Discrete State Model for Kinesin-1 with Rate Constants Modulated by Neck
Linker Tension
Abstract
Kinesin-1 is a homodimeric molecular motor protein that uses ATP and a hand-over-hand motion to
transport cargo along microtubules. How kinesin converts chemical energy into directed motion is a
question that has been actively studied since its discovery. Even at the most coarse-grained level of
chemical kinetics, understanding is still lacking. Minimal kinetic models are often developed to both
explain kinesin’s hand-over-hand forward-stepping behavior and to infer important kinetic rate
constants from experimental data. These minimal models are often limited to a handful of two-headed
states on a core cycle and have been essential for the current level of understanding. However, it is not
always clear how to evolve these core-cycle models to explain more complex behavior such as non-
processive motion. We have taken a different approach and have developed a kinetic model without a
pre-defined core cycle. Our model includes 80 two-headed states and permits transitions between any
two states that differ by a single catalytic or binding event. We constrain the rate constants as much as
possible by published experimental data. We define many of the remaining unknown rate constants
based on mechanical strain in the kinesin neck linkers and their docking state. We present a one-
dimensional model for neck-linker modulation of head binding and unbinding rates and nucleotide
binding and unbinding rates. We show that our model reproduces a run length (processivity) and run
time in the range of experimental results. The core cycles that emerge are slightly different than those
commonly discussed. We also explore how processivity and speed change with neck linker length. Our
modeling applications are available as LabVIEW open-source code and compiled executables for PCs,
which will allow other research groups to adapt the model and rate constants and may aid in general
understanding of molecular motor behavior.
Introduction
Kinesin is a family of motor proteins that catalyzes ATP hydrolysis and steps along a microtubule via a
series of stochastic transitions [1-3]. Kinesin-1 (herein referred to as simply “kinesin”) is an often studied
member of this family. It has an essential role in anterograde axonal transport [4-10]. Kinesin can walk
about a micron along the microtubule in a second. It does this through a cycle that involves hydrolyzing
one ATP per step. This stepping cycle has been probed extensively through many different experiments
and tools including optical traps, analysis of chimera from different kinesin family members, Förster
resonance energy transfer (FRET), and gliding motility assays [11-17]. This has led to an understanding of
the frequent transitions that under normal conditions the kinesin steps through in order to travel along
the microtubule. Details of the ordering of the transitions are still debated. For example, the exact order
of ATP binding and the mechanical step of kinesin moving forward are argued, and these steps are
sometimes combined [18].
There are a couple of important characteristics of the kinesin stepping cycle. The first is that one ATP is
hydrolyzed per step, providing energy for directed transport along the microtubule [14,19]. Under
*Manuscript
Click here to download Manuscript: kinesin model doc.doc

normal conditions ATP binds to the head, is hydrolyzed into ADP and inorganic phosphate (Pi) which are
then released. Another important feature is that there is coordination between the two heads. The neck
linker domains can transmit strain which is modulated by the nucleotide binding states of the two
heads. This coordination allows for high processivity. Kinesin can walk hundreds of steps before
detaching from the microtubule.
The neck linker has been reported to be within a range of 14-15 amino acids (aa) long or 5.32-5.7 nm,
assuming a contour length of .38 nm per aa [20-23]. It is believed that coordination of the heads is
assisted by a nucleotide dependent docking mechanism of the neck linker. When ATP or ADP-Pi is bound
to the catalytic core, the neck linker will dock to the head through a short amino acid sequence on the
head named switch I which chemically interacts with the Pi [20-27]. Conversely the neck linker is found
in an undocked state when the head is empty or bound to ADP. Though this docking mechanism has
been extensively explored it is not known exactly how or if the neck linker coordinates a long processive
kinesin motion.
Many researchers have developed models to explain kinesin’s processivity, force generation, and other
physical aspects. These models include ratchet models [28-30], elastically coupled Brownian heads [31-
35], and discrete-state stochastic models[20,22,36-40]. While these models have produced invaluable
insight into kinesin, there are still many unanswered questions especially concerning how the neck linker
physically impacts kinesin’s behavior and how the behavior changes under various conditions.
In this paper we describe a discrete-state model of kinesin, analyzed by stochastic simulation and
analytical Markov chain theory. There are two aspects of our model that have not been typically
included in prior work. First, we do not impose strong restrictions on allowed transitions between
states, even if these states are considered forbidden or rare. This allows us to analyze rare transitions, in
particular those leading to two-headed detachment. On the other hand, our permissive model requires
knowledge of many more rate constants beyond those on a core cycle. The second feature we include is
a physics-based model of how the kinesin neck linker strain modulates rate constants. We model the
neck linker as a worm-like chain (WLC) and use Kramers’ reaction rate theory to model force-based
modulation of head binding and unbinding rates. We also include explicit chemical gating based on
potential neck linker strain.
In this paper we describe the numerous rate constants we used in our model and our methods for
estimating or calculating unknown rate constants. The rate constants may serve as a useful review of
existing published rate constants for kinesin-1. We demonstrate that our model produces results
agreeing with many published experiments using both Monte Carlo and Markov chain analysis. Finally,
we explore how observables such as speed and processivity are affected by changing the neck linker
length and thus the strain. The software applications presented have been written in LabVIEW 7.1 and
are available as open-source on SourceForge at http://sourceforge.net/projects/herskowkinesin/files/.

Methods
Model Description
As mentioned above, we have created a permissive model that allows for rare states and transitions and
does not explicitly define a core cycle. The model is defined by a vector of possible two-headed states
and a matrix of transition rates. An individual head can be either bound or unbound to the microtubule
and can have four nucleotide states (ATP, ADP-Pi, ADP, or no nucleotide). We have limited the
nucleotide state to not allow binding of Pi by itself. We do this to reduce complexity of the model and
are motivated by the low concentration of Pi in solution and the lack of discussion of this state in the
literature [41-43]. Two headed states can be defined as combinations of one headed states. When both
heads are bound, however, an additional property defines relative front/back position of the heads.
When one or both heads are unbound, there is no front / back property.
This results in 80 unique two-headed states. The transition rate matrix has a size of 80 x 80, but with
only 6 or seven potentially non-zero entries per row. This is because transitions are restricted to one
chemical reaction or binding event at a time. For example, an ATP head can transition to an ADP-Pi head
(hydrolysis) or an empty head (ATP release), but cannot transition to an ADP-only head, since that would
require two simultaneous events: either ATP release followed by ADP binding, or hydrolysis followed
and Pi release. This results in a sparse matrix with 416 allowed transitions. Of these, there are 148
unique transitions. These rate constants are the core of the model. In the following sections, we discuss
our methods for obtaining these rate constants, which includes the literature, mechanical and chemical
gating, and empirical fitting. In supplemental Table S1 we provide a list of all the transition rates we
used for the data shown in this paper. When available, we provide the published range and when
necessary our reasons for the value we have used.
Use of published rate constants
The first thing we did was scour the literature for well-accepted published rate constants. Since kinesin
is well studied, we were able to find rates for many of the transitions [15,16,28,34,36,44-59]. Of the 148
unique rate constants 64 were taken from literature. This number does not account for the 8 inorganic
phosphate release rates explained in the Empirical Fitting section below.
Hancock et al. hypothesized that rate constants for a singly-bound head are similar to those for
monomeric kiensin constructs [50]. We used this reasoning for 12 unique transition rates extracted from
literature [28,40,60,61]. This included the nucleotide-dependent head unbinding rates that are used as
k0 in equation 2.
Besides the inorganic phosphate release rates described below, we set the rate constants within the
published ranges we found. We did not pick the center of these ranges, but instead made some
adjustments to produce results for run length and run time that agreed with predictions. Unfortunately
we did not record our exact method for doing this during the initial phases of our research, so we
cannot describe it completely here. Many of the times, we agreed with a specific reference, and in Table
S1 we designate these rate constants. However, we cannot state our specific reasons for choosing the
particular reference.

