Dynamic variations of cell populations given distinct impacts of Aβ on M1 macrophages (the value of α₁₃).

<p>Variations in the (a) M₁, (b) N_d and (c) Aβ populations over 20 years for three values of α₁₃  =  1× (black), 10× (red), and 50× (blue) the value reported in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0015176#pone-0015176-t001" target="_blank">Table 1</a> for the path Aβ → M₁. As α₁₃ increases, M₁ and N_d also increase and, consequently, there is an associated decrease in neuronal survival. This is also illustrated through Eqs. (1) and (2) of the mathematical model.</p

Dynamic simulation of various cell populations during the progression of Alzheimer's disease.

<p>The (a) N_s (black), M₁ (red) and Aβ (blue), and (b) N_d (black) and A_p (blue) populations over 20 years for the rates reported in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0015176#pone-0015176-t001" target="_blank">Table 1</a>. The removal rate α_r stabilizes the net number of Aβ molecules after three years so that there is only a gradual increase in N_d and corresponding decline in N_s thereafter. The microglia populations are also consequently relatively stable.</p

Schematic of the AD mechanism that incorporates feedback influences from surviving and dead neurons, N_s and N_d, quiescent and proliferating astroglia A_q and A_p, reactive and normal microglia, M₁ and M₂, and Aβ.

<p>The rates associated with the pathways are included in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0015176#pone-0015176-t001" target="_blank">Table 1</a>.</p

Sensitivities of the cell types to the initial conditions.

<p>Initial values X(0) of the initial cell populations and the number of molecules of Aβ in an arbitrary local volume and orders of magnitude for the sensitivity coefficients S(N_{j, j = s,d})  =  dN_j/d(X(0)) determined after 20 years for tenfold perturbations, i.e., 10× and 10⁻¹×, in these initial values.</p

Mathematical parameters describing the functional interactions among various cell types.

<p>The rates α_i associated with the pathways of the AD mechanism, and the sensitivities of the N_s and N_d populations to variations in the values of α_i. The values for the sensitivity coefficients S(N_{j, j = s, d})  =  dN_j/dα_i are determined after 20 years for ±2.5% perturbations in each α_i value. A cell population is more sensitive to a change in a rate that produces a larger value of |S(N_j)|. Positive S(N_j) imply that a rate contributes to an increase in N_j while a negative value entails a corresponding population decrease.</p

Dynamic variations of cell populations given distinct Aβ removal rate.

<p>Variations in the (a) M₁, (b) A_p, (c) Aβ, and (d) N_d populations over 20 years for three values of α_r  =  1× (black), 10⁻¹× (red), and 10⁻²× (blue) the value reported in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0015176#pone-0015176-t001" target="_blank">Table 1</a> for the Aβ removal rate. As α_r decreases, there is an increase in neuropathogenesis so that all four populations increase.</p

Computational simulation captures the dynamic features of the experimental data.

<p>(A) The network motif responsible for the transient induction of <i>Tnfα</i> and the persistent induction of <i>Lcn2</i>. (B) Computational simulation of the transient induction of <i>Tnfα</i> and persistent induction of <i>Lcn2</i>. Circles denote actual experimental data. Lines represent computational simulations.</p

LPS induces transient recruitment of c-Jun to the promoters of <i>Tnfα</i> and <i>C/ebpδ</i>, and induces prolonged recruitment of C/EBPδ to the promoter of <i>C/ebpδ</i>.

<p>WT kidney fibroblasts were treated with or without LPS for a time course. Nuclear lysates were then subjected to ChIP analysis to examine relative binding to the promoter of <i>C/ebpδ</i> (A) or <i>Tnfα</i> (B).</p

<i>Socs1</i> and <i>Atf3</i>, negative regulators of TLR4 signaling, are not induced and IRAK-1 remains intact upon LPS stimulation in kidney fibroblasts.

<p>(A) The expressions of <i>Socs1</i> and <i>Atf3</i> were not induced after stimulation with LPS. Wild-type kidney fibroblasts were either untreated or treated with 100 ng/mL LPS for 4, 6, or 10 hours. <i>Socs1</i>, <i>Atf3</i>, and <i>Il-6</i> transcripts were measured by real time RT-PCR assays and standardized against <i>Gapdh</i> levels. Each experiment was performed in triplicate. Data is depicted as means +/− standard deviation. (B) LPS does not cause the degradation of IRAK-1. Wild-type kidney fibroblasts were either untreated or treated with 100 ng/mL LPS for either 2 or 4 hours. Whole cell lysates were harvested and analyzed by Western blot with IRAK-1 specific antibodies.</p

LPS stimulation induces a persistent induction of LCN2 in kidney fibroblasts.

<p>(A) LPS (100 ng/ml) induces a transient induction of <i>Tnfα</i> mRNA. (B) LPS (100 ng/ml) induces a persistent induction of <i>Lcn2</i> mRNA Transcript levels were measured by qRT-PCR as described above. The results are expressed as means +/− standard deviation performed in triplicate. (C) LCN2 protein levels persist after 24 hours of LPS stimulation. The levels of LCN2 were visualized by western blot.</p