Often, complex molecules are described in terms of their atomic masses. But what

Question

Often, complex molecules are described in terms of their atomic masses. But what is more relevant in biology is how they take up space. (For proteins, their shapes are particularly important.) Let's see if we can get an approximate idea of the physical size of a protein molecule by doing various estimations.

An important molecule in the internal mechanisms of cells is Actin. This is measured as having a mass of about 42 kDa (= 42,000 Daltons, where 12 Daltons is defined as the mass of a carbon atom). Let's see if we can estimate how big it is using very crude estimates. Of course eventually we will want to know how big it actually is and what its shape is, but getting a scale would help us determine what measurement tools might be appropriate.

In order to estimate the size of Actin, we'll first make an estimate of how many atoms it has, then, using the average size of an atom, we'll consider different models of how it might be arranged to get an idea of its size.

A. We could look up the chemical composition of Actin to get exactly how many atoms it contains. But let's see how "the estimation game" does instead. Actin is a biological molecule, so it's probably made up of mostly carbon, oxygen, nitrogen, and hydrogen, with a few other stray atoms tossed in. Use an "average sized biological atom" to estimate the number of atoms in Actin.

_______ atoms

B. Given the radius of an average atom let's consider a simple model of Actin. Suppose Actin is tightly packed into a sphere or cube. For estimation purposes we could model each atom as a cube. If you built up a cube of the total number of atoms you found in A, what would be the dimension of each side of the cube?

______ nm

Explanation / Answer

For A)

Let us first identify the molar masses of each atom:

MW of H = 1 g/mol

MW of C = 12 g/mol

MW of N = 14 g/mol

MW of O = 16 g/mol

Average = MW of (H +C+N+O) / total n

Average = (1+12+14+16)/(4)

Average = 10.75 g/mol approx... so we could say that, in average, the atoms of the molecule are 10.75 g /mol

but we are interested "per atom" so

Mass of Actin = 42000 Da

1 Da = 1 g/mol

42000 Da = 42000 = 42000 g per mol of Actin

and we know that...

1 mol of Actin = 42000 g

mol of Actin = mass/MW = 42000/ 10.75 = 3906.97 mol of Actin

1 mol = 6.022*10^23 atoms

3906.97 mol = 3906.97*6.022*10^23 = 2.352*10^27 atoms are present in ACTIN

B)

V of cube = L^3

1 atom = 1 cube

radius of average atom =  2.5*10^-10 m (since they range from 1*10^-10 to 10*10^-10 m)

Volume of 1 atom:

Assume Length = 2*R = 2*2.5*10^-10 = 5*10^-10 m

change to nm

nm 10^9 to m

so

5*10^-10 m * 10^9 = 50 nm

Lenght of cube = 50 nm

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