Neck Linker modulation of rate constants
Using an extensible WLC model, we can approximate the tension in the neck linker in different docking
configurations. Calculating this tension allows us to modulate the rate for a bound head to detach from
the microtubule using the Bell equation [62]. It also allows us to calculate the rate at which an unbound
head can bind to the next and previous binding sites. These two rate modulation methods are explained
in the Mechanical Strain Gating section. Finally, we hypothesize that when the tension in the neck linker
is great, switch I would not be able to bind to the inorganic phosphate, thus the neck linker would not be
able to dock. This prevents a bound head from entering a docked state which increases the nucleotide
release rate. This is explained in the Chemical Strain Gating section.
Mechanical Strain Gating
We model the neck linker as an extensible WLC. The following interpolation equation describes the
relationship between the force and the extension of a WLC [63]

00
2
00 4
1)1(4
1
K
F
L
x
K
F
L
x
Tk
FP
B
 
Equation 1
where F is the force, x is the extension length, P=0.8 nm is the persistence length [21,29,64], kBT=4.1 pN-
nm is the thermal energy, K0=1000 pN is the stretch modulus [65,66], and L0 = N*0.38 nm is the contour
length, dependent on the number of undocked amino acids (N). We use N=26 as the number of amino
acids in the two fully-undocked neck linkers of the dimer, for L0 = 9.88 nm. The 13 amino acid length of a
single neck linker is within the published range, 12-17 aa [20-22,67-69], of neck linker lengths. We use
this model, as opposed to a hookean approximation because the hypothetical forces encountered from
the various docking states are well outside of the low-force linear regime.
When one of the neck linkers goes from an undocked to a docked configuration, two parameters
change. First, the number of free amino acids between the two kinesin heads changes by the amount of
docked amino acids. This number is debated; for this work, we use 10 amino acids [26,70,71]. The
second parameter that changes is the position of the attachment of the free amino acid chain to the
kinesin head. We use a highly-simplified one-dimensional model for the docking and say that the
attachment position shifts towards the plus end of the microtubule by the number of amino acids
multiplied by the contour length per amino acid. This effectively assumes that there is enough binding
energy to stretch the neck linker to its contour length, a force of about 109 pN for the WLC parameters
we use. If both heads are bound, neck linker docking or undocking either reduces or increases the strain
between the two bound heads, depending on whether the change in docking state occurs in the front or
rear head. See Figure 1 for the strain forces in the various docking states.
The mechanical strain affects our model in two ways. The first is by modulating the rate constants for
head unbinding from the tubulin binding site. Strain increases the unbinding rate exponentially
according to the Bell equation [62].

 
l
l
dxxF
ek
kr 
)(
0
Equation 2

where k0 is the unbinding rate with no force applied, l is the distance from the unbound equilibrium
position to the position at its binding site, and  is the distance from the binding site to the transition
state. Delta has been measured experimentally to be 2.5-3 nm [13,72,73] and we use 2.5 nm in this
work. We assume that the delta is the same whether force is applied by the neck linker or an external
force probe, and that it is constant over the force range. Figure 1 shows the unbinding rate increase
factors for the various docking states. We were able to calculate 32 unique detaching rates using
equation 2, marked in yellow in supplemental Table S1.
The second way neck linker strain affects rate constants is by modulation of the rate of head binding to
tubulin binding sites. We first made the assumption that when the head detaches from the microtubule
it does not rebind before quickly finding an equilibrium position over the bound head. This rate of
reaching equilibrium can be estimated from the Smoluchowski equation and the WLC forces. It is of the
order of 109s-1 and rapid enough to ignore in our model. Neck linker docking of the heads affects the
equilibrium position of the undocked head relative to its forward and backward tubulin binding sites, as
illustrated in Figure 2. The equilibrium position affects the rate constant for binding to the forward or
backward binding site. We model this landscape as a WLC potential coupled with an absorbing potential,
which creates a cusp. The minimum of the energy landscape is placed at the head equilibrium location.
Hanngi, et al. 1990 [74] reports the rate for a particle to escape a cusp shaped barrier.
Tk
E
B
b
B
cusp
B
b
eTk
E
Tk
xDUk 2
)('' 0
Equation 3
In the previous equation
cuspk
is the escape rate to get over the barrier, D is the diffusion constant,
)('' 0xU is the second spatial derivative of the energy landscape evaluated at the energy minimum, and
bE is the cusp barrier height. In this case bE is the energy of the WLC at the distance to the binding
site. The distance of the cusp from the equilibrium position is equal to the distance to the forward or
backward binding site from the equilibrium position. Thus, the magnitude of
bE depends strongly on
the docking states of the bound and unbound heads. It is worth noting that this equation depends
strongly on
bE and less on the curvature at the equilibrium position, but does not depend on the energy
potential after the cusp. In addition to the assumptions already described, we also explicitly assume that
there is no reduction in binding rates due to configuration of the binding interfaces, for example,
rotation of the head relative to the binding site. That is, binding to the microtubule is instantaneous
once the head diffuses a distance equal to the distance from the binding site. Using equation 3 we were
able to calculate 32 unique stepping/binding rates, marked in orange in supplemental Table S1.
Chemical Gating
In addition to head binding and unbinding rates, neck linker docking may also affect nucleotide binding
stability. ADP binds more weakly to the head than ATP or ADP-Pi [46,61]. This could be due to stabilizing
interactions between the switch I and the inorganic phosphate [75].

According to the parameters used above in Figure 1, the tension in the neck linker when an undocked
head is bound behind a bound docked head would be 1041 pN, and when both bound heads are docked
the tension is increased to 2631 pN. Such high tensions in the neck linker and consequently on the
switch I, would likely prohibit the switch from binding to the inorganic phosphate thus the neck linker
would not be able to dock to the head. Because it is highly unlikely that there is enough binding energy
to sustain this force we make the assumption that these docking configurations are forbidden, and
therefore the inorganic phosphate cannot bind to the switch I. Because of this, binding of ATP is not
stabilized and its unbinding rate from the kinesin head is the same as ADP’s unbinding rate. These rate
constants are colored blue in supplemental Table S1. In most cases, our gating of the nucleotide
unbinding rate is in contrast to much chemical gating literature, where gating modulates the nucleotide
binding rate [18,20,22]. In some cases, though, we use specific published rate constants which may
imply strong chemical gating of nucleotide binding rates. For example our ATP binding rates of 3 Ms-1
when the empty head is in front and 0.3 Ms-1 when the empty head is in back [34].
Empirical fitting of inorganic phosphate release rates
Without changing the rates of inorganic phosphate release well outside of published experimental
ranges, we were unable to produce results that matched expected run time and run length. This same
problem was encountered by the model of Muthurkrishnan et al. [22] and Shastry et al. [20]. The
literature reports a range of 13 to 100 s-1 [36,47,54,58]. However, release of inorganic phosphate must
occur during every productive hydrolysis cycle, which occurs at a rate of 100/s. Shasta et al. point out
that this is incongruous with such a low rate of phosphate release. They empirically adjust their rate to
250 / s for the step of bound/ADP-Pi in back of a bound/empty head [20]. We arrived at a similar
conclusion and needed to adjust our rate to 250 /s for all of the release rates except when ADP-Pi is
behind an undocked head. For the cases of an ADP-Pi head bound behind a bound ADP or empty head,
we used a Pi release rate of 25/s. This is in range of published rate constants but we don’t have a
structural reason for using the published range for only these particular constants. However, we found
that if the rate constant for phosphate release behind an ADP head were also 250 / s it would frequently
enter the ADP/ADP state, which leads to a reduction of processivity. We use 25/s for phosphate release
behind the empty head as well, reasoning that the chemical gating should be the same for both cases. In
the case of Shastry et al. [20], they only consider phosphate release from behind a bound empty head.
For consistency, we kept the inorganic phosphate release at 25 s-1 when in back of an empty head, even
though it didn’t affect our run time or length.
Agent-Based Stochastic Simulation
We used an agent-based implementation of the model for stochastic simulation [76,77]. Each kinesin
head is an agent identical to the other head and handled independently. Each agent is a state machine
with 8 states—bound or unbound in each of the 4 nucleotide states. We initially thought this would
reduce the complexity of the simulation, using a state machine with only 8 states instead of 80 if we
considered both heads at once. However the need to modulate rate constants based on the state of the
partner agent required many nested case structures for each state, and thus we did not realize a gain in
simplicity. Identical results should be obtained with an 80 state machine, but we did not attempt to
show this. As an example, Figure 3 shows the possible transitions from a bound/ATP head with an

