BioQuant, Heidelberg University, Im Neuenheimer Feld 267, 69120 Heidelberg, Germany

Institute for Theoretical Physics, , Philosophenweg 19, 69120 Heidelberg, Germany

Abstract

Background

Focal adhesions are integrin-based cell-matrix contacts that transduce and integrate mechanical and biochemical cues from the environment. They develop from smaller and more numerous focal complexes under the influence of mechanical force and are key elements for many physiological and disease-related processes, including wound healing and metastasis. More than 150 different proteins localize to focal adhesions and have been systematically classified in the adhesome project (

Results

We have developed a kinetic model for RNA interference of focal adhesions which represents some of its main elements: a spatially layered structure, signaling through the small GTPases Rac and Rho, and maturation from focal complexes to focal adhesions under force. The response to force is described by two complementary scenarios corresponding to slip and catch bond behavior, respectively. Using estimated and literature values for the model parameters, three time scales of the dynamics of RNAi-influenced focal adhesions are identified: a sub-minute time scale for the assembly of focal complexes, a sub-hour time scale for the maturation to focal adhesions, and a time scale of days that controls the siRNA-mediated knockdown. Our model shows bistability between states dominated by focal complexes and focal adhesions, respectively. Catch bonding strongly extends the range of stability of the state dominated by focal adhesions. A sensitivity analysis predicts that knockdown of focal adhesion components is more efficient for focal adhesions with slip bonds or if the system is in a state dominated by focal complexes. Knockdown of Rho leads to an increase of focal complexes.

Conclusions

The suggested model provides a kinetic description of the effect of RNA-interference of focal adhesions. Its predictions are in good agreement with known experimental results and can now guide the design of RNAi-experiments. In the future, it can be extended to include more components of the adhesome. It also could be extended by spatial aspects, for example by the differential activation of the Rac- and Rho-pathways in different parts of the cell.

Background

Cells adhere to flat surfaces through focal adhesions, which are integrin-based contacts between the cell and the extracellular matrix

Focal adhesions are not only signaling hubs, they also provide the mechanical linkage between the extracellular matrix and the actin cytoskeleton. For this purpose, they contain a large range of different connector proteins, including talin, vinculin, paxillin, and

Schematic presentation of focal adhesions

**Schematic presentation of focal adhesions.** Schematics of the situation of interest. **(A)** Cartoon of an adherent cell. During spreading and migration the cell adheres to ligands of the extracellular matrix (ECM), for example fibronectin, at the leading edge through nascent adhesions. They develop into focal complexes in the lamellipodium (LP), which can then mature into focal adhesions in the lamella (LM). Focal adhesions are typically connected to stress fibers that either run from one focal adhesion to another (ventral stress fibers) or end in the actin network (dorsal stress fibers). **(B)** Enlarged view of a focal adhesion with the main molecular components. The transmembrane protein integrin binds to the fibronectin on the ECM. The connection to the actin stress fibers, which can contract due to the myosin II motor molecules, is made by talin. This basic mechanical link is enhanced by proteins like vinculin, paxillin, or

Focal adhesions are the result of a complex maturation process, which is strongly related to the overall spatial coordination in an adherent cell

The maturation of FXs into FAs has been shown to depend on the presence of physical force
_{0} an internal force scale of the order of pico-Newtons

Focal adhesions are not only important for cell adhesion, but also for cell migration, division, and fate. Being essential for cell migration, they are key elements for many physiological and disease-related processes, including wound healing

One technique capable of such a systems level approach is the systematic use of RNA-interference (RNAi)

First siRNA-screens have also been conducted for focal adhesions. In

In order to systematically and quantitatively understand the experimental results with their often counterintuitive relations, theoretical models for focal adhesions are required. In the literature several models for the force-mediated dynamics of focal adhesions have been proposed

Different models have been suggested to model the effect of RNAi. A very global view has been introduced by Bartlett & Davis, who published a model that consists of twelve ordinary differential equations

Here we introduce a kinetic model based on the clutch model by Macdonald et al.

