Can Mechanical Stress Therapies be used in COVID-19 outbreak?

: Understanding the workings of the novel coronavirus (SARS-CoV-2) is crucial to develop counter therapeutic measures. SARS-CoV-2 gains entry into human cell by binding its receptor Binding Domain (RBD) of Spike protein (S1) to ACE2 receptors. In order to study the effect of mechanical stress on the RBD of SARS-CoV-2, it is modelled as viscoelastic material using Burgers Model. Strain response of RBD under constant stress is analyzed, which gives useful insights into the conformational transitions of RBD at 0K and physiological temperatures. The theoretical underpinning has shown that with increase in the number of stress cycles, the binding affinities of RBD conformational states to ACE2 receptor decrease, decreasing the binding reaction rate between ACE2 receptor and SARS-CoV-2. This analysis gives theoretical evidence that ultrasonic therapy and photo therapy (UV) can be potential candidates to reduce binding reaction rates between ACE2 and SARS-COV-2.

This fusion process is triggered when receptor-binding Domain (RBD) of S1 subunit binds with angiotensin-converting enzyme 2 (ACE2) of host cells found in lungs arteries, heart, kidney and intestines [8,9]. Wrapp, et al [7] showed two conformational states of RBD using cryo-electron microscopy. They referred two-conformations as "up" conformation for receptor accessible state and "down" conformation as receptor inaccessible state. The up-conformation is thought to be less stable [10][11][12][13]. However, the conformational transitions is critically dependent on temperature [14]. Generally, a protein at cryo-temperatures remains relatively fixed in a particular conformation state and at room temperatures the proteins transitions from one conformation state to the other [14]. The transitions of conformational states can be describe by analogies with non-biological systems such as glass [15][16][17][18] and spin glasses [15][16][17]. The experimental evidence of two-conformational states as presented by Wrapp et al, are two of the many states RBD can transition to depending on the temperature and each conformation state of RBD has different binding Barrier Height to bind with ACE2. Depending on the barrier Heights, certain conformations of ACE2 have high binding affinity than others, shown at cryotemperatures by Wrapp, et al [7].
The purpose of this paper is to qualitatively study the conformational transitions of RBD using constant mechanical stress. The logic being to create non-equilibrium state of RBD using mechanical stress and get insights into the transitions to equilibrium states. The first step is to model the RBD, akin to amorphous systems, since amorphous systems share features with proteins [19]. To serve this purpose, RBD is modelled as a viscoelastic material using 4-element Burger's Model. Excellent reviews of using viscoelasticity for biomaterial modelling have been elegantly exposed, which justifies the RBD of S protein to be viscoelastic in nature. Considerable work is done to describe cellular mechanics using elastic modulus [20]. Furthermore, viscosity measurements are carried out in E-coli plasma membrane [21] and methods are developed to accurately measure energy dissipations using Atomic Force Microscope [22]. However, no data is available for the mechanics of viral protein domain, either experimental or otherwise. Given the constraints, the best one can do is use qualitative analysis using generic solutions of the model. To serve this purpose, the typical strain response of RBD under constant stress, which is analogous to the creep test in materials, is presented. Based on the strain response, the theoretical underpinning of equilibrium energy levels (EELs) of RBD and their corresponding conformational states at 0K temperature is presented, which gives several useful insights into qualitatively characterizing the conformational states at physiological temperatures. Using the premise of EELs and Conformational States, the binding affinity of RBD and ACE2 is discussed in terms of binding Barrier energies, and a region and region is characterized where number of high affinity conformational state is high and low, respectively. Based on these regions it is hypothetically reasoned that at a given temperature T, the conformational states of RBD will transition to low binding affinity region as the number of constant stress cycles increases.
Lastly, the use of ultrasonic therapy and phototherapy in transitioning to low affinity region and reducing the binding rate of RBD and ACE2 is discussed.