unbound/ADP head. The ATP head can unbind from the microtubule, hydrolyze to form ADP-Pi, or
release ATP. The other head can release ADP, bind behind the ATP head, capture inorganic phosphate,
or bind in front of the ATP head. The most likely transition is for the unbound head to bind in front of
the ATP head. The ATP head has a binds relatively strongly to the microtubule so it is unlikely to unbind
from the microtubule. While hydrolysis is fast and expected in other two headed states, in this case it is
three orders of magnitude slower than the forward stepping rate. The same is true for ATP release from
the bound head. ADP is strongly attached to an unbound head [61]. Inorganic phosphate is unlikely to
bind to the unbound head with its extremely low concentration, and it is unlikely for the unbound head
to bind to the previous binding site since it has to travel 12.0 nm as opposed to a 4.4 nm distance to the
next site. This makes a huge difference in the rate of forward or backward binding as seen in Figure 1.
We used a Monte Carlo method to determine which path the kinesin will take from the current state. A
random number, rand, between 0 and 1 is chosen and converted to an exponentially distributed time, ti,
according to the following equation,
)ln(1 randkt ii

, where ki is the rate constant for the i
th
transition. The system is moved to the state according to the transition with the shortest time [77]. The
process is repeated for the new state, with new rate constants. If the transition is a head unbinding or
binding event, then the stalk position moves forward or backward according to neck linker docking
configurations.
For the work reported here, each single run starts with the system in unbound ADP with a bound ATP,
and ends when both heads are unbound simultaneously. The states of the heads, stalk positions, and
cumulative time are recorded for each transition. Most reported results are the result of an average of
1000 individual runs per condition. This application is called Kinetic Monte Carlo.exe available at
http://sourceforge.net/projects/herskowkinesin/files/.
Markov Analysis
Using a kinetic Monte Carlo technique is the simplest way to analyze this model, and it allows for
measuring the variance of observables. Complementary and exact solutions for average run length,
most frequented states, most probable transitions, run time and other observables can be obtained
from Discrete Time Markov chain (DTMC) and Continuous Time Markov chain (CTMC) theories.
DTMC
To calculate run length we analyze the DTMC that is embedded in the full CTMC. The embedded DTMC
is calculated through








 

ij
ij
q
q
p
ij
ij
ij
ij
0
Equation 4
where
iiq is the transition rate from state i to state j [78]. The diagonal terms are 0 since the state
cannot make a transition from state i to itself. We use the DTMC instead of the CTMC because we are

only interested in the number of steps taken. It is simpler to use DTMC for this purpose since we are not
interested in the time it takes which would require CTMC modeling.
To compute the average distance the kinesin travels, we first looked at the probability that the system
will return to the initial state. To calculate this probability we first need to look at the probability that
the system will return to the initial state after n steps. This probability is expressed by




1
1
)()()()( n
l
ln
jj
l
ij
n
ij
n
ij pfpf
Equation 5
)(nijf is the probability that the first time the system enters state j after starting in state i is after n steps.
)(nijp is the i,j element of the embedded DTMC raised to the n
th power [78]. This quantity is the
probability that starting in state i the system will be in state j after n steps. So to calculate the probability
that the system will ever transition into state j we use equation 6.




1
)(
n
n
ijij ff
Equation 6
Thus
*iif is the probability of starting in state i and ever transitioning to state i
*. i* is the same state as i
but with the opposite head in front. )(*niif is the probability to transition to the i
* n times [78]. We made
the assumption that each time the system travels from i to i* the kinesin took a step. Thorn et al.
reported a 99.3% chance of finishing a cycle after starting [59]. For the rate constants used in this report,
DTMC analysis also showed a 99.3% chance.
DTMC analysis also allows calculation of the most-visited states and the most-popular transitions. First
the probability matrix needs to be rewritten into canonical form. If there are b absorbing states (states
where both heads are detached) and m transient states then the probability matrix takes the canonical
form of





 0
RSP
Equation 7
where S is an m by m matrix, R is an m by b matrix, 0 is an b by m zero matrix, and I is an b by b identity
matrix. In our model there are 16 absorbing states (b=16) and 64 transient states (m=64). The
fundamental matrix, N, is calculated by
1)(  SN Equation 8
where the exponential -1 denotes the inverse of )( S . The elements of the fundamental matrix nij is
the average number of times the system is in state j if it started in state i. N, and P are used to calculate
the most frequented states [79].

To calculate the most popular transitions we take nij and multiply it by the probability, pjk, to go from
state j to state k. This allows us to find the average number of times each transitional step is taken.
Finally, we can use the R matrix to calculate the most probable absorbing state (completely detached
state).
NRD  Equation 9
where D is a matrix whose elements dij is the probability for a system whose initial state, i, will be
absorbed in state j [79].
CTMC
To calculate run time we used continuous time Markov chain (CTMC) analysis, since we needed to
consider the time spent in each state. We first created the infinitesimal generating matrix, Q, out of the
transition rates. The off-diagonal elements qij are the transition rates from state i to state j. The
diagonals qii are calculated as




ij ijii
qq
Equation 10
and represent the rate of staying in state i. Q was then used to create the differential equation:

QtPdt
tdP )()( 
Equation 11
where P(t) is a matrix whose elements pij(t) are the probability that starting in state i the system is in
state j at time t [78].
The solution to this differential equation is
QtePtP )0()(  Equation 12
where is the initial state. This can be more simply evaluated using the eigenvalues and
eigenvectors so that the solution is:
1)0()(  AAePtP t Equation 13
where A is an eigenvector, A-1 is its inverse, and  is its eigenvalue matrix. This has the advantage of it
being simpler to calculate the exponential of a diagonalized matrix.
To calculate the run time, we looked at the probability of finding the system in a detached state as a
function of time. There are 16 unique detached states; however both heads unbound with ADP is by far
the most common, detaching by this route over 99.96% of the time. Thus it is a good approximation to
consider only the probability of ending in the two-head unbound ADP state.

Using DTMC and CTMC analyses to probe other characteristics from this collection of transition rates
proved to be increasingly complicated and difficult. The simplest and thus more convincing method is to
use the stochastic simulation, though Markov chain analyses are quicker. However it is important to
note that analytical Markov chain analyses may be useful for future work, including analysis of variance
via maximum caliber methods [80,81]. All software used to analyze the data is called Markov Chain
Analysis.exe available at http://sourceforge.net/projects/herskowkinesin/files/.
Extracting Velocity and KM from the Kinetic Monte Carlo Simulations
To calculate velocity for a given run, we chose to use the best fit slope of the position versus time data,
using least-squares fitting in LabVIEW 7.1. Seen in Figure 4 is an example of this best fit line over a single
processive run. A group of 1000 runs will produce a spread of measured speeds as shown in Figure 5.
We used a kernel density estimation (KDE) method to approximate the underlying probability density
function (PDF) for that group of speeds [82]. The peak of this PDF was used as the resultant speed for
that set of conditions. For example each data point in Figure 8 is produced from the peak of the PDF for
one hundred individual runs at a given set of conditions. KDE is an alternative to histogram methods for
estimating PDFs. KDE is performed by summing up a kernel function centered at each data point, or
mathematically written as




n
i
i
h h
xxKnhxf 1 )(
1)(
Equation 14
where h is a smoothing parameter called the bandwidth, xi are the data points, and )( h
xxK i
is the
kernel function. We used the standard Gaussian kernel:
2
2
1
2
1)( 

 
 h
xx
i
i
eh
xxK 
Equation 15
Figure 5 shows an example of the PDF produced from the KDE of 1000 speed measurements. For this
work we used a high bandwidth of 200 nm/s because we are only concerned with finding a single peak
as opposed to looking for speed changes or pauses. Smaller bandwidths sometimes produced multiple
peaks which are not desirable for our purposes here. The higher bandwidth produced a larger spread
than was intrinsic to the data, as seen in Figure 5.
To calculate the Michaelis-Menten constant we best fit the speed versus concentration data using Igor
Pro 5.05A to

MKATP
ATPvATPv  ][
][])([ max
Equation 16
and we extract Km, the Michaelis-Menten constant. vmax is the maximum velocity the kinesin reaches at
saturating ATP concentrations. Igor Pro 5.05A uses a Levenberg-Marquardt algorithm to best fit the
curve.

