Supplemental Protocol S1
Pattern recognition algorithm for identifying and measuring Ca2+ spikes in
YFP:CFP ratio line-graph readouts for intracellular cameleon sensors
The aim of the algorithm is to fit a pattern defined by f (t ) to an observed Ca2+
spike y (t ) .
This consists in minimizing the J value defined by:
J (a, b, ,  ) 
1
T f
T f

0
( y(t   )  af (t /  )  b) 2 dt
applying the constraint a  amin .
The mean and energy of the pattern is defined by:
E1 
1
Tf
Tf

0
f (t )dt E 2 
1
Tf
Tf

0
(1)
( f (t )) 2 dt
The local mean and the local energy of the peak is defined by:
M 1y ( ,  ) 
1
T f
1
M ( ,  ) 
T f
2
y
T f

0
T f

0
y (t   )dt
(2)
y (t   )dt
and its cross-correlation with the pattern by:
Ryf ( ,  ) 
1
T f
T f

0
y(t   ) f (t /  )dt
(3)
The minimization of J with respect to a and b leads to:
1
( R yf ( ,  )  E 1 M 1y ( ,  ))
E  (E1 )2
(4)
1
*
2
1
1
b ( ,  )  2
( E M y ( ,  )  E R yf ( ,  ))
E  (E1 )2
a * ( ,  ) 
2
If a*  amin , then the optimal solution is defined by:
a *  amin
b* ( ,  )  M 1y ( ,  )  amin E 1
(5)
The minimization of J is then achieved by minimizing over  ,
J (a* , b* , ,  )  M y2 ( ,  )  (a* ) 2 E 2  (b* ) 2  2a* Ryf ( ,  )  2b*M 1y ( ,  )  2a*b* E1
(6)
The algorithm is structured as follows:
 Select a pattern f (t ) and compute its mean and energy by (1)
 Fix a value of  and  on the grid defined over the set [ min , max ]  [ min ,  max ]
o Compute the local mean and energy of the signal and the crosscorrelation of the pattern by (2) and (3)
o Compute the optimal values of the bias and the amplitude a * and b *
by (4)
o If a*  amin , substitute the values of a * and b * by those defined by (5)
o Compute J (a * , b* , , ) according to (6) and record this value
 Compute the local maxima of J (a * , b* , , ) over all the values of  , and
record the N first values  i* and  i* , N being the number of peaks predefined manually.
2
The above figure illustrates the theoretical pattern [ f (t)  t exp(t /T) where T stands
for a time-constant (dashed green line)] superimposed on an observed peak
(continuous blue line). The pattern is defined by a  bf ((t   )/ ) where
a is the bias


(local mean value of the pattern), b is the amplitude of ratio changes depending on
the signal power,  is the time delay between ratio changes and  is a scale factor.



Figure Legends for Supplemental Movies S1 and S2
Supplemental Movie S1. Visualizing the nuclear Ca2+ spiking variability and cellautonomy in adjacent growing root hairs. YFP:CFP-ratio changes during nuclear Ca2+
spiking elicited by 10-9 M NF in six elongating M. truncatula root hairs expressing
NupYC2.1. Relative changes in nuclear Ca2+ levels were monitored with FRET-based
ratiometric confocal imaging and then pseudocolor-coded according to ImageJ plugin
Ratio Plus (see “Material and Methods”). Root hairs were imaged simultaneously at 5
sec intervals and the movie duration is 10 min.
Supplemental Movie S2.
Spatio-temporal distribution of NF-elicited intranuclear
Ca2+ spiking in a single M. truncatula root hair expressing NupYC2.1. YFP:CFP ratio
changes, reflecting modulations in nuclear Ca2+ levels, were monitored with FRETbased confocal imaging and then pseudocolor-coded according to ImageJ plugin
Ratio Plus (see Material and Methods). Images were recorded every 5 sec and the
movie duration is 10 min.