A local sensitivity analysis of Ca²⁺-calmodulin binding and its influence over PP1 activity

Abstract

Synapses are the site of signal transmission between neurons (neurotransmission). Long term synaptic plasticity refers to synaptic efficacy being modulated in response to neurotransmission events. This change can last from minutes to years. In postsynaptic excitatory synapses, increasing synaptic efficacy (known as long term potentiation (LTP)) is a molecular mechanism of memory formation, while decreasing efficacy (long term depression (LTD)) induces memory loss. Postsynaptic LTP and LTD are modulated when Ca2+ fluxes into postsynaptic neurons and binds to the signal transducer protein called calmodulin (CaM). Upon binding four Ca2+ ions, CaM becomes active (as CaM4) and integrates the signal. That is, CaM4 can bind and activate proteins that pertain LTP (kinases), and also protein phosphatases which induce LTD. The ratio of kinase: phosphatase activity determines the direction of synaptic plasticity. Interestingly, activity of the key LTD- inducing protein, "protein phosphatase 1" (PP1) is coordinated by other CaM4- sensitive proteins. PP1 is inactive when bound to protein inhibitor 1 (i-1). Phosphorylation of i-1 prevents it from dissociating from PP1, thereby blocking its activity. At basal Ca2+, i-1 is phosphorylated due to kinase activity, meaning PP1 activity gets blocked. Synaptic activity can then cause intracellular Ca2+ influx to the cell which alters the phosphorylation state of i-1. This is because Ca2+ binds CaM, then CaM4 activates "protein kinase A" (PKA) and "protein phosphatase 2B" (PP2B) which phosphorylate and dephosphorylate i-1 respectively. These proteins thereby modulate PP1 activity by collectively controlling the phosphorylation status of i-1. When Ca2+ levels begin to rise, PP2B gets preferential activation due to having a faster CaM4 binding rates than PKA, resulting in net dephosphorylation of i-1 and subsequent activation of PP1. If CaM4 levels escalates further, more PKA gets activated which has greater catalytic activity than PP2B. This means increased phosphorylation of i-1 and subsequent suppression of PP1. PP1 activity can therefore be modelled as a function of CaM4 formation, meaning its activation is affected by CaM binding to Ca2+. CaM has two separate lobes (the N- and C-lobes) which have different mechanisms of binding cooperativity to Ca2+. In the current study, mathematical modelling is used to determine to influence each of these CaM cooperativities/binding rates. Here, a detailed Ca2+-CaM binding model based on Mass Action fed into simplified Hill equations of PKA/PP2B regulation over PP1 activity were used. To determine the influence of each lobe, Ca2+ binding/unbinding rates to CaM, a local sensitivity analysis (LSA) was performed over a range of Ca2+ concentrations. Since PP1 activity is dependent on CaM4 formation, PP1 activation was used as an output for the LSA. From the analysis, it is evident that C-lobe has more stable binding than the N-lobe across all Ca2+ levels.