”, “1,2”) to encode molecules. In BigSMILES sequence, the stochastic object and the bonding descriptors were two new joined elements compared with basic SMILES grammar. We further introduced several additional definition so as the composition information of each repeated subunit in the stochastic object could be expressed, which was not included in BigSMILES. Take DM0.6BU0.4 as an example, it could be written as: {[>]NC(C)(C)C(C[NH3+])C=O.[+rn = 60], NC(CCCC)CC=O[<].[+rn = 40]}, where “[+rn = 60]” showed that the DM subunit has the ratio of 60%. “>” and “<” were two conjugate types of boding descriptors showing how repeat units were linked. For simplicity, we omitted exterior strings (since they are all same for our cationic-hydrophobic β-amino acid polymers) and we used the simplification style. Other cationic-hydrophobic polymers were defined like such. After collecting all characters involved, the one-hot encoding of the BigSMILES strings could be generated as the input. All the sequences are written manually and it is hard to be applied to large-scale datasets for further performance comparison, since there is still not mature toolkit for polymers.Graph representation. Similarly, we construct graph representation for random polymers according to the BigSMILES syntax, shown in Supplementary Fig. 10. In BigSMILES syntax, bond descriptors are introduced to specify where and how repeat units can be joined with another repeat unit. Bonding descriptors are placed on atoms of a repeat unit that could form direct bonds with another repeat unit. In BigSMILES, there are two types of bonding descriptors: one is the “$” descriptor, or AA-type descriptor, which means it can only be connected with the same descriptors; the other is the “<” and “>” descriptors, or AB-type descriptor, which means one descriptor should be connected with the conjugate descriptor. These rules are translated into our tasks to represent a cationic-hydrophobic amphiphilic β-amino acid polymer.Predictive networkWe testified the property prediction performance using various of representations and we set Morgan fingerprints, which was widely used in polymer property prediction35, as baseline. In this study, we mainly used the following combinations according to three proposed multi-modal representations with properly designed network structures for specific tasks71,72: 1) Descriptor vector (from Descriptor_Init to Descriptor_Opt), 2) Sequence vector, 3) Graph vector, 4) Sequence vector and Descriptor vector (Seq+Descriptor_Opt), 5) Graph vector and Descriptor vector (Graph+Descriptor_Opt), 6) Sequence vector, graph vector and Descriptor vector (Seq+Graph+Descriptor_Opt). Noted that we used the optimized descriptors for fusing since they had reached better model performance.Network architecturesFor situation 1), we transformed the descriptor feature Ff by subtracting the means and dividing by the standard deviations as normalization process and we simply trained a Fully-connected Feed-forward Neural Network (FFN) for prediction. The dimensionality of the input feature Fj is [B, ND] and the dimensionality of the input layer of FNN is [ND, Df], where B is the number of batch size, ND is the number of descriptors used and Df is the dimensionality of the hidden layers in FNN. For 2), we used the bidirectional Gate Recurrent Unit (GRU)73,74 to extract the hidden information embedded in Sequence vector, and can be formulated as,$$\left\{\begin{array}{l}\overrightarrow{{h}_{k}}=\overrightarrow{{{{{{\bf{GRU}}}}}}}({t}_{k},\, \overrightarrow{{h}_{k-1}}),\quad \\ \overleftarrow{{h}_{k}}=\overleftarrow{{{{{{\bf{GRU}}}}}}}({t}_{k},\, \overleftarrow{{h}_{k-1}}),\quad \end{array}\right.$$
(2)
where tk was the token embedding, and \(\overrightarrow{{h}_{k}},\, \overleftarrow{{h}_{k}}\) were bidirectional hidden states for the kth token of a string embedded by GRU, and the current hidden state hk was obtained as,$${h}_{k}=(\overrightarrow{{h}_{k}},\, \overleftarrow{{h}_{k}}).$$
(3)
Finally, we used Fs to denote the contextual representation of a sequence string with length n as,$${F}_{s}=({h}_{0},\, {h}_{1},\cdots \,,\, {h}_{n}).$$
(4)
The dimensionality of the input sequence vector is [B, n] and the dimensionality of the sequence embedding is [n,Ds], where B is the number of batch size, n is the number of each input sequence and Ds is the dimensionality of the hidden layers in GRU. The final dimensionality of the sequence feature Fs is [B,Ds].For 3), we apply a Bidirectional Message Communication GNN75, which makes full use of the node message for more effective message interactions to extract the local information embedded in the graph. The network structures can be seen in Supplementary Fig. S11 and the pseudocode of the model were concluded in Supplementary Information as Algorithm 1.Specifically, the input of the algorithm is each polymer graph G=\(({{{{{\mathcal{V}}}}}},\, {{{{{\mathcal{E}}}}}})\) and all of its atom attributes xv(\(\forall v\in {{{{{\mathcal{V}}}}}}\)) and bond attributes \({x}_{{e}_{vw}}\)(\(\forall {e}_{vw}\in {{{{{\mathcal{E}}}}}}\)). The initial node feature \({h}_{v}^{0}\) is simply the atom attributes, while the initial edge feature \({h}_{{e}_{vw}}^{0}\) is the bond attributes. Then, according to the network depth T, a T steps message aggregation and update procedure is applied. In each step t, each node message vector \({m}_{v}^{t+1}\) is aggregated according to its incoming edges and each edge message vector \({m}_{{e}_{vw}^{t+1}}\) is aggregated according to its neighbor nodes, shown as,$$\left\{\begin{array}{ll}{m}_{v}^{t+1}={{{{{\bf{MAX}}}}}}({h}_{{e}_{uv}}^{t})\odot {{{{{\bf{SUM}}}}}}({h}_{{e}_{uv}}^{t}),\, u\in {{{{{\mathcal{N}}}}}}(v),\\ {m}_{{e}_{vw}}^{t+1}={{{{{\bf{MEAN}}}}}}({h}_{v}^{t},\, {h}_{w}^{t}),\hfill\end{array}\right.$$
