Chapter 17, Problem 12Q

Summary Introduction

To calculate: The average time required for a small particle, a protein, and a membrane vesicle to diffuse from one side to another side.

Introduction: Cell is the basic unit of the life. It consists of many molecules to carry out biological processes. The molecules across the cell can move or diffuse. Different molecules take different time to travel from one place to another side of the cell.

Explanation of Solution

Calculation:

Given,

$\begin{array}{l}\text{Approximate}\text{time}\text{(t)}\text{is}\text{cacluted}\text{as follows:}\\ \text{t}\text{=}{\text{x}}^{\text{2}}\text{/2D}\mathrm{..............}\text{ (1)}\\ \text{Where}\\ \text{t}\text{=}\text{Time}\text{taken}\\ \text{x}=\text{Distance}\\ \text{D}\text{=}\text{Diffusion}\text{coefficient}\end{array}$

$\begin{array}{l}\text{Diffusion}\text{coefficient for small}\text{molecule}\text{=}\text{5}\text{×}{\text{10}}^{\text{-6}}{\text{cm}}^{\text{2}}\text{/sec}\\ \text{Diffusion}\text{coefficient for a protein}\text{=}\text{5}\text{×}{\text{10}}^{\text{-7}}{\text{cm}}^{\text{2}}\text{/sec}\end{array}$

$\begin{array}{l}\text{Diffusion}\text{coefficient for a vesicle}\text{= 5}\text{×}{\text{10}}^{\text{-8}}{\text{cm}}^{\text{2}}\text{/sec}\\ \text{Distance}(x)\text{=}\text{10}\text{μm}\text{=}\text{10}\text{cm}\end{array}$

Average time for a small protein molecule can be calculated by substituting the value of diffusion coefficient (D) for small molecule and x in equation (1),

$\begin{array}{l}\text{t}\text{=}{{\text{(10}}^{\text{-3}}}^{\text{)}}\text{/}\text{(2}\text{×}\text{5}\text{×}{\text{10}}^{\text{-6}}\text{)}\\ \text{=}\text{0}\text{.1}\text{seconds}\end{array}$

Average time for a small protein molecule can be calculated by substituting the value of diffusion coefficient (D) for a protein and x in equation (1),

$\begin{array}{l}\text{t}\text{=}{{\text{(10}}^{\text{-3}}}^{\text{)}}\text{/}\text{(2}\text{×}\text{5}\text{×}{\text{10}}^{\text{-7}}\text{)}\\ \text{=}\text{1}\text{second}\end{array}$

Similarly, the time required for a membrane vesicle is

$\begin{array}{l}\text{t}\text{=}{{\text{(10}}^{\text{-3}}}^{\text{)}}\text{/}\text{(2}\text{×}\text{5}\text{×}{\text{10}}^{\text{-8}}\text{)}\\ \text{=}\text{1}0\text{seconds}\end{array}$

Conclusion

The time required for a small particle, a protein, and a membrane vesicle to travel 10µm is 0.1 second, 1 second, and 10 seconds, respectively.

Summary Introduction

To calculate: The time required for a membrane vesicle to travel 10 cm long axon.

Introduction: Cell is the basic unit of the life. It consists of many molecules to carry out biological processes. The molecules across the cell can move or diffuse. Different molecules take different time to travel from one place to another side of the cell.

Explanation of Solution

$\begin{array}{l}\text{Given,}\\ \text{Distance}\text{(x)}\text{=}\text{10cm}\end{array}$

Substituting the value of x and diffusion coefficient (D) of a membrane coefficient in equation (1), time (t) is

$\begin{array}{l}\text{t}\text{=}{\text{(10)}}^{\text{2}}\text{/}\text{(2}\text{×}\text{5}\text{×}{\text{10}}^{\text{-8}}\text{)}\\ \text{=}{\text{10}}^{\text{9}}\text{seconds}\end{array}$

Conclusion

The time required for a membrane vesicle to travel 10 cm is 10⁹ seconds.

Summary Introduction

To calculate: The time required for a membrane vesicle when it travels along microtubule at $\text{1}\text{μm/sec}$.

Introduction: Cell is the basic unit of the life. It consists of many molecules to carry out biological processes. The molecules across the cell can move or diffuse. Different molecules take different time to travel from one place to another side of the cell.

Explanation of Solution

Calculation:

Given,

$\begin{array}{l}\text{Speed}\text{of}\text{microtuble}\text{along}\text{microtuble}\text{is}\text{=}\text{1}\text{μm}\text{/}\text{sec}\\ \text{ =}{\text{10}}^{\text{-3}}\text{cm/sec}\end{array}$

Time required to travel a 10 cm long axon for a membrane vesicle along with microtubule is

$\begin{array}{l}\text{=}\frac{\text{1}}{{\text{10}}^{\text{-3}}}\text{×}\text{10}\\ \text{=}\text{0}\text{.0001sec}\end{array}$

Conclusion

The time required for a membrane vesicle along with microtubule to travel 10 cm is 0.0001 seconds.