We analyze theoretically the problem of cargo transport along microtubules by motors of two species with opposite polarities. We consider two different one-dimensional models previously developed in the literature. On the one hand, a quite widespread model which assumes equal force sharing, here referred to as mean field model (MFM). On the other hand, a stochastic model (SM) which considers individual motor-cargo links. We find that in generic situations the MFM predicts larger cargo mean velocity, smaller mean run time and less frequent reversions than the SM. These phenomena are found to be consequences of the load sharing assumptions and can be interpreted in terms the probabilities of the different motility states. We also explore the influence of the viscosity in both models and the role of the stiffness of the motor-cargo links within the SM. Our results show that the mean cargo velocity is independent of the stiffness while the mean run time decreases with such a parameter. We explore the case of symmetric forward and backward motors considering kinesin- 1 parameters, and the problem of transport by kinesin-1 and cytoplasmic dyneins considering two different sets of parameters previously proposed for dyneins.
Transport of cargo driven by multiple molecular motors along microtubules has become a very active subject of research because of its relevance for many cellular functions [1,2,3,4]. In recent years, a myriad of experiments and models have attempted to understand the way in which motors work together [4,5,6,7,8,9], and, still, there are many fundamental details which remain unclear and deserve further research, most particularly for the case of bidirectional transport by two motor species.
The complexity of the multiple motor systems and the difficulties for controlling the experiments are often quite important so that performing the connection between models and experiments must be done carefully. Models involve always many parameters, including for instance detachment and attachment rates, stall forces, motor stiffness and viscosity of the media. Usually, many of these parameters are a priori not well known in the experiments, and even more fundamental features such as the number of motors, or whether more than a single species is participating on the transport, remain unclear. Thus, distinct models may provide different fitting of the experimental data and, consequently, different interpretations. Moreover, recent in vivo experiments [10] have revealed important differences with in vitro systems. In this context, a detailed knowledge of the consequences of specific modeling assumptions as well as the comparison of different kinds of models becomes quite relevant. The aim of this paper is to contribute in these two important aspects.
References [11] and [12] have originated a modeling framework that has largely contributed to the understanding of transport by several motors. The model introduced in [11] deals with cargo transport by a single class of motors, while in [12] the formalism is extended to account for bidirectional transport associated to tug of war between two motor types with opposite polarities. Assuming certain force-velocity relations, and specific attachment and detachment probabilities for individual motors, the model enables the calculation of the probabilities of different motility states characterized by different number of motors, and the reproduction of trajectories and velocity distributions as well. In a series of papers [7,13,14,15] the model was further developed and several effects and transport conditions have been analyzed, providing a deep physical insight on the problem. An important assumption of the model is that all the motors of the same polarity simultaneously engaged to the microtubule share equally the load. In real systems, however, fluctuations of the distances between motor-microtuble binding position and motor-cargo binding position may lead to nonnegligible differences between the forces supported by the different motors [8,16,17,18]. Consequently, the model would eventually fail to predict exact quantitative results. In reference [17], the model was referred to as mean field due to the equal sharing of load approximation. We will keep such a name throughout this work.
Several models have gone beyond the mean field approach by considering independent motor-cargo links for each motor, and incorporating different degree of detail in their description of individual motor properties [8,9,17,19,20]. Although such models generally provide less instrumental (and less elegant) formulations than the mean field model, and they mostly lack analytical results, they may be more successful in predicting numerical results for multiple motors through simulations based on individual motor parameters. In a different but related context, models in references [21] and [22] consider the load applied only to the leading motor and constitute thus interesting extreme examples of models beyond mean field. Although not directly connected to our approach for processive motors on microtubules, studies on non-processive motors [23,24] and general ratchet models [25] provide also relevant analysis of bidirectional motion in many motor systems.
In this paper we investigate bidirectional cargo transport by two opposing teams of processive motors within two different models. On the one hand, the mean field model. On the other hand, a recently introduced [19] stochastic model which considers independent cargo-motor links for individual motors, allowing for uneven load sharing. In this way, at the same time that we investigate how cargo transport depends on the system parameters, we are able to clearly identify the consequences of the assumption of equal load sharing. Our work follows the spirit of the paper by Kunwar and Mogilner [17]. There, the authors compared results from both kind of models focussing on the case of cargo transport by a single team of motors, and provided also an analysis of the velocity distributions for bidirectional transport. Moreover, they studied the influence of the non linearities of the force-velocity relations of individual motors.
Our studies focus on analyzi
This content is AI-processed based on open access ArXiv data.