(5)
where MAX, SUM, MEAN are the corresponding aggregating strategy, ⊙ is an element-wise multiplication operator. Then the obtained message vectors of node and edge \({m}_{v}^{t+1}\),\({m}_{{e}_{vw}}^{t+1}\) are concatenated with the corresponding current hidden states to be sent to the communicate function which use an addition operator as communicative kernel to calculate the communicative vector \({p}_{v}^{t+1}\),\({p}_{{e}_{vw}}^{t+1}\). Then the hidden state of the node and edge are updated with skip connection as,$$\left\{\begin{array}{ll}{h}_{v}^{t+1}={U}_{v}^{t}({p}_{v}^{t+1},\, {h}_{v}^{0})={{{{{\bf{ReLU}}}}}}({h}_{v}^{0}+{{{{{{\bf{W}}}}}}}_{{{{{{\bf{v}}}}}}}\cdot {p}_{v}^{t+1}),\hfill \\ {h}_{{e}_{vw}}^{t+1}={U}_{e}^{t}({p}_{{e}_{vw}}^{t+1},\, {h}_{{e}_{vw}}^{0})={{{{{\bf{ReLU}}}}}}({h}_{{e}_{vw}}^{0}+{{{{{{\bf{W}}}}}}}_{{{{{{\bf{e}}}}}}}\cdot {p}_{{e}_{vw}}^{t+1}),\end{array}\right.$$
(6)
where ReLU is the rectified linear unit and Wv, We are learned matrices. After T step iteration, a GRU based readout function is applied to the final node representation \({h}_{v}^{T}\) to get the graph-level representation Fg as,$${F}_{g}={{\sum}_{v\in {{{{{\mathcal{V}}}}}}}}{{{{{\bf{GRU}}}}}}({h}_{v}^{T}).$$
(7)
The dimensionality of the input atom vector and bond vector in graph are [B, Nv, Fv] and [B, Ne, Fe], and the dimensionality of the atom embedding and bond embedding in Bidirectional Message Communication GNN are [Fv, Dg] and [Fe, Dg], where B is the number of batch size, Nv, Ne are the atom number and bond number in each input molecular graph, Fv and Fe are the number of attributes for each atom and bond and Dg is the dimensionality of the hidden layers in GNN. The final dimensionality of the graph feature Fg is [B, Dg]. For 1)-3), the network structures can be seen in Supplementary Fig. 11.Since 4), 5) and 6) involved multiple polymer vectors, we developed a multi-modal polymer representation method with adjustable network blocks for specific representations. A core motivation was how to learn more abundant chemical information from limited data points and how to find connections and differences between information in diverse representations. From feature descriptors, various basic chemical or calculated information could be gained. In contrast, from sequence or graph representations, distributions of atoms and bonds on spatial and numerical were explicitly displayed, while more implicit information, which might not be calculated through a specific equation, was generally learned with the help of data-driven deep learning. Since the available data are very limited, to learn better polymer feature for few-shot prediction, we tempted to merge various representations which is one of the main contributions of our work.The main structure included several customized representation learning blocks to extract implicit information from various representations (descriptors, sequence and graph here), and this process could be formulated as,$${F}_{j}={{{{{\bf{Combine}}}}}}({F}_{f},\, {F}_{s},\, {F}_{g}),$$
(8)
where Combine was the function to assemble different representations with adding and stacking, and Fj was the joint feature by stacking all the vector features with the dimensionality of [B, Dj], Dj = D + ND (D = Df = Ds = Dg). According to the different input representations in 4), 5) and 6), different blocks are inserted as shown in Supplementary Fig. 12.Then a Transformer-based feature combination block was built with the input of Fj. The Transformer had been proved as a powerful model on various fields through its power on extracting comprehensive information. To find connections between the learned implicit information from Sequence and Graph representation and the explicit information embedded in descriptors, we further used descriptors Ff as the attention bias in the self-attention mechanism, and this process could be formulated as:$$Q={F}_{j}{W}_{Q},\, K={F}_{j}{W}_{K},\, V={F}_{j}{W}_{V},$$
(9)
$${{{{{\bf{Attention}}}}}}({F}_{j})={{{{{\bf{softmax}}}}}}(Q{K}^{\top }/\sqrt{{d}_{K}}+{F}_{f})V,$$
(10)
where WQ, WK, WV were the corresponding projecting matrices of Q (query), K (keys), V (values), dK was the dimension of keys, Attention was the self-attention mechanism in Transformer and softmax was the softmax function. With the calculation of the Transformer block and feedforward network (FNN) block, we got the final predictions of the properties with the dimensionality of [B,1],$$P={{{{{\bf{FNN}}}}}}({{{{{\bf{Transformer}}}}}}({F}_{j},\, {F}_{f})).$$
(11)
Predictive model training settingsWe randomly split the training data Dtrain_aug into 8:1:1 train/valid/test ratios and we applied bayesian optimization to find the optimal hyper-parameters. Then we used the optimized parameters to retrain the model for 10 independent runs with different random seeds. Specifically, a dynamic changed learning rate was used with the Adam optimizer with mean squared error (MSE) loss to train the model. We set an initial learning rate as 10−4 and it would be doubled as a max learning rate in 5 warm up training epochs, and finally the learning would return the 10−4 as a final value. The training epoch and the batch size were set as 100 and 16 respectively. In each epoch, if the validation MSE reduced, the model would be saved. The parameters of each block of GNN, GRU, Transformer and FNN were all recorded in Supplementary Table 2. In addition, since the operation of random data splitting would cause uneven distribution of training data, we applied the