Methods

Model definition

In Figure

Scheme of the kinetic model

**Scheme of the kinetic model.** The overall model scheme reveals the main design principles. The mRNA transcription and degradation are depicted on the left hand side. After the translation of the proteins, these are assembled to focal complexes (ACI). Focal complexes can in turn mature to focal adhesions (ACI#). The assembly process is regulated by Rac and the maturation process is regulated by force and Rho. Depending on the force model used, the reactions marked with a star are either promoting (slip bonds) or suppressing (catch bonds) focal adhesion or focal complex disassembly.

Mathematically this scheme corresponds to twelve ordinary differential equations that will be explained in detail below. Due to the use of ordinary differential equations, we have no explicit spatial resolution, however, our choice of species and reactions includes an implicit spatial assembly order (layer-like structure) and mirrors the spatial segregation of focal complexes and focal adhesions. Modeling spatial processes with ordinary differential equations has been used successfully before, mainly in the context of compartment models. Examples in the context of cell adhesion are the original clutch model for focal adhesions

Each differential equation in our model describes the dynamic behavior of one species. These species are: MA - messenger RNA for actin, MC - messenger RNA for the so called connector complex, which represents all proteins that are located between actin and integrin in the focal adhesion (most prominently talin), MI - messenger RNA for integrin, A - actin, C - connector complex, I - integrin, AC - complex where the connector complex is bound to actin, CI - complex where the connector complex is bound to integrin, ACI - full complex (focal complex), ACI# - mature full complex (focal adhesion), RAC - active Rac concentration, RHO - active Rho concentration. Apart from the mRNA part and the Rac/Rho regulation steps, we use mass action kinetics throughout our model.

RNA-interference

We start with a description of the messenger RNA (mRNA). The change in the concentrations of the mRNA is dependent on two processes: basal production rate with rate constant _{MX} and basal degradation rate with rate constant _{MX}. An additional degradation term comes from the siRNA-treatment:

The RNAi-term is implemented in our model in the following way:

as suggested by Khanin & Vinciotti

In practice, usually only one component is knocked down. Then only the corresponding RNAi-term has to be included. The most reasonable choice seems to knock down the connector complex (for example talin), because integrins and actin are vital to the system. For example, cells lacking integrin are not capable to adhere on a 2D surface

Assembly and maturation process

The next three equations describe the change in the concentrations of actin, connector complex, and integrin in their monomeric forms:

Although in the cell actin can occur in many different forms, including monomeric, dendritic and bundled ones, for simplicity here we only introduced one species A; however, the different functions of actin are partially represented in the way this species interacts with the other ones. Likewise we introduce only one connector complex C, although in the adhesome, many different components might carry such a function. The concentration of the proteins A, C and I increases as they get translated from the accompanying mRNA or as higher order complexes disassemble. Degradation and incorporation into complexes decrease the concentration. Here and in the following equations, _{X} denotes the correspondent disassembly rate constant and _{X} denotes the correspondent assembly rate constant. The translation and degradation rate constants of protein X are given by _{T, X} and _{X}, respectively. The assembly of the intermediate complexes into focal complexes also depends on the Rac concentration, as Rac is known to promote the assembly of focal complexes

The rate equations for the intermediate complexes AC or CI are

We note that these equations are generic for the first steps in the assembly of a three-component complex and that more specific assembly pathways can be implemented by a suitable choice of reaction constants. For example, if actin A cannot bind to the connector complex C because the complex CI has to form first in order to recruit actin polymerization factors like formin in order to assembly the ACI complex, one simply could set the reaction rate _{AC} to zero. Here we refrain from such special choices, but in the results section we will comment on the effect of partially switching off one assembly pathway. For the fully assembled complex ACI we have

while for the force-activated mature complex ACI# we have

We note that apart from the equations (1)-(3) and the last two terms in equations (5)-(7), all terms appear at least twice, once with a positive sign and once with a negative sign. This is the direct consequence of our model mainly describing an assembly process. Thus, the only external fluxes in the system are the translation of new proteins from mRNA and the degradation of monomeric proteins. We also note that all but the translation reactions in the assembly system are reversible, as indicated in Figure

