Transport proteins are proteins that facilitate the movement of substances (ions, small molecules, macromolecules) across biological membranes.
Let's analyze the options:
(a) Sodium-potassium pump (Na\(^+\)/K\(^+\)-ATPase): This is an active transport protein (an ion pump) that moves Na\(^+\) ions out of the cell and K\(^+\) ions into the cell against their concentration gradients, using ATP. It is a transport protein.
(b) Mechano-Sensitive ion Channels: These are ion channels that open or close in response to mechanical stimuli (e.g., stretch, pressure, touch). When open, they allow the passage of ions across the membrane. Thus, they are involved in ion transport and are a type of transport protein (specifically, a channel protein).
(c) The sodium-calcium exchanger (NCX): This is a transport protein that uses the electrochemical gradient of sodium ions (moving Na\(^+\) into the cell) to drive the transport of calcium ions (Ca\(^{2+}\)) out of the cell (or vice-versa depending on conditions). It is an example of secondary active transport (an antiporter). It is a transport protein.
(d) Lactose permease: This is a membrane transport protein (a symporter) found in bacteria like E. coli. It transports lactose across the cell membrane into the cell, along with a proton (H\(^+\)). It is a transport protein.
All the options listed are indeed types of transport proteins or are directly involved in transport across membranes. The question asks "Which of the following is not a transport protein?" This suggests there might be a subtlety in definition or one option is fundamentally different in classification.
Mechano-sensitive ion channels are proteins that form channels for ion transport, gated by mechanical force. Pumps, exchangers, and permeases are also proteins facilitating transport.
If the question is trying to distinguish between different *types* of transport mechanisms where one is not primarily "just a transporter" but a sensor-transducer that then transports:
Ion channels are typically considered transport proteins.
Perhaps the question is flawed, as all listed are involved in transport. However, if "transport protein" is used in a more restrictive sense to mean carriers or pumps that bind and move specific solutes, then ion channels (which form pores) could be considered a slightly different category, though still facilitating transport.
The provided checkmark is on (b) "Mechano-Sensitive ion Channels".
One reason this might be considered "not a transport protein" in a very narrow sense is if the emphasis is on their gating mechanism (mechano-sensation) rather than just the transport function once gated. However, they fundamentally transport ions.
This is a problematic question if all options are involved in transport. Let's assume the distinction is based on primary classification where the "mechano-sensitive" aspect is considered primary over the "ion channel/transport" aspect for the purpose of this question.
\[ \boxed{\text{Mechano-Sensitive ion Channels (this is debatable as they are ion transport channels)}} \]