Extracting observables from Markov analysis
To calculate the expected run time and run length, we used the relation:




0
)( dxxxPx
Equation 17
where x is either the run time or the run length parameter and P(x) is the probability density function
from Markov theory. We evaluated this numerically with a dx of 8.2nm or .001 s.
Software for this Analysis
We used three different custom programs to produce the data seen in this paper. The workings of these
programs have been discussed above. The names and summaries of their duties are listed below:
 Kinetic Monte Carlo
o Allows the user to perform kinetic Monte Carlo simulations with prescribed rate
constants.
 Analyze Simulations from Kinetic Monte Carlo Simulations
o Analyzes a grouping of kinetic Monte Carlo simulations and extracts (all the following
quantities are averaged over the group) run time, run length, ATP/step ratio, speed,
most probable states, most probable transitions, most probable detached states, and
view individual runs.
 Markov Chain Analysis
o Uses Markov Chain theory to analyze prescribed rate constants. This software calculates
run time, run length, most probable states, most probable transitions, most probable
dethatched states, and creates the transition matrix.
These are provided as open sources at http://sourceforge.net/projects/herskowkinesin/files/. A tutorial
video created by CamStudio is also available at this site called Kinesin Model Tutuorial.
Results
Reproduction of Widely-Accepted Experimental Results
Except when stated otherwise, the following parameters were used for all results reported below: 1000
micromolar ATP concentration, 100 micromolar ADP concentration, 0.1 micromolar Pi concentration, 8.2
nm tubulin dimer spacing, 4.1 pN-nm kBT value. Neck linker properties are described in the methods. All
analyses were started with the same initial state of bound ATP with an unbound ADP head.
As described in the method section, we adjusted some rate constants and neck linker properties to
match correct run time and run length values. Figure 6 shows the histogram of the run length created
from the kinetic Monte Carlo simulation in red with the function predicted by DTMC in black. The
average run length of 1,298 nm is close to the range of published values of 600 to 1,200 nm [59,83].

The run time seen in Figure 7 has an average value of 1.31 s which is within the published range 0.75 to
2.89 s [17,59]. The CTMC curve in black shows a sharp increase at 0 time. This is because kinesin cannot
detach instantaneously from the initial state, but needs to cycle through other states before it can
detach. We calculated a velocity of 1080 nm/s which is close to the range of the accepted experimental
speed of 600- ~1,000 nm/s [20,27,84].
After setting rate constants and neck linker properties, we found that the ATP coupling ratio and ATP
Michaelis-Menten constant were also in acceptable range. From the 1000 runs used in Figures 6 and 7,
we found a ratio of ATP consumed to step taken of 1.03, and a ratio close to 1 is generally accepted
[85,86]. To calculate the Michaelis Menten constant, we performed 100 simulations at each ATP
concentration from 0 micromolars to 1,000 micromolar in variable increments. We computed the speed
for each concentration, producing the Michaelis-Menten curve shown in Figure 8. The best fit Michaelis-
Menten constant, Km, was 37.6 M within the published range of 13-60 M [17,85-87].
Most Probable State for Complete Detachment
Using DTMC, we found a 99.96% chance of two-head detachment occurring with ADP bound to both
heads. This result is not surprising since an ADP bound head has the weakest attachment to the
microtubule [88].
Core Cycle
One of our goals when developing this model was to see which core cycle(s) emerged having
constrained rate constants as much as possible by neck linker physics and published ranges without
removing any possible states. Figure 9 shows the core cycles we found using the rate constants
described here. We only include transitions that occur at least 10 times per processive run as computed
from DTMC. None of the three ATP-turnover cycles seen in Figure 9 are the most common cycle
described in the literature, which involves an ADP head bound behind an empty, followed by ADP head
unbinding and ATP binding to the empty bound head. A likely reason for this is that we do not inhibit
ATP binding to the front head, regardless of docking state of rear head [18,20,22,27]. This allows for
states seen in the center and right of the figure, ATP-ATP and ADPPi-ATP. In our model we did not forbid
these states, we only forbid neck linker docking of front head in these states as described in methods.
The outer cycle in Figure 9 is similar to Shastry 2010 [20], which includes allows ATP binding to the ADPPi
- empty state. However, other differences remain.
If we include strict front-head gating of ATP binding in our model, we can recover the more popular core
cycles. When we reduced front head ATP binding drastically we found the core cycle shown in Figure 10.
The rate constants we used for this core cycle can be found along with the open source software at
http://sourceforge.net/projects/herskowkinesin/files/ called front “head gating rate constants 2.dat”. In
order to get run length (514 nm) and run time (.92 s) in the correct range we needed to change the
inorganic phosphate release in back of a bound empty head to 250 s-1.
We also recovered popular core cycles by lowering the ATP and ADP concentrations but otherwise
keeping the conditions similar to reported above. We lowered the ADP concentration because the
processivity was too short with the 100 micromolar concentration we used for the other calculations

and it is difficult to report a core cycle when the molecule does not take processive steps. With an ATP
and ADP concentration of 3 micromolar, we found the core cycle seen in Figure 10. It is very similar to
the case of front-head gating, except the unbound ADP head with the bound empty head more
frequently rebinds behind the empty head (red arrow).
However, it was not our intention to reproduce the core cycle by modulating rate constants, but instead
to see which cycles emerged from our rate constant literature search and neck-linker modeling. Our
open source software platform should allow other researchers to reintroduce this or other types of
gating and explore the repercussions.
Changing the Neck Linker Length
A feature of our software is that it allows for easily investigating the effect of neck linker length on
observables such as speed and processivity. We investigated these effects as we changed the neck linker
length from 24 to 34 amino acids (26 amino acids was the standard length used). Figure 11A shows the
processivity and Figure 11B shows the resulting speed. We observed a maximum in speed for the default
neck linker length of 26 amino acids. The speed decreased by a factor of 2 when the neck linker was
lengthened by 8 amino acids. The processivity steadily increased as the neck linker was lengthened,
almost doubling with a neck linker change from 32 to 34 amino acids.
In our model, increasing the neck linker length decreases the tension between the two bound heads.
This decreases the rate at which a bound head detaches from the microtubule. On the other hand, it
increases the rate the unbound head can reach a binding site. This decreases the speed by increasing
the time of the two-headed states, but increases the processivity by increasing the chance of binding
when unattached. The increased likelihood of backward steps also contributes to a decrease in speed
and tempers the increase in forward processivity. The sharp decrease in processivity seen in the 24 aa
neck linker can be attributed to the shorter neck linker increasing the unbinding rates drastically while
decreasing the stepping rate. This causes the kinesin to spend most of its time with only a single head
bound, causing a decrease in processivity. Table 1 shows the unbinding factor and stepping rates
associated with each neck linker length.
Since our physics-based model of the neck linker is highly simplified, the quantitative results are less
important than the qualitative trends. The trends of increased processivity and decreased speed with
increased neck linker length do not agree with Yildiz [23] or Miyazono [21] or Shastry [20]. Disagreement
with these experiments could be explained by a number of differences between our model and
experimental conditions. In our model, as the neck linker length is changed, the mechanical gating
changes dramatically—affecting head binding and unbinding rates. However, we do not include any
effect of changing neck linker tension on chemical gating. The fact that we do not agree with experiment
may indicate that chemical gating is significantly affected by neck linker length. It is also possible that
our assumption of one dimensionality could cause these differences especially as the neck linker gets
longer.