ensembling technique, which is a common technique in machine learning. Multiple independently trained models with different random seeds were combined to produce an averaging predictions so as to prevent overfitting on partial results. After training, the unseen testing data Dtest was used to evaluate the performance of the model, using the R-squared coefficient (R2, higher R2 means better performance of the model) and root-mean-squared error (RMSE, lower RMSE means better performance of the model) as metrics. The implementation of the model relies on Pytorch and RDKit package.Scaffold-decorator generative networkTake the hydrophobic subunit “BU” as an example, its SMILES string was “NC(CCCC)C C=O”, which could also be seen as that a side chain “[*]CCCC” was decorated to the scaffold “NC([*])CC=O”, where “[*]” was the special attachment token for substitution. For scaffold with more than one substitution, a symbol “∣” was introduced to differentiate decorations76. Therefore, the core problem of polymer design could be transformed as finding the optimized decoration for the specific scaffold to formulate subunits for polymer with desirable properties. We summarized the whole designing procedure in two stages. Firstly, we pre-trained a GRU-based molecular scaffold-decorator with the ability of generating valid subunits. Secondly, a reinforcement learning fine-tuning stage was adopted to explore the chemical space for optimal polymers. When fine-tuning, each reasonable molecule would be recorded for the convenience of final analysis and evaluation.Network architecturesThe implementation of scaffold-decorator network was totally an encoder-decoder architecture with attention mechanism. The encoder was a bidirectional RNN sequenced with an embedding layer and three layers of bidirectional GRU cells of 256 dimensions. Then the hidden states were sent to the decoder, which was a single direction RNN sequenced with an embedding layer, three layers of GRU cells of 256 dimensions. Finally, an global attention layer as adopted to sum up the output of the encoder and the decoder, and a liner layer was connected to calculate the probability of each possible token xi. The model was trained to maximize the Negative Log-Likehood (NLL) loss written as:$$\,{{\mbox{NLL}}}\,({{{{{\bf{S}}}}}})=-{{\sum}_{i=1}^{n}}\log P({x}_{i}| {x}_{ < i},\,{{\mbox{scaffold}}}),$$
(12)
where P(xi∣x<i) was the probability when sampling the ith token of decoration sequence S with given the previous tokens and the input scaffold.Graph grammar distillationA direct idea was that the subunits for which we would like to explore had similar structures thus these structures must distributed closely in the huge chemical space (Supplementary Fig. 24). Generally, our β-amino acids have similar structures with natural α-amino acids. However, if we pre-training our model with large-scale public data, those rules for constructing complex structures or undesirable chemical elements (e.g., Br,Cl) may also be embedded in the model. Thus, it takes a long time for further RL fine-tuning to adjust the parameters to avoid generating those subunits. Thereby, we first collected all cationic and hydrophobic β-amino acids in our data and several natural α-amino acids structures (Supplementary Fig. 23). Then, we used a hyper-graph based data-efficient graph grammar learning method (DEG)77 to collect various graph grammar rules from the given amino acids. Thus, various grammar rules were learned automatically from the training data, and specific rules could be learned according to the given data if needed. By doing so, we extracted grammar knowledge and we recombined these grammar to construct a distilled set of molecules. Then, we similarly used the RECAP rules to slice molecules, gaining 0.3 million pairs of scaffold-decoration data. We took these data to pre-train a generative model with the same structures above and constructed a more-focused chemical space embedded in the model for further exploration, so as to accelerate the search efficiency under multi constraints for RL agent.Reinforcement learningTo further guide our generative model pre-trained by graph grammar distillation toward relevant areas in chemical space according to customized requirements, we adopted REINVENT 2.078. It is a recently developed reinforcement learning method for de novo drug design, for fine-tuning to carry out a constellation of specific tasks of design. By fine-tuning, various user-defined requirements could be satisfied to generate molecules of interest. In our cases, we realized the following requirements: 1) polymer generation under various scaffold subunit structures (e.g., “NC([*])CC=O”, “NCC(C=O)1[*]C1”, “NC1[*]C1C=O”), 2) polymer generation under multi-objective constraints (e.g., carbon numbers, ring number and MICS.aureus/MICE.coli/HC10 thresholds).The main roles in REINVENT 2.0 included a prior model MPrior, an agent model MAgent and a score modulating block. The prior model was the pre-trained scaffold-decorator generative model introduced above, while the agent model shared the identical network structures and the initialization parameters of the agent model as completely the same as the prior model. The score modulating block could be regarded as the environment which fed back rewards according to the targeted scoring functions.Then we introduced the reinforcement learning cycle. First, the agent model Magent sampled batch of SMILES decorations for a specific scaffold, and the decorated polymer were scored according to the scoring function \({S}_{{{{{{\rm{score}}}}}}}\) (introduced in Eq. (15)). Among each course of sampling molecules, the agent chose the next possible token, seen as the action Aaction, according to the current token sequence, regarded as the state Sstate in the RL framework. Thus, the agent learned a conditional probability p(A∣S) to generate the desired molecules when the episodes go on. To train the agent model, we used the NLL, similar to Eq. (12), to represent the agent likelihood of the generated decoration sequence S as NLL(S)Agent. Then S would be given to the prior model MPrior to calculate the augmented likelihood with the score \({S}_{{{{{{\rm{score}}}}}}}({{{{{\bf{S}}}}}})\). Ultimately, the loss of the agent could be calculated as:$$\,{{\mbox{NLL}}}\,{({{{{{\bf{S}}}}}})}_{{{{{{\rm{Augmented}}}}}}}=\,{{\mbox{NLL}}}\,{({{{{{\bf{S}}}}}})}_{{{{{{\rm{Prior}}}}}}}-\sigma {S}_{{{{{{\rm{score}}}}}}}({{{{{\bf{S}}}}}}),$$