Rac and Rho signaling

As stated in the introduction, the Rac/Rho regulatory network is very complex

_{RAC} and _{RHO} are the parameters that determine how strongly the activation of Rac and Rho from its inactive forms depends on the concentration of the focal complexes and the focal adhesions, respectively. _{RAC}, _{RHO}, _{RAC}, and _{RHO} are parameters that control the characteristics of the Hill function describing the double negative feedback. _{RAC} and _{RHO} are Hill coefficients and

Effect of force

In the clutch model by Macdonald et al.

with

The first two substitutions describe the physical rupture of bonds under force. The exponential dependence on force

The equation (18) for the force implements several important aspects of the system. ^{2} versus 2.0±1 nN/^{2}), possibly due to larger compactification of the focal adhesion

Force has different effects on focal adhesions and our kinetic equations show that they tend to work in different directions: while focal complexes mature to focal adhesions under force due to a variety of molecular and physical effects, including changes in composition, the slip bond behavior tends to disrupt the higher order complexes on all levels. Catch bonds might have evolved in the context of cell adhesion to further counterbalance the disrupting effect of force. We explore this scenario in our model by changing the sign in the exponential functions in equations (14), (15), and (17):

The functional form for the force and its effect on focal complex maturation remain unchanged in the catch bond model. We note that the pure slip and the pure catch bond cases are the two extreme cases which however are good indicators for the possible dynamics of focal adhesion assembly and knockdown. For this reason, we will mostly discuss these cases throughout the paper. Nevertheless we will comment on the effect of mixtures between slip and catch bonds later on in the results section.

Initial conditions, parametrization and implementation

As will be reported in the results section, our model shows bistability between two states which are dominated by focal complexes and focal adhesions, respectively. Because these two states are stabilized by the Rac and Rho signaling parts, respectively, in the following we work with two sets of initial conditions (ICs) reflecting these two states. The **Rac-IC** has 1.0 for [ACI] and [RAC] while the **Rho-IC** has 1.0 for [ACI#] and [RHO]. If we include the RNA-part, [MA], [MC], and [MI] are initially set to 0.5. The initial concentrations of all other species will be set to zero.

For a complex kinetic model as presented here, it is difficult to completely explore parameter space and therefore the informed use of parameter values is crucial for model predictions. Macdonald et al. determined some of the parameter sets used in
_{
t
o
t
a
l
}]= [ AC]/([ C]+[ AC]+[ CI]+[ ACI]+[ ACI

where _{1} is the value of a parameter from parameter set 1, and _{2} is the value of the same parameter from set 2.

All mRNA degradation rate constants were set to the same value for simplicity. Production and degradation rates were chosen as to achieve a typical concentration of 1. Protein translation rates were determined in a similar manner. Motivated by experimental observations, for the maximum degradation rate

The parameter _{siRNA} is chosen such that the steady state is reached approximately two days after beginning of siRNA-treatment.

The parameters for the Rho and Rac activation processes are chosen to be 1 for _{RAC}, _{RHO}, _{RAC}, and _{RHO}, a choice that has been made before for Rac/Rho systems
_{RAC} = _{RHO} = 4 in order to achieve a sharp transition. In order to keep our model simple and reflecting the lack of information on the exact processes that lead to the activation of Rac and Rho at focal complexes and focal adhesions, we also set the remaining coupling parameters _{RAC} and _{RAC} to 1.

We used Mathematica (Wolfram Research Inc., Champaign, Il, USA,

Results and discussion

Model without RNA-part

We first investigated our model without the RNA-part. By disregarding the external fluxes due to translation and degradation, we focus on the assembly part of our model. Then the three species A, C, and I have constant overall concentrations. In principle, the no-flux assumption reduces the number of independent variables and allows us to rewrite the system of equations. In order to allow comparison with the full model, however, here we keep the original definitions. We first investigated the slip bond model as shown in the two upper panels of Figure

Dynamics of the model without RNA-part

**Dynamics of the model without RNA-part.** Model without RNA-part. (Upper left panel) Slip bond model with Rac-IC. Note the very short time scale of below one minute for focal complex assembly, the high level of focal complexes and the very low (close to zero) level of focal adhesions. (Upper right panel) Effect of Rho-IC. Now the time scale is about 30 minutes. The result is a high steady state level of focal adhesions and a much lower level of focal complexes. (Lower left panel) Dynamics of the catch bond model with Rac-IC. The result is similar to the slip bond case due to the low level of force. (Lower right panel) Dynamics of the catch bond model with Rho-IC. The time scale remains the same as in the slip bond model, however, the steady state level of focal adhesions is noticeably higher as the focal adhesions are more stable in the catch bond case. Parameter set PS1 was used for these plots.

