This paper is dedicated to the study how HE particle spectra, which are measured in cosmic ray physics and astrophysics, are influenced by the specifics of collider spectrum of protons.LHC experiments are providing us with the proton spectra at very high energy (VHE) measured in center-of-mass system. A QCD phenomenological study of previous years gave us the Quark-Gluon String Model for the modeling of baryon and meson production spectra in full kinematical range from centrally produced hadrons up to very forward ones. In 1990, I have applied the method for the recalculation the collider distribution of neutral pions into the description of gamma spectrum from supernovae that was measured in the laboratory system. Here, I used the same method. The main statement of this study is that the features of leading spectra of cosmic protons, neutrinos and gamma are to be formed already in first collision of UHE proton at the power source of cosmic particles. The specifics of collider spectrum of protons are as following: the growing distribution at the central rapidityes, which reflects in the "knee" of cosmic proton spectrum, and the triple-Pomeron peak at the end of c.m.s. spectrum that leads to the enhancements in spectra of leading cosmic protons, neutrinos, gamma-photons, and as I assume, positrons too. These conclusions desire for more experimental facts to be collected and new observations to be made.