Summary
We developed an 80-state model for kinesin behavior that can be analyzed by stochastic simulation and
Markov analysis. Unlike many existing models, we did not restrict the model to known core cycles. To do
so, a large number of rate constants needed to be determined. We were able to set these rate constants
by literature search and modeling of the neck linker for physical and chemical gating. To match
experimental behavior, only the rate constant for inorganic phosphate release needed to be adjusted
well outside of the published range. We were able to reproduce the expected results for run time, run
length, speed, and processivity.
The advantage of our expanded-state model is that it allows for exploration of the behavior as rate
constants are adjusted over a wide range, without the need to predefine a core cycle that may be
changing over this range of parameters. We demonstrated an example of this as we explored the
behavior as the neck linker length was changed. We also saw the core cycle change between high and
low ATP concentration. The expanded-state model also allowed us to explore the most likely means of
two-headed detachment. We expect to leverage this feature in future studies investigating the potential
effects of osmotic stress and water isotope on kinesin processivity and speed. Finally, it is easy to limit
the model and analyze published core cycles by setting the branch rates to zero.
We have begun work to add the ability to apply an external force to the kinesin. However this work
remains complicated by the need to adjust many rate constants such as head unbinding, head rebinding,
and chemical gating. Furthermore, forces add vectorially and depend on the location of force
application.
All of the software used in this report is open source and available via
http://sourceforge.net/projects/herskowkinesin/files/. A Tutorial video is available as well.
Acknowledgements
We thank Susan Atlas, Andy Maloney, Igor Kuznetsov, and Evan Evans technical discussions. We thank
Brian Josey for organizing our initial rate constants table. INCBN IGERT. LJH partially supported by NSF
Grant DGE-0549500. LJH and SJK supported by DTRA basic research grant HDTRA-1-09-1-0018.

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Figure 1. Docking configurations for the two head bound states and their associated
tension, neck linker contour length and extension, and head detachment rate enhancement
factor. Color coding indicates nucleotide state of the head: white no nucleotide, red ATP, purple
ADP-Pi, blue ADP. There are a total of four possible docking configurations for two head bound
states. These are seen in the “Unrestricted Configuration” column. We modeled the neck linker
using an extensible worm-like chain, Equation 1, with a persistence length of 0.8 nm, thermal
energy value of 4.1 pN-nm, elastic modulus of 1000 pN/nm, and a varying neck linker contour
length and extension. After calculating the tension in each unrestricted configuration we came to
the conclusion that the neck linker could not stably dock in the front head when there is a high
force pulling backwards as seen in the undocked/docked and docked/undocked configurations.
Though not shown in the table the neck linker contour length and extension for undocked/docked
is 6.08 nm and 12.0 nm respectively. For docked/docked the parameters are 2.3 nm and 8.2 nm
respectively. Thus in our model prohibitive tension causes the front head to be in an undocked
state regardless of nucleotide status. The changes this has on the configurations can be seen in
the column labeled “Configuration used in model”. The first two rows are allowed while the last
two rows show prohibited front head docking. The resulting tensions from the actual
configurations used are shown in the fourth column. Finally the unbinding rate enhancement
factor, r, which is the ratio of the kinesin’s head detachment rate with the tension compared to
the rate with no force applied (calculated using Equation 2) is shown in the last column.
Figure 2. Forward and backward binding rates for an unbound head for differing two-
headed docking configurations. When a head detaches from the microtubule it quickly finds an
equilibrium position over the bound head. This is because the tension in the neck linker is a
minimum in the least extended position. The four different two-headed docking configurations
are shown in the table. Unlike Figure 1, all docking configurations are allowed, since only one
head is bound and there is no neck linker tension. This equilibrium position is the minimum of a
potential energy landscape determined by the worm-like chain behavior of the flexible
(undocked) portions of the two neck linkers. To model binding, we placed ac sup at the location
of the forward and backward binding sites as seen in the “Energy Landscape Diagrams” row.
Even though each landscape should have two cusps, in most cases the energy becomes
exceptionally large and effectively prohibits binding in a direction, forward or backwards. The
rates for reaching the forward and backward binding sites are computed using Equation 3 using a
diffusion constant of 5.05x108 nm/s2, 4.1 pN-nm thermal energy, and the same parameters for
the worm0like chain mentioned above. Eb is the energy value from the worm-like chain potential
at each binding site. When the contour length is too short or the distance to the binding site too
large, the rate for reaching a binding site effectively becomes zero. Note by putting a cusp at the
binding site, we are modeling binding as immediate if the molecule reaches that extension. This
is the simplest model, and we do not account for the need for correct 3-D orientation of the
binding sties or other factors. Color coding and neck linker representation same as in Figure 1.
Figure 3. Transitions from an ATP head bound to the microtubule and an ADP-head
unbound (top, middle). Rates are in units of inverse second and are described in the text. The
most likely transition is forward binding of the ADP head, due to the docked neck linker (black
horizontal line) on the ATP head. Color coding indicates nucleotide state of the head: white no
nucleotide, red ATP, purple ADP-Pi, blue ADP.

Figure 4. Example of distance versus time (red trace) for a single stochastic simulation. The
linear least squares fit is shown as blue line and has a slope of 1187 nm/s.
Figure 5. Speed for 1000 individual stochastic simulations (red crosses) and kernel density
estimation (KDE) for speed probability density function (PDF, black curve). Each individual
speed is the least squares fit slope of an individual run (see Figure 4). For KDE a bandwidth of
200 nm/s was used, in order to ensure a single peak in the PDF (see methods).
Figure 6. Processive run length results. A histogram of run length for the 1000 stochastic
simulations is shown in red, while the calculated run length probability from DTMC is shown in
black. The expected run length from DTMC is 1,298 nm and close to the published range of
experimental averages.
Figure 7. Processive run time results. Histogram of run time for 1000 stochastic simulations
(red) is shown, along with calculated frequency from CTMC (black). The CTMC curve shows a
minimum at zero time because more than one transition must occur to reach the most likely
detached state (ADP bound to both heads), given our starting state (ATP head bound to MT,
ADP head detached).
Figure 8. Speed versus ATP concentration from stochastic simulations. Each speed point
(red curve) is the most likely speed found from kernel density estimation of 100 individual
stochastic simulations. The blue curve shows the best fit to the Michaelis-Menten relation, with a
KM of 37.6 M and a vmax of 1117 nm/s. This KM is in the range of published experimental
measurements.
Figure 9. Most probable transitions resulting from our unconstrained model. For the main
rate constants we used, we found the most likely transitions show here. Arrows indicate direction
of transition. We only show transitions that occur at least an average of 10 times per processive
run, as calculated by DTMC. Three core cycles can be seen in the picture, all proceeding
clockwise. None of these are the cycle most commonly described in the literature, though we can
recover that cycle by constraining the ATP binding to front head (marked by stars) as seen in
Figure 10 and described in text. The nucleotide binding state of the heads are represented by
color: white for no nucleotide, red for ATP, purple for ADP-Pi, blue for ADP. The neck linker is
represented by the black lines, and docking is indicated by a straight horizontal segment, while
undocked is curved upwards.
Figure 10. Most likely transitions after addition of front head gating of ATP binding. Only
transitions that occur an average of 10 or more times per processive run (as calculated by
DTMC) are shown. In contrast to Figure 9, here the rate constants for binding of ATP to the front
head was forbidden if the rear head is in the ATP state. This is sometimes referred to as front
head gating of ATP binding. In addition to reducing these rate constants close to zero, we also
increased a rate of phosphate release to produce a reasonable run length and time (marked with
STAR on figure, see text). Color coding and neck linker representation same as in Figure 1.
The core cycle for the low ATP and ADP case follows the same cycle as the front head gating
except the unbound ADP head more frequently rebinds behind the empty head in the low
concentration case. This is shown with the red arrow. Only transitions that occur an average of
10 or more times per processive run (as calculated by DTMC) are shown.

