We propose two approaches for determining the native basins in off-lattice models of proteins. The first of them is based on exploring the saddle points on selected trajectories emerging from the native state. In the second approach, the basin size can be determined by monitoring random distortions in the shape of the protein around the native state. Both techniques yield similar results. As a byproduct, a simple method to determine the folding temperature is obtained.Chains of beads on cubic or square lattices, with some effective interactions between the beads, often serve as simple models of proteins (see for instance [1]). A more realistic modelling, however, requires considering off-lattice systems. Simple off-lattice heteropolymers have been discussed recently by Iori et al [2], Irback et al [3], Klimov and Thirumalai [4] and by the present authors [5]. The purpose in using such models is to understand the basic mechanism of folding to the native state. In lattice models, the native state is usually non-degenerate and it coincides with the ground state of the system. Delineating boundaries of the native basin in off-lattice systems, however, is difficult, especially when the number of degrees of freedom is large, yet it is essential for studies of almost all equilibrium and dynamical properties of proteins. For instance, stability of a protein is determined by estimating the equilibrium probability to stay in the native basin: the temperature at which this probability is 1 2 defines the folding temperature, T f . The native basin consists of the native state and its immediate neighbourhood, as shown schematically in figure 1, and it should not be confused with the whole folding funnel. The latter involves a much larger set of conformations which are linked kinetically to the native state.In most studies, such as in [3,4], the size of a basin is declared by adopting a reasonable but ad hoc cutoff bound. Systematic approaches, however, are needed and will be presented here. The task of delineating of the native basin is facilitated by introducing the concept of a distance between two conformations a and b, δ ab . The distance should be defined in a way that excludes effects of an overall translation or rotation. There are two definitions of δ ab , for a sequence of N monomers, that we shall use. The first one is [2, 6]:
We describe the O(α 0 ) constraints on the target space geometry of the N = (2, 1) heterotic superstring due to the left-moving N = 1 supersymmetry and U(1) currents. In the fermionic description of the internal sector supersymmetry is realized quantum mechanically, so that both tree-level and one-loop effects contribute to the order O(α 0 ) constraints. We also discuss the physical interpretation of the resulting target space geometry in terms of configurations of a (2 + 2)-dimensional object propagating in a (10 + 2)-dimensional spacetime with a null isometry, which has recently been suggested as a unified description of string and M-theory.
Dynamic properties of the resonant tunnelling structures (RTS) as an example of the dynamic nature of nanoelements are studied. Hysteresis and 'plateaulike' behaviours of the time-averaged current-voltage (I -V ) curve of resonant tunnelling structures may be obtained through analysing the high-frequency current oscillations in such structures. Our study shows that 'soft' generation of oscillations leads to the characteristic 'plateaulike' I -V form and 'rigid' generation of oscillations leads to 'hysteresis' I -V behaviour. The analysis is obtained by investigation of the limit cycles of the dynamical system corresponding to the modified equivalent circuit of the RTS developed by Buot and Jensen. In this paper it is clarified that RTS may be used not only as a device for generation of THz oscillations but it may also be used as the dynamic trigger which has two stable states: the stable limit cycle and stable static state.
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