Questions & explanations
1. Given the HP sequence HPHPPH, find a compact 2D lattice shape that maximizes H-H contacts. How many contacts can you make?
One possible shape is a 3x2 rectangle. Place beads: position 1 (H) at (0,0), 2 (P) at (1,0), 3 (H) at (1,1), 4 (P) at (0,1), 5 (P) at (0,2), 6 (H) at (1,2). Contacts: H at (0,0) touches H at (1,1)? No, diagonal doesn't count. Only orthogonal neighbors: (0,0) touches (1,0) P, (0,1) P; no H-H. (1,1) H touches (1,0) P, (0,1) P, (1,2) H? Yes, (1,1) and (1,2) are orthogonal neighbors, so one H-H contact. Also (1,2) H touches (0,2) P. So only 1 H-H contact. A better shape: a zigzag: (0,0)H, (1,0)P, (1,1)H, (0,1)P, (0,2)P, (1,2)H gives contacts: (0,0)H with (1,1)H? No, diagonal. (1,1)H with (1,2)H? Yes, that's 1. So still 1. Actually, with 6 beads, maximum H-H contacts is 2 if you make a 2x3 rectangle: H at corners? Let's try: positions: (0,0)H, (1,0)P, (2,0)H, (2,1)P, (1,1)P, (0,1)H. Contacts: (0,0)H with (0,1)H? Yes, 1. (2,0)H with (2,1)P? No. (0,1)H with (1,1)P? No. So only 1. Actually, with 3 H's, max contacts is 2 if they form a line: e.g., (0,0)H, (1,0)H, (2,0)H? But sequence has P in between. So answer: 1 contact is possible.
2. How can single-molecule studies distinguish between induced fit and conformational selection in molecular recognition?
Induced fit means binding causes a conformational change, while conformational selection means the protein samples different shapes and the ligand binds to one. Single-molecule FRET (Foerster resonance energy transfer) can tell them apart. In conformational selection, the protein shows spontaneous fluctuations between states before ligand is added. The ligand then binds preferentially to one state, reducing fluctuations. In induced fit, the protein is mostly in one state without ligand, and binding triggers a new conformation. By watching individual molecules, researchers see the order of events: if a conformational change occurs before binding, it's selection; if after, it's induced fit. Many systems use a mix of both.
3. How can single-molecule methods distinguish between specific and non-specific adhesion?
Specific adhesion involves receptor-ligand pairs, while non-specific adhesion is due to general forces like electrostatics. Single-molecule force spectroscopy measures the force-distance curve. Specific bonds show a characteristic unbinding force that depends on the pulling speed. Non-specific interactions have a broad distribution and lower forces. Also, specific bonds can be blocked by adding free ligand or antibodies. By recording many events, researchers can separate the two types. For example, integrin-fibronectin bonds show a peak at 80 pN, while non-specific adhesion gives a flat background. This allows quantification of receptor density and binding probability.
4. Give an example of how single-molecule methods reveal the mechanism of cooperative binding in an allosteric enzyme.
Cooperative binding means that binding of one ligand affects binding of another. For the enzyme aspartate transcarbamoylase (ATCase), single-molecule fluorescence labels each subunit. Researchers observe that binding of the first substrate molecule induces a conformational change that increases affinity for the next substrate. This is seen as a shift in FRET (Foerster resonance energy transfer) signal. The enzyme exists in a low-activity T state and a high-activity R state. Substrate binding stabilizes the R state, making it easier for more substrate to bind. Single-molecule data show that the transition between states is concerted: all subunits change together.
5. If an enzyme has a very high k_2 (fast product formation), how does that affect the steady-state assumption?
If k_2 is very high, product formation is fast, so the enzyme-substrate complex breaks down quickly into product. The steady-state assumption may still hold if substrate is in excess, but the complex concentration may be low. The Michaelis constant K_M becomes larger because k_2 adds to the numerator. The reaction rate can be high because k_cat (which equals k_2) is large. The steady-state assumption requires that the complex concentration does not change rapidly; fast product formation can still maintain steady state if substrate replenishes the complex. However, if k_2 is extremely high, the complex may be depleted quickly, and the assumption may break down.
