Isotherm kinetics of PIP2 bound gelsolin inactivation

Actin monomers (G-actin) and filaments (F-actin) have dynamical rearrangement thus manage cellular motility, division and transport processes. The gelsolin (GSN) regulates the remodeling of cytoskeleton. After the activation of GSN by calcium ions, it can sever actin filaments then capped at its barbed end. In the cytoplasm, GSN manages the cellular motions and morphology. Phosphatidylinositol 4,5-bisphosphate (PIP2) is involved in signal transduction and the regulation of the actin cytoskeleton by regulation of actin-binding proteins. GSN can bind to PIP2 and thus can be localized in the near of the plasma membrane and released from the end of F-actin. We test here with isoperibol calorimetry the enthalpy change, within the interplay between GSN and F-actin under nano-, micro- and millimolar calcium concentrations and express the importance of PIP2 binding for the inactivation of GSN. As we have demonstrated here that PIP2 binding stabilizes the structure of gelsolin and reduces its actin monomer binding activity under nanomolar calcium as the typical cytoplasmic calcium concentration of resting cells. The gelsolin shows partial activity under micromolar and total activity with strong responses under millimolar calcium. If gelsolin-capped filaments point at the plasma membrane helps the binding between gelsolin and PIP2, and hence, filament uncapping in case of resting cells. We presume that the low free calcium concentration keeps on the structure of gelsolin which is able to bind actin within the cooperativity of actin bound calcium. Gelsolin can help to manage monomer pool far from the membrane and it can be linked to a basic sensory mechanism which drives the direction of filament growth in the near of the membrane.

As previously shown the free calcium concentration in resting cells changing on the nanomolar level [55,56], and in non-resting state can reach the micromolar levels [57,58]. Cytoplasmic free magnesium levels are regulated in the nanomolar range but it does not have effect on GSN activity [49,59,60]. Interestingly, the reduction of calcium levels cannot cause directly the GSN release from actin, but a single calcium ion is still trapped in the complex [61]. The main concern with GSN inactivation is that it still depolymerizing actin filaments in the presence of millimolar EGTA provided nanomolar free calcium level [62,63]. Possibly, only the PIP2 binding can fully inhibit any activity of GSN [49]. Structural rearrangement of F-actin and its binding molecules can be studied by DSC [64][65][66]. We probe here the isothermal enthalpy change within the interplay between GSN and F-actin under nano-, micro-and millimolar calcium concentrations and express the importance of PIP2 binding for the total inactivation of GSN. We can postulate that GSN shows remarkable thermal response to actin, addition under nanomolar calcium concentration which can be reduced by PIP2 binding. Figure 1 shows isothermal heatflow kinetics as well as the denaturation of mixing GSN with F-actin under different Ca 2+ conditions, or in the presence of PIP2. All isotherm assays were taken 16 h but we focused on the first relevant 180 min after the relapse of the heatflow subsequently after the mixing effect, between the minimum (ΔQ initial ) and the maximum points (ΔQ top ) (Fig. 1A). The heatflow was dropped down (2.4 µW) ( Table 1) if 12.8 µM GSN (1 mg mL −1 ) was added to nanomolar Ca 2+ containing buffer then increased slowly (1.7 ± 0.3 × 10 -4 µW s −1 ) in the first 3 h (Fig. 1B). In case of 46 µM F-actin (2 mg mL −1 ) bound GSN in a ratio of 1: 3.6; under nanomolar Ca 2+ concentration, there were two remarkable exothermic peaks. The first peak was increased quickly 9.1 ± 2.5 W in the first 15 min by the rate of 82 ± 1.2 × 10 -4 µW s −1 , after a minor reduction it was followed by a second peak in 63 min. If GSN was formed complexes with 1.6 µM PIP2 [49] in the presence of nanomolar Ca 2+ and F-actin, the heatflow was increased quickly with multiple rates (totally 4.6 ± 0.7 µW with an average rate of 17 ± 2.5 × 10 -4 µW s −1 ) in 65 min. Just after the isothermal processes we performed denaturation with heating rate of 0.3 K min -1 (Fig. 1C). GSN in the presence of nanomolar Ca 2+ shows a main transition at 39.5 °C ( Table 2). GSN and F-actin in the presence of nanomolar Ca 2+ shows four transitions at 33, 40, 54 and 60 °C and the GSN-PIP2 complex with F-actin show three transitions at 36, 56 and 60.5 °C. PIP2 binding shifted the main peak from 33 to 36 °C, however in case of free GSN the biggest transition was observable at 39.5 °C. Figure 1D shows that the isothermal heatflow of F-actin was dropped down (endothermic 3.6 µW)( Table 1) by mixing with millimolar Ca 2+ containing buffer then it was increased by 3.23 µW first in a quick step 100 ± 0.8 × 10 -4 µW s -1 then slowly 6 ± 1.5 × 10 -4 µWs −1 in the first hour. The previously described two exothermic peaks of GSN and F-actin under nanomolar Ca 2+ were turned to be reduced in the presence of micromolar Ca 2+ . Interestingly, we observed a minor drop (endothermic 1.36 µW) of the heatflow then it was followed by an exothermic change 3.84 ± 1.2 µW with the rate of 37 ± 0.8 × 10 -4 µW s −1 . If GSN was added to F-actin in the presence of millimolar Ca 2+ , the heatflow showed a big drop 9.7 µW at the beginning of the process then it was increased by 7.7 ± 2.8 µW with a relatively quick rate 17 ± 1.2 × 10 -4 µW s −1 in the first two hours. Figure 1E shows that the shape of thermal denaturation curves in each cases from panel C seems to be Ca 2+ dependent. F-actin in the presence of milimolar Ca 2+ shows a main transition at 60 °C (

