In conventional particle accelerators, protons are produced in long pulses, in which the average inter-proton distance is in the order of tens of centimeters or more. Therefore, the radiobiology of conventionally accelerated protons is primarily governed by the interaction of a single proton with the cell. In a laser-plasma interaction scheme, the accelerated protons come as a single bunch of particles (less than 1 ps in duration) with inter particle distances that are many orders of magnitude shorter than those in conventional particle accelerators. As laser-accelerated protons traverse the medium, they not only interact with each other, but also with the host medium. It is shown that when the average distance between protons in a cluster is less than or equal to their velocity divided by the characteristic frequency of the collective excitations supported by the medium, the cluster's linear stopping power increases and can reach several times that of sparsely distributed protons. As a result, the elevated radio biological effectiveness of the proton cluster may take place and conditions for its experimental observation are presented.