{S = 1,2, …, Nstates}

{rates(j,k) = rate constant for j → k, rates(j,j) = 0}

for clock=1:clockmax do

t = clock * dt

rates = updaterates(S, rates)

{updaterates(S, rates) updates row S of the matrix rates, since that is the only row that will be used in the current time step}

ratesum = sum(rates(S, :))

if rand < ratesum * dt then

cp = cumsum(rates(S,:) / ratesum)

{cumulative summation of the rates in the state S and its normalization}

r = rand {random number between 0 and 1 with uniform distribution}

forS = 1:Nstates do

if r < cp(S) then

break

end if

end for

end if

end for