6. How does WaterLOGSY use water molecules to detect ligand binding?
WaterLOGSY relies on magnetization transfer from water to the protein and then to the ligand. First, water protons are selectively inverted. Through chemical exchange and NOE (Nuclear Overhauser Effect), the inverted magnetization spreads to the protein. Bound ligands receive this inverted magnetization via intermolecular NOE from the protein. When the ligand dissociates, it carries the inverted magnetization into solution. In the NMR spectrum, bound ligands show a negative signal (inverted), while free ligands that interact only with bulk water show a positive signal. The difference between inverted and non-inverted water experiments highlights binders.
7. How can single-molecule studies distinguish between proofreading and kinetic discrimination in splicing?
Proofreading involves checking and rejecting incorrect substrates, while kinetic discrimination relies on speed differences. Single-molecule assays measure binding and dissociation rates for correct vs. incorrect pre-mRNA. For proofreading, they observe that incorrect substrates bind but are quickly released after ATP hydrolysis. For kinetic discrimination, correct substrates trigger faster conformational changes. By tracking individual molecules, researchers see that both mechanisms operate at different steps. For example, U1 snRNP binding uses kinetic discrimination, while later steps involve proofreading. This dual strategy ensures high fidelity.
8. How does the Briggs-Haldane approach differ from the Michaelis-Menten rapid equilibrium assumption?
The Michaelis-Menten rapid equilibrium assumption says the enzyme-substrate complex forms and breaks down quickly, reaching equilibrium before product forms. The Briggs-Haldane steady-state assumption instead says the complex concentration stays constant, not necessarily at equilibrium. This makes the Briggs-Haldane model more widely applicable, especially when product formation is not much slower than complex breakdown. The two models give the same form of rate equation but different definitions of the Michaelis constant. The Briggs-Haldane constant includes both breakdown steps, while the rapid equilibrium constant only includes dissociation.
9. How does the presence of non-specific binding affect Kd determination in NMR titration?
Non-specific binding can complicate Kd determination because the observed signal changes may arise from multiple binding events with different affinities. This can lead to a poor fit to a simple one-site binding model. To account for non-specific binding, one may need to use a more complex model that includes a non-specific binding term or use a competition experiment. Alternatively, one can subtract the non-specific contribution by using a control ligand that does not bind specifically. If non-specific binding is strong, the apparent Kd may be overestimated (weaker binding) because the ligand is partitioned into non-specific sites.
10. How does the simultaneous iterative reconstruction technique (SIRT) improve upon WBP?
SIRT is an iterative algorithm that refines the reconstruction by repeatedly comparing the forward projections of the current volume with the measured projections. It starts with an initial guess, then computes the difference between the calculated and measured projections. This difference is back-projected to update the volume, and the process repeats. SIRT produces higher-quality reconstructions with fewer artifacts than WBP, especially when the tilt range is limited. However, it is computationally slower because it requires many iterations. SIRT also handles missing wedge effects better by enforcing consistency with the data.
11. What is WaterLOGSY and what does it detect?
WaterLOGSY stands for Water-Ligand Observed via Gradient Spectroscopy. It is an NMR method to detect ligand binding to a protein. It uses the water molecules in the sample to transfer magnetization. The experiment compares two spectra: one where water magnetization is inverted, and one where it is not. Ligands that bind to the protein receive negative magnetization from water via the protein, while non-binders receive positive magnetization from bulk water. The difference spectrum shows binding ligands with negative signals, while non-binders give positive signals. It is a sensitive technique for screening compound libraries.
12. Compare the NMR approaches to study phosphorylation versus glycosylation of proteins.
Phosphorylation is often studied using 31P NMR, which directly detects the phosphate group. The 31P signal is sensitive to the environment and can show multiple phosphorylation states. Glycosylation is usually studied via 1H or 13C NMR, focusing on sugar anomeric protons. Phosphorylation typically causes larger chemical shift changes in the protein backbone than glycosylation. Glycosylation often involves more complex, heterogeneous structures. Both require comparing modified and unmodified samples. For phosphorylation, site-specific mutants can help, while for glycosylation, enzymatic removal of sugars is common.