(13)
$$\,{{\mbox{loss}}}\,={[{{\mbox{NLL}}}{({{{{{\bf{S}}}}}})}_{{{{{{\rm{Augmented}}}}}}}-{{\mbox{NLL}}}{({{{{{\bf{S}}}}}})}_{{{{{{\rm{Agent}}}}}}}]}^{2},$$
(14)
where σ was the scalar value to scale up the output of the score function. During the training process, we collected all valid generated molecules for data analysis, and molecules with desired properties would be further filtered out for experimental validation.Generative model training settingsFor the graph grammar distillation pre-training process, the training epoch, batch size and the learning rate were set as 450, 256 and 10−3 respectively. The dimensionality of hidden layers of GRU was set as 256. For the reinforcement learning fine-tuning process, the training epoch, batch size and the learning rate were set as 450, 30 and 10−9 respectively. Also, we use the negative log likelihood (NLL) loss to train the model and the implementation of the model relies on Pytorch and RDKit package. All hyperparameters are concluded in Supplementary Table 5.Score and metricIn this study, we aimed to find more potential cationic and hydrophobic subunit combinations with specific composition rations, which satisfied the desired properties: MICS.aureus < 25, MICE.coli > 25 and HC10 > 100. Moreover, we designed several penalty rules or customized constraints to accelerate the learning process with narrowing down the scope of exploration. The final score function \({S}_{{{{{{\rm{score}}}}}}}({{{{{\bf{S}}}}}})\), which could also be seen as the reward in RL, was written as:$${S}_{{{{{{\bf{score}}}}}}}({{{{{\bf{S}}}}}})={S}_{{{{{{\rm{property}}}}}}}({{{{{\bf{S}}}}}})+{S}_{{{{{{\rm{penalty}}}}}}}({{{{{\bf{S}}}}}})+{S}_{{{{{{\rm{constrain}}}}}}}({{{{{\bf{S}}}}}}),$$
(15)
where Sproperty, Spenalty, Sconstrain were three different parts of target activities, penalty of irrationality and customlized constraints for scoring.Property scoreWe used the previously trained predictive network to calculate the value of MICS.aureus, MICE.coli and HC10 respectively. For all the calculated values, we applied score transformations (sigmoid for HC10 and reverse sigmoid for MICS.aureus and MICE.coli) so that each component returned a value between [0,1] (the higher the better). This operation helped to avoid one-sided impacts of single-properties and adjust the influence of multi-parameter objectives, and the property scoring function could be written as:$${S}_{{{{{{\rm{property}}}}}}}({{{{{\bf{S}}}}}})=a * {{{\mbox{MIC}}}}_{S. \, aureus}({{{{{\bf{S}}}}}})+b * {{{\mbox{MIC}}}}_{{{{{E.}}}}\, {{{{coli}}}}}({{{{{\bf{S}}}}}})+c * {{\mbox{}}}{{{{{{\rm{HC}}}}}}}_{10}{{\mbox{}}}({{{{{\bf{S}}}}}}),$$
(16)
where a, b and c were adjustable weights showing that which the agent should put more focus on. They were decided by customized design demands. In this work, we focused more on the antimicrobial activity and hence, we set a larger value for a = b = 2 than c = 1.Penalty scoreTo improve the rationality and correctness of the generated molecules, we designed several structural penalties as the penalty scoring function,$${S}_{{{{{{\rm{penalty}}}}}}}({{{{{\bf{S}}}}}})=\left\{\begin{array}{l}-5,\, {{\mbox{ when molecule is invalid}}} \,,\hfill \quad \\ -3,\, {{\mbox{ when unexpected elements exist}}} \, .\quad \end{array}\right.$$
(17)
Constrain scoreTo further constrain the structures of the generated molecules, we also designed several constraints which can be used alternatively,$${S}_{{{\rm{constrain}}}}({{{\bf{S}}}})=\left\{\begin{array}{ll}C/2,\quad &{C}_{{{\rm{number}}}} \, \le \, X,\\ -2,\quad &{C}_{{{\rm{number}}}} \, > \, X,\\ \end{array}\right.+\left\{\begin{array}{ll}-3,\quad &R \, > \, Y,\\ 0,\quad &R \, \le \, Y,\end{array}\right.$$
(18)
where Cnumber was the carbon number of the final decorated molecule, R was the ring number and X, Y were adjustable constants to decide how many carbon atoms or how many circles should be generated. As discussed before, to prove the rationality of the generated polymers, we set X = 11 and Y = 1 in our exploration settings to prove the toxicity without chemical structural rationality.Evaluation settingsTo exactly find new candidate polymers with desired properties, we set three situations to evaluate the performance of the generative model pre-trained by graph grammar distillation. It is worth noting that in all situations, we fixed the cationic monomer as DM and MM structures and focused on designing new hydrophobic monomers. This helped to improve the synthetic possibility for final validation. Even new cationic monomers were not taken into consideration. It was still a challenging problem since there still existed multi-constraints (structures, properties etc.) and should be taken into consideration to adjust hydrophobic subunits. Details are outlined below: Task 1: Cationic: DM/MM, hydrophobic: any scaffold, reward design:$${S}_{{{{{{\rm{score}}}}}}}({{{{{\bf{S}}}}}})=2 * {{{\mbox{MIC}}}}_{S.aureus}({{{{{\bf{S}}}}}})+{S}_{{{{{{\rm{penalty}}}}}}}({{{{{\bf{S}}}}}}).$$
