Dynamics of interacting molecular motors

The dynamics of the sperm flagellum has been recently studied with particular attention to its fluctuations [1]. It has been found that the precision of the flagellar beating is close to that of an individual dynein motor (L1) powering its motion, which in turn is close to the bound dictated by the thermodynamic uncertainty relation (TUR) [2]. To explain this observation, we have generalised a well-established schematic model of the flagellum [3] (T1,T4,T10) to include explicit interactions between molecular motors. Our model shows that strong motor-motor couplings prevent the noise from decreasing at the collective level (as many motors actuate together the axoneme) and significantly limit the precision of the whole flagellum. In contrast, recent experiments [4] show that, by inhibiting individual motors at random, the fluctuations of flagellar oscillations scale with number of active dynein motors. Given this novel experimental information, we aim to make significant progress in understanding fluctuations and interactions in assemblies of biological nanomotors by using the theoretical tools of stochastic thermodynamics and massive computer simulations.

The CNR unit will develop efficient GPU simulations (T1,T4,T10) of flagellar models. From a theoretical point of view the Edinburgh group will focus on the extensions of the TURs to many-body systems. Theoretical work to this end will build on the description of work extraction from large collections of active particles (e.g., molecular motors) [5], extending results obtained for the average work to include its fluctuations. Moreover, we will revisit the model of [3] in the light of recent insights from stochastic thermodynamics, analysing its entropy production which may be affected by an increasing number of idle cycles in the state space of many interacting motors. The results of [6] allow the entropy production to be related to the coherence of oscillations, which can be compared to the results obtained previously using the TUR for currents. A possible explanation for reduced precision in flagellar oscillations is correlated noise [7]. We will study whether this could be interpreted as environmental noise in a variation of the models that features fluctuations in the driving chemical potential differences. Finally, we will test these theoretical and numerical results on novel experiments on E. coli bacteria performed in Rome. In E. coli, each motor is connected to one single flagellum and the motor is actuated by several stators. Thus we will determine if couplings among stators re relevant also in the flagellar dynamics of this bacterium.

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[1] Maggi, C, et al. (2023) PRX Life 1:013003 [2] Hwang, W, & Hyeon, C. (2018) J Phys Chem Lett 9:513 [3] Jülicher, F, & Prost, J. (1997) Phys Rev Lett 78:4510 [4] Sharma, A, et al. (2024) bioarxiv DOI:10.1101/2024.06.25.600380 [5] Pietzonka, P, et al. (2019) Phys Rev X 9:041032 [6] Oberreiter,L, et al. (2022) Phys Rev E 106: 014106 [7] Costantini, G, & Puglisi, A. (2024) J. Stat. Mech. 024003