Modelling RBD using 4 element Burgers Models
Receptor binding Domain (RBD) of S1 protein is modelled using a 4-element Burgers model [23], which is the combination of Maxwell model and Kelvin-Voight Model connected in series.
Burgers model is a constitutive model for linear viscoelasticity, where elasticity and viscosity components are modelled as the linear combinations of springs and viscosity respectively. The configuration of springs with elasticity 1 , 2 and dashpots with viscosity 1 , 2 is shown in Figure 1A and the corresponding equation is given by equation 1. is analyzed and is abstracted for RBD, since proteins share features with amorphous materials [19]. The strain Response under constant stress [23] is given by equation 2.
where 0 is the constant stress. The typical response is shown in Figure 1B, which shows that after a stress loading cycle, a permanent strain stays in the RBD, giving rise to permanent structure changes in RBD, due to breaking of the sacrificial bonds and dissipation of energy.
This is an important insight as after every loading cycle permanent structure change occurs in RBD which results in changes in the conformational states, RBD can attain. The next section uses this insight to develop theoretical underpinning based on the energy levels and corresponding conformational states at these levels.

Theoretical Underpinning
Strain Response of RBD shows that a certain energy is dissipated after a stress loading cycle.
This energy dissipation brings RBD to a new energy level, as a results of breakage of sacrificial bonds depending on the viscosity and structure of RBD. Every energy level corresponds to specific conformational states, since the structure at every energy level is different. Furthermore, the number of conformational states of a molecular structure is dependent on the temperature, with low temperatures corresponding to fixed conformational states of the molecular structure.
To serve this purpose, it is vital to analyze RBD at absolute zero temperature where conformations are fixed and will only respond to external stimulus.

Equilibrium Energy Levels (EELs) and Conformational States (CS) at 0K Temperature
Consider an arbitrary RBD with total internal energy 0 at 0K temperature. This internal energy corresponds to a fixed conformational state of RBD. At time ( ) a stress is applied which corresponds to * energy added to RBD, increasing the internal energy to ∆ 0 where ∆ 0 = 0 + * . This causes RBD to change into a new temporary conformation until * is constantly applied.
At ( ) RBD is unloaded, hence * is removed, RBD jumps to new energy level 1 after a certain amount of relaxation time . 1  time and is same for every loading cycle, the EELs of RBD of S1 protein at 0K Temperature is shown in Figure 2.
As mentioned above, each EEL of RBD has a fixed equilibrium CS given by . The transition period from one EEL to the other corresponds to non-equilibrium conformational states given by ̅ . Both equilibrium and non-equilibrium ̅ prefusion conformational states of RBD of S1 protein have specific binding Energy Barrier to bind with ACE2 receptor, which corresponds to specific binding affinities of different CS to ACE2 receptor. Let the binding Energy Barrier for equilibrium CS be and non-equilibrium CS be ̅̅̅̅ . The typical binding reaction between equilibrium and non-equilibrium CS of RBD of S1 protein and ACE2 receptor is given by equation 3 and 4 respectively RBD conformational states with low and ̅̅̅̅ will generally have high binding affinity with ACE2 receptor, making certain conformations to fuse easily with ACE2 than others. Likewise certain CS will have zero affinity to bind with ACE2, as energy barrier of reaction are large to overcome. Wrapp. Et al have shown a CS denoted by "down" CS at cryo-temperatures which have zero affinity to bind with ACE2 receptor [7].
The next step is to establish a region where CS have high affinity to fuse with ACE2 receptor.
For any biological reaction, the molecular structure of reactants is of paramount importance, as certain molecular bonds are broken and new bonds are made during the chemical reaction. So, for RBD to bind with ACE2, the structural integrity of RBD will have significant impact on the binding affinity with ACE2. It has been shown, after every load cycle, sacrificial bonds are broken, deforming the structure of RBD. The exact sacrificial bond breakage during each cycle requires further study, however, it is fairly straightforward to establish that after enough load cycles, large number of bonds will be broken in RBD, making it structurally unfavorable to bind with ACE2. Furthermore, low energy levels generally have high stabilities and have to overcome large energy Barriers. Using these premises, it can be hypothesized that as the number of load cycles increase, the binding affinities of CS of RBD with ACE2 will decrease, because of structural deterioration and high binding energy barriers. An arbitrary RBD of S1 protein of SARS-CoV-2 shows high binding affinity with ACE2 receptor because of its genetic makeup. So using stress loading cycles, one can deform molecular structure of RBD, making it unfavorable to bind with ACE2. No information is available yet about the sacrificial bonds which will break upon loading. The best one can do is establish a region starting from its natural state where it has high binding affinity. As the number of load cycles increase, the binding affinity of both and ̅ will tend to decrease for the reasons mentioned earlier. Consider an RBD in its natural state with EEL 0 , which has high binding affinity to react with ACE2. After a number of load cycles, the structure however deformed may still have the CS capable to bind with ACE2 with high affinity. Let this region be denoted by Region A (Figure 2). As one move away from Region A towards Region B (Figure 2), the binding affinities of CS both and ̅ will decrease, because of structural deformations and high energy barriers. After a certain number of load cycle, the structure will become unfavorable for binding with ACE2.