(19)
Task 2: Cationic: DM/MM, hydrophobic: any scaffold, reward design:$${S}_{{{{{{\rm{score}}}}}}}({{{{{\bf{S}}}}}})= 2 * {{{\mbox{MIC}}}}_{S. \, aureus}({{{{{\bf{S}}}}}})+2 * {{{\mbox{MIC}}}}_{{{{{E. \, coli}}}}}({{{{{\bf{S}}}}}})\\ +1 * {{\mbox{}}}{{{{{{\rm{HC}}}}}}}_{10}{{\mbox{}}}({{{{{\bf{S}}}}}})+{S}_{{{{{{\rm{penalty}}}}}}}({{{{{\bf{S}}}}}})+{S}_{{{{{{\rm{constrain}}}}}}}({{{{{\bf{S}}}}}}),$$
(20)
where X = 11, Y = 1. Task 3: Cationic: DM, hydrophobic: NC([*])C C(=O), reward design:$${S}_{{{{{{\rm{score}}}}}}}({{{{{\bf{S}}}}}})= 1 * {{{\mbox{MIC}}}}_{S. \, aureus}({{{{{\bf{S}}}}}})+1 * {{{\mbox{MIC}}}}_{{{{{E. \, coli}}}}}({{{{{\bf{S}}}}}})+3 * {{\mbox{}}}{{{{{{\rm{HC}}}}}}}_{10}{{\mbox{}}}({{{{{\bf{S}}}}}}) \\ +{S}_{{{{{{\rm{penalty}}}}}}}({{{{{\bf{S}}}}}})+{S}_{{{{{{\rm{constrain}}}}}}}({{{{{\bf{S}}}}}}),$$
(21)
where X = 11, Y = 1.Task 1 was designed to evaluate the performance of the model pre-trained by graph grammar distillation and the model pre-trained by ChEMBL. Task 2 referred to analysis the distributions of the generated polymers with evaluations by the predictive model, aiming at further find the desirable area with more possible optimal candidates under multiple-constrains. Following the results in Task 2, we made further qualifications on a specific scaffold structure, aiming exploring more candidate polymer with specific scaffold for real-work synthesis, as Task 3. Note that we defined a high weight for HC10 which was mainly due to the fact that for polymers with a fixed DM subunit, most polymers showed undesirable property on HC10 and we gave more weights on it.MaterialsAll chemical reagents and solvents were used without further purification. Anhydrous dichloromethane (DCM) and anhydrous Tetrahydrofuran (THF) were purchased from Sigma-Aldrich. Ethyl acetate (EtOAc) and other solvents were purchased from Shanghai Titan Technology Co., Ltd. Synthesized chemicals were purified using a SepaBean machine equipped with Sepaflash columns produced by Santai Technologies Inc in China. The water used in these experiments was obtained from a Millipore water purification system with a resistivity of 18.2 MΩ.cm. 3-(4,5-Dimethylthiazol-2-yl)-2,5-diphenyltetrazolium bromide (MTT) was purchased from MACKLIN regent, Shanghai. Dulbecco’s modified Eagle medium (DMEM) were purchased from Hyclone (USA).Cell linesHuman umbilical vein endothelial cell line (HUVEC) and the African green monkey kidney fibroblasts (COS7) cells were obtained from the Cell Bank of the Chinese Academy of Sciences (Shanghai, China).MeasurementsNuclear magnetic resonance (NMR) spectra were collected on a Bruker spectrometer at 400 MHz using CDCl3 as the solvent and 600 MHz using D2O as the solvent. The corresponding chemical shifts were referenced to residual protons in the deuterated NMR solvents. High resolution electrospray ionization time-of-flight mass spectrometry (HRESI-MS) was collected on a Waters XEVO G2 TOF mass spectrometer. Gel permeation chromatography (GPC) was performed on a Waters GPC instrument equipped with a refractive index detector (Waters 2414) using dimethylformamide (DMF), supplemented with 0.01 M LiBr, as the mobile phase at a flow rate of 1 mL min−1 at 50 °C. The GPC were equipped by a Tosoh TSKgel Alpha-2500 column (particle size 7 μm) and a Tosoh TSKgel Alpha-3000 column (particle size 7 μm) linked in series. Relative number-average molecular weight (Mn), degree of polymerization (DP) and dispersity index (D) were calculated from a calibration curve using polymethylmethacrylate (PMMA) as standards. Before GPC characterization, all samples were filtered through 0.22 μm polytetrafluoroethylene (PTFE) filters. Optical density (OD) value and fluorescence value were recorded on a multifunction microplate reader (SpectraMax M2).Synthesis of β-lactams(±)-3-tert-Butyloxycarbonylaminomethyl-4,4-dimethyl azetidin-2-one (3, β-lactam DM, Supplementary Fig. 57) was synthesized by following previously reported procedure43. Briefly, 3,3-Dimethylallyl bromide (15.0 g, 0.1 mol) and potassium phthalimide (20.4 g, 0.11 mol) potassium phthalimide was mixed in 300 mL DMF. The reaction mixture was stirred vigorously at room temperature for 16 h and then poured into 800 mL ice water with vigorous stirring to result precipitate. The precipitate was collected by filtration and washing with ethanol to give the crude product. After removing the solvent under vacuum, the intermediate compound 1 (Supplementary Fig. 57) was directly used without purification (20.0 g, 93.0%). 1H NMR (400 MHz, CDCl3, Supplementary Fig. 58): δ 7.90-7.78 (m, 2H), 7.72-7.66 (m, 2H), 5.27 (dt, J = 7.2, 1.2 Hz, 1H), 4.5 (d, J = 7.2 Hz, 2H), 1.83 (s, 3H), 1.70 (s, 3H). HRESI-MS (Supplementary Fig. 59): m/z calculated for C13H14NO2 [M+H]+: 216.1025; Found: 216.1024.To a solution of the intermediate compound 1 (20.0 g, 0.093 mol) in dichloromethane (50 mL) was added chlorosulfonyl isocyanate (10.4 mL, 0.11 mol) under N2 atmosphere. The reaction mixture was stirred for 30 min at 0 °C and then warmed up to room temperature for 72 h. Then the reaction mixture was poured into a suspension of Na2SO3 (41.6 g, 0.33 mol) and Na2HPO4 (46.9 g, 0.33 mol) in water (800 mL) and was stirred for 12 h. The aqueous phase was extracted with dichloromethane (3 × 500 mL). The organic phase was combined and then dried over anhydrous magnesium sulfate and concentrated under vacuum to give the crude product. The crude product was purified by recrystallization from ethyl acetate and hexane to afford maleimide-protected DM (compound 2, Supplementary Fig. 57) as white solid (14.6 g, 60.8%). 