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Research Papers

Modeling of Transient Transport of Soluble Proteins in the Connecting Cilium of a Photoreceptor Cell

[+] Author and Article Information
A. V. Kuznetsov

Department of Mechanical
and Aerospace Engineering,
North Carolina State University,
Campus Box 7910,
Raleigh, NC 27695-7910
e-mail: avkuznet@eos.ncsu.edu

Manuscript received February 29, 2012; final manuscript received August 13, 2012; published online January 18, 2013. Assoc. Editor: Debjyoti Banerjee.

J. Nanotechnol. Eng. Med 3(3), 031001 (Jan 18, 2013) (9 pages) doi:10.1115/1.4007567 History: Received February 29, 2012; Revised August 13, 2012

A minimal mathematical model describing mass transport in the connecting cilium (CC) of a photoreceptor cell in response to a suddenly increased protein concentration at the base of the CC is developed. Dimensionless governing equations and dimensionless parameters are identified. Analytical solutions are obtained for concentrations of free (diffusion-driven) and motor-driven proteins. The obtained solutions make it possible to predict mass transfer in the CC as a function of two dimensionless transport parameters involved in the model: the diffusivity of free soluble proteins and the transition rate from the diffusion-driven to the motor-driven state. Sensitivities of the obtained solutions to these two parameters are discussed.

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References

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Figures

Grahic Jump Location
Fig. 1

(a) Sketch of a photoreceptor cell: OS, the outer segment; CC, the connecting cilium; IS, the inner segment; A, the axon; and N, the nucleus. (b) Kinetic diagram showing soluble proteins transported anterogradely by molecular motors and free soluble proteins transported by diffusion as well as a possible transition between these two protein populations resulting from the attachment of free proteins to ITF complexes transported by anterograde motors.

Grahic Jump Location
Fig. 2

(a) Number density of free soluble proteins transported in the CC by diffusion; (b) number density of soluble proteins transported anterogradely along the axoneme by molecular motors; and (c) total concentration of soluble proteins transported along the axoneme. D0*=0.1 μm2/s, γ*=1 s−1.

Grahic Jump Location
Fig. 3

(a) Diffusion-driven flux of soluble proteins; (b) motor-driven flux of soluble proteins; and (c) total (diffusion plus motor-driven) flux of soluble proteins in the CC. D0*=0.1 μm2/s, γ*=1 s−1.

Grahic Jump Location
Fig. 4

Similar to Fig. 2, but now the diffusivity of free soluble proteins is reduced by a factor of 10: D0*=0.01 μm2/s

Grahic Jump Location
Fig. 5

Similar to Fig. 3, but now the diffusivity of free soluble proteins is reduced by a factor of 10: D0*=0.01 μm2/s

Grahic Jump Location
Fig. 6

Similar to Fig. 2, but now the diffusivity of free soluble proteins is increased by a factor of 5: D0*=0.5 μm2/s

Grahic Jump Location
Fig. 7

Similar to Fig. 3, but now the diffusivity of free soluble proteins is increased by a factor of 5: D0*=0.5 μm2/s

Grahic Jump Location
Fig. 8

Similar to Fig. 2, but now the value of the kinetic constant describing the probability of protein transition from the free to the anterograde motor-driven kinetic state is reduced by a factor of 10: γ*=0.1 s−1

Grahic Jump Location
Fig. 9

Similar to Fig. 3, but now the value of the kinetic constant describing the probability of protein transition from the free to the anterograde motor-driven kinetic state is reduced by a factor of 10: γ*=0.1 s−1

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