Differential expression of smooth muscle contractile proteins has been associated with organismal development [1], contractile phenotypes [2]–[4], and pathologies, e.g. preterm labour, hypertrophic bladder, or airway hyper-responsiveness [5]–[7]. While the role of the smooth muscle myosin isoforms has been extensively investigated [7]–[9], the functional implications of the differential expression of specific actin and actin-regulatory protein isoforms remain elusive [4].

In smooth muscle, actin isoforms are expressed from four different genes, yielding “vascular muscle” - and “enteric muscle” -actin, as well as non-muscle (cytoplasmic) - and -actin. The muscle isoforms are associated with the contractile apparatus, the non-muscle isoforms with cytoskeletal structures [5]. Muscle -actin is generally associated with tonic, -actin with phasic smooth muscles [5], [10], [11]. An anti-proportional relationship between the absolute levels of - and -actin has been established [2]. Disease-related expression differences in - vs. -actin have been found [6]. Functional differences between - and -isoforms were searched for in molecular mechanics experiments, but, to our knowledge, no differences were detected [12]–[15]. Insight from tissue level mechanics seems lacking, too [4].

Smooth muscle tropomyosin affects the weak to strong binding of ATP-activated myosin to actin: tropomyosin can be in an ON state supporting myosin strong binding, or an OFF state hindering myosin strong binding [10], [16]. When regulated by caldesmon-calmodulin, dependent on the caldesmon-calmodulin activation state, smooth muscle tropomyosin is stabilized in the open or the closed state, increasing or decreasing the rate of myosin cycling compared to the rate without any tropomyosin being present [10], [17]. Tropomyosin forms chains along actin filaments by a head-to-tail overlap of consecutive tropomyosin molecules. This overlap leads to an increased cooperativity in the switching between the ON and the OFF state. Compared to striated muscle tropomyosin isoforms, a stronger cooperativity between tropomyosin displacement due to stronger end-to-end binding between tropomyosin molecules is observed, as well as a greater bias for the ON conformation [16], [18], [19]. Similar to striated muscle tropomyosin, smooth muscle tropomyosin facilitates cooperative binding of myosin to actin: above a critical ratio of myosin heads per actin monomer, myosin heads cooperatively displace tropomyosin into the ON state so that further myosin binding is facilitated; below a critical density or activation by phosphorylation, tropomyosin remains mostly in the OFF state [20], [21] and inhibits myosin cycling [10], [19].

Tropomyosin is expressed from the same two genes in non-muscle, striated muscle, and smooth muscle cells. In smooth muscle, alternative splicing yields two smooth muscle specific isoforms (tropomyosin- and tropomyosin-), one from each gene [22]. In vivo, tropomyosin- and tropomyosin- mostly occur as heterodimers, making functional differentiation between the isoforms difficult [10], [22]. In disease states, however, expression differences between both isoforms can be observed [6], raising the question of functional differences between these two isoforms, especially in interaction with other differentially expressed contractile protein isoforms. Crystallized N-terminal fragments of tropomyosin- and tropomyosin- displayed differences in the heterodimerization properties of tropomyosin- vs. tropomyosin- and a greater head-to-tail overlap of tropomyosin- than that of tropomyosin- [23]. These structural results were interpreted as indication of negligible differences in tropomyosin's interface for actin binding and more important differences in the surfaces available for mediation of actin-myosin interactions as well as the binding of other proteins [23]. However, actin affinity (in terms of binding constants) of smooth muscle tropomyosin- was found to be times greater than that of tropomyosin- [24], [25].

In this study, we use an in vitro motility assay to investigate differences in the propulsion of “vascular” -actin vs. “enteric” -actin by smooth muscle myosin in the presence of smooth muscle tropomyosin-, tropomyosin-, or in the absence of tropomyosin, see Fig. 1 A and Tab. 1. We develop and simulate a mathematical model to establish the differences in actin-myosin interaction kinetics that underlie the experimentally observed differences.

Using our specifically developed analysis software, we extracted the following features of actin sliding: mean sliding velocity (), the motile fraction (), the average run time (), and the average stop time () (Fig. 1 B, C). These features were extracted for the different experimental conditions (Tab. 1) and resolved by actin filament length () (Fig. 2). For A-Tm a consistent increase is apparent (Fig. 2 A). , , and do not immediately suggest consistent differences, (Fig. 2 B–D). In spite of high filament counts (Fig. 2 D, inset), the width of the confidence intervals compared to potential differences makes a direct, conclusive inference difficult, especially for and at .

