Multi-barrier unfolding of the double-knotted protein, TrmD-Tm1570, revealed by single-molecule force spectroscopy and molecular dynamics

This study combines single-molecule force spectroscopy and molecular dynamics simulations to reveal that the double-knotted TrmD-Tm1570 protein exhibits unique mechanical unfolding pathways and higher stability than its single-knotted counterparts, suggesting that native contacts alone are insufficient for its complete folding and that chaperone assistance may be required.

The Gist

Imagine a protein not as a simple string of beads, but as a piece of yarn that nature has tied into a complex knot. Most proteins have no knots, some have one simple knot (like a shoelace tied once), but the star of this study is a rare "double-knotted" protein called TrmD-Tm1570. It's like a single piece of yarn that has been tied into two separate, deep knots, one inside the other, making it incredibly tangled.

Here is the story of how scientists tried to understand how this protein works, how it falls apart, and why it's so tricky to study.

1. The Mystery of the "Self-Tying" Yarn

Scientists have long wondered: How does a protein tie itself into a knot?
For proteins with just one knot, the answer is usually that they can "self-tie." Imagine a person threading a needle; the protein folds itself, and the end of the chain slips through a loop to create the knot.

However, when the researchers tried to simulate the double-knotted TrmD-Tm1570 on a supercomputer, they hit a wall.

• The Analogy: Think of trying to tie two complex knots in a single rope while blindfolded. The computer models tried millions of times to fold the protein from a loose string into its final knotted shape, but it never happened. The protein just couldn't tie the second knot on its own.
• The Conclusion: Nature likely doesn't leave this protein to its own devices. It probably needs a "helper" (a molecular chaperone) to guide the rope through the loops, much like a human assistant helping you tie a complicated knot.

2. The "Un-tying" Game: Four Ways to Untangle

Since the protein couldn't tie itself in the simulation, the scientists flipped the script and asked: "How does it come undone?"

They simulated pulling the protein apart and found four different ways it could unravel.

• The Analogy: Imagine two people holding hands, each wearing a heavy backpack with a complex lock (the knot). To get free, they have to take off the backpacks.
  • Pathway A: Person 1 takes off their backpack, unlocks it, and then Person 2 does the same.
  • Pathway B: They both take off their backpacks first, then unlock them one by one.
  • Pathway C & D: A mix of the above, where one person unlocks while the other is still struggling with their pack.

The most common way they found was that the two parts of the protein (TrmD and Tm1570) could actually untie themselves independently. One part would unravel and un-knot, while the other stayed knotted for a while, before finally letting go.

3. The "Tug-of-War" Experiment

To see if this matched reality, the scientists used a high-tech tool called Optical Tweezers.

• The Analogy: Imagine holding a piece of DNA with two tiny, invisible laser beams (like tweezers made of light). They gently pulled the protein apart, stretching it like a rubber band, and measured how much force was needed to break it.

What they found:

• The Stronger Knot: One part of the protein (Tm1570) was much harder to pull apart than the other (TrmD).
• Why? It comes down to where the knot sits. In Tm1570, the knot is tucked deeper inside, closer to the end of the rope, making it harder to pull loose. In TrmD, the knot is a bit more exposed.
• The "Stuck" State: Even when they pulled the protein until it was fully stretched out, the knot didn't disappear. It stayed tied, just like a knot in a rubber band that stays knotted even when you stretch the band to its limit.

4. Why Does This Matter?

This study is a big deal for a few reasons:

1. Complexity: It shows that double knots are so complex that they likely need help from the cell to form. This changes how we think about how proteins are built.
2. Stability: The double knot makes the protein incredibly tough. It's like a super-reinforced structure that resists heat and physical pulling.
3. The Future: There are over 1,200 proteins predicted to have these double knots. Understanding how TrmD-Tm1570 works is like finding the first key to a locked room; it helps us understand how all these other complex, knotted proteins function, how they degrade (break down), and how we might be able to target them for medicine.

The Big Takeaway

Nature is a master knot-tyer, but some knots are so complex that even the protein can't tie them alone. It needs a helper. Once tied, these double knots act like super-strong anchors, making the protein incredibly stable and difficult to break, even when you pull on it with all your might. This research helps us understand the "rules of the knot" in the microscopic world of life.

Technical Summary

1. Problem Statement

Protein folding is a fundamental challenge in structural biology, particularly regarding proteins with complex topologies like knots. While single-knotted proteins (e.g., trefoil knots) are known to sometimes self-fold, double-knotted proteins (specifically the composite $3_1\#3_1$ topology) represent a rare and poorly understood class.

• The Specific Challenge: The paper focuses on TrmD–Tm1570, a fusion protein from Calditerrivibrio nitroreducens containing two deep trefoil knots ($3_1$) in its N-terminal (TrmD) and C-terminal (Tm1570) domains.
• Key Questions:
  1. Can double-knotted proteins self-fold into their native state without external assistance (chaperones)?
  2. What are the mechanical and thermal unfolding pathways of such complex topologies?
  3. How does the presence of a second knot affect the stability and folding kinetics of individual domains compared to their single-knotted counterparts?

2. Methodology

The study employed a multi-modal approach combining biophysical experiments, coarse-grained molecular dynamics (MD) simulations, all-atom simulations, and AI-driven data analysis.

