Enhanced Conformational Sampling of Nanobody CDR H3 Loop by Generalized Replica-Exchange with Solute Tempering

The variable domains of heavy-chain antibodies, known as nanobodies, are potential substitutes for IgG antibodies. They have similar affinities to antigens as antibodies, but are more heat resistant. Their small size allows us to exploit computational approaches for structural modeling or design. Here, we investigate the applicability of an enhanced sampling method, a generalized replica-exchange with solute tempering (gREST) for sampling CDR-H3 loop structures of nanobodies. In the conventional replica-exchange methods, temperatures of only a whole system or scaling parameters of a solute molecule are selected for temperature or parameter exchange. In gREST, we can flexibly select a part of a solute molecule and a part of the potential energy terms as a parameter exchange region. We selected the CDR-H3 loop and investigated which potential energy term should be selected for the efficient sampling of the loop structures. We found that the gREST with dihedral terms can explore a global conformational space, but the relaxation to the global equilibrium is slow. On the other hand, gREST with all the potential energy terms can sample the equilibrium distribution, but the structural exploration is slower than with dihedral terms. The lessons learned from this study can be applied to future studies of loop modeling.

Scattering, Quantum Current, and Resonant Tunneling

Having examined free particles and particles that are confined in space by a potential energy term, we now consider the impact of a disturbance in the flat energy landscape for a free particle. By disturbance we means some kind of fixed “obstacle” which is either a positive (repelling) or negative (attractive) potential. We are interested in determining the impact on the free particle. Continuing to work mostly in one dimension, the particle described by a plane wave corresponding to momentum moving in the positive direction (a positive k−vector in the x−direction), we study elastic scattering. In one dimension, this means that we determine the probability that the particle is transmitted (continuing in the forward direction) or reflected (now moving in the backward direction.) We will also determine the nature of the solution inside the potential and in the case that the potential energy maximum is greater than the kinetic energy of the particle, we will show that the particle tunnels through the barrier. Interestingly, when we have two barriers, we can find conditions where the probability that the particle is transmitted is unity. This is the result of resonance, a feature of the wave-like nature of the particle’s wave function.

Quantum Dynamics: Resonance and a Quantum Flip-Flop

This chapter begins the discussion of the time evolution of an active quantum system. From the earlier chapters, time dependent physics has been observed through the presence of the time evolution of the phase of each eigenstate. The Hamiltonian itself is time independent. This represents the same kind of evolution of a classical system like the vibration of a tuning fork when it has been struck or the oscillation of an LC circuit if the capacitor is charged to some voltage and then the switch is closed. In the quantum case, the Hamiltonian has also been time independent. The time evolution evolves according the full-time dependent Schrödinger equation, depending only on a single initial condition of the state vector or wave function and the corresponding time evolution of the phase factor for each eigenstate. However in this chapter, we consider the case of when there is a time dependent Hamiltonian such as a sinewave generator or laser. As in the case of resonant tunneling, we see the importance in dynamics of resonant coupling. With an oscillating potential energy term, we see the presence of Rabi oscillations in the probability amplitude of a two-state system on resonance, which can be viewed as a quantum flip-flop between two states of a quantum bit (qubit).

Alternative approach to time evolution of quantum systems

This study focuses on the temporal evolution of quantum systems based on epistemological and ontological arguments and reconsiders some fundamental concepts of quantum theory. Initially, the time dependent Schrödinger wave equation (TDSWE) is criticized for the lack of a potential energy term and thereafter, a novel time dependent momentum operator is defined which eventually leads to an alternative TDSWE, including a potential energy term that remains in harmony with current theory. The wave nature is then generally examined by comparing time evolutions of classical and Schrödinger waves, dissimilarities then carefully inspected and ultimately a novel second order TDSWE is suggested. Finally, time evolution of the probability density is discussed in light of this new approach, and additionally some further insights and conclusions are briefly outlined that conform with the standard theory.

Size of the early universe and GUP

This paper presents the effects of the Generalized Uncertainty Principle (GUP), i.e. its classical version expressed through the deformed Poisson brackets in the phase–space of a one-dimensional minisuperspace Friedmann cosmological model with a mixture of non-interacting dust and radiation. It is shown, in the case of this model, that starting from the specific representation of the deformed Poisson algebra, which corresponds to the change of the potential energy term of the oscillator, the size of the early universe can be related to its inflationary GUP expansion.

SURFACE ROTATIONAL DISORDERING IN CRYSTALLINE C60

We present a theory of surface rotational disordering of crystalline fullerene. Realistic intermolecular interactions are implemented, in a layer-by-layer mean field theory. The crucial new ingredient turns out to be a one-body potential energy term, or "crystal field," is totally different at the surface, therefore locally frustrating bulk order. This frustration causes a severe surface order parameter reduction, and a first order surface rotational disordering transition, well below the corresponding bulk one. Preliminary results are in agreement with recent experiments, confirming a first order surface rotational transition of C 60(111) at a transition temperature lower than the bulk one.

SYMPLECTIC STRUCTURE OF ISOSPIN PARTICLES IN YANG-MILLS FIELDS

Using Dirac’s constraint analysis, we explore the Hamiltonian formalism of isospin particles in external Yang-Mills fields without kinetic and potential energy term. We consider an example of isospin particle in ’t Hooft-Polyakov magnetic monopole field and discuss possible quantization condition of magnetic charge in terms of geometric quantization.

Estimation of the Properties of Quarks. I. Vector Quark?Quark Interaction

From the sum rules for hadron scattering, the nucleon form factors, and the masses of the hadrons, the properties of quarks are estimated as: 2 Ge V Jc2 ;:; quark mass ;:; 30 Ge V Jc2, 0�1 fm ;:; range of the quark-quark interaction ;:; 0�25 fm. The hadrons are described by a relativistic independent quark model using the Dirac equation with a potential energy term for the effective interaction.

Flight Efficiency of Air-Breathing Engines

SummaryThe overall effective efficiency of a jet-propelled flight may be defined as the net useful work that is done in accelerating the vehicle, raising it to height and combating its drag, divided by the calorific value of the propellants used. The analysis presented here shows that for a single-stage vehicle this overall efficiency is equal to the integral of the fractionwith respect to each element of propellants used. In this expression u'is the effective jet velocity (allowing for jet deflection, this is √(1 + k2) times the actual exhaust velocity), υ the vehicle velocity, q the fuel/air ratio and H the calorific value of the fuel in dynamic units. The mean lift/drag ratio of the vehicle is taken as 1/k, so that the last three terms of the numerator represent the work lost in dragging, raising and accelerating each element of propellant to the range R, height h and flight velocity υ at which it is burnt. The fraction may therefore be considered as the efficiency with which that element of propellant is used with respect to the whole flight plan.For advanced air-breathing projects—by-pass engines up to aircraft speeds around Mach 2 and ramjets between Mach 4 and 9—the analysis shows that the sum of the υ-dependent terms in the efficiency factor is practically constant. The potential energy term is insignificant in the normally accepted flight corridor. Thus the overall efficiency with which propellants are consumed in covering a range R1 at flight speed υ js closely approximated to by the fractionand the useful work done by the mass mm of propellants isThe vehicle mass (including engine, payload, and so on) that can be dragged over the range R1 by unit mass of propellants can then be calculated.Although such simplified expressions cannot substitute for the final detailed analysis of a projected flight plan, it is hoped that they will prove more useful in preliminary analysis than the figures based entirely on cruise performance which have often been quoted in the past.