Abstract

We introduce a discrete-time variational principle inspired by the quantum clock originally proposed by Feynman and use it to write down quantum evolution as a ground-state eigenvalue problem. The construction allows one to apply ground-state quantum many-body theory to quantum dynamics, extending the reach of many highly developed tools from this fertile research area. Moreover, this formalism naturally leads to an algorithm to parallelize quantum simulation over time. We draw an explicit connection between previously known time-dependent variational principles and the time-embedded variational principle presented. Sample calculations are presented, applying the idea to a hydrogen molecule and the spin degrees of freedom of a model inorganic compound, demonstrating the parallel speedup of our method as well as its flexibility in applying ground-state methodologies. Finally, we take advantage of the unique perspective of this variational principle to examine the error of basis approximations in quantum dynamics. The insulin-like growth factor-I (IGF-I) is a key regulator of skeletal muscle growth in vertebrates, promoting mitogenic and anabolic effects through the activation of the MAPK/ERK and the PI3K/Akt signaling pathways. Also, these results show that there is a time-dependent regulation of IGF-I plasma levels and its signaling pathways in muscle. The insulin-like growth factor-I (IGF-I) is a key regulatory hormone that controls growth in vertebrates. Particularly, skeletal muscle growth is strongly stimulated by this hormone. IGFI stimulates both proliferation and differentiation of myoblasts, as well as promoting myotube hypertrophy in vitro and in vivo. The mitogenic and anabolic effects of IGF-I on muscle cells are mediated through specific binding with the IGF-I receptor (IGF-IR). This ligand-receptor interaction promotes the activation of two major intracellular signaling pathways, the mitogen-activated protein kinases (MAPKs), specifically the extracellular signal-regulated kinase (ERK), and the phosphatidylinositol 3 kinase (PI3K)/Akt. The MAPK (RAF/MEK/ERK) is a key signaling pathway in skeletal muscle, where its activation is absolutely indispensable for muscle cell proliferation. Biologically active polypeptides derived from the E domain that forms the C-terminus of the insulin-like growth factor I (IGF-I) splice variant known as mechano growth factor which have been demonstrated neuroprotective and cardioprotective properties, as well as the ability to increase the strength of normal and dystrophic skeletal muscle. Ligands selected from phage-displayed random peptide libraries tend to be directed to biologically relevant sites on the surface of the target protein. Protein-peptide interactions form the basis of many cellular processes. Consequently, peptides derived from library screenings often modulate the target protein’s activity in vitro and in vivo and can be used as lead compounds in drug design and as alternatives to antibodies for target validation in both genomics and drug discovery of predicted (Propeptide-Fc)/MGF peptide mimicking interactive chemo-polypharmacophoric agent comprising Feynman’s clock new variational principles, and parallel-in-time quantum dynamics of high free binding energy properties towards Wnt7a/Fzd7 signalling Akt/mTOR anabolic growth IGF-I/PI3K/Akt -I/MAPK/ERK pathways.

Keywords

Feynman’s clock, variational principle, parallel-in-time quantum dynamics; predicted chemo-polypharmacophoric; (Propeptide-Fc)/MGF peptide mimickin interactive of high free binding energ properties towards Wnt7a/Fzd signalling Akt/mTO anabolic growt IGF-I/PI3K/Akt -I/MAPK/ERK pathways.