1H NMR (400 MHz, CDCl3, Supplementary Fig. 60): δ 7.89-7.81 (m, 2H), 7.77-7.67 (m,2H), 6.00 (br, 1H), 4.09 (dd, J = 8.0, 14.0 Hz, 1H), 3.91 (dd, J = 8.0, 14.0 Hz, 1H), 3.41 (t, J = 8.0 Hz, 1H), 1.47 (s, 3H), 1.45 (s, 3H). HRESI-MS (Supplementary Fig. 61): m/z calculated for C14H15N2O3 [M+H]+: 259.1083; Found: 259.1084.To a solution of above compound 2 (14.6 g, 56.5 mmol) in methanol (200 mL) was added a solution of hydrazin hydrate (80% solution in water, 14 mL). The reaction mixture was stirred at 70 °C for 12 h to result precipitate. After removing the precipitate by filtration, the filtrate was coevaporated with toluene (3 × 200 mL) for removing the residual hydrazine hydrate. The residue, di-tert-butyl dicarbonate (Boc2O, 24.6 g, 113.0 mmol) and triethylamine (15.3 mL, 113.0 mmol) were mixed in 500 mL methanol. The reaction mixture was refluxed for 6 h. After filtration, the solvent was concentrated under vacuum to give the residue. The residue was dissolved in dichloromethane (200 mL) and then washed sequentially with hydrochloric acid solution (1 N), sodium hydroxide solution (1 N) and brine (200 mL). The organic phase was dried over anhydrous magnesium sulfate and then concentrated under vacuum to give the crude product, which was directly purified by column chromatography to obtain β-Lactam DM (compound 3, Supplementary Fig. 57) as white solid (9.7 g, 75.2%). 1H NMR (400 MHz, CDCl3, Supplementary Fig. 62): δ 5.9 (s, 1H), 4.9 (s, 1H), 3.66-3.56 (m, 1H), 3.28 (t, J = 10.2 Hz, 1H), 2.97 (t, J = 7.8 Hz, 1H), 1.45 (s, 3H), 1.43 (s, 9H), 1.37 (s, 3H). 13C NMR (100 MHz, CDCl3, Supplementary Fig. 63): δ 169.01, 155.79, 79.58, 58.24, 54.80, 37.07, 28.62, 28.37, 22.86. HRESI-MS (Supplementary Fig. 64): m/z calculated for C11H20N2NaO3 [M+Na]+: 251.1372; Found: 251.1371.4-(2-methylpropyl)azetidin-2-one (compound 4, β-lactam iPen, Supplementary Fig. 57) was synthesized according to the method reported in previous literature66. Briefly, to a solution of 5-Methyl-1-hexene (3.5 g, 35.6 mmol, 1.0 equiv.) in dichloromethane (10 mL), chlorosulfonyl isocyanate (3.3 mL, 37.4 mmol, 1.05 equiv.) was added at 0 °C under N2 atmosphere. The reaction mixture was stirred for 3 days at room temperature then monitored by thin layer chromatography (TLC). The reaction was quenched via carefully transferring into the buffer (200 mL) consisting of anhydrous sodium sulfite (13.5 g, 106.8 mmol, 3.0 equiv.) and disodium hydrogen phosphate (15.2 g, 106.8 mmol, 3.0 equiv.), the mixture was stirred for overnight and extracted with dichloromethane (3 × 100 mL), then the organic layer was combined and dried over anhydrous MgSO4. After removing the solvent under vacuum, the crude product was purified by silica gel column chromatography to afford β-lactam iPen (compound 4) as colorless oil (2.1 g, 41.7% yield). 1H NMR (400 MHz, CDCl3, Supplementary Fig. 65): δ 6.06 (s, 1H), 3.60-3.54 (m, 1H), 3.04 (ddd, J = 14.8, 4.8, 2 Hz, 1H), 3.04 (dq, J = 14.8, 1.2 Hz, 1H), 1.69-1.49 (m, 3H), 1.26-1.10 (m, 2H), 0.89 (d, J = 6.8 Hz, 6H). 13C NMR (100 MHz, CDCl3, Supplementary Fig. 66): δ 168.87, 48.22, 43.09, 35.07, 33.14, 27.70, 22.34. HRESI-MS (Supplementary Fig. 67): m/z calculated for C8H15NNaO [M+Na]+:164.1051; Found 164.1053.Synthesis of β-amino acid polymersAll polymerizations of β-lactams were carried in nitrogen-regulated glove box at room temperature. Initiator (tBuBzCl), β-lactams (DM and iPen) and the base catalyst LiHMDS were dissolved in dry THF to a concentration of 0.2 M respectively. The positive charge and hydrophobic composition of β-amino acid polymers was controlled by the initial feed ratio of tBuBzCl: DM: iPen. Briefly, 2 mL β-lactams with different volume ratios of DM: iPen were mixed, after adding 100 μL tBuBzCl solution in THF and 300 μL LiHMDS in THF into the mixture sequentially, the reaction mixture was stirred for 12 h. When the polymerization reaction was completed, the reaction mixture was poured into cold petroleum ether (PE, 45 mL) to precipitate out the crude product as a white solid, followed by centrifugation (2810 g) to remove the solvent. The crude product was dissolved in 2 mL THF followed by pouring cold petroleum ether (45 mL) to precipitate out the crude product. The N-Boc protected polymers were purified by dissolution-precipitation process using THF/PE (2 mL/45 mL) three times and vacuum drying for overnight to give a white solid. The number-average molecular weight (Mn) and polydispersity index (D) were characterized by GPC using N, N-dimethylformamide (DMF) as the mobile phase.N-Boc protected polymers were dissolved in trifluoroacetic acid (2 mL). Then the mixture was under shaking for 2 h at room temperature. After removing the solvent under a nitrogen flow, the residue was dissolved in methanol (1 mL), followed by addition of cold MTBE (45 mL) to precipitate out the crude polymers. The crude polymers were purified by three times of dissolution-precipitation process using methanol/MTBE (1 mL/45 mL) and vacuum drying for overnight. The purified polymers were dissolved in Milli-Q water and lyophilized to obtain a white powder in the form of TFA salt (>80.0% yield), which was further characterized by 1H NMR and used for antibacterial assay.Minimum inhibitory concentration (MIC) assay11 strains of gram positive and negative bacteria were respectively cultured in Luria-Bertani (LB) medium for 9 h at 37 °C under shaking at 200 rpm. After centrifugation at 4000 rpm for 5 min, the bacteria in the culture medium were collected and re-suspended in Mueller-Hinton (MH) medium to 2 × 105 CFU mL−1 as the working suspension. The deprotected polymer DMxiPeny libraries were respectively diluted to concentrations ranging from 3.13 μg mL−1 to 400 μg mL−1 by a two-fold gradient dilution in a 96-well plate. After mixing equal volumes of bacterial cells suspension (50 μL) and DMxiPeny solution (50 μL) in each well, the 96-well plates were incubated at 37 °C for 9 h to collect OD values on a SpectraMax®M2 plate reader. MH medium was used as the blank; bacteria in MH medium was used as positive control. The percentage of bacterial cells survival was calculated from the equation below:$$\,{{\mbox{Cell growth}}}\,(\%)=\frac{{{{{{{\rm{OD}}}}}}}_{600}^{{{{{{\rm{polymer}}}}}}}-{{{{{{\rm{OD}}}}}}}_{600}^{{{{{{\rm{blank}}}}}}}}{{{{{{{\rm{OD}}}}}}}_{600}^{{{{{{\rm{control}}}}}}}-{{{{{{\rm{OD}}}}}}}_{600}^{{{{{{\rm{blank}}}}}}}}\times 100.$$
