B Cell Differentiation Model for Identifying Predictors of Responses to Rituximab‐Mediated B Cell Depletion in Rheumatic Diseases

ABSTRACT

Rituximab (RTX), an anti‐CD20 monoclonal antibody, has been used to treat autoimmune diseases such as rheumatoid arthritis (RA). However, variability in therapeutic response to RTX remains a challenge. Here, a systems model is developed to mimic B cell differentiation leading to antibody‐secreting cells (ASCs), including plasmablasts (PBs) and plasma cells (PCs). The model features the localization of B cell subsets in the bone marrow and secondary lymphoid organs and incorporates the internalization process of the CD20–RTX complex. To reproduce clinical data from patients with RA receiving RTX and glucocorticoids, pharmacokinetic models for the drugs were built and respective pharmacodynamic profiles of CD19⁺ and CD20⁺ cells and PBs were well captured by optimizing model parameters, which were estimated with good precision. As ASCs are the primary source of pathogenic autoantibodies in RA, the extent and duration of ASC depletion were hypothesized as drivers of therapeutic response to RTX. Global sensitivity analyses identified the CD20–RTX binding affinity and elimination rate constant (i.e., Fcγ‐mediated degradation, internalization) as major determinants of both CD19⁺ cells and ASCs. The influence of baseline PBs and PCs on ASCs was also suggested, providing potential mechanisms underlying responder and non‐responder variability. The model accurately reproduced the temporal changes in CD19⁺ cells after combination treatment with RTX and glucocorticoids suggesting successful model validation. This study provides a mechanistic framework and insights into key drivers of responses to CD20‐depletion treatment using B cell dynamics as an indirect biomarker of clinical endpoints, which might ultimately improve therapeutic outcomes.

Study Highlights.

• What is the current knowledge on the topic?

  • ○
    Rituximab, an anti‐CD20 monoclonal antibody, has advanced the treatment of autoimmune diseases such as rheumatoid arthritis by depleting B cells. However, variability in patient response and early relapse remain therapeutic challenges.
• What question did this study address?

  • ○
    This study developed a systems model that represents B cell differentiation and each B cell subset localization in the bone marrow and lymph organs to identify key drivers of therapeutic response to rituximab using cellular dynamics as a biomarker of clinical efficacy.
• What does this study add to our knowledge?

  • ○
    The model captured the pharmacokinetics of rituximab and glucocorticoids and temporal changes in B cells following each drug alone and in combination. Rituximab‐mediated CD20 binding, Fcγ‐mediated degradation and internalization, and baseline B cell subsets were identified as predictors of B cell behavior, providing potential mechanistic insights into responder and non‐responder variability.
• How might this change drug discovery, development, and/or therapeutics?

  • ○
    The model provides a framework for studying potential drivers of variability in rituximab responses, which may ultimately improve therapeutic outcomes by guiding dosing strategies considering patient‐specific biomarkers.

1. Introduction

The pathophysiology of autoimmune diseases such as rheumatoid arthritis (RA) and systemic lupus erythematosus (SLE) is influenced by cytokines and autoantibodies [1]. In RA, inflammation induced by cytokines and tissue damage caused by autoantibodies occur in the synovium, cartilage, and joints, which are the primary affected areas [1]. Autoantibodies play a major role in other autoimmune diseases such as SLE, Sjögren's syndrome (SjS), systemic sclerosis (SSc), IgG4‐related disease (IgG4‐RD), and neuromyelitis optica spectrum disorder (NMOSD) [1, 2]. These autoantibodies are produced by plasmablasts (PBs) and plasma cells (PCs), which are the final products of B cell differentiation in the bone marrow (BM) [3, 4].

B cells have been targeted for the treatment of autoimmune diseases as the source of antibody‐secreting cells (ASCs). Rituximab (RTX) is anti‐CD20 monoclonal antibody and has significantly advanced the treatment of such disorders [2, 3], as supported by evidence of the association between achieving complete peripheral B cell depletion and clinical responses (e.g., DAS28 and autoantibody titers) [5, 6]. One major challenge is that most patients relapse early, with high numbers of CD27⁺ cells (including ASCs) likely associated with less clinical response even after CD20⁺ cell depletion therapy with RTX [6, 7]. Several mechanisms have been hypothesized to explain the variability in responses to RTX treatment: pre‐treatment levels of specific B cell subsets [8], internalization of CD20 expressed on the cell surface [9], and the efficacy of B cell depletion in the BM [10]. A comprehensive study to assess the role of the low‐affinity Fcγ receptor (FCGR) variants in the largest RA and SLE cohorts showed a major contribution of FCGR3A to RTX responses, with ex vivo data characterizing FcγRIIIa expression and NK‐cell‐mediated cytotoxicity [11]. However, a comprehensive testing of the above hypotheses has not been evaluated.

