Diffusion-trapping model of receptor trafficking in dendrites

Bressloff, Paul C.; Earnshaw, Berton A.

doi:10.1103/physreve.75.041915

Cited by 49 publications

(47 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…Let p(x, t) denote the probability density (per unit area) that a surface receptor is located within the dendritic membrane at position x at time t. Similarly, let R j (t), S j (t) denote the probability that the receptor is trapped at the surface of the jth spine or within an associated intracellular pool, respectively. A simple version of the 1D diffusion-trapping model of AMPA receptor trafficking takes the form (Bressloff and Earnshaw, 2007;Earnshaw and Bressloff, 2008) …”

Section: Diffusion Along Spiny Dendritesmentioning

confidence: 99%

“…However, it is still unclear to what extent intracellular diffusion is anomalous in the long-time limit rather than just at intermediate times. This motivates studying diffusion in the presence of obstacles and transient traps whereby normal diffusion is recovered asymptotically (Bressloff and Earnshaw, 2007;Santamaria et al, 2006;Saxton, 1994Saxton, , 2007.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Stochastic models of intracellular transport

2013

View full text Add to dashboard Cite

The interior of a living cell is a crowded, heterogenuous, fluctuating environment. Hence, a major challenge in modeling intracellular transport is to analyze stochastic processes within complex environments. Broadly speaking, there are two basic mechanisms for intracellular transport: passive diffusion and motor-driven active transport. Diffusive transport can be formulated in terms of the motion of an over-damped Brownian particle. On the other hand, active transport requires chemical energy, usually in the form of ATP hydrolysis, and can be direction specific, allowing biomolecules to be transported long distances; this is particularly important in neurons due to their complex geometry. In this review we present a wide range of analytical methods and models of intracellular transport. In the case of diffusive transport, we consider narrow escape problems, diffusion to a small target, confined and single-file diffusion, homogenization theory, and fractional diffusion. In the case of active transport, we consider Brownian ratchets, random walk models, exclusion processes, random intermittent search processes, quasisteady-state reduction methods, and mean field approximations. Applications include receptor trafficking, axonal transport, membrane diffusion, nuclear transport, protein-DNA interactions, virus trafficking, and the self-organization of subcellular structures.

show abstract

Section: Diffusion Along Spiny Dendritesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Stochastic models of intracellular transport

2013

View full text Add to dashboard Cite

show abstract

“…Given the fact that the radius of the spine neck is typically at the submicron level, which is much smaller than any other length scale of the system, we can take into account the discreteness of spines by representing the spine density as a sum of Dirac delta functions Bressloff and Earnshaw 2007;Meunier and d'Incamps 2008;Bressloff 2009):…”

Section: Pulsating Waves In the Presence Of Discretely Distributed Spmentioning

confidence: 99%

Propagation of CaMKII translocation waves in heterogeneous spiny dendrites

Bressloff

2012

J. Math. Biol.

View full text Add to dashboard Cite

CaMKII (Ca 2+ -calmodulin-dependent protein kinase II) is a key regulator of glutamatergic synapses and plays an essential role in many forms of synaptic plasticity. It has recently been observed experimentally that stimulating a local region of dendrite not only induces the local translocation of CaMKII from the dendritic shaft to synaptic targets within spines, but also initiates a wave of CaMKII translocation that spreads distally through the dendrite with an average speed of order 1µm/s. We have previously developed a simple reaction-diffusion model of CaMKII translocation waves that can account for the observed wavespeed and predicts wave propagation failure if the density of spines is too high. A major simplification of our previous model was to treat the distribution of spines as spatially uniform. However, there are at least two sources of heterogeneity in the spine distribution that occur on two different spatial scales. First, spines are discrete entities that are joined to a dendritic branch via a thin spine neck of submicron radius, resulting in spatial variations in spine density at the micron level. The second source of heterogeneity occurs on a much longer length scale and reflects the experimental observation that there is a slow proximal to distal variation in the density of spines. In this paper, we analyze how both sources of heterogeneity modulate the speed of CaMKII translocation waves along a spiny dendrite. We adapt methods from the study of the spread of biological invasions in heterogeneous environments, including homogenization theory of pulsating fronts and Hamilton-Jacobi dynamics of sharp interfaces.

