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I understand that in closed systems, once reactions reach equilibrium, they can no longer be used to power other reactions. If a cell was a closed system (which it is not), being at equilibrium would mean that it's dead, for it needs a continuous input of energy from the environment.

I know that the cells are open systems, and my teacher mentions that cells can never be at equilibrium. But, I am confused because can't cells be at dynamic equilibrium (where rates of reactions = rates of products)? So my next question is: can the cells not exist at static equilibrium? I am not quite understanding the differences between equilibrium, dynamic, and static. And, when something is at dynamic equilibrium, why does this mean that the concentrations of reactants and products are not necessarily equal?

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There are some things that should be addressed first.


Chemical-Equilibrium

This is a condition at which the forward reaction rate is equal to the backward reaction rate for a reversible reaction.

$$\ce{A<=>[k_f][k_r]B}$$

In this case, $k_f.A=k_r.B$, at the equilibrium, if the reactions are first-order. If $k_f>k_r$, then the concentration of B would be higher than the concentration of A, at equilibrium point.


Steady-State

It is a state of the system at which the overall concentration of all the components (reactants and products) remain constant with time, or oscillate at a constant amplitude and frequency. Mathematically, the differential equations that denote the system (as mentioned by Dexter) would equate to zero.

If this condition applies only for one or more but not all the components of the system, then it is said to be in a Quasi-Steady-State.

If there are only two species which inter-convert but do not get formed or degraded, then steady state would be same as the chemical equilibrium. However, it is to be noted that chemical-equilibrium is a property of a reversible reaction whereas steady state is the property of the system.


Coming to your main question, I do not know what your teacher really had in mind, but this is my explanation.

According to the above definitions, you cannot say that the cell is in equilibrium because the cell is a system and not a reaction. The usage of the term "equilibrium" varies between different fields of study and physicists do use steady-state and equilibrium interchangeably. However, this is not the practice among chemists and biochemists.

Having said that, I would say that a cell does attain a steady state. I think what your teacher wanted to imply was that a cell constantly responds to the external stimuli (which is randomly changing) and therefore never remains at any given steady state for a long time.

Can the cells not exist at static equilibrium?

No, they don't. In fact the term "static equilibrium" in never used in chemistry because it never really happens. At a static equilibrium all the rates have to be zero, whereas in a dynamic equilibrium the rates have to balance each other out. Static equilibrium usually applies only for macroscopic objects (which do not include molecules).

A note on stochasticity: Chemical reactions follow probabilistic kinetics i.e. the reactions occur with some probabilities, instead of fixed rates (these probabilities can be unequal for different reactions). Chemical systems can be approximated by deterministic models at the thermodynamic-limit which reflects the "average" behaviour of the system.

when something is at dynamic equilibrium, why does this mean that the concentrations of reactants and products are not necessarily equal?

See the first section. Similar logic applies for steady-state. The steady state concentrations depend on the kinetic parameters.

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If a cell was a closed system (which it is not),

Yes, you are right. Cell is not closed system.

my teacher mentions that cells can never be at equilibrium

No. It depends on your definition of equilibrium and which kind of equilibrium. E.g.: Cellular membranes are most of the time in chemical equilibrium to maintain their resting potential.

can't cells be at dynamic equilibrium (where rates of reactions = rates of products)?

Yes. Most of cellular processes are assumed to be in dynamic equilibrium which is correct in most of macroscopic phenomenons. Microscopically, everything is stochastic.

Most of cellular processes are assumed to be in dynamic equilibrium.

I am not quite understanding the differences between equilibrium, dynamic, and static. And, when something is at dynamic equilibrium

Look here!

And, when something is at dynamic equilibrium, why does this mean that the concentrations of reactants and products are not necessarily equal?

Suppose system A -> B -> C -> A, with reaction rates v1, v2 and v3. If you write differential equations for this system, $$ \frac{dA}{dt} = v3\times C - v1\times A\\ \frac{dB}{dt} = v1\times A - v2\times B\\ \frac{dC}{dt} = v2\times B - v3\times C $$ Now at equilibrium, $$ v3\times C = v1\times A = v2\times B $$ Now you can put your v1,v2 and v3 in such way that concentrations of A, B, C will be different. In this care system can be in dynamic equilibrium even when concentrations of A, B and C are not same.

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  • $\begingroup$ The condition that you are referring to, is specifically called the steady state in chemical and biochemical texts because chemical equilibrium is a different phenomenon. Physicists, generally use the term "equilibrium" to mean steady state. $\endgroup$ – WYSIWYG Sep 7 '15 at 8:47
  • $\begingroup$ This is better than all of our mathematical explanations. ! $\endgroup$ – Dexter Sep 7 '15 at 14:13
  • $\begingroup$ The video is nice.. But I think there are field specific differences (which are quite subtle). $\endgroup$ – WYSIWYG Sep 7 '15 at 14:49

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