τ f a s t d V f a s t d t = ∑ i w i E i δ ( t − t i s y n ) − V f a s t {\displaystyle \tau _{fast}{\frac {dV_{fast}}{dt}}=\sum _{i}w_{i}E_{i}\delta (t-t_{i}^{syn})-V_{fast}}
d s p i k e : V f a s t + V B A P > V d s p i k e , t h r e s h + V d s p i k e , r e f r a c t o r y {\displaystyle dspike:V_{fast}+V_{BAP}>V_{dspike,thresh}+V_{dspike,refractory}}
s o m a : V s o m a > V t h r e s h , s o m a ( 1 − a C R E B ) − V s o m a , r e f r a c t o r y {\displaystyle soma:V_{soma}>V_{thresh,soma}(1-a_{CREB})-V_{soma,refractory}}
τ d s p i k e d V d s p i k e d t = ( E d s p i k e − V f a s t − V B A P ) ∑ i δ ( t − t i d s p i k e ) − V d s p i k e {\displaystyle \tau _{dspike}{\frac {dV_{dspike}}{dt}}=(E_{dspike}-V_{fast}-V_{BAP})\sum _{i}\delta (t-t_{i}^{dspike})-V_{dspike}}
V s o m a = ∑ j ( V f a s t , i + B i V d s p i k e , i ) − R a d a p t I a d a p t {\displaystyle V_{soma}=\sum _{j}(V_{fast,i}+B_{i}V_{dspike,i})-R_{adapt}I_{adapt}}
τ a d a p t d I a d a p t d t = I a d a p t , 0 ∑ i δ ( t − t i s o m a ) − I a d a p t {\displaystyle \tau _{adapt}{\frac {dI_{adapt}}{dt}}=I_{adapt,0}\sum _{i}\delta (t-t_{i}^{soma})-I_{adapt}}
τ B A P d V B A P d t = E B A P ∑ i δ ( t − t i s o m a ) − V B A P {\displaystyle \tau _{BAP}{\frac {dV_{BAP}}{dt}}=E_{BAP}\sum _{i}\delta (t-t_{i}^{soma})-V_{BAP}}
τ C a d C a d t = a C a s i g m o i d ( V f a s t + V d s p i k e + V B A P ) ∑ i δ ( t − t i s y n ) − C a {\displaystyle \tau _{Ca}{\frac {dCa}{dt}}=a_{Ca}sigmoid(V_{fast}+V_{dspike}+V_{BAP})\sum _{i}\delta (t-t_{i}^{syn})-Ca}
E T a g = ∫ 0 t ( E T a g m a x − E T a g ) C D P ( C a ( t ) ) + + ( E T a g − E T a g m i n ) C D P ( C a ( t ) ) − {\displaystyle ETag=\int _{0}^{t}(ETag_{max}-ETag)CDP(Ca(t))_{+}+(ETag-ETag_{min})CDP(Ca(t))_{-}}
P R P s ( t ) = ∑ i t − t i τ 1 e 1 − t − t i τ 2 {\displaystyle PRPs(t)=\sum _{i}{\frac {t-t_{i}}{\tau _{1}}}e^{1-{\frac {t-t_{i}}{\tau _{2}}}}}
τ W e a r l y d W e a r l y d t = E T a g ( t ) ( W m a x − ( W l a t e + W e a r l y ) ) − W e a r l y {\displaystyle \tau _{W_{early}}{\frac {dW_{early}}{dt}}=ETag(t)(W_{max}-(W_{late}+W_{early}))-W_{early}}
τ a C R E B d a C R E B d t = ∑ i a C R E B , 0 δ ( t − t i C R E B ) − a C R E B {\displaystyle \tau _{a_{CREB}}{\frac {da_{CREB}}{dt}}=\sum _{i}a_{CREB,0}\delta (t-t_{i}^{CREB})-a_{CREB}}
W e a r l y → τ W l a t e p r o t e i n s → W l a t e {\displaystyle W_{early}\rightarrow _{\tau _{W_{late}}}^{proteins}\rightarrow W_{late}}
w ( t ) = W e a r l y ( t ) + W l a t e ( t ) {\displaystyle w(t)=W_{early}(t)+W_{late}(t)}
τ B t a g d B t a g d t = B t a g , 0 ∑ i δ ( t − t i d s p i k e ) − B t a g {\displaystyle \tau _{B_{tag}}{\frac {dB_{tag}}{dt}}=B_{tag,0}\sum _{i}\delta (t-t_{i}^{dspike})-B_{tag}}
d B j d t = 1 τ B j B t a g , j ( B m a x − B j ) + 1 τ B H B ( 1 − ∑ j B j N ) {\displaystyle {\frac {dB_{j}}{dt}}={\frac {1}{\tau _{B_{j}}}}B_{tag,j}(B_{max}-B_{j})+{\frac {1}{\tau _{B_{H}}}}B(1-{\frac {\sum _{j}B_{j}}{N}})}
d W j d t = 1 τ W H B ( 1 − ∑ j W j N s y n ) {\displaystyle {\frac {dW_{j}}{dt}}={\frac {1}{\tau _{W_{H}}}}B(1-{\frac {\sum _{j}W_{j}}{N_{syn}}})}