Quantitative systems pharmacology (QSP) is a mechanism‐based modeling framework that integrates pharmacological mechanisms of action with related human biology. QSP enables the identification of determinants of therapeutic responses within the scope of the system [12]. A small systems model has been developed previously to characterize temporal patterns of cytokines and the inflammatory marker C‐reactive protein (CRP) in rheumatoid arthritis [13]. This model identified predictors of therapeutic responses with CRP as a biomarker; however, it did not include B cell properties. Although models describing the pharmacokinetics of B cells have been reported, most do not consider the differentiation process of B cells in the BM or their localization in tissues such as the BM and secondary lymphoid organs (SLOs) [14, 15, 16]. To address such modeling challenges, we developed a B cell differentiation (BCD) model that emulates the differentiation and localization of B cells to relevant tissues. The differentiation model was based on published data of B cell subsets in both human BM and peripheral blood quantified by flow cytometry [17] and the number and ratio of B cells and plasma cells in various tissues throughout the human body [18]. The aim of this study is to reproduce the temporal patterns of B cells after the administration of RTX alone or in combination with glucocorticoids. Considering ASCs as the source of autoantibodies and their significant association with RA responses [19], the degree and duration of ASC depletion were hypothesized to be primary determinants of clinical response. To predict the variability in ASC responses to RTX, sensitivity analysis was conducted to identify key determinants and potential sources of variability of RTX effects on ASCs.

2. Methods

2.1. Workflow of Parameter Optimization and Model Validation

As shown in Figure 1 (Steps 1 and 2), model PK parameters for RTX and concomitant glucocorticoids were optimized during fitting to extracted clinical data (studies listed in Table 1). In the sub‐model for RTX‐mediated CD20 internalization, parameters regarding the internalization process were set (Step 3). Subsequently, effects of glucocorticoids on CD19⁺ cells were incorporated into the BCD model (Step 4), followed by the CD20⁺ cell depletion effect by RTX alone (Step 5) based on temporal patterns for internal data. Using the final model, a global sensitivity analysis (GSA) for B cell behaviors was evaluated (Step 6). Lastly, the final model was validated with external data (studies listed in Table 1) by comparing the simulated ranges of B cells and corresponding subsets (Step 7).

FIGURE 1.

Workflow of model calibration and validation in this study. Input and external testing data were extracted from the literature (Table 1). ASCs, antibody‐secreting cells; GCs, glucocorticoids; GSA, global sensitivity analysis; MB, memory B cells; MP, methylprednisolone; NB, naïve B cells; PB, plasmablasts; PNL, prednisolone; PNS, prednisone; RTX, rituximab. Trapezoid and rounded rectangles represent input and reference data.

TABLE 1.

Overview of clinical studies and data for glucocorticoids and rituximab in RA patients.

Type	Drug	Measurements	Dose regimen	References
I	Methylprednisolone (MP)	MP	100 mg (i.v.)	[20]
		CD19+ cells	100 mg (i.v.) at day 1, 15 a	[21]
I	Free prednisolone (fPNL)	fPNL	16.4, 49.2 mg/day (i.v.)	[22]
		CD19+ cells	≤ 12.5 mg/day (i.v.) at day 1, 15 a	[23]
I	Prednisone (PNS)	PNS	20.0, 50.0 mg/day (p.o.)	[24]
		CD19+ cells	60 mg/day at day 2, 4–7 and 30 mg/day at day 8–14 (p.o.)	[21]
I	Rituximab (RTX)	RTX	500, 1000 mg at day 1, 15 (i.v.)	[25]
			1000 mg at day 1, 15 (i.v.)	[23]
		CD20+ cells	1000 mg at day 1, 15 (i.v.)	[3]
	RTX and MP	PB	RTX 1000 mg at day 1, 15 with MP 100 mg b	[19]
E	RTX and PNL	CD19+ cells	RTX 1000 mg at day 1, 15 with PNL ≤ 12.5 mg/day	[23]
	RTX and MP		RTX 1000 mg at day 1, 15 with MP 100 mg b	[19]

Abbreviations: E, external data to validate the model; I, internal data for model development. PB, plasmablasts.