In the upper right panel of Figure

We next investigated our model for the case of catch bond behavior as shown in the two lower panels of Figure

We further investigated the robustness of our results in regard to variations of the initial conditions and found that the stability region for the Rac-state is relatively small. In Figure

Dependence on initial conditions

**Dependence on initial conditions.** Dynamics of the slip bond and catch bond model without the RNA-part and with initial conditions ACI=0.9, ACI#=0.1, RAC=1, RHO=0. Although there is only a small deviation from the Rac-IC, both models run into a steady state with a high amount of focal adhesions. Again the catch bond model leads to a higher amount of ACI# than the slip bond model. This sensitivity with respect to the initial conditions is very dependent on the parameter set. Both the sub-minute and the sub-hour timescales are visible in both plots. Parameter set PS1 was used for these plots.

In order to further elucidate the bistable behavior of our system, we performed a bifurcation analysis. In Figure
_{RHO}, which describes the influence of the Rho-concentration on the force. For small _{RHO}, the system is bistable, leading to a high amount of ACI# for Rho-IC and a very small amount of ACI# for Rac-IC. Bistability is found for 0.15 < _{RHO} < 3.3. For _{RHO} > 3.3 the system is no longer bistable and both initial conditions lead to the same high amount of focal adhesions. The number of focal adhesions increases with an increasing value of _{RHO} as subsequently the force and thus, ACI# increases. For large _{RHO} the difference between the slip bond and the catch bond model becomes clear. In the slip bond model the system adapts a steady state characterized by a low amount of focal adhesions, as the high force levels disrupt the focal adhesions. Focal adhesions in the catch bond model however remain at a high amount as the increasing force decreases their disassembly rate. Thus, we conclude that our model is bistable between Rac- and Rho-states, and that catch bonds further stabilize the Rho-state.

Bifurcation analysis

**Bifurcation analysis.** One-parameter bifurcation diagram showing the bistable region resulting from the two initial conditions (Rac-IC and Rho-IC) for the amount of focal adhesions (ACI#) in dependence of _{RHO} that describes the influence of the Rho concentration on the force. Parameter set PS1 was used for these plots.

Full model with RNA and assembly parts

We now turn to the main focus of this paper, the effect of RNAi on focal adhesions. To this purpose, we now include the effect of RNA-synthesis, degradation and interference, that is we turn on the external fluxes. As motivated above, we focus on a knockdown of the connector molecules. We first note that due to the parameter choice of the translation and degradation reaction constants the steady states for the full model differ from the ones for the model without the RNA-part, thus, their exact values cannot be compared directly to the results from the preceding section. For the following analysis, we choose parameter values which allow us to explore all relevant regimes. In the upper left panel of Figure

Effect of RNAi

**Effect of RNAi.** Simulation of knockdown. (Upper left panel) Dynamics of the slip bond model with Rac-IC. The timescale of the siRNA mediated knockdown is about two days. Both the amount of focal complexes and focal adhesions is reduced by about 75-80%. (Upper right panel) Dynamics of the slip bond model with Rho-IC. The knockdown leads to a reduction of about 70% of the amount of focal adhesions. (Lower left panel) Dynamics of the catch bond model with Rac-IC. The result is comparable to the slip bond case. (Lower right panel) Dynamics of the coupled catch bond model with Rho-IC. Here the knockdown leads only to a reduction of about 40% of the amount of focal adhesions, which is considerably less than the 70% reduction in the slip bond case. Parameter set PS3 was used for these plots.

