Is the process of long term potentiation (LTP) definitively linked with brain plasticity? Given that the process of Long Term Potentiation (LTP) is one of the processes that increases synaptic efficacy:

Is it reasonable to conclude that the process of LTP is sufficient and necessary to control plasticity of circuits within the brain?   

Can we assume that the biochemical factors that modulate LTP are also intrinsically linked with brain plasticity?
Although LTP might be necessary for brain plasticity, I would doubt that it is also sufficient. There is quite a lot of literature about homeostatic plasticity (for a review, see Turrigiano &amp; Nelson, 2004) and synaptic scaling (for another review, see Turrigiano, 2008) which seem to be necessary to keep LTP working in the long run. 

References
Turrigiano GG, Nelson SB (2004) Homeostatic plasticity in the developing nervous system. Nature Reviews Neuroscience 5, 97-107. Full text

Turrigiano GG (2008) The self-tuning neuron: synaptic scaling of excitatory synapses. Cell 135, 422-435. Full text