Hideyo is a Japanese scientist working on biopolymers and looking for the persis

Question

Hideyo is a Japanese scientist working on biopolymers and looking for the persistence length of actin filaments. He extracted actin from leg and back muscles of rabbit. F-actin 0.25 mg/ml) was labeled with rhodamine-phalloidin (R415, Invitrogen, USA). Experiments were performed at room temperature (23°C). Fluorescence micrographs were obtained for path persistence length measurements in these experiments (Figure 1). The cosine correlation function ( average value for N=74-164 samples) against the distance (s) along the contour length or the curve length of the filaments. In order to obtain s and 8(s), the leading ends of F actin were manually tracked using the computer pointer device relying on a custom-designed algorithm (Figure 2). From the values of cosine correlation function, Figure 3 is obtained and the nonlinear regression fits a straight line to curve length smaller than 20 um. For a segment of F-actin (s-20 m) determine the persistence length and the flexural rigidity of F-actin shown in open circle symbols in Figure 3. Fis ure l Fluorescent image of F-Actin. Scale bar: 10 m 10 s 15 s Figure 2 Image sequences depicting movement of actin filaments (F-actin) when they are sliding on hcavy mcromyosin for 13 s in the in vitro motility assay. Images represent snapshots (0.5 s exposure timc) obtained at 5 s interval. Different arrows denote the tip of individual F-actin during their sliding on HMM. Scale bars: 10 m 0.0 0.5 1.5 20 40 path length (um) 60 80 Figure 3 Semi-logarithmic diagram of cosine correlation functions plotted against path length, s. Open circles are experimental data for actin filaments (F-actin). Lines are obtained using non-linear regression.

Explanation / Answer

The cosine correlation factor (CCF) : <cos((0) (s)) >

Now, persistence lengths (Lp) of actin is calculated by fitting the CCF to an exponential function:

<cos((0) (s)) > = exp(s / (2Lp)) ---- (1)

where, Lp is the persistence length of F-actin. And, s (segment of F-actin)= 20um

From figure 3,

the value of CCF we get is 0.999 which is ~1

therefore, from the above equation 1,

Lp = 10um

Flexural rigidity (EI) can be calculated from the following equation,

Lp= EI / kT,

where, k= boltzman constant (1.3806x10^-23), and T is the temperature in kelvin (296K)

therefore, EI= Lp x kT

so, EI = 4.086x 10^(-26) Nm2

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