• Protein Systems:

  • TrmD–Tm1570: The double-knotted fusion protein (residues 1–433).
  • TrmD: Single-knotted N-terminal domain (residues 1–240).
  • Tm1570: Single-knotted C-terminal domain (residues 241–433).
  • Note: All proteins were engineered with terminal cysteines for optical tweezer attachment.

• Experimental Techniques:

  • Optical Tweezers (OT): Single-molecule force spectroscopy was used to perform constant-velocity mechanical unfolding and refolding experiments (20 nm/s and 500 nm/s). This allowed for the measurement of contour length changes and force-extension profiles.
  • Differential Scanning Fluorimetry (DSF): Used to assess thermal stability and melting temperatures.

• Computational Simulations:

  • Coarse-Grained (CG) Models:
    • SBM-C$\alpha$ (Structure-Based Model): Used to simulate folding and unfolding pathways based on native contacts.
    • UNRES: A different CG model used to verify folding capabilities.
    • Thermal Unfolding: Simulations performed by increasing temperature to identify unfolding pathways.
    • Mechanical Unfolding: Constant-velocity pulling simulations mimicking OT experiments.
  • All-Atom MD: Explicit solvent simulations (CHARMM36 force field) performed to validate end-to-end distances and knot core stability.
  • AI/Data Analysis: Self-Organizing Maps (SOM) were utilized to cluster high-dimensional simulation trajectories and identify dominant unfolding pathways and force-extension patterns.

3. Key Contributions & Results

A. Folding Limitations: The "Self-Tying" Barrier

• Finding: While single-knotted proteins (TrmD and Tm1570 individually) could successfully self-fold into their native knotted states in CG simulations (albeit with low success rates typical of SPOUT family proteins), the double-knotted TrmD–Tm1570 failed to fold in any of the tested simulations.
• Implication: Native contacts alone are insufficient to drive the formation of a double knot. The authors hypothesize that the double-knotted protein likely requires ribosomal assistance or molecular chaperones to navigate the topological barriers during de novo folding.

B. Unfolding Pathways (Mechanical and Thermal)

The study identified four distinct unfolding and untying pathways for the fusion protein, characterized by the order of domain unfolding and knot untying:

1. Pathway 1 & 2: TrmD unfolds/unties first, followed by Tm1570.
2. Pathway 3 & 4: Tm1570 unfolds/unties first, followed by TrmD.

• Reversibility: Optical tweezer experiments confirmed that the unfolding process is reversible. However, the stretched state often remains knotted, indicating that the knot does not immediately untie upon stretching but rather tightens or persists until specific structural barriers are overcome.
• Dominant Pathway: Pathway 2 (TrmD unfolds first, followed by Tm1570) was the most populated in simulations, consistent with experimental degradation data showing TrmD is less stable than Tm1570.

C. Mechanical Stability and Knot Depth

• Stability Hierarchy: Tm1570 is mechanically and thermally more stable than TrmD.
  • Reason: The knot core in Tm1570 is located closer to the C-terminus (residues 113–158) compared to TrmD (residues 85–129). The deeper knot in TrmD (relative to the pulling direction in some contexts) and its specific structural constraints make it more susceptible to mechanical rupture.
• Force-Extension Profiles:
  • TrmD: Exhibited two main unfolding events (total $\Delta L \approx 45.8$ nm).
  • Tm1570: Exhibited three main unfolding events (total $\Delta L \approx 53.3$ nm).
  • Fusion (TrmD–Tm1570): Showed a complex profile with multiple peaks, but crucially, only 45% of traces showed complete unfolding. The remaining traces retained structure, attributed to the persistence of the knots which resist mechanical force.
• Knot Tightening: Simulations revealed that knots tighten significantly during the final stages of mechanical unfolding, acting as a "safety lock" that prevents full extension until high forces are applied.

D. AI-Driven Trajectory Clustering

• The use of Self-Organizing Maps (SOM) allowed the researchers to reduce the complexity of thousands of simulation trajectories into distinct clusters. This confirmed that while multiple pathways exist, specific dominant routes (like Pathway 2) are statistically favored, providing a robust statistical basis for the proposed mechanisms.

4. Significance

• Topological Complexity: This study provides the first comprehensive characterization of the unfolding mechanism of a naturally occurring double-knotted protein ($3_1\#3_1$).
• Folding Paradox: It highlights a critical limitation in current structure-based models: they can simulate the folding of single knots but fail for double knots, suggesting that cellular machinery (chaperones) is essential for the biogenesis of such complex topologies.
• Mechanical Resilience: The findings demonstrate that knotted proteins possess unique mechanical stability properties where the knot acts as a barrier to degradation and unfolding. The persistence of knots in the stretched state suggests a potential biological role in resisting proteolytic degradation or mechanical stress.
• Broader Impact: With over 1,200 predicted double-knotted proteins (including membrane proteins), understanding the TrmD–Tm1570 system offers a blueprint for investigating the folding, stability, and function of this entire class of entangled proteins.

Conclusion

The paper concludes that the double-knotted TrmD–Tm1570 protein represents a complex system where self-folding is kinetically trapped without external assistance, while mechanical unfolding follows a multi-barrier pathway where the two domains can untie independently. The study underscores the importance of knot depth and position in determining protein stability and suggests that the evolution of double knots may be tightly coupled with the evolution of chaperone systems.