EELs and CS at Physiological Temperatures
Using the analysis at 0K temperature, one can get useful insights at the physiological ̅̅̅̅̅ corresponds to low binding affinities with ACE2 receptor. As established for 0K temperature, it can be hypothesized that as the number of load cycles increase, the binding affinities of CS will decrease, and energy levels of RBD will transition from high affinity Region A to low affinity Region B (Figure 2).

Zero Affinity and greater than Zero Affinity CS
Consider an arbitrary RBD at physiological temperature with total conformational states (both equilibrium and non-equilibrium) at all EELs to be .

Therapeutic Options at Physiological Temperatures
The viscoelastic nature of RBD of SARS-CoV-2 makes ultrasound therapy suitable to apply mechanical energy to RBD. Viscoelastic materials coverts mechanical energy from vibrations of ultrasound energy to thermal energy. Sacrificial bonds in the materials are broken as a result, deforming their structure. Ultrasonic therapy is therefore a viable therapeutic option for mechanically loading the RBD of SARS-CoV-2, and reducing the binding reaction rate R between RBD and ACE2 receptor. However, the analysis of conformations so far is done using constant stress and mechanical stressing by ultrasound waves are oscillatory, which requires dynamic mechanical analysis, but the principles of conformational transitions and binding affinities at constant stress holds.
Phototherapy using ultraviolet (UV) electromagnetic waves can be another viable option.
Considerable research has already been elegantly exposed on the effect of UV on SARS-CoV-1. under UV irradiation [25]. UV irradiation uses energy in the form of photons to break sacrificial bonds in RBD, reducing number of CS with binding affinities greater than zero and as a consequence reducing binding reaction rate between ACE2 and SARS-CoV-2. However, both these therapeutic options require further progresses both experimentally and theoretically.
Nonetheless, these options are worth exploring as potential candidates for reducing the reaction rate between SARS-CoV-2 and ACE2 receptor.

Conclusion
To develop useful therapeutic countermeasures against SARS-CoV-2, which has caused global pandemic, understanding the workings of the virus is of utmost importance. Understanding the conformational transitions of Receptor Binding Domain of SARS-CoV-2 is vital to know and alter the binding affinities and reaction rate between SARS-CoV-2 and ACE2 receptor. (B) Strain Response under constant stress cycle. Stress is applied at ( ), which corresponds to instantaneous strain 1 due to elasticity 1 of spring. Followed by the increase in strain to 2 due to elasticity and viscosity 2 and 1 respectively. The strain continue to increase until 3 because of viscosity of dashpot 2 . At ( ), the stress is unloaded which corresponds to a sudden decrease in strain to 4 due to elasticity 1 of spring. The strain continue to decrease at a decreasing strain rate due to elasticity 2 and viscosity 1 of spring and dashpot respectively. Permanent strain in the system remain equal to after one stress cycle which is due to the viscosity 2 of dashpot. The system in this case RBD has permanent structural changes after the loading cycle. corresponds to non-equilibrium conformational states ̅̅̅ . is more stable than ̅ . Each and ̅ has different binding Barrier Energies and binding affinities with ACE2 receptor. Region A has hypothesized to have more and ̅ with high binding affinities to ACE2 receptor than Region B.