A Refined Reaction-Diffusion Model of Tau-Microtubule Dynamics and Its Application in FDAP Analysis

Abstract

Fluorescence decay after photoactivation (FDAP) and fluorescence recovery after photobleaching (FRAP) are well established approaches for studying the interaction of the microtubule (MT)-associated protein tau with MTs in neuronal cells. Previous interpretations of FDAP/FRAP data have revealed dwell times of tau on MTs in the range of several seconds. However, this is difficult to reconcile with a dwell time recently measured by single-molecule analysis in neuronal processes that was shorter by two orders of magnitude. Questioning the validity of previously used phenomenological interpretations of FDAP/FRAP data, we have generalized the standard two-state reaction-diffusion equations by 1), accounting for the parallel and discrete arrangement of MTs in cell processes (i.e., homogeneous versus heterogeneous distribution of tau-binding sites); and 2), explicitly considering both active (diffusion upon MTs) and passive (piggybacking upon MTs at rates of slow axonal transport) motion of bound tau. For some idealized cases, analytical solutions were derived. By comparing them with the full numerical solution and Monte Carlo simulations, the respective validity domains were mapped. Interpretation of our FDAP data (from processes of neuronally differentiated PC12 cells) in light of the heterogeneous formalism yielded independent estimates for the association (∼2 ms) and dwell (∼100 ms) times of tau to/on a single MT rather than in an MT array. The dwell time was shorter by orders of magnitude than that in a previous report where a homogeneous topology of MTs was assumed. We found that the diffusion of bound tau was negligible in vivo, in contrast to an earlier report that tau diffuses along the MT lattice in vitro. Methodologically, our results demonstrate that the heterogeneity of binding sites cannot be ignored when dealing with reaction-diffusion of cytoskeleton-associated proteins. Physiologically, the results reveal the behavior of tau in cellular processes, which is noticeably different from that in vitro.

Annexins A2 and A6 interact with the extreme N terminus of tau and thereby contribute to tau's axonal localization

“…Based on the effective diffusion constants, Ͼ90% of the constructs were bound to microtubules, which is consistent with previous data on the tau-MT interaction in processes of living cells (16,32). To directly estimate the pseudo-first-order association rate (k* on ϭ k on [MT] eq , where [MT] eq is the equilibrium concentration of tau-binding sites on MTs) and the dissociation rate (k off ), we used a previously developed refined reaction-diffusion model of the tau-MT interaction (33). Absence of E1 led to a moderate but significant increase in k* on but did not influence k off (Fig.…”

“…The microscope was enclosed in an incubation chamber maintained at 37°C and 5% CO 2 (Solent Scientific, Fareham, UK). Photoactivation of a neurite's segment 6 m in length and automated image acquisition of 112 frames after photoactivation with a frame rate of 1/s were performed as described previously (33). Analysis of individual FDAP curves to estimate directly the pseudo-first-order association rate (k * on ) and the dissociation rate (k off ) of tau to/from microtubules was performed as described previously (32).…”

Mechanisms of protein misfolding: Novel therapeutic approaches to protein-misfolding diseases

“…The data showed that tau-microtubule dynamics differ in vitro and in vivo. In particular, it was shown that diffusion of bound tau was negligible in vivo contrary to the findings that tau diffuses along MT lattice in vitro [19].…”

“…Deeper insight into the tau-microtubule interactions have also been provided by FDAP analysis [19]. The data showed that tau-microtubule dynamics differ in vitro and in vivo.…”

International Meeting Molecular Neurodegeneration: News and Views in Molecular Neuroscience in Health and Disease. Delmenhorst, Germany, July 20–22, 2015

“…There was a discussion on new methods for discerning the levels of free tubulin relative to microtubules in the axons of cultured neuronal cells (Igaev et al 2014), as well as discussion on how a straightforward drug approach could be used to quantify the levels of stable and labile microtubule mass.…”