The same system with Rho-IC is shown in the upper right panel of Figure

In the lower left panel of Figure

In Figure

Knockdown results summary

**Knockdown results summary.** Summary of steady state results for connector knockdown. The amount of ACI and ACI# is shown for wild type conditions and after the knockdown of the connector complex for both the slip bond (blue bars) and the catch bond model (red bars) with the two different initial conditions. In the upper panels, values below 0.001 are displayed as 0.001 and in the lower panels, values below 0.01 are displayed as 0.01. Focal adhesions are most stable under knockdown due to their stabilization through Rho-signaling. Stabilization is further increased by catch bond behavior. Parameter set PS3 was used for these plots.

Application to specific knockdowns

Our model not only predicts situations in which the amount of adhesions goes down. One interesting example for the opposite effect is the knockdown of Rho or Rho signaling related components. We included this by reducing the total amount of Rho from 1 to 0.2 in a time-dependent manner representing the knockdown time scale. The results are shown in Figure

Knockdown of Rho and of an additional regulating species

**Knockdown of Rho and of an additional regulating species.****(A)** Effect of Rho knockdown. While the steady state amount of focal adhesions decreases, the amount of focal complexes increases due to the increased amount of Rac. The slip bond model with parameter set PS2 and Rho-IC was used for this plot. **(B)** Effect of a knockdown of an additional species Z acting on the degradation of C (see inset). Degradation of Z leads to an increased amount of C and a subsequent increase in the concentrations of both focal complexes and focal adhesions. The slip bond model with parameter set PS3 and Rho-IC was used for this plot.

Another knockdown of interest requires a slight modification of the model which underlines the modular structure of our general model. We assume that the degradation of C is under the control of an additional species Z that itself is now knocked down. A scheme representing these changes can be found as an inset in Figure

Another target of the additional regulator Z could be a member of the kindlin family of proteins. Kindlin is known as an integrin binding and activating protein

More specific model assumptions

We next discuss the effect of making more specific assumptions on the assembly pathways. As mentioned in the methods section, assuming that CI needs to be assembled first to recruit actin polymerization promoting factors (e.g. formins and the Arp2/3 complex recruited to sites of adhesions) that allow actin to bind amounts to removing the reaction A+C from the system by setting the corresponding reaction rate to zero. The effect of this is shown in Figure

Effect of a specific assembly pathway and of a mixture of slip and catch bonds

**Effect of a specific assembly pathway and of a mixture of slip and catch bonds.****(A)** Effect of switching off the reaction of A and C to AC. The steady state values differ from before, however, the general picture remains the same, indicating that our model is capable of dealing with different pathway structures. The catch bond model with parameter set PS1 and Rho-IC was used for this plot. **(B)** Effect of a mixture of slip and catch bonds. The steady state amount of focal adhesion decreases almost linear with the fraction of slip bonds in the system. Results are shown for the full model before and after the knockdown. Parameter set PS3 and Rho-IC were used for this plot.

Another possible extension of the model is the consideration of mixtures of catch and slip bond behaviour. In Figure

in all appropriate differential equations, whereby

Sensitivity analysis

In order to predict the effect of a knockdown in more detail, we next performed a sensitivity analysis based on ideas from metabolic control analysis
_{
k
} of the

Here the rate _{
k
} is defined as the difference in the forward and backward reaction rates and _{
k
} can be any parameter that influences _{
k
}. It is important for computations to choose the parameters in such a way that they have an influence only on one reaction, which means that _{
k
}/_{
k
}≠0 and _{
k
}/_{
l
}=0 for

with

The results of the sensitivity analysis are shown in Figure

Sensitivity Analysis

**Sensitivity Analysis.** Concentration control coefficients from sensitivity analysis. (Left panel) Concentration control coefficients (CCCs) for ACI# with respect to the degradation rates of the mRNA for the slip bond model for 300 different parameter sets. Both, for the Rac-IC as well as for the Rho-IC a knockdown of integrin would be most effective for the majority of the parameter sets. Nevertheless, there are parameter sets for which a knockdown of actin would yield the best results. The effectivity of the knockdown of the connector species remains constant for Rac-IC. For most parameter sets the focal adhesions are more stable for Rho-IC. (Right panel) Results for the catch bond model. For Rac-IC the result is comparable to the slip bond model. For Rho-IC, the absolute values of the CCCs are much smaller, indicating that the focal adhesions are much more stable if we assume catch bond behavior.