Figure 11. Effect of changing neck linker length on processivity (A) and speed (B).
Changing the neck linker length changes the tension in the undocked portions of the neck linker.
We did not adjust the number of amino acids involved in docking. The default neck linker length
used throughout this report was 26 amino acids, with a docking number 10 aa.

Table 1. Effect of changing neck linker length on kinesin head unbinding and binding
rates.
Neck Linker
Length (aa)
Contour
length (nm)
Docked
contour
length (nm)
r Unbound Binding Rates (s-1)
Docked
Undocked
Undocked
Undocked
Docked
Undocked
Docked
Docked
Undocked
Undocked
4.4 nm 8.2 nm 4.4 nm 12 nm 8.2 nm 8.2 nm
24 9.12 5.3 1.23x103 4.56x106 5.43x104 0 0 0.184
26 9.88 6.1 109.445 3.51x104 4.90x105 0 0 36.7518
28 10.6 6.8 35.5 2.58x103 1.28x106 0 0 679.021
30 11.4 7.6 18.4 544 2.15x106 0 0 4.05x103
32 12.2 8.4 11.9 196 2.93x106 0 0 1.34x104
34 12.9 9.1 8.71 95.5 3.59x106 0 0 3.13x104
We changed the neck linker length from 24 to 34 amino acids (26 amino acids was used for all
figures created in this paper unless stated otherwise). This table shows the contour length and
docked contour length used to calculate r (the ratio of kinesin head detachment rate with a force
compared to the detachment rate with no force) and the unbound head binding rates. As shown in
Figure 1, there are only two different configurations when both heads are bound (although this
assumption may become less valid as the neck linker length increases), and the neck linker
extension is shown below each of these cases. For the unbound head binding rates, there are four
different configurations. However, an unbound undocked head with a bound docked head has the
same rates when traveling forward and backward as an unbound docked head with a bound
undocked binding backward and forward. For simplicity we combined these into one column.
The distances shown below each configuration is the distance to the closest binding site. Since
docked/docked and undocked/undocked equilibrium positions are located exactly between two
binding sites, the head needs to travel 8.2 nm to reach either binding site. r is calculated using
Equation 2 while the unbound binding rates are calculated using Equation 3. As the neck linker
length increases, the tension between the two bound heads decreases, thus r decreases as well.
This means that the kinesin heads remain bound to the microtubule longer. The binding rates
increase as the neck linker gets longer since there is now less force prohibiting the neck linker
from diffusing that distance. However there still remains a bias for forward binding due to the
forward bias in the equilibrium position. This causes a longer processivity since it decreases the
time in the one-head bound state, thus reducing the probability of complete detachment. The
velocity decreases due to the longer time spent with both heads bound to the microtubule.

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Supporting Information
Click here to download Supporting Information: Supplemental Table 1.pdf

The table below shows the rate constants used for the analysis in the paper expect when explicitly
stated otherwise. The columns provide the transition name, the rate used, the range from literature
when applicable, the references for that range, and finally if needed a reason explaining why this rate
is used. The table is color coded to show the method for obtaining the rate constant, as described in
the following text. Uncolored rows represent rates which were obtained from publication. In some
cases we chose one particular publication over another (that reference is shown in bold), or we
adjusted the rate constant within the published range. Unfortunately this was early in our research
project, and we do not have information stating our particular reason for choosing the rate constant,
other than it being within the published range.
The orange bands designate when the rate is calculated using Hanggi’s rate equation for escaping an
energy barrier with a cusp as described in the manuscript. This equation is seen below:
Tk
E
B
b
B
cusp
B
b
eTk
E
Tk
xDUk 2
)('' 0
Equation 1
In the previous equation is the escape rate to get over the barrier, D is the diffusion constant,
is the second spatial derivative of the energy landscape evaluated at the energy minimum, and
is the cusp barrier height. In this case is the energy of the WLC extended from the equilibrium
position to the binding site. All of these rates are for an unbound head stepping and binding to an
adjacent binding site. In these rows the contour length, L0, and distance to the binding site, d, are
specified. The WLC parameters are given in the manuscript.
The rows are colored yellow when we used Bell’s equation to calculate the unbinding rate.
 
l
l
dxxF
ekk 
)(
0
Equation 2
where is the unbinding rate with no force applied, l is the distance from the unbound equilibrium
position to the position at its binding site (i.e. the neck linker is significantly extended when the head is
bound), and is the distance from the binding site to the transition state. For this work we used a  of
2.5 nm (see main text for references). In each of these cases the neck linker tension accelerates
unbinding above the rate of unbinding under no tension, k0. The extension of the neck linker is labeled
in the table as s. The rates for k0 are obtained from the literature ( blllaa nkk color coding).
The green rows indicate the two rate constants for which we could not find published rates and which
were not produced by our modeling. In these two cases we could only find a similar transition but for a
bound head not an unbound head. So for both of these rates we used the published bound head rate
constant. These two rates come from a rare state and thus do not impact the results regardless of their
particular values.
When our chemical gating model changed the rate constants we colored these rows purple. There are
two different configurations in which we felt that the neck would not dock to the kinesin head: when a

bound docked head is in front of a bound undocked head and when both bound heads are docked. We
did not note when the rate is affected by chemical gating and the Bell equation simultaneously. Those
rows were left yellow. However because we specify the contour length and distance the docking
configuration could be deduced using Figure 1.
The blue rows are the inorganic phosphate release rows. We could not keep these rates within the
published range and observe correct run time and run length (similar to Shastry et al as noted in the
main text). We decided to raise the inorganic phosphate release to 250 /s except for when ADP-Pi was
in front of an undocked state. Then we lowered the value to 25 /s which is within range but different
from the other rates for no reason other than it lowered the run length and run time too much if set to
250 s-1.
These rate constants can be loaded into our software using the file “Rate Constants used.dat” at
https://sourceforge.net/project/admin/explorer.php?group_id=362373.
Table S1. Transitions rates used in the Paper
Transition Rate Range Reference Reason
Unbound ADP Release ADP 2.000E-3 .002-.1 [1-4]
Unbound ADP Capture P 2.000E+1 25 [1]
Unbound Empty Bind ADP 6.000E+0 6 [4]
Unbound Empty Bind ATP 4.000E+0 4 [1]
Unbound ADP Stepping with
Empty Forward
3.675E+1 Equation 1: L0=9.88 nm
d=8.2 nm
Unbound ADP Stepping with
Empty Backward
3.675E+1 Equation 1: L0=9.88 nm
d=8.2 nm
Unbound ATP Hydrolyze to ADP-
P
1.000E+1 6-10 [1,4,5]
Unbound ATP Release ATP 5.000E+1 150 Could not find this value so
used the value from the
bound case
Unbound ADP-P Release P 2.500E+2 20-250 [1,2,6]
Unbound ADP-P Form ATP 2.500E+1 Could not find this value so
used the bound ATP
synthesis rate
Unbound Empty Stepping with
Empty Forward
3.675E+1 Equation 1: L0=9.88 nm
d=8.2 nm
Unbound Empty Stepping with
Empty Backward
3.675E+1 Equation 1: L0=9.88 nm
d=8.2 nm
Unbound ADP Stepping with
ADP-P Forward
4.900E+5 Equation 1: L0=6.08 nm
d=4.4 nm
Unbound ADP Stepping with
ADP-P Backward
0.000E+0 Equation 1: L0=6.08 nm d=12
nm
Unbound ADP Stepping with
ADP Forward
3.675E+1 Equation 1: L0=9.88 nm
d=8.2 nm
Unbound ADP Stepping with 3.675E+1 Equation 1: L0=9.88 nm

