Free energy landscape with two barriers and a transient intermediate state determining the unfolding and folding dynamics of cold shock protein

Cold shock protein (Csp) is a typical two-state folding model protein which has been widely studied by biochemistry and single molecule techniques. Recently two-state property of Csp was confirmed by atomic force microscopy (AFM) through direct pulling measurement, while several long-lifetime intermediate states were found by force-clamp AFM. We systematically studied force-dependent folding and unfolding dynamics of Csp using magnetic tweezers with intrinsic constant force capability. We found that Csp mostly folds and unfolds with a single step over force range from 5 pN to 50 pN, and the unfolding rates show different force sensitivities at forces below and above ~8 pN, which determines a free energy landscape with two barriers and a transient intermediate between them along one transition pathway. Our results provide a new insight on protein folding mechanism of two-state proteins.


Introduction
Most small single domain proteins fold to unique three-dimensional structure, and the thermodynamics of protein folding and unfolding can be described by two-state model with highly populated native state and unfolded state only 1,2 .
But the detailed mechanism of protein folding/unfolding, such as transition pathway, properties of transition state, and existence of intermediate states, needs further study by newly developed highly sensitive techniques.
Theoretically, funnel-shaped free energy landscape with native state at the bottom provides a general picture of proteins folding 3,4  Single molecular manipulation techniques apply force to tilt the free energy landscape, and record the conformation transition process of single protein through extension and force signals 6 . Force-dependent transition rate and detection of short-lived intermediate states provide hints to study the complex free-energy landscape of proteins 7

. Cold shock protein B (Csp) from
Thermotoga maritima is a model protein to study protein folding dynamics with a single peptide chain of 66 amino acids. Csp has a highly conserved single domain structure which can interact with single stranded DNA or RNA 8,9 . Csp functions as nucleic acid chaperons to prevent the formation of DNA/RNA secondary structures at low temperature 10 . Previous bulk experiment and single molecular fluorescence experiment both suggested that Csp is a typical twostate model protein [11][12][13] . Single-molecule force spectroscopy by atomic force microscope (AFM) measured force-induced unfolding of Csp at constant pulling speeds from 100 nm s -1 to 2000 nm s -1 . Single-step unfolding signal of Csp is consistent with two-state model, and pulling-speed-dependent unfolding forces gave unfolding distance = 0.49 nm 14   The obtained fitting parameters, especially , show large discrepancy between the above two measurements. Additionally, the obtained is bigger than previous results by AFM 14 . Therefore, we suspect that force-dependent unfolding rates cannot be described by Bell's model. Theoretically modelindependent unfolding rate can be obtained from unfolding force distribution P( ), but it requires large amount of data to give an accurate P( ) 25 . Four independent measurements give = 6.6 ± 0.2 pN and = 14 ± 1 nm which is consistent with the recorded step size ( Supplementary Fig. 1).
In order to explore the unfolding rate at higher force range, we did the force jump experiment from 10 pN to 50 pN (Fig. 3). Firstly, we hold the protein at force 1 pN and changed force to various high values abruptly to record unfolding step of Csp. After observing unfolding step of Csp, we decreased force to 1 pN and kept force of 1 pN for 20 sec to make Csp fold to native state.
We suppose that the folding transition state is the same as the unfolding transition state in force range of 5-7 pN, then folding transition state has a size of 0 = 4.2 nm. Then the force-dependent folding rates can be fitted with Supplementary Eq. (11) with a zero-force folding rate 0 = 400±100 s -1 (blue solid curve in Fig. 4a and 4b).
Based on the force-dependent unfolding and folding rates, we can get the force dependent folding free energy ( ) according to Supplementary Eq.

⇌ →
We found that the unfolding rate is not sensitive to location of state I along the unfolding pathway (Fig. 4c). As we cannot detect state I directly in recorded time course of extension, state I must be not very stable. We suppose that state I has free energy ~14 and located at position in the middle of TS1 and TS2, the force-dependent unfolding rates can be fitted with analytical equations of NIU model derived by Pierse and Dudko 27 (Fig. 4a，Supplementary Note 2).
Interdependence between parameters is given in Supplementary Fig. 5.

Discussion
In summary, force-dependent unfolding and folding rate of Csp at a force range from 5 pN to 50 pN were measured directly by magnetic tweezers, especially the force-dependent folding rate which is not measured before.  Fig. 4). One possibility is that the protein was injured at some unknown position during such long-time measurement.
We found that force-dependent unfolding rate cannot be fitted with Bell's model. Unfolding of Csp is more sensitive to force when force is smaller than 8 pN, and less sensitive to force at force range greater than 8 pN. A similar phenomenon has been found in GB1 protein 28 . As shown in Fig. 4c, TS1 with  Protein with N-terminus AviTag and C-terminus SpyTag was flowed into chamber and incubated for 25 min, then streptavidin-coated paramagnetic beads M270 were flowed into the chamber to form tether.
Home-made magnetic tweezers were used to apply stretching force to Csp protein tether to study its force-dependent folding and unfolding dynamics.
Constant loading rates between 0.25 pN s -1 and 6 pN s -1 were used by moving magnets with different speeds. Force jump experiments were done by moving magnets rapidly in less than 0.15 sec. Details of magnetic tweezers design can be referenced to our previous publication 19 .

Data availability
The authors declare that all data supporting the findings of this study are available within the article and its supplementary information files.