(22)
The MIC value was defined as the lowest concentration of an antimicrobial agent to completely inhibit microbial growth. Measurements were performed in duplicates, and the experiments were repeated at least twice.Hemolysis assayFresh human blood was washed with Tris-buffered saline (TBS, pH = 7.2) for three times and the collected human red blood cells (hRBCs) were diluted to 5% (v/v) with TBS to obtain working suspension. DMxiPeny solution were diluted to concentrations ranging from 3.13 to 400 μg mL−1 by a two-fold gradient dilution in a 96-well plate. After mixing an equal volume of hRBCs suspension and DMxiPeny solution, 96-well plates were incubated at 37 °C for 1 h. TBS was used as the blank, the mixture of Triton X-100 (0.1% in TBS) and hRBCs was used as the positive control. After centrifugation, 80 μL of the supernatant in each well was transferred to another 96-well plate and the optical density (OD) value was collected at 405 nm. The percentage of hemolysis was calculated from$$\,{{\mbox{hemolysis}}}\,(\%)=\frac{{{{{{{\rm{OD}}}}}}}_{405}^{{{{{{\rm{polymer}}}}}}}-{{{{{{\rm{OD}}}}}}}_{405}^{{{{{{\rm{blank}}}}}}}}{{{{{{{\rm{OD}}}}}}}_{405}^{{{{{{\rm{control}}}}}}}-{{{{{{\rm{OD}}}}}}}_{405}^{{{{{{\rm{blank}}}}}}}}\times 100.$$
(23)
The HC50 was defined as the concentration of a compound to cause 50% hemolysis. Measurements were performed in triplicate. The experiments were repeated three times independently.All sourced blood for hemolysis assays were donated by the Shanghai RuiJin Rehabilitation Hospital before the blood is disposed as scheduled and no recruitment information was supplied to the researchers of this project as per the agreement with University of East China University of Science and Technology Human Ethics Approval, therefore recruitment information are unknown.Cytotoxicity assayThe cytotoxicity of β-amino acid polymers was studied using MTT assay. Specifically, COS-7 and HUVEC cells were respectively incubated in Dulbecco’s Modified Eagle’s Medium (DMEM) containing FBS (10%) and penicillin/streptomycin (1%) at 37 °C in a humidified atmosphere containing 5 °C CO2. Cells were seeded in a 96 well plates at 5000 cells in 100 μL DMEM medium for each well and the plates were incubated at 37 °C in a humidified atmosphere containing 5% CO2 for 24 h. Different concentrations of DMxiPeny solution ranging from 400 μg mL−1 to 3.13 μg mL−1 were prepared and added to HUVEC and COS-7 cells, respectively. The plates were incubated for another 48 hours. An aliquot of 10 μL MTT solution (5 mg mL−1) in phosphate buffered saline (PBS) was added in each well and the plate was incubated for 4 h. After removing the supernatant, 150 μL DMSO was added in each well and then the plate was shaken for 15 min before measuring the absorbance at 570 nm on a microplate reader. The untreated cells were used as positive control, DMEM solution was used as blank. The percentage of cell viability was calculated from$$\,{{\mbox{Cell viability}}}\,(\%)=\frac{{{{{{{\rm{A}}}}}}}_{570}^{{{{{{\rm{polymer}}}}}}}-{{{{{{\rm{A}}}}}}}_{570}^{{{{{{\rm{blank}}}}}}}}{{{{{{{\rm{A}}}}}}}_{570}^{{{{{{\rm{control}}}}}}}-{{{{{{\rm{A}}}}}}}_{570}^{{{{{{\rm{blank}}}}}}}}\times 100.$$
(24)
The IC50 was defined as the minimum concentration to cause 50% inhibition. All experiments were carried out with three replicates. Each experiment was repeated at least twice.Synthesis of dye-labeled (DM0.8
iPen0.2)20
The dye-labeled β-amino acid polymer (DM0.8iPen0.2)20 was synthesized according to the protocol in our previous study79. Briefly, the initiator Dye-NHS ester, co-initiator LiHMDS, DM monomer and iPen monomer were dissolved in dried tetrahydrofuran (THF) to the solution with a final concentration of 0.2 M inside a glove box. DM (1.6 mL), iPen (0.4 mL) and Dye-NHS ester (0.1 mL) were mixed and stirred. Subsequently, LiHMDS (0.3 mL) was quickly added into the mixture. The reaction mixture was stirred for 6 h at room temperature and then quenched with 5 drops of MeOH. After removing the solvent under N2 flow, the residue was dissolved in THF (1 mL) and transferred to a centrifuge tube, followed by slowly addition of cold PE (45 mL) into the mixture to precipitate out a yellow product. The N-Boc protected polymer was further purified via three times of dissolution-precipitation process using the solvent of THF/PE (1 mL/45 mL) then vacuum dried and characterized by GPC using DMF containing 10 mM LiBr as mobile phase. This polymer was dissolved in 2 mL TFA and stirred at room temperature for 2 h to remove the Boc protection. After removing the TFA under N2 flow, the residue was dissolved in MeOH (1 mL), followed by slow addition of cold methyl tert-butyl ether (MTBE, 45 mL) to precipitate out a yellow product. The N-Boc deprotected polymer was further purified via three times of dissolution-precipitation