Re: How does a cell evolve from a single-cell to a multicellular organism??

You've asked an interesting question, actually two questions, one about 
the origin of multicellularity and another about differentiation during 
development.  Your basic information is correct. Prior to cell division, 
genetic material is copied.  As you probably know, the DNA molecule has 
two complementary halves; each half acts as a template to form a new 
complementary half.  Mitosis is a process that separates the two identical 
sets of chromosomes.  Usually mitosis is coupled with cytokinesis, a 
process that divides the cytoplasm producing two separate cells.  Since 
multicellular organisms arise from a single cell, every cell has exactly 
the same genetic information.

It seems most logical to answer the last question first.  First 
multicellularity exists in a range of different forms.  In some 
multicellular organisms all cells are identical and therefore perform 
similar functions.  In other multicellular organisms cells may 
differentiate into specialized forms for specialized functions. In simple 
organisms, only occasional cells may have specialized functions.  In 
others virtually all cells may become specialized to form familiar tissues 
and organs.  But while all these specialized cells are genetically 
identical, different sets of genes, different portions of these genetic 
instructions, are being followed.  The developmental process is how cells 
obtain information about their "location" and what set of instructions to 
follow. Developmental biology studies how genes are regulated, turned on 
and turned off, as an organism develops from a single cell.  It's sort of 
like a map to a city.  All maps are identical, but different people follow 
different routes to arrive at different destinations.

Very simple organisms have much simpler genetic programs.  Consider a very 
simple organism, a filamentous algae.  A filament is a chain of identical 
cells, although some filamentous algae do produce specialized cells. The 
developmental program, in descriptive language, says to a cell, divide at 
right angles to your long axis.  This set of instructions is simply 
repeated to produce a filament.  If a second set of instructions was 
added, a more complex form could be produced.  For example, every 10th 
time, divide parallel to your long axis then return to dividing at right 
angles.  This will produce a branching filament.  Obviously more complex 
forms develop from the addition of new sets of instructions, which must be 
derived from the instructions that already exist.  In other words, you 
wouldn't expect a whole new set of instructions to just magically appear; 
you might however expect a new set of instructions that are just a little 
different from some set of instructions the cell already has.  And we know 
how such differences happen, mutations during DNA duplication.

Now let's address your first question.  How did multicellularity arise?  
Obviously from a small change in the instructions on how to divide into 
two separate cells, the most common form of asexual reproduction.  If for 
example you were to watch a large number of Chlamydomonas cell divide, you 
will occasionally see a double cell resulting from a failure of 
cytokinesis.  Perhaps this happens because of some mutation that causes  a 
failure to separate.  Most likely the failure will result in the early 
death of the double cell.  This is a form of natural selection and an 
example of how it works, in this case by weeding out mutations. But 
suppose the mutation only causes separation failure, say once every 20 
divisions or so.  Since it works OK 19 out of 20 times, the mutated 
instructions survive in the population even if the one of 20 dies.  But 
how could this become the regular case?  If for some reason the double 
cell found itself at an advantage, where it thrived instead of died, then 
natural selection would be reversed to favor the mutation.  Now I have no 
idea about what might cause selection for a double cell that could lead to 
multiple celled colonies and finally a magnificent organism like Volvox.  

However, let's consider another example, a very simple seaweed, a single 
celled algae anchored to a rock.  Space is very limited on something like 
a rock, so a larger size would allow this simple seaweed to compete better 
for space and therefore light.  So maybe it spreads out broadly, and this 
works fine, until a different simple seaweed moves into the adjacent 
space.  Rather than have a short, broad cell, the new seaweed produces a 
tall, slender cell that shades the short, broad cell, so the tall slender 
cell is a better competitor for light under these conditions.  Maybe a 
third even taller seaweed arrives, but this competitive race will end 
because there is a size limitation on single cells for both functional 
reasons (cells must maintain a functional volume to surface area) and 
structural reasons (big water balloons break easier than small water 
balloons).  If one of these single celled seaweeds had a mutation to its 
genetic program for dividing and failing separate every 20th time, similar 
to the one described above, then the production of a filament would be of 
real competive advantage allowing an even bigger size via 
multicellularity.  So that's the basic answer.  What was originally a 
mistake in the genetic instructions to divide and separate became 
instructions for making a simple multicellular organism (divide the cell, 
but don't separate), and for some reason, in this case compeition for 
light, the multicellular condition was an advantage.  

This is how evolution works.  A random process, mutation, causes variants, 
many of which aren't functional at all.  But some variants exist.  
Changing environmental conditions select among variants, favoring some and 
not others.  Favored sets of instructions, even altered ones, become a 
part of the organism's genetic instructions.  Complex sets of 
developmental instructions represent an accumulation of successful 
mistakes.  

Again think of the map analogy.  You learn a new route to a new location 
by retracing part of an old route and adding some new instructions to it.  
Where's the new Thai restaurant (I'm always hoping)?  Well, you know how 
to get to the grease-burger palace?  Well, rather than turning right by 
the school, just go one block further and turn right.  I found it by 
accidentally missing the turn.  And then you discover you like Thai food 
so much, you never return to the burger palace.  So now the instructions 
have become the route to phad thai not to fries.  Where's the bicycle shop 
where you got the cool recumbent bike that replaced your gas guzzler 
(still always hoping)?  Well, you know how to get to Bangkok Palace?  See 
how things develop?