In the left panel of Figure

The right panel of Figure

Conclusions

In this paper we have presented a kinetic model to describe the effect of RNAi on focal adhesions. To this end we have combined model elements for siRNA mediated knockdown, focal adhesion assembly, force generation and regulation. We have successfully parametrized our model as to reproduce the three basic time scales relevant in this context, namely a sub-minute time scale for focal complex assembly, a sub-hour time scale for the adaptation of the focal adhesions to the changed environmental conditions, and a much longer time scale that is given by the time it takes the RNAi to be at its maximum level (roughly 48 hours).

Mechanical force plays different roles at focal adhesions. On the one hand, it physically disrupts focal adhesions, while on the other hand, it leads to a reinforcement effect. The second effect strongly depends on Rho-signaling. During recent years, it has been shown that stabilization of focal adhesions is also achieved by the peculiar property of some molecular bonds to become more stable under force (catch bonds). To explore the consequences of this feature, throughout the paper we have explored both a traditional slip bond model and a catch bond model. Our results strongly depend on these models, thus proving the importance of choosing the correct dissociation model under force.

Our first important result is that the system is bistable, with the two possible states differing in being either low or high in the amount of focal adhesions. Because these states are stabilized by the two positive feedback loops from the Rac- and Rho-pathways, we have called them Rac- and Rho-states. The typical initial conditions leading to these states are called Rac- and Rho-ICs. In general, the Rac-state is less stable and also more susceptible to RNA-interference. In contrast, the Rho-state is quite stable and also more robust in regard to RNA-interference, especially in the catch bond model. This main feature of our model is in line with the general view of the Rac-Rho-system leading to different and mutually exclusive cellular phenotypes

A sensitivity analysis was used to systematically investigate the effect of RNAi over a large range of parameter sets. Independent of using Rac-IC versus Rho-IC or slip versus catch bond models, we found that a knockdown of integrins would be most efficient. However, because integrins are essential for proper cell function, it is more realistic to knock down the connector component, which we found to yield the second strongest effects on focal adhesions. We found that for Rho-IC in general the absolute concentration control coefficients were considerably smaller than for Rac-IC, especially in the catch bond case, in agreement with our earlier conclusion that the Rho-state is more stable than the Rac-state.

Our model now allows us to predict the effect of RNAi on focal adhesions, thus being a potentially very useful tool to guide corresponding experiments. For a given cellular system of interest, one first has to identify a parameter set for our model which best corresponds to the experimental system. Using explicit integration or the sensitivity analysis, one then could predict the most efficient strategy to knockdown specific features of the system, for example focal complexes or focal adhesions. Using the examples of Rho and calpain with its effects on talin and kindlin, we have shown how our model can be adjusted to more specific situations of interest.

One important aspect emerging from our model is the role of initial conditions. Bistability leads to the effect that the choice of initial conditions becomes important. Throughout this work we have therefore distinguished between Rac- and Rho-ICs. A practical consequence of this finding is that in experiments one has to differ between setups in which knockdown has been performed after or before the last plating step. Because spreading (like migration) corresponds to the Rac-state, while mature adhesion corresponds to the Rho-state, a knockdown during mature adhesion might have much less effect than a knockdown before replating after trypsination. In the future our model can be used to pursue this aspect further and to investigate whether there is a difference in the results between the two fundamentally different ways to implement a knockdown.

There are several limitations to our model which might be addressed in future work. In order to establish the appropriate conceptual basis for our system of interest, we have focused on three generic protein components, thus neglecting further known details of the complex composition of focal adhesions. In the future, the model could be complemented by more detailed models for the hierarchical structure of adhesion contacts, for example the interplay between integrins, talin, vinculin and the actin cytoskeleton. For actin, a more detailed modelling might introduce different species to account for its different functional contexts (monomeric in the cytoplasm, dendritic in the lamellipodium and bundled in the lamella). Then the model might also be extended by a more explicit model for actin polymerization, including species representing formins or Arp2/3.