process using the solvent of MeOH/MTBE (1 mL/45 mL) then vacuum dried and dissolved in Milli-Q water. Subsequently, the solution was subjected to lyophilization to give a final dye-labeled polymer (DM0.8iPen0.2)20, which was used for confocal imaging.Time-lapse fluorescent confocal imaging assayThe confocal imaging assay for drug-resistant S. aureus and drug-resistant E. coli was conducted according to the protocol in our previous study80. Briefly, the dye-labeled (DM0.8iPen0.2)20 (4 × MBC, green fluorescence) and propidium iodide (40 mM, red fluorescence) were mixed in equal volumes to prepare a working solution. In addition, the bacteria were cultured in LB medium at 37 °C for 6 h to obtain the bacterial suspension, the bacterial suspension was washed by PBS buffer and then diluted in MH medium to achieve a working suspension with a cell density of 1 × 107 CFU mL−1. 10 μL of the bacterial suspension was dropped into a glass-bottomed cell culture dish for 10 min to allow the bacteria to attach to the bottom. Subsequently, 10 μL of working solution was added to the bacterial drop. The confocal images were captured at the various time points for three channels: bright field, 488 nm (green fluorescence) and 562 nm (red fluorescence), respectively. These images were used to record the bactericidal process.Outer membrane permeabilization assayThe outer membrane permeabilization assay for drug-resistant E. coli was conducted according to the protocol in our previous study43. Briefly, the bacteria were cultured in LB medium at 37 °C for 6 h to obtain the bacterial suspension, the bacterial suspension was washed by PBS buffer and then diluted in HEPES medium (5 mM HEPES, 20 mM glucose, pH = 7.4) to achieve a working suspension with a cell density of 3 × 108 CFU mL−1, followed by addition of 1-N-phenyl-naphthylamine (NPN) dye at a final concentration of 10 μM. 90 μL of working suspension containing NPN was added to each well of a 384-well plate. The fluorescence changes (excitation λ = 350 nm, emission λ = 420 nm) were recorded on a SpectraMax®M2 plate reader (Molecular Devics, USA). Once the fluorescence intensity remained stable, 10 μL of (DM0.8iPen0.2)20 was added to the bacterial solution, and the fluorescence intensity was recorded continuously.Cytoplasmic membrane depolarization assayThe cytoplasmic membrane depolarization for drug-resistant S. aureus and drug-resistant E. coli was conducted according to the protocol in our previous study43. The drug-resistant bacteria were cultured in LB medium at 37 °C for 6 h, and then the bacterial suspension was diluted in HEPES medium (5 mM HEPES, 20 mM glucose, pH = 7.4) to achieve a working suspension with a cell density of 1 × 107 CFU mL−1, followed by addition of 3, 3’-dipropylthiadicarbocyanine iodide (diSC3(5)) dye at a final concentration of 0.8 μM. The bacterial suspension was incubated for 1 h, followed by the addition of KCl to a final concentration of 0.1 M to balance the cytoplasmic and external K+ concentration. 90 μL of bacterial suspension containing diSC3(5) was added to each well of a 384-well plate. The fluorescence changes (excitation λ = 622 nm, emission λ = 673 nm) were recorded on a SpectraMax®M2 plate reader (Molecular Devics, USA). Once the fluorescence intensity remained stable, 10 μL of (DM0.8iPen0.2)20 and 0.1% Triton X-100 as the positive control was separately added to the bacterial solution and the fluorescence intensity was recorded continuously.Cytoplasmic membrane permeabilization assayThe cytoplasmic membrane permeabilization assay for drug-resistant S. aureus and drug-resistant E. coli was conducted according to the protocol in our previous study43. The drug-resistant bacteria were cultured in LB medium at 37 °C for 6 h, and then the bacterial suspension was diluted in HEPES medium (5 mM HEPES, 5 mM glucose, pH = 7.4) to achieve a working suspension with a cell density of 1 × 108 CFU mL−1, followed by addition of propidium iodide (PI) dye at a final concentration of 10 μM. 150 μL of bacterial suspension containing PI was added to each well of a corning 96-well plate. The fluorescence changes (excitation λ = 535 nm, emission λ = 617 nm) were recorded on a SpectraMax®M2 plate reader (Molecular Devics, USA). Once the fluorescence intensity remained stable, 10 μL of (DM0.8iPen0.2)20 was added to the bacterial solution and the fluorescence intensity was recorded continuously.SEM characterization of bacteria morphologyThe SEM characterization for drug-resistant S. aureus and drug-resistant E. coli was conducted according to the protocol in our previous study79. Briefly, the drug-resistant bacteria were cultured in LB medium at 37 °C for 9 h, and then the bacterial suspension was diluted in LB medium to achieve a working suspension with a cell density of 1 × 107 CFU mL−1, followed by addition of (DM0.8iPen0.2)20 at a final concentration of 1 × MBC. The bacterial suspension was incubated at 37 °C for 30 min. An untreated bacteria suspension was used as the control. (DM0.8iPen0.2)20 treated and untreated bacteria were collected by centrifugation at 1700 × g for 5 min. They were washed with phosphate buffer saline (PBS) once and then fixed with 4% glutaraldehyde in phosphate buffer (PB) at 25 °C overnight. The bacteria were further washed with PBS and dehydrated with gradient ethanol (EtOH) solutions (30, 50, 70, 80, 90, 95, and then 100% ethanol). The samples were dried in air and then used for Field Emission Scanning Electron Microscopy (FESEM) characterization.Reporting summaryFurther information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

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