Having trouble with a global fit to several curves of intensity vs. frequency to extract an exchange rate.

I am trying to simulate data representing intensity vs. frequency for a system that exhibits (slow) exchange between a free and ligand bound state during serial addition of the ligand. Using the equations below I plan to extract the rate of exchange and I am also allowing a variable to be adjustable which scales the intensity over the series to a account for issues which decrease intensity other than direct ligand binding. I have gone through the equation line by line, and it seems acceptable, but when i try to run the fitting .m file, I get the following error:

Error using nlinfit (line 142) Error evaluating model function 'lnshp_exchange'.

Error in fit_lnshp_exchange (line 30) [beta,R]=nlinfit(x,y,@lnshp_exchange, beta0);

Caused by: Error using / Matrix dimensions must agree.

I am fairly new to matlab, and previous data and model functions have been simpler. The function .m file and fitting .m file I am trying to use are below:

FUNCTION file:

function f = lnshp_exchange(a,x) %a(1) is k (the rate), a(2) is c (the weighting function allowing each %spectrum to vary in intensity) global K L v1 v2 Tp1 Tp2

t=1/(a(1)*L*(1+K));

p1=K*a(1)*L*t;

p2=1-p1;

w=(v1+v2)*(1/(2-x(i)));

W=v1-v2;

P=t*((1/Tp1*Tp2)-4*pi^2*w^2+pi^2*W^2)+(p1/Tp1)+(p2/Tp2);

Q=t*(2*pi*w-pi*W*(p1-p2));

R=2*pi*w*(1+t*((1/Tp1)+(1/Tp2)))+pi*W*t*((1/Tp1)-(1/Tp2)+pi*W*(p1-p2));

f=a(2)*(P*(1+t*(p2/Tp1 + p1/Tp2))+Q*R)/(P^2+R^2);

end

FITTING file:

%lnshp_exchange.m

% simulation of lineshape to extract kon rate

%used to extract kon from titration lineshape analysis wiht known Kd

%k is kon, p1 is protein population, p2 is PL complex population, K is Kd,

%v1 is P shift, v2 is PL shift, Tp1 is T2 of protein, Tp2 is T2 of PL

%complex % %

K=0.0000033;

L=0;

Tp1=4.96;

Tp2=7.25;

v1=12.212;

v2=13.114;

 x = [13.627  13.549  13.471  13.393  13.315  13.236  13.158  13.08  13.002  12.924  12.846  12.768  12.689  12.611  12.533  12.455  12.377  12.299  12.221  12.142  12.064  11.986  11.908  11.83  11.752]; 
y = [-1065.0592  -1211.71057  -856.98804  -531.41229  -893.48578  -986.63025  -918.69916  -109.00397  831.30347  993.21808  294.64252  -152.99203  -315.96314  146.8889  301.44775  838.57312  8316.95019  67597.40625  134763.2188  87617.96875  16666.29883  3421.37939  1571.36316  410.51562  72.57593
    -1703.73584  -168.12866  789.64722  47.88208  1053.0144  2968.02295  4267.29297  2023.13257  2187.24414  1070.43872  494.38843  441.92407  982.57385  2506.96777  5016.04541  8904.80859  21991.72266  58715.40625  81474.96875  51473.53906  16955.95312  7286.82764  5943.39551  1376.10278  1042.12024
-39.62695  700.45947  880.60693  1672.54761  5490.44434  10250.34961  10380.7793  6425.10059  6905.46533  6553.79688  6200.93555  5450.68262  4783.33496  5999.4292  7567.62451  11676.40039  25238.00391  44612.70703  48212.02734  31467.79102  14820.61523  7434.34668  4969.66113  3741.05395  1968.92871
1043.43018  1107.2915  867.73779  5146.99512  10612.75098  15606.82129  17111.01367  15553.41211  13606.79297  11644.58398  9904.29102  8363.57617  8394.67383  9185.61426  11504.78906  15183.7041  18597.78906  19856.51953  18239.32031  14534.8418  10632.95703  7895.86572  5961.84131  2730.13037  844.76611
955.84497  2015.80225  2387.98047  4048.4624  11210.70312  16925.08203  19031.31055  17363.96484  14155.95312  12351.83789  12254.92773  12554.97559  8054.34082  7015.4541  9957.03027  12886.91992  15665.52832  16681.64844  15349.11035  11559.93652  6778.93994  2888.54883  2653.48828  1996.67981  462.49243
816.61426  1340.49951  2559.72241  4974.0498  11448.54688  18123.99414  22077  21455.01172  17330.70312  13263.42481  12302.31055  12430.32227  10510.09863  8609.22852  8700.05859  11117.88281  13825.72266  13037.2832  10703.99121  7670.78467  4957.00293  2900.64209  1040.67224  2628.21582  2260.03833
1724.04956  1974.71899  3508.62842  6614.21143  14141.95898  22662.28711  29631.51758  30185.56836  24522.78125  20425.20117  17182.12695  14347.07422  11488.67969  9485.25684  8113.57764  7390.01367  6137.35059  4852.66846  4065.29761  1038.77881  2389.02588  2390.88355  1635.01221  887.71338  418.07263
1017.89062  3290.80713  2461.18628  6337.92041  10516.60254  27073.01367  47504.57031  49338.07031  32321.31836  17756.05273  10994.10547  7089.5957  5681.59668  5528.44141  3266.34937  1683.14502  1117.92139  1018.42493  1810.63977  1372.02917  409.14453  208.14368  503.91351  749.15692  609.94269
478.78796  276.61523  943.86523  3912.71606  10665.20508  26013.48047  49891.15625  52589.57031  32083.81641  14279.88379  7967.62402  2074.96045  1551.20606  2382.36328  1204.91748  660.64294  433.22656  293.98059  877.6582  425.44501  306.06085  582.08484  762.74091  773.78149  848.60443
-212.7782  806.15381  1836.09131  2703.93774  6954.34522  24789.8418  52799.79297  55614.00391  30688.68164  11702.89648  7908.93018  7220.44189  991.13086  176.91162  426.85034  595.06372  1902.92786  1999.74829  261.81982  127.63409  1488.17212  819.18957  809.03778  547.50305  402.78043
421.03442  679.49683  1223.23584  1319.02173  7267.28906  27667.15625  57490.22656  59154.5625  30209.49023  10021.16992  5106.10645  2895.95361  263.38672  4925.26855  535.75537  470.86707  656.37109  723.2934  -176.93835  -80.99463  460.82233  592.15222  624.12665  -272.06909  -973.29181
144.40857  243.18066  855.50024  1911.75195  7785.42334  24537.07617  53844.03125  56273.88672  29028.33984  12262.52441  8271.73731  4480.6875  752.30762  290.34033  593.19531  956.20917  722.90625  289.04041  86.98852  193.8642  372.54791  40.64154  29.01819  -144.94244  -311.20447
712.8313  30.62354  297.38672  1315.11987  5841.479  24975.31641  58066.73438  60861.19141  30210.11523  11398.08008  9358.29785  7345.10352  4206.13623  648.10962  1151.78479  1603.72144  994.3385  783.32489  472.1008  347.92139  159.12595  182.41538  -399.45337  2497.44824  336.76511];

beta0=[1*10.^6 0.8];

[beta,R]=nlinfit(x,y,@lnshp_exchange, beta0);