The resolved features represent a simultaneous measurement of values, whose interdependence cannot be judged a priori. We applied a Principal Component Analysis (PCA) to reduce the dimensionality of our data and remove correlations between values, which would otherwise inflate statistical significance. Transformation into the three Principal Components (PCs) explaining most of the variance indicates that consistent differences between the experimental conditions exist (Fig. 3 A, B). Our statistical analysis detected no differences between A, A, and A-Tm, which will therefore be referred to as baseline conditions that show no effect; A-Tm, A-Tm, and A-Tm are all different from the baseline conditions, as well as from each other (Fig. 3 C, D). To support the conclusions from our statistical analysis, we executed a hierarchical cluster analysis. Based on the relatively large reduction of linkage when going from four to five clusters, a number of four clusters was chosen (Fig. 3 E). In the PC space, the four clusters appear similar to the above separation into one baseline and three regulated conditions (Fig. 3 F, G). Indeed, the four clusters form a clear representation of the A, A, A-Tm baseline conditions, and the three distinctly regulated conditions A-Tm, A-Tm, and A-Tm, (Fig. 3 H). Thus, two independent methods of statistical assessment indicate that only A-Tm, A-Tm, and A-Tm are significantly regulated, while for each of them the regulation affects actin sliding in the in vitro motility assay in a distinctly different manner (Fig. 3 I).

Next, we wanted to attribute the differences that had been detected using PCA to molecular mechanical features. Thus, we evaluated the motility features' fold changes relative to A, averaged over . For A-Tm, is statistically significantly increased to 1.12 times the baseline value (Fig. 4 A). For A-Tm, is decreased to 0.96-fold, is increased by a factor of 1.6 relative to the baseline value, though both changes show up only as strong trends (Fig. 4 B, C). For A-Tm, is elevated 1.3-fold, which also shows up as a strong trend only (Fig. 4 D). When and are analyzed together, the joint fold changes for A-Tm become statistically significant (Fig. 4 E). When only short actin is considered, is statistically significantly elevated to 1.7 times the baseline value (Fig. 4 F). Note that each condition's differences are found in different features, which is coherent with the PCA finding that the regulated conditions are each affected by tropomyosin in a distinct manner.

To theoretically understand the regulatory effect that tropomyosin has on actin-myosin interactions, we constructed a mathematical model of the kinetics of a myosin-coated surface interacting with actin filaments of different length . Stochastic simulations of our model produce time courses (Fig. 1 C). Averaging these time courses gives , all other features of actin sliding can be extracted in exactly the same way as from experimental data. Our model is an extension of our earlier model of the group action of myosins propelling actin filaments in the in vitro motility assay [26]. Briefly, the model assumes that myosin moves actin by two mechanical steps, the main power stroke and a secondary mechanical step preceding myosin detachment [27], [28]. When several myosins are simultaneously bound to the same actin filament, they are mechanically coupled via the filament. Thus, the individual myosins' steps cause a change in the mechanical configuration of the overall system of bound myosins and the actin filament. Consequently, mechanical work might have to be exerted on or might be released from the actin-myosin system during the execution of an individual myosin's mechanical step. This mechanical work affects the strain-dependent rates of both mechanical transitions, the main power stroke and the secondary pre-detachment step. The overall number of myosin binding sites that are accessible on a given actin filament () is assumed to be proportional to . Using the helix repeat of actin (0.0355 μm) as an approximate binding site distance [27], [29], the ranges were adjusted to correspond to the ranges used in the different analysis steps. For details regarding our mathematical model, see Text S1.

A set of model parameters was determined to mimic the baseline condition (Fig. 5). These baseline parameters were altered so as to mimic the changes in resolved features that were observed experimentally for the A-Tm, A-Tm, and A-Tm conditions (Fig. 5). The scalar fold changes in motility features were determined in the same way as from the experimental data (Fig. 6). The resolved motility features as well as the fold changes capture the experimentally observed differences between the baseline conditions and the conditions that exhibited statistically significant effects.

The changes in model parameters that were necessary to mimic the experimentally observed differences point towards the aspects of actin-myosin interaction kinetics that are changed in the different conditions (Fig. 7). For A-Tm, all kinetic rates (, , ) are increased 1.15-fold. For A-Tm, the impact of mechanical coupling between myosins on the rate of the mechanical transitions () is increased by a factor of 1.2. For A-Tm, is reduced to of the baseline value, and is reduced to of the baseline value.

We developed an automated video analysis software which executes the following steps. Raw video data are preprocessed (image enhancement and frame merging to a time resolution of s) and turned into binary images. Filament objects and their properties are extracted from individual frames using connected components methods. Filaments are tracked throughout consecutive frames based on their centroid position and area. Frame-to-frame velocities () are calculated from centroid displacements between two consecutive frames. Filament length () and travelled path lengths are determined based on a transformation of image objects into rectangles of same area and perimeter, the longer edge representing lengths. A filament's mean trace velocity () is determined by dividing the total distance that the filament's tip has travelled by the time the filament was present for (). Filament traces with filament crossing events or signs of irregular motion were removed by a machine-learning algorithm, which was trained on subset of our data that we scored by hand. The automated video analysis was assessed using computer-generated mock motility videos, the automated quality control was evaluated against hand-scored data sets. For details see Text S1.

Statistical significance was assumed for . Statistical comparisons were executed by bootstrapping of the compared statistic; statistical significance was assumed where no overlap exists between the confidence intervals of the compared conditions. For details see Text S1.