Burgeoning interest in the area of bacteria powered bio-hybrid micro-robotic systems motivates a fundamental question on how one achieves optimal cargo-carrying capacity in such systems. Here we demonstrate a process to attach oil-droplet cargos to cell bodies of flagellated single bacteria which allowed us to probe cargo-carrying capacity of single bacteria over cargo sizes as large as 200 times a single cell volume. The most remarkable finding from our studies is that , for a given cargo size, the swim-speed is maximized when the rotational drag coefficient of the flagella is tuned to the torque-speed  characteristics of the bacterial flagellar motor . This tuning criterion discovered in our analysis is not satisfied by wild-type bacteria such as E. coli . Operating in the tuned regime leads to swim-speed enhancements in excess of 4 times relative to wild-type condition. This result provides a simple design rule to achieve optimal cargo transport for future bio-hybrid or synthetic flagellated micro-swimmers. Additionally, our study also reveals the existence of an anomalous propulsion regime where swim-speed increases with increasing load  . Finally, the experimental data was found to be consistent with a propulsion matrix based analytical model .
In a classic paper, Edward Purcell analysed the dynamics of flagellated bacterial swimmers and derived a geometrical relationship which optimizes the propulsion efficiency. Experimental measurements for wild-type bacterial species E. coli have revealed that they closely satisfy this geometric optimality. However, the dependence of the flagellar motor speed on the load and more generally the role of the torque-speed characteristics of the flagellar motor is not considered in Purcell's original analysis. Here we derive a tuned condition representing a match between the flagella geometry and the torque-speed characteristics of the flagellar motor to maximize the bacterial swimming speed for a given load. This condition is independent of the geometric optimality condition derived by Purcell and interestingly this condition is not satisfied by wild-type E. coli which swim 2-3 times slower than the maximum possible speed given the amount of available motor torque. Our analysis also reveals the existence of an anomalous propulsion regime , where the swim speed increases with increasing load (drag) . Finally, we present experimental data which supports our analysis .
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Burgeoning interest in the area of bacteria powered bio-hybrid micro-robotic systems motivates a fundamental question on how one achieves optimal cargo-carrying capacity in such systems. Here we demonstrate a process to attach oil-droplet cargos to cell bodies of flagellated single bacteria which allowed us to probe cargo-carrying capacity of single bacteria over cargo sizes as large as 200 times a single cell volume. The most remarkable finding from our studies is that , for a given cargo size, the swim-speed is maximized when the rotational drag coefficient of the flagella is tuned to the
In a classic paper, Edward Purcell analysed the dynamics of flagellated bacterial swimmers and derived a geometrical relationship which optimizes the propulsion efficiency. Experimental measurements for wild-type bacterial species E. coli have revealed that they closely satisfy this geometric optimality. However, the dependence of the flagellar motor speed on the load and more generally the role of the
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characteristics of the flagellar motor is not considered in Purcell's original analysis. Here we derive a tuned condition representing a match between the flagella geometry and the torque-speed
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bacterial flagellar motor . This tuning criterion discovered in our analysis is
flagellar motor to maximize the bacterial swimming speed for a given load. This condition is independent of the geometric optimality condition derived by Purcell and interestingly this condition is
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bacteria such as
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. Operating in the tuned regime leads to swim-speed enhancements in excess of 4 times relative to wild-type condition. This result provides a simple design rule to achieve optimal cargo transport for future bio-hybrid or synthetic flagellated micro-swimmers. Additionally, our study
which swim 2-3 times slower than the maximum possible speed given the amount of available motor torque. Our analysis
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where swim-speed
, where the swim speed
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(drag)
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the experimental data was found to be consistent with a propulsion matrix based analytical model
we present experimental data which supports our analysis