Another major limitation is the restriction to a kinetic approach, assuming a well-mixed system. Although our model represents the layered nature of adhesions and the segregation into focal complexes and focal adhesions, it does not represent their complex spatial coordination. Our approach does not account for the number, spatial distribution, size or shape of the adhesion sites, but only makes statements on the average phenotype expected for different conditions, including knockdowns. Future work is required to include the spatial dimension, either by using partial differential equations or particle-based simulations. In the future, our approach might be combined with detailed spatial models for the localization, size, and shape of adhesion sites

To conclude, our work introduces a flexible modeling framework for cell-matrix adhesions which represents many of their biochemical and physical features as they are currently known. It is especially suited to study the effect of RNA-interference and makes specific predictions about its effectiveness. Thus, it is an ideal starting point to guide and analyze corresponding experiments.

Appendix

The basic parameter sets (PS) used in the model are listed in Table

**Focal adhesion parameters**

**Parameter**

**PS1**

**PS2**

**PS3**

**Source**

_{A}

10000

1000

10

_{A}

1

100

1

_{I}

100

1000

100

_{I}

100

100

100

_{AC}

0.1

0.01

100

_{AC}

10

10

10

_{CI}

10

10000

0.01

_{CI}

100

10

100

_{ACI}

10

10

10

this paper

0.001

0.001

0.001

this paper

0.001

0.001

0.001

this paper

1.0

1.0

1.0

this paper

**RNAi parameters**

**Parameter**

**PS1**

**PS2**

**PS3**

**Source**

_{MA}

17.3

17.3

17.3

this paper

_{MC}

17.3

17.3

17.3

this paper

_{MI}

17.3

17.3

17.3

this paper

_{MA}

17.3

17.3

17.3

this paper

_{MC}

17.3

17.3

17.3

this paper

_{MI}

17.3

17.3

17.3

this paper

_{T,A}

2.07681

0.735221

1.03706

this paper

_{T,C}

2.07437

0.0206286

1.03476

this paper

_{T,I}

2.59193

0.652918

2.08517

this paper

_{A}

10

10

10

this paper

_{C}

10

10

10

this paper

_{I}

10

10

10

this paper

60.0

60.0

60.0

this paper

[ siRNA]_{MAX}

1.0

1.0

1.0

this paper

_{siRNA}

10^{−4}

10^{−4}

10^{−4}

this paper

0.1

0.1

0.1

this paper

4.5

4.5

4.5

**Rac & Rho parameters**

**Parameter**

**PS1**

**PS2**

**PS3**

**Source**

_{RAC}

1.0

1.0

1.0

this paper

_{RHO}

1.0

1.0

1.0

this paper

_{RAC}

1.0

1.0

1.0

_{RHO}

1.0

1.0

1.0

_{RAC}

1.0

1.0

1.0

_{RHO}

1.0

1.0

1.0

_{RAC}

4

4

4

this paper

_{RHO}

4

4

4

this paper

1.0

1.0

1.0

this paper

_{RAC}

1.0

1.0

1.0

this paper

_{RHO}

1.0

1.0

1.0

this paper

Abbreviations

FX: Focal complex; FA: Focal adhesion; RNAi: RNA interference; A: Actin; C: Connector complex; I: Integrin; AC: Actin-connector complex; CI: Connector-integrin complex; ACI: Full complex; ACI#: Mature full complex; Rac-IC: Rac initial conditions (ACI(0)=Rac(0)=1, ACI#(0)=Rho(0)=0); Rho-IC: Rho initial conditions (ACI(0)=Rac(0)=0, ACI#(0)=Rho(0)=1); Z: Additional regulatory species

Competing interests

The authors declare that they have no competing interests.

Authors’ contributions

MH and USS developed the model and MH conducted the numerical analysis. MH and USS wrote the manuscript. Both authors have read and approved the final manuscript.

Acknowledgements

This work was supported by the BMBF-program MechanoSys (grant number 0315501C). USS is a member of the Heidelberg cluster of excellence CellNetworks. We thank Holger Erfle and Vytaute Starkuviene for a critical reading of an early version of the manuscript and Benny Geiger for helpful discussions.