ADP Backward d=8.2 nm
Unbound ADP Stepping with
ATP Forward
4.900E+5 Equation 1: L0=6.08 nm
d=4.4 nm
Unbound ADP Stepping with
ATP Backward
0.000E+0 Equation 1: L0=6.08 nm d=12
nm
Unbound Empty Stepping with
ADP-P Forward
4.900E+5 Equation 1: L0=6.08 nm
d=4.4 nm
Unbound Empty Stepping with
ADP-P Backward
0.000E+0 Equation 1: L0=6.08 nm d=12
nm
Unbound Empty Stepping with
ADP Forward
3.675E+1 Equation 1: L0=9.88 nm
d=8.2 nm
Unbound Empty Stepping with
ADP Backward
3.675E+1 Equation 1: L0=9.88 nm
d=8.2 nm
Unbound Empty Stepping with
ATP Forward
4.900E+5 Equation 1: L0=6.08 nm
d=4.4 nm
Unbound Empty Stepping with
ATP Backward
0.000E+0 Equation 1: L0=6.08 nm d=12
nm
Unbound ATP Stepping with
ADP-P Forward
0.000E+0 Equation 1: L0=2.28 nm
d=8.2 nm
Unbound ATP Stepping with
ADP-P Backward
0.000E+0 Equation 1: L0=2.28 nm
d=8.2 nm
Unbound ATP Stepping with
ADP Forward
0.000E+0 Equation 1: L0=6.08 nm d=12
nm
Unbound ATP Stepping with
ADP Backward
4.900E+5 Equation 1: L0=6.08 nm
d=4.4 nm
Unbound ATP Stepping with ATP
Forward
0.000E+0 Equation 1: L0=2.28 nm
d=8.2 nm
Unbound ATP Stepping with ATP
Backward
0.000E+0 Equation 1: L0=2.28 nm
d=8.2 nm
Unbound ATP Stepping with
Empty Forward
0.000E+0 Equation 1: L0=6.08 nm d=12
nm
Unbound ATP Stepping with
Empty Backward
4.900E+5 Equation 1: L0=6.08 nm
d=4.4 nm
Unbound ADP-P Stepping with
ADP-P Forward
0.000E+0 Equation 1: L0=2.28 nm
d=8.2 nm
Unbound ADP-P Stepping with
ADP-P Backward
0.000E+0 Equation 1: L0=2.28 nm
d=8.2 nm
Unbound ADP-P Stepping with
ADP Forward
0.000E+0 Equation 1: L0=6.08 nm d=12
nm
Unbound ADP-P Stepping with
ADP Backward
4.900E+5 Equation 1: L0=6.08 nm
d=4.4 nm
Unbound ADP-P Stepping with
ATP Forward
0.000E+0 Equation 1: L0=2.28 nm
d=8.2 nm
Unbound ADP-P Stepping with
ATP Backward
0.000E+0 Equation 1: L0=2.28 nm
d=8.2 nm
Unbound ADP-P Stepping with
Empty Forward
0.000E+0 Equation 1: L0=6.08 nm
d=4.4 nm

Unbound ADP-P Stepping with
Empty Backward
4.900E+5 Equation 1: L0=6.08 nm
d=4.4 nm
Bound Empty in front of Bound
ATP Binding ATP
3.000E+0 1-3.8 [2,4,6-12]
Bound Empty in front of Bound
ATP Binding ADP
2.500E-1 .25 [13]
Bound Empty in front of Bound
ATP Unbinding
7.661E-1 Equation 2: L0=6.08 nm
s=4.4 nm
Bound Empty in back of Bound
ATP Binding ATP
3.000E-1 .3-3.8 [2,4,6-12]
Bound Empty in back of Bound
ATP Binding ADP
2.500E-1 .25 [13]
Bound Empty in back of Bound
ATP Unbinding
2.460E+2 Equation 2: L0=9.88 nm
s=8.2 nm
Bound Empty in front of Bound
ADP-P Binding ATP
3.000E+0 1-3.8 [2,4,6-12]
Bound Empty in front of Bound
ADP-P Binding ADP
2.500E-1 .25 [13]
Bound Empty in front of Bound
ADP-P Unbinding
7.661E-1 Equation 2: L0=6.08 nm
s=4.4 nm
Bound Empty in back of Bound
ADP-P Binding ATP
3.000E-1 .3-3.8 [2,4,6-12]
Bound Empty in back of Bound
ADP-P Binding ADP
2.500E-1 .25 [13]
Bound Empty in back of Bound
ADP-P Unbinding
2.460E+2 Equation 2: L0=9.88 nm
s=8.2 nm
Bound Empty in front of Bound
ADP Binding ATP
3.000E+0 1-3.8 [2,4,6-12]
Bound Empty in front of Bound
ADP Binding ADP
2.500E-1 .25 [13]
Bound Empty in front of Bound
ADP Unbinding
2.460E+2 Equation 2: L0=9.88 nm
s=8.2 nm
Bound Empty in back of Bound
ADP Binding ATP
3.000E-1 .3-3.8 [2,4,6-12]
Bound Empty in back of Bound
ADP Binding ADP
2.500E-1 .25 [13]
Bound Empty in back of Bound
ADP Unbinding
2.460E+2 Equation 2: L0=9.88 nm
s=8.2 nm
Bound Empty in front of Bound
Empty Binding ATP
3.000E+0 1-3.8 [2,4,6-12]
Bound Empty in front of Bound
Empty Binding ADP
2.500E-1 .25 [13]
Bound Empty in front of Bound
Empty Unbinding
2.460E+2 Equation 2: L0=9.88 nm
s=8.2 nm
Bound Empty in back of Bound
Empty Binding ATP
3.000E-1 .3-3.8 [2,4,6-12]
Bound Empty in back of Bound 2.500E-1 .25 [13]

Empty Binding ADP
Bound Empty in back of Bound
Empty Unbinding
2.460E+2 Equation 2: L0=9.88 nm
s=8.2 nm
Bound Empty with Unbound
Anything Binding ATP
2.000E+1 20 [14]
Bound Empty with Unbound
Anything Binding ADP
1.500E+0 1.5 [15]
Bound Empty with Unbound
Anything Unbinding
7.000E-3 .0009-.2 [3,6]
Bound ATP in front of Bound
ATP Becoming ADP-P
8.000E+0 8-300 [2,6,8-10,16,17]
Bound ATP in front of Bound
ATP Releasing ATP
5.000E+2 30-600 [2-4,6,8,9,11,12,16,18] In our chemical gating
theory this acts like ADP
bound head
Bound ATP in front of Bound
ATP Unbinding
7.661E-1 Equation 2: L0=6.08 nm
s=4.4 nm
Bound ATP in back of Bound ATP
Becoming ADP-P
8.000E+2 100-800 [2,6,8-10,16,17]
Bound ATP in back of Bound ATP
Releasing ATP
5.000E+1 30-200 [2,4,6-8,12,15]
Bound ATP in back of Bound ATP
Unbinding
7.661E-1 Equation 2: L0=6.08 nm
s=4.4 nm
Bound ATP in front of Bound
ADP-P Becoming ADP-P
8.000E+0 8-300 [2,6,8-10,16,17]
Bound ATP in front of Bound
ADP-P Releasing ATP
5.000E+2 30-600 [2-4,6,8,9,11,12,16,18] In our chemical gating
theory this acts like ADP
bound head
Bound ATP in front of Bound
ADP-P Unbinding
7.661E-1 Equation 2: L0=6.08 nm
s=4.4 nm
Bound ATP in back of Bound
ADP-P Becoming ADP-P
8.000E+2 100-800 [2,6,8-10,16,17]
Bound ATP in back of Bound
ADP-P Releasing ATP
5.000E+1 30-200 [2,4,6-8,12,15]
Bound ATP in back of Bound
ADP-P Unbinding
7.661E-1 Equation 2: L0=6.08 nm
s=4.4 nm
Bound ATP in front of Bound
ADP Becoming ADP-P
8.000E+0 8-800 [2,6,8-10,16,17]
Bound ATP in front of Bound
ADP Releasing ATP
5.000E+0 .01-300 [2-4,6,8,9,12,15] In our chemical gating
theory this acts like ADP
bound head
Bound ATP in front of Bound
ADP Unbinding
2.460E+2 Equation 2: L0=9.88 nm
s=8.2 nm
Bound ATP in back of Bound
ADP Becoming ADP-P
8.000E+2 100-800 [2,6,8-10,16,17]
Bound ATP in back of Bound
ADP Releasing ATP
5.000E+1 30-200 [2,4,6-8,12,15]
Bound ATP in back of Bound 7.661E-1 Equation 2: L0=6.08 nm