^a Placebo group for rituximab dose.

^b Data were used during only the first treatment course, in which administration timing was explicit.

2.2. Pharmacokinetic Models

Simple pharmacokinetic (PK) models for glucocorticoids such as methylprednisolone (MP), prednisone (PNS), and prednisolone (PNL) were constructed to describe the plasma concentration time‐course based on clinical data for each study drug (Step‐1 in Figure 1). PK for RTX was defined by a minimal physiologically based pharmacokinetic (mPBPK) model (Step‐2 in Figure 1) with a minor modification to include distribution to the BM [26]. Ordinary differential equations (ODEs) for RTX PK are defined in Equations ((1), (2), (3), (4), (5)). For the corticosteroids, model diagrams are shown in Figure S1 and the model equations are reported in Supporting Information S1.

$$\begin{array}{c}\begin{array}{c}\frac{{\mathit{dC}}_{s,\mathrm{RTX}}}{\mathit{dt}}=\frac{\text{In}{\left(t\right)}_{\mathrm{RTX}}}{V_s}+L_{\mathrm{tot}}·\frac{C_{\mathrm{ly},\mathrm{RTX}}}{V_s}-\left(1-{\sigma }_{1,\mathrm{RTX}}\right)·L_1·\frac{C_{s,\mathrm{RTX}}}{V_s}\hfill \\ -\left(1-{\sigma }_{2,\mathrm{RTX}}\right)·L_2·\frac{C_{s,\mathrm{RTX}}}{V_s}-\left(\frac{C_{s,\mathrm{RTX}}}{V_s}-\frac{C_{\mathrm{bm},\mathrm{RTX}}}{V_s·K_{p,\mathrm{bm}}}\right)·Q_{\mathrm{bm}}\hfill \\ -{\mathit{CL}}_{\mathrm{RTX}}·\frac{C_{s,\mathrm{RTX}}}{V_s},C_{s,\mathrm{RTX}}^0=0\hfill \end{array}\hfill \end{array}$$ (1)

$$\begin{array}{c}\frac{{\mathit{dC}}_{\mathrm{ti},\mathrm{RTX}}}{\mathit{dt}}=\left(1-{\sigma }_{1,\mathrm{RTX}}\right)·L_1·\frac{C_{s,\mathrm{RTX}}}{V_{\mathrm{ti}}}-\left(1-{\sigma }_L\right)·L_1·\frac{C_{\mathrm{ti},\mathrm{RTX}}}{V_{\mathrm{ti}}};C_{\mathrm{ti},\mathrm{RTX}}^0=0\hfill \end{array}$$ (2)

$$\begin{array}{c}\begin{array}{c}\frac{{\mathit{dC}}_{\mathrm{le},\mathrm{RTX}}}{\mathit{dt}}=\left(1-{\sigma }_{2,\mathrm{RTX}}\right)·L_2·\frac{C_{s,\mathrm{RTX}}}{V_{\mathrm{le}}}-\left(1-{\sigma }_L\right)·L_2·\frac{C_{\mathrm{le},\mathrm{RTX}}}{V_{\mathrm{le}}};C_{\mathrm{le},\mathrm{RTX}}^0=0\end{array}\hfill \end{array}$$ (3)

$$\begin{array}{c}\begin{array}{c}\frac{d{C}_{\mathrm{ly},\mathrm{RTX}}}{\mathit{dt}}=\left(1-{\sigma }_L\right)·\left(L_1·\frac{C_{\mathrm{ti},\mathrm{RTX}}}{V_{\mathrm{ly}}}+L_2·\frac{C_{\mathrm{le},\mathrm{RTX}}}{V_{\mathrm{ly}}}\right)-L_{\mathrm{tot}}·\frac{C_{\mathrm{ly},\mathrm{RTX}}}{V_{\mathrm{ly}}};C_{\mathrm{ly},\mathrm{RTX}}^0=0\end{array}\hfill \end{array}$$ (4)

$$\begin{array}{c}\begin{array}{c}\frac{d{C}_{\mathrm{bm},\mathrm{RTX}}}{\mathit{dt}}=\left(\frac{C_{s,\mathrm{RTX}}}{V_{\mathrm{bm}}}-\frac{C_{\mathrm{bm},\mathrm{RTX}}}{V_{\mathrm{bm}}·K_{p,\mathrm{bm}}}\right)·Q_{\mathrm{bm}};C_{\mathrm{bm},\mathrm{RTX}}^0=0\end{array}\hfill \end{array}