Figure 1.
Representation of the molecular events simulated in the mathematical model.
Molecules included in the model as variables are the following: HIV, REC (CD4 and CXCR4 or CCR5 receptors for HIV-1 infection on lymphocyte cell-surface), FILAMIN, MOESIN (phosphorylated and active; dephosphorylated and non-active), COFILIN (a, active; i, inactive), and ACTIN. Molecules recruited at the HIV-1-triggered capping regions are indicated by the c subscript, while non-capped molecules outside this region are indicated by the nc subscript. As it is assumed that gelsolin remains constant during the whole process, it is not incorporated as a variable in the model. Numbered arrows (from 1 to 13) are the processes included in the model, and dashed arrows are the interactions from the molecules to the processes (black are positive, red are negative). Gelsolin acts by remodeling the amount and size of actin filaments, so the total amount of actin and its reorganization is reduced by higher expression of gelsolin (negative influence of GELSOLIN on processes 4 and 10, see Material and Methods for details); furthermore, appropriate levels of gelsolin facilitate, through the orchestrated severing and remodeling of actin filaments, the capping of actin filaments at viral entry regions (positive effect of GELSOLIN on process 6). Continuous arrows serve as an additional explanation of molecular events taking place during the invasion. Thus, red arrows represent depolymerization of actin filaments, blue arrows represent components which assist the depolymerization of actin filaments (e.g., active cofilin and inactivation of moesin in fusion pore formation), the green arrow indicates actin monomer incorporation to the growing actin filaments, and the purple arrow represents the actin severing and remodeling by gelsolin, thereby controlling the size of actin filaments and the amount of filaments reorganized to the viral entry regions on the plasma membrane of target cells.
Figure 2.
Rate constant values of the model processes.
Rate constants from 1 to 13 correspond to the processes named from 1 to 13 in Figure 1. Mean values for the 12 selected solutions (see Material and Methods) are represented by the bars; standard deviation measures are included.
Figure 3.
Model fitting and parameter estimation.
These panels represent the 12 solutions - one for each of the predicted dynamics - which best predict the experimental ratio between total actin and total moesin as measured by Barrero-Villar et al. 2009 [10] (black solid circles). RECratio: receptor ratio inside the cap; FILAMIN ratio: filamin-A ratio inside the cap; MOESIN ratio+ACTIN ratio: ratio of moesin within the cap over the total amount of actin and moesin, plus ratio of actin within the cap over the total amount of actin and moesin; ACTIN ratio: proportion of actin in the cap; MOESIN ratio: proportion of moesin in the cap; COFILINi: inactive cofilin ratio with respect to the total amount of cofilin; COFILINa: proportion of active cofilin over the total amount of cofilin; HIV: virus units per lymphocyte. The HIV variable correlates with the intensity of the signal inside the lymphocyte triggered by the virus.
Figure 4.
Model verification of the moesin role on the HIV-1 viral entry process.
Panel A shows the total amount of functional moesin on the peak of activated moesin (at 90 minutes after infection) as determined by Barrero-Villar et al. 2009 [10]. Panel B shows the result of the MOESINratio value obtained from the model by modifying the parameter rate K6 (related with the total amount of moesin). The red color refers to N-Moe (a dominant negative N-terminal fragment of the protein which impedes the physiological function of the intact moesin); the black refers to the control conditions and the green to the FL-Moe (an intact form of the protein which increases the total amount of moesin inside the lymphocyte).
Figure 5.
Comparison of the model predictions for two alternative roles of gelsolin in the cap formation.
Red bars represent the experimental measurements of actin capping in a control situation or after over-expressing gelsolin. Blue bars represent the model prediction with the standard deviation of all solutions selected (see Material and Methods). A. A set of scenarios is evaluated in the model assuming different actin capping influences of gelsolin. In “a” K7 was increased by 50%, assuming that gelsolin has a negative effect on actin capping. In “b”, K6 was increased to mimic a gelsolin activation on the actin capping by increasing the actin remodeling dynamics. B. Model verification of scenario “b” shown in panel A. The measured and the predicted maximum peak of the capping of receptors on the gelsolin over-expressed cell lines are shown. C. In “a” K6, the parameter that models gelsolin stimulation of actin capping, takes the value of 0.75 times the value in Control; in “b” this figure is 0.5 times.
Figure 6.
Model evaluation of the role of filamin on virus infectivity.
Red curves and bars refer to the control situation, while the blue ones represent the predicted response after a decrease in the total amount of filamin-A. A. Virus-induced actin aggregation time course. B. Virus infectivity in control and filamin down-regulated conditions according to Jiménez-Baranda et al. 2007 [15].
Figure 7.
Model prediction and experimental verification of the LIMK1 signaling pathway knockdown and the actin polymerization inhibitor Lat-A on the virus infectivity.
A. Black line displays the original solution showed in Figure 1 while the red line represents the model prediction of the COFILINa variable after inhibition of the LIMK signaling pathway by a 50%. B. Black line displays the original solution showed in Figure 1; red line represents the model prediction of the ACTIN variable after inhibition of the LIMK signaling pathway by a 50%. C. The black lines (control condition where cofilin is active before infection) show the model's predicted dynamics of the actin capping. Pink lines show the solutions obtained when the initial state of cofilin, just before infection, was inactive. Dark blue lines represent the predicted dynamics of the actin capping after the activation of virus signaling on the cofilin. Light blue lines represent an increase of the intensity of the activation signaling of cofilin by the virus D. Experimental measurements of infectivity of the virus in increased initial concentrations of the actin-severing factor Lat-A (Yoder et al. 2008, [7]). E. Black line displays the original solution showed in Figure 1 while the red line represents the model prediction of the COFILINa variable after inhibition of the WAVE2 signaling pathway by a 50%. F. Black line displays the original solution showed in Figure 1; red line represents the model prediction of the ACTIN variable after inhibition of the WAVE2 signaling pathway by a 50%.
Figure 8.
Model verification of the cofilin activity decay.
Red dots and line represent the dynamics of the active cofilin during the invasion of HIV-1 as determined by Yoder et al. 2008 [7]. These observations are compared with the predicted dynamics (blue line) of the same model variable (Cofa).