Discussion and conclusions
The aim of our present work is to show thermodynamical changes due to the activation and inactivation of gelsolin. Heat flow follows the structural entropy change as increases with structural stabilization.
Under nanomolar Ca 2+ concentration, GSN responded with a minor isothermal change to the mixing of sample. GSN addition to F-actin resulted a strong exothermic change linked to the reduction of their structural entropy. Possibly, free actin monomers were depleted by GSN binding [62,63] which mechanism can be described as the Type I. Ca 2+ binding sites [67] are partially saturated, and thus initialized a structural change of GSN for a cooperative binding to actin monomer. Here we found that the actin binding leads to a lower thermodynamical stability of GSN. The PIP2 binding was stabilized the structure of GSN similar to the free form with slow and weak response to the actin addition (Fig. 2). In good agreement with our previous results, since the intrinsic tryptophan of GSN responds with increased emission to PIP2 addition, the response was a less flexible structural dynamics of GSN [49]. At the end of the isotherm assays, the majority of actin was denatured around 60 °C, it can be interpreted by the hydrolyzation of ATP due to the long term processes [68]. Under micromolar Ca 2+ concentration, the Ca 2+ binding to Type II. binding sites [67] were initialized structural change of GSN and the mixing of sample can make fragments of long actin filaments and all newly exposed barbed end can be quickly capped by the partially active GSN. However, a slow structural transition in all capped actin filaments was observable.
Under millimolar Ca 2+ concentration, the fully active GSN can do very fast severing within the mixing of the sample and induced a relatively big endotherm drop of the heat flow at the beginning of the process. Then subsequently, there was a relatively slow exotherm change which can be explained by the capping and within caused slow structural rearrangement of short filaments. However, if we mixed F-actin with buffer only it shows a very fast then a very slow isothermal process, possibly it was a recovery after certain fragmentations. As Nag et al. Here we have demonstrated that PIP2 binding stabilized the whole structure of gelsolin and possibly reduced its actin monomer binding activity under nanomolar calcium as the typical cytoplasmic calcium concentration of resting cells. If gelsolin-capped filaments point at the plasma membrane, the local concentration of gelsolin increases by forming PIP2 clusters [70]. All the conditions which help the binding between gelsolin and PIP2, and hence, filament uncapping in case of resting cells. The total inactivation of gelsolin is required PIP2.
We can presume that the low free calcium concentration keeps on the structure of gelsolin which is able to bind actin within the cooperativity of actin bound calcium (Fig. 2). Gelsolin can help to manage monomer pool far from the membrane and it can be linked to a basic sensory mechanism which influences the direction of filament growth in the near of the membrane.

DSC measurements
The actin samples were freshly prepared before all measurements. The isotherm kinetics analysis was made by a SETARAM Micro-DSCII calorimeter on room temperature, 22 °C for 16 h. After the third hour of measurements, we observed the continuous dropping of heat flow which can be described by the decay of ATP and actin filaments. We used Hastelloy designed pair of "mixing batch" vessels for isotherm measurements (V lower = 500 µL, V upper = 200 µL) in the reference vessel the GSN was mixed with buffer only and in the sample one with F-actin in the presence of nanomolar, micromolar or millimolar free Ca 2+ (calculated by MaxChelator, https:// somapp. ucdmc. ucdav is. edu) and after it subsequently undergone for denaturation measurements. Kinetics measurements were carried out with an isotherm program then finally denatured by heating up them with 0.3 K/ min up to 80 °C. MOPS buffer was used as a reference. The reference and sample vessels were equilibrated with a precision of ± 0.1 mg; this way we did not need to do any correction between vessels' heat capacity. The first point of our analysis was the minimum of the heat flow change (ΔQ initial ) after a single sharp peak which shows the mixing effect, and thus the curve was increased slowly to the maximum point (ΔQ top ) (Fig. 1A). The exponential fitting resulted the time rate (k) of the peaks, the measurements were started in 5 min after reaching the thermal equilibrium between the vessels, but we used for the analysis the part of the curve after the mixing effect. Actin and gelsolin based molecular events were happened only in the first three hours then all curves decreased slowly possibly by the decay of ATP thus the most reasonable time duration of kinetics was analyzed in the first 10,800 s. All kinetic processes were terminated with heat denaturation assays. With the help of a two-point SETARAM peak integration setting, the denaturation calorimetric enthalpy was calculated from the area under the heat absorption curve, and then, the results [denaturation or melting temperature (T m ) and calorimetric enthalpy (ΔH cal ) data of samples] were compared. This method is identical with the protocol as we applied in our previous study [64].