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My question is, where does energy come from for passive translocase's conformational changes? I argue it can't be concentration gradient, as concentration is only statistical phenomenon at micro scale, and has nothing to do with energy of individual molecules and interactions. I also don't want to cover electric gradient, as it involves obvious electric forces.

I couldn't find any diagrams like this about this theme, so I would appreciate very much if someone provides me with one:

enter image description here

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  • $\begingroup$ I am not sure that the concentration gradient provides the energy for conformation changes in passive protein transporters (or at least the molecular mechanism), but your statement about a concentration gradient being unable to energy is obviously incorrect or Mitchell's hypothesis would have been thrown out years ago. Instead it won a Nobel Prize. (And that involves an electric gradient as well, whether or not you want to cover it.) $\endgroup$
    – David
    Feb 14, 2022 at 11:49
  • $\begingroup$ @David thank you for your response. concentration of molecules doesn't correlate to energy of each particle, but temperature does. i did not want to cover electric forces as they are already obvious, moreover, not all particles have charge, e.g. glucose. $\endgroup$
    – niko papiashvili
    Feb 14, 2022 at 12:08
  • $\begingroup$ I said concentration gradient, not concentration. There is a page in Berg et al. that derives the thermodynamic expression for the free energy change represented by a concentration gradient. Unfortunately this is no longer available online. $\endgroup$
    – David
    Feb 14, 2022 at 13:22

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Type of transport to be considered

The term used in the question — passive translocase — is not a standard description of any transporter protein. From the description I shall assume we are talking about what is called Passive Transport or Facilitated Diffusion. This is defined in the Wikipedia article on the topic as follows:

Facilitated Diffusion… is the process of spontaneous passive transport (as opposed to active transport) of molecules or ions across a biological membrane via specific transmembrane integral proteins. Being passive, facilitated transport does not directly require chemical energy from ATP hydrolysis in the transport step itself; rather, molecules and ions move down their concentration gradient reflecting its diffusive nature.

Although most structural information is available for ion transport, because of the specification of the question, I shall consider the transport of glucose (and other neutral sugars) by the proteins GLUT1 and GLUT3

The molecular concentration gradient supplies the energy for transport

Before considering the molecular interactions between the sugar and the transporter protein, it is necessary (because of the assertion otherwise in the question) to assert that the net difference in concentration of sugar between the two sides of the membrane supplies the overall energy for transport.

The free energy change in transporting a neutral species from one side of a membrane at a concentration c1 to the other side at a concentration c2 is:

ΔG = RTln(c2/c1) = 2.303RTlog10(c2/c1)

For example, if c1 = 10–1 M and c2 = 10–3 M, one can calculate the change in Free Energy as –11.3 kJ/mol.

General aspects of the thermodynamics of conformation changes in proteins

Many protein, e.g. allosteric proteins such as haemoglobin, can adopt two (or more) conformations differing only slightly in Gibbs Free Energy. Clearly, the conformation with the lower free energy will be favoured. However the position of the equilibrium between the two states can be changed by the specific binding of a small molecule which can favour the disfavoured structure, because the protein–ligand complex has a different, and lower, free energy than that of the free protein.

Ligand stablization of conformtion

A general alternating model of transporters was proposed by Jardetzky as long ago as 1966, assuming three characteristic features:

  1. A cavity in the transporter to accommodate the substrate
  2. Two different transporter conformations to allow for the molecular cavity to be open to one side of the membrane in one conformation and to the opposite side in the other
  3. A binding site for substrates in the cavity, the substrate affinity of which may be different in the two conformations.

Detailed thermodynamics of the GLUT transporters

Zhang and Han (Biophysics Reports 2016) performed the kind of thermodynamic analysis solicited in the question in the light of structural information on GLUT transporters of the major facilitator superfamily (MFS). They considered two conformation states — Cin and Cout, with and without bound substrate in a four step model:

Four step transporter model

They also presented a free-energy landscape of the type requested, concluding that the lower free energy of Cout after transport was due to loss of energy as heat.

Energy Landscape of GLUT transporters

For a full explanation it is, of course, necessary to consult the original paper.

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  • $\begingroup$ Thank you very much for your expertize. I wonder weather lower free energy of Cout after transport increases after regaining thermal energy from surroundings. That should finally answer my question. $\endgroup$
    – niko papiashvili
    Feb 15, 2022 at 16:10
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    $\begingroup$ @nikopapiashvili — I'm not an expert on transporters, and I do find this a bit puzzling myself. I would need to read and think a bit more about this. There are some protein chemists on the list that are more knowledgeable than me on thermodynamics. Perhaps they will chip in. $\endgroup$
    – David
    Feb 15, 2022 at 18:31

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