Abstract:Resolving distinct biochemical interaction states when analyzing the trajectories of diffusing proteins in live cells on an individual basis remains challenging because of the limited statistics provided by the relatively short trajectories available experimentally. Here, we introduce a novel, machine-learning based classification methodology, which we call perturbation expectation-maximization (pEM), that simultaneously analyzes a population of protein trajectories to uncover the system of diffusive behaviors… Show more
“…Importantly, pEMv2 is rooted in physical principles of stochastic processes. Applying non-physical clustering methods to the same data, such as k-means clustering, lead to poor characterization of the underlying diffusive states [17].…”
Section: Discussionmentioning
confidence: 99%
“…Here, we extend the original pEM framework [17] to now include non-normal modes of diffusion, i.e. we lift the short-time-diffusion approximation.…”
Section: A Maximum Likelihood Frameworkmentioning
confidence: 99%
“…However, as described in detail in Ref. [17] and summarized in the Methods (Sec. IV), suitably perturbing the likelihood surface, namely pEM, is a computationally efficient means to reach the global maximum likelihood.…”
Section: A Maximum Likelihood Frameworkmentioning
confidence: 99%
“…[17]. The traditional approach for analyzing the diffusive properties of individual particle trajectories is by fitting each trajectory's time-averaged mean * simon.mochrie@yale.edu square displacement (taMSD) to a corresponding diffusion model [18].…”
The stochastic motions of a diffusing particle contain information concerning the particle's interactions with binding partners and with its local environment. However, accurate determination of the underlying diffusive properties, beyond normal diffusion, has remained challenging when analyzing particle trajectories on an individual basis. Here, we introduce the maximum likelihood estimator (MLE) for confined diffusion and fractional Brownian motion. We demonstrate that this MLE yields improved estimation over traditional mean square displacement analyses. We also introduce a model selection scheme (that we call mleBIC) that classifies individual trajectories to a given diffusion mode. We demonstrate the statistical limitations of classification via mleBIC using simulated data. To overcome these limitations, we introduce a new version of perturbation expectation-maximization (pEMv2), which simultaneously analyzes a collection of particle trajectories to uncover the system of interactions which give rise to unique normal and/or non-normal diffusive states within the population. We test and evaluate the performance of pEMv2 on various sets of simulated particle trajectories, which transition among several modes of normal and non-normal diffusion, highlighting the key considerations for employing this analysis methodology.
“…Importantly, pEMv2 is rooted in physical principles of stochastic processes. Applying non-physical clustering methods to the same data, such as k-means clustering, lead to poor characterization of the underlying diffusive states [17].…”
Section: Discussionmentioning
confidence: 99%
“…Here, we extend the original pEM framework [17] to now include non-normal modes of diffusion, i.e. we lift the short-time-diffusion approximation.…”
Section: A Maximum Likelihood Frameworkmentioning
confidence: 99%
“…However, as described in detail in Ref. [17] and summarized in the Methods (Sec. IV), suitably perturbing the likelihood surface, namely pEM, is a computationally efficient means to reach the global maximum likelihood.…”
Section: A Maximum Likelihood Frameworkmentioning
confidence: 99%
“…[17]. The traditional approach for analyzing the diffusive properties of individual particle trajectories is by fitting each trajectory's time-averaged mean * simon.mochrie@yale.edu square displacement (taMSD) to a corresponding diffusion model [18].…”
The stochastic motions of a diffusing particle contain information concerning the particle's interactions with binding partners and with its local environment. However, accurate determination of the underlying diffusive properties, beyond normal diffusion, has remained challenging when analyzing particle trajectories on an individual basis. Here, we introduce the maximum likelihood estimator (MLE) for confined diffusion and fractional Brownian motion. We demonstrate that this MLE yields improved estimation over traditional mean square displacement analyses. We also introduce a model selection scheme (that we call mleBIC) that classifies individual trajectories to a given diffusion mode. We demonstrate the statistical limitations of classification via mleBIC using simulated data. To overcome these limitations, we introduce a new version of perturbation expectation-maximization (pEMv2), which simultaneously analyzes a collection of particle trajectories to uncover the system of interactions which give rise to unique normal and/or non-normal diffusive states within the population. We test and evaluate the performance of pEMv2 on various sets of simulated particle trajectories, which transition among several modes of normal and non-normal diffusion, highlighting the key considerations for employing this analysis methodology.
“…6,7 Koo et al recently analyzed the location of the fluorescent reporter, mEos2, when fused to either full-length RhoA, fulllength RhoC, or the HV domain of either RhoA or RhoC. 8 The authors found a similar number of diffusion states for mEos2 when attached to either full-length GTPase or its corresponding HV domain, suggesting the HV domain alone dictates much of the diffusibility of RhoA and RhoC within cells, potentially through its intermolecular interactions. Moreover, the HV domain chimeras of RhoA and RhoC were found to be dissimilar.…”
RhoA and RhoC GTPases are 92% identical but demonstrate unique regulation and function. Phosphorylation of Ser188 has widely been reported to inhibit RhoA activity. RhoC possesses Arg188 in place of Ser188 but retains a canonical upstream PKA recognition sequence. We report here that RhoC-R188S was a PKA substrate in vitro and exhibited less GTP loading compared to wild-type RhoC when expressed in cells. Transiently expressed RhoC was found to be significantly more membrane associated than RhoA. Membrane association of RhoC-R188S and RhoC-R188A were similar to each other and wild-type RhoA, suggesting that Arg188 directly promotes RhoC membrane binding. The positive influence of Arg188 on RhoC membrane association was evident in a constitutively active (Q63L) background. In accordance, RhoA-S188R was significantly more membrane associated than either RhoA or RhoA-S188A. Altogether, these data suggest that swapping residue 188 identity effectively flips the membrane binding profile of wild-type RhoA and RhoC through positive arginine contribution rather than negative phosphoserine regulation.
Single-particle tracking (SPT) enables the ability to noninvasively probe the diffusive motions of individual proteins inside living cells at sub-diffraction-limit resolution. The stochastic motions of diffusing Rho GTPases encode information concerning its interactions with binding partners and with its local environment. By identifying Rho GTPases' diffusive states, insight can thus be gained into the spatiotemporal in vivo biochemistry inside live cells at a single-molecule resolution. Here we present perturbation expectation-maximization (pEM), a computational method which simultaneously analyzes a population of protein trajectories to uncover the system of diffusive behaviors: (1) the number of diffusive states, (2) the properties of each such diffusive state, and (3) the probabilities of each trajectory to a respective diffusive state. We provide a step-by-step guide to pEM and discuss considerations for its practical applications, including pEM's capabilities and limitations.
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