show abstract

“…This Markovian model corresponds to the phenomenological approach for spine-dendrite interaction [12]. Consider now the non-Markovian case when both waiting time PDFs c i are gamma distributions c i ðtÞ ¼ [14], i.e., hx 2 ðtÞi $ t , where 0 < < 1.…”

Section: Prl 101 218102 (2008) P H Y S I C a L R E V I E W L E T T Ementioning

confidence: 99%

“…In recent years, the development of confocal microscopies and other techniques allow one to study the transport and biochemical reactions on the microscopic level of a single spine and a parent dendrite [7][8][9]. There are several models for the particle transport and chemical reactions inside biological microdomains [10][11][12][13]. Santamaria et al [14] found recently that the transport of biologically inert particles (fluorescein dextran) in spiny dendrites is very slow in comparison to the standard diffusion.…”

mentioning

confidence: 99%

Non-Markovian Model for Transport and Reactions of Particles in Spiny Dendrites

Fedotov

Méndez

2008

Phys. Rev. Lett.

View full text Add to dashboard Cite

Motivated by the experiments [Santamaria et al., Neuron 52, 635 (2006)] that indicated the possibility of subdiffusive transport of molecules along dendrites of cerebellar Purkinje cells, we develop a mesoscopic model for transport and chemical reactions of particles in spiny dendrites. The communication between spines and a parent dendrite is described by a non-Markovian random process and, as a result, the overall movement of particles can be subdiffusive. A system of integrodifferential equations is derived for the particles densities in dendrites and spines. This system involves the spine-dendrite interaction term which describes the memory effects and nonlocality in space. We consider the impact of power-law waiting time distributions on the transport of biochemical signals and mechanism of the accumulation of plasticity-inducing signals inside spines. Dendritic spines are essential elements of most brain regions because they form a surface for receiving synaptic inputs. For the Purkinje cells of the cerebellar cortex, over 90% of their excitatory synapses are located on dendritic spines. They are believed to play a very important role in regulating neuronal activity [1][2][3]. The heads of spines have an active membrane; therefore, the spiny dendrites can sustain the propagation of an action potential. The propagation rate depends on the spatial distribution of spines along dendrites. Much theoretical work has been devoted to studying the interaction of spines with dendrites on the macroscopic level. Baer and Rinzel [4] proposed a cable theory for excitable spiny dendrites and found that the spread of local excitation strongly depends on a spinestem resistance. There are many extensions of this work that take into account the dynamic structure of spines and their changes in response to synaptic activity [5]. Coombes and Bressloff suggested the simplified version of classical theory based on FitzHugh-Nagumo model [6]. Note that these cable models are phenomenological and not derived from the transport and biochemical reactions equations for ions in spiny dendrites. In recent years, the development of confocal microscopies and other techniques allow one to study the transport and biochemical reactions on the microscopic level of a single spine and a parent dendrite [7][8][9]. There are several models for the particle transport and chemical reactions inside biological microdomains [10][11][12][13]. Santamaria et al. [14] found recently that the transport of biologically inert particles (fluorescein dextran) in spiny dendrites is very slow in comparison to the standard diffusion. The mean-square displacement is hx 2 ðtÞi $ t with < 1 [15,16]. The authors suggested that the main reason for this anomalous diffusion is that the dendritic spines act as the traps of particles. Henry et al. [17] addressed this problem by proposing a cable model derived from fractional Nernst-Planck equations. Whereas many studies have been devoted to the coupling between spines and dendrites, they are either phenomenological cable ...

show abstract

Diffusion-trapping model of receptor trafficking in dendrites

Cited by 49 publications

References 28 publications

Stochastic models of intracellular transport

Stochastic models of intracellular transport

Propagation of CaMKII translocation waves in heterogeneous spiny dendrites

Non-Markovian Model for Transport and Reactions of Particles in Spiny Dendrites

Contact Info

Product

Resources

About