ADP Unbinding s=4.4 nm
Bound ATP in front of Bound
Empty Becoming ADP-P
8.000E+0 8-800 [2,6,8-10,16,17]
Bound ATP in front of Bound
Empty Releasing ATP
5.000E+0 .01-300 [2-4,6,8,9,12,15] In our chemical gating
theory this acts like ADP
bound head
Bound ATP in front of Bound
Empty Unbinding
2.460E+2 Equation 2: L0=9.88 nm
s=8.2 nm
Bound ATP in back of Bound
Empty Becoming ADP-P
8.000E+2 100-800 [2,6,8-10,16,17]
Bound ATP in back of Bound
Empty Releasing ATP
5.000E+1 30-200 [2,4,6-8,12,15]
Bound ATP in back of Bound
Empty Unbinding
7.661E-1 Equation 2: L0=6.08 nm
s=4.4 nm
Bound ATP with anything
unbound Becoming ADP-P
4.000E+2 200->300 [14,19]
Bound ATP with anything
unbound Releasing ATP
2.000E+2 200 [14]
Bound ATP with anything
unbound Unbinding
7.000E-3 .007-.9 [6]
Bound ADP-P in front of Bound
ATP Releasing P
2.500E+2 13- >100 [4,8,11,12] Adjusted rate constant
Bound ADP-P in front of Bound
ATP Forming ATP
2.500E+1 18-25 [1,6]
Bound ADP-P in front of Bound
ATP Unbinding
7.661E-1 Equation 2: L0=6.08 nm
s=4.4 nm
Bound ADP-P in back of Bound
ATP Releasing P
2.500E+2 13- >100 [4,8,11,12] Adjusted rate constant
Bound ADP-P in back of Bound
ATP Forming ATP
2.500E+1 18-25 [1,6]
Bound ADP-P in back of Bound
ATP Unbinding
7.661E-1 Equation 2: L0=6.08 nm
s=4.4 nm
Bound ADP-P in front of Bound
ADP-P Releasing P
2.500E+2 13- >100 [4,8,11,12] Adjusted rate constant
Bound ADP-P in front of Bound
ADP-P Forming ATP
2.500E+1 18-25 [1,6]
Bound ADP-P in front of Bound
ADP-P Unbinding
7.661E-1 Equation 2: L0=6.08 nm
s=4.4 nm
Bound ADP-P in back of Bound
ADP-P Releasing P
2.500E+2 13- >100 [4,8,11,12] Adjusted rate constant
Bound ADP-P in back of Bound
ADP-P Forming ATP
2.500E+1 18-25 [1,6]
Bound ADP-P in back of Bound
ADP-P Unbinding
7.661E-1 Equation 2: L0=6.08 nm
s=4.4 nm
Bound ADP-P in front of Bound
ADP Releasing P
2.500E+2 13- >100 [4,8,11,12] Adjusted rate constant
Bound ADP-P in front of Bound 2.500E+1 18-25 [1,6]

ADP Forming ATP
Bound ADP-P in front of Bound
ADP Unbinding
2.460E+2 Equation 2: L0=9.88 nm
s=8.2 nm
Bound ADP-P in back of Bound
ADP Releasing P
2.500E+1 13- >100 [4,8,11,12]
Bound ADP-P in back of Bound
ADP Forming ATP
2.500E+1 18-25 [1,6]
Bound ADP-P in back of Bound
ADP Unbinding
7.661E-1 Equation 2: L0=6.08 nm
s=4.4 nm
Bound ADP-P in front of Bound
Empty Releasing P
2.500E+2 13- >100 [4,8,11,12] Adjusted rate constant
Bound ADP-P in front of Bound
Empty Forming ATP
2.500E+1 18-25 [1,6]
Bound ADP-P in front of Bound
Empty Unbinding
2.460E+2 Equation 2: L0=9.88 nm
s=8.2 nm
Bound ADP-P in back of Bound
Empty Releasing P
2.500E+1 13- >100 [4,8,11,12]
Bound ADP-P in back of Bound
Empty Forming ATP
2.500E+1 18-25 [1,6]
Bound ADP-P in back of Bound
Empty Unbinding
7.661E-1 Equation 2: L0=6.08 nm
s=4.4 nm
Bound ADP-P with Anything
Unbound Releasing P
8.100E+1 81 [14]
Bound ADP-P with Anything
Unbound Forming ATP
2.500E+1 18-25 [1,6]
Bound ADP-P with Anything
Unbound Unbinding
7.000E-3 1.67-20 [2,3] It is generally accepted that
this off rate is similar ATP
and empty unbinding so it
was adjusted.
Bound ADP in front of Bound
ATP Capture P
2.000E+1 25 [1]
Bound ADP in front of Bound
ATP Release ADP
5.000E+2 30-600 [2-4,6,8,9,11,12,16,18]
Bound ADP in front of Bound
ATP Unbinding
2.736E+3 Equation 2: L0=6.08 nm
s=4.4 nm
Bound ADP in back of Bound
ATP Capture P
2.000E+1 25 [1]
Bound ADP in back of Bound
ATP Release ADP
5.000E+2 30-600 [2-4,6,8,9,11,12,16,18]
Bound ADP in back of Bound
ATP Unbinding
8.787E+5 Equation 2: L0=9.88 nm
s=8.2 nm
Bound ADP in front of Bound
ADP-P Capture P
2.000E+1 25 [1]
Bound ADP in front of Bound
ADP-P Release ADP
5.000E+2 30-600 [2-4,6,8,9,11,12,16,18]
Bound ADP in front of Bound
ADP-P Unbinding
2.736E+3 Equation 2: L0=6.08 nm
s=4.4 nm

Bound ADP in back of Bound
ADP-P Capture P
2.000E+1 25 [1]
Bound ADP in back of Bound
ADP-P Release ADP
5.000E+2 30-600 [2-4,6,8,9,11,12,16,18]
Bound ADP in back of Bound
ADP-P Unbinding
8.787E+5 Equation 2: L0=9.88 nm
s=8.2 nm
Bound ADP in front of Bound
ADP Capture P
2.000E+1 25 [1]
Bound ADP in front of Bound
ADP Release ADP
5.000E+0 .01-300 [2-4,6,8,9,12,15]
Bound ADP in front of Bound
ADP Unbinding
8.787E+5 Equation 2: L0=9.88 nm
s=8.2 nm
Bound ADP in back of Bound
ADP Capture P
2.000E+1 25 [1]
Bound ADP in back of Bound
ADP Release ADP
5.000E+0 .01-300 [2-4,6,8,9,12,15]
Bound ADP in back of Bound
ADP Unbinding
8.787E+5 Equation 2: L0=9.88 nm
s=8.2 nm
Bound ADP in front of Bound
Empty Capture P
2.000E+1 25 [1]
Bound ADP in front of Bound
Empty Release ADP
5.000E+0 .01-300 [2-4,6,8,9,12,15]
Bound ADP in front of Bound
Empty Unbinding
8.787E+5 Equation 2: L0=9.88 nm
s=8.2 nm
Bound ADP in back of Bound
Empty Capture P
2.000E+1 25 [1]
Bound ADP in back of Bound
Empty Release ADP
5.000E+0 .01-300 [2-4,6,8,9,12,15]
Bound ADP in back of Bound
Empty Unbinding
8.787E+5 Equation 2: L0=9.88 nm
s=8.2 nm
Bound ADP with Anything
Unbound Capture P
2.000E+1 25 [1]
Bound ADP with Anything
Unbound Release ADP
1.100E+2 110 [15]
Bound ADP with Anything
Unbound Unbinding
2.500E+1 1-25 [6]
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