Dynamic Fiber Bundle Model of Biopolymer Deformation
- PDF / 361,298 Bytes
- 6 Pages / 612 x 792 pts (letter) Page_size
- 94 Downloads / 224 Views
1187-KK06-02
Dynamic Fiber Bundle Model of Biopolymer Deformation Mark H. Jhon12 and Daryl C. Chrzan12 Department of Materials Science and Engineering, University of California–Berkeley, Berkeley, California 94720, U.S.A. 2 Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, U.S.A.
1
ABSTRACT A statistical model is developed to study the loading-rate dependent mechanical response of biopolymer arrays. Using the kinetic Monte Carlo method, bundles of fibers are studied under load-controlled and displacement-controlled conditions. INTRODUCTION Structural biological materials such as bone, antler, and nacre are composites consisting of mineral platelets in an organic matrix [1]. The properties of the matrix will influence the mechanical properties of the composite. These materials exhibit strain-rate dependent mechanical properties [2,3]. Single molecule experiments on some biopolymers have shown that they exhibit discrete unfolding events and a jagged load-extension trace [4,5]. As a result, sacrificial bonds present in the biopolymer have been proposed as one source for the remarkable toughness of natural composites such as nacre [5]. A two-state statistical model for the single polymer model was introduced by Rief et al. to model titin [6,7]. A fixed-time step Monte Carlo method was used to simulate the dynamics of the system. This computational scheme was also extended to study coupled systems of 20 molecules: by allowing a number of molecules to share a common load, some many-polymer effects could be studied [8]. However, this type of fiber-bundle model (FBM) is still a mean-field model that does not incorporate spatial correlations. In order to perform systematic studies of larger systems, it is necessary to develop a more efficient computational algorithm. To this end, a kinetic Monte Carlo (KMC) method is developed based on rare event statistics. This extends the analysis of the single polymer model studied in [9]. THEORY A schematic of the FBM is depicted in Fig. 1. The elastic response of the biopolymer is modeled using the worm-like chain model [10].
kT Fwlc (x, Lc ) = B p
−2 1 x 1 x 1 − − + Lc 4 Lc 4
(1)
The entropic restoring force is a function of the thermal energy kBT , the contour length of the polymer Lc , and the persistence length, p . The initial contour length of the i th polymer chain is drawn from a uniform distribution Li = [0, Lmax ] . The rate at which the i th has an
unfolding event is given by N iω u ( Fi ) , where N i is the number of folded domains on the i th polymer and Fi is the applied force on the polymer. Fi may be computed by using a load sharing law depending on the loading conditions. Under displacement controlled conditions, x(t ) = vt .
Figure 1. Schematic diagram of fiber bundle model. The circles represent modules that may unfold discretely. The polymer may be strained under load-controlled (specified F ) or displacement-controlled (specified x ) conditions.
The unfolding rate has an exponential depe
Data Loading...
