The authors wish to note the following: "We wish to acknowledge that during the writing of our manuscript we had access to an unpublished preprint from the Princeton group of H. Yang and coauthors, which similarly dealt with the theory of feedback control of Janus particles based on optically heated self-thermophoretic motion of Janus particles (photon nudging).* Through the state-of-the-art realization of 3D control, they analyzed the statistics and traveling time for a hot microswimmer in light of the optimal strategy for run-and-tumble motion of Escherichia coli. They developed a rigorous theory for evaluating on-time (self-propulsion period) and off-time (rotational diffusion period) distributions by making use of the first-passage time distribution (FPTD), which agreed with exponential tails known in biology. The optimum acceptance angle for self-propulsion was determined as 90 degrees for photon nudging, similar to the prediction for the optimal chemotactic strategy for E. coli (27). The same paper (27) hinted to us to use the probability distribution function with absorbing boundary conditions in solving the heat (diffusion) equation. The solution can be found in Selmke's paper* and our paper, as well as Zauderer's book (25). However, the normalization factor, which is necessary to compare the theory and the simulation, cannot be found to the best of our knowledge except for in our paper. FPTD is used to formulate the exact solution of the average displacement during active Brownian motion (ABM) in our paper, while in Selmke's paper,* it is used either to obtain exponential tails in on-time/offtime distribution or to obtain an asymptotic form to conclude the optimal acceptance angle to be 90 degrees. Our results revealed that the optimal angle varies from 0 to 90 degrees depending on signal to noise ratio for the deterministic feedback. Therefore, the usages and conclusions are very different."Accordingly, we wish to add the following text on page 1 in the right column: 'Researchers have been inspired by chemotactic behaviors of microorganisms and implemented such functions to self-propelled particles (11, 12, 34) for targeting their motion. Run-and-tumble is a well-known strategy for tactic behavior of E. coli, and it has been thoroughly compared with ABM of self-propelled particles from the view point of statistical mechanics (35)(36)(37)(38). The concept of run-and-tumble has been applied to Janus particles (13). The optimization of the run-andtumble algorithm for controlling microswimmers has been carried out rigorously using a first-passage time approach (Selmke et al., unpublished*).' "We apologize for the oversight in removing the reference to Selmke et al., which had been included in an earlier version of the paper. The reference was deleted because PNAS does not allow citations to unpublished work." Published under the PNAS license.www.pnas.org/cgi

We study the active dynamics of self-propelled asymmetrical colloidal particles (Janus particles) fueled by an AC electric field. Both the speed and direction of the self-propulsion, and the strength of the attractive interaction between particles can be controlled by tuning the frequency of the applied electric field and the ion concentration of the solution. The strong attractive force at high ion concentration gives rise to chain formation of the Janus particles, which can be explained by the quadrupolar charge distribution on the particles. Chain formation is observed irrespective of the direction of the self-propulsion of the particles. When both the position and the orientation of the heads of the chains are fixed, they exhibit beating behavior reminiscent of eukaryotic flagella. The beating frequency of the chains of Janus particles depends on the applied voltage and thus on the selfpropulsive force. The scaling relation between the beating frequency and the self-propulsive force deviates from theoretical predictions made previously on active filaments. However, this discrepancy is resolved by assuming that the attractive interaction between the particles is mediated by the quadrupolar distribution of the induced charges, which gives indirect but convincing evidence on the mechanisms of the Janus particles. This signifies that the dependence between the propulsion mechanism and the interaction mechanism, which had been dismissed previously, can modify the dispersion relations of beating behaviors. In addition, hydrodynamic interaction within the chain, and its effect on propulsion speed, are discussed. These provide new insights into active filaments, such as optimal flagellar design for biological functions.

Understanding the constraints that shape the evolution of antibiotic resistance is critical for predicting and controlling drug resistance. Despite its importance, however, a systematic investigation of evolutionary constraints is lacking. Here, we perform a high-throughput laboratory evolution of Escherichia coli under the addition of 95 antibacterial chemicals and quantified the transcriptome, resistance, and genomic profiles for the evolved strains. Utilizing machine learning techniques, we analyze the phenotype–genotype data and identified low dimensional phenotypic states among the evolved strains. Further analysis reveals the underlying biological processes responsible for these distinct states, leading to the identification of trade-off relationships associated with drug resistance. We also report a decelerated evolution of β-lactam resistance, a phenomenon experienced by certain strains under various stresses resulting in higher acquired resistance to β-lactams compared to strains directly selected by β-lactams. These findings bridge the genotypic, gene expression, and drug resistance gap, while contributing to a better understanding of evolutionary constraints for antibiotic resistance.

No abstract

The fitness landscape represents the complex relationship between genotype or phenotype and fitness under a given environment, the structure of which allows the explanation and prediction of evolutionary trajectories. Although previous studies have constructed fitness landscapes by comprehensively studying the mutations in specific genes, the high dimensionality of genotypic changes prevents us from developing a fitness landscape capable of predicting evolution for the whole cell. Herein, we address this problem by inferring the phenotype-based fitness landscape for antibiotic resistance evolution by quantifying the multidimensional phenotypic changes, i.e., time-series data of resistance for eight different drugs. We show that different peaks of the landscape correspond to different drug resistance mechanisms, thus supporting the validity of the inferred phenotype-fitness landscape. We further discuss how inferred phenotype-fitness landscapes could contribute to the prediction and control of evolution. This approach bridges the gap between phenotypic/genotypic changes and fitness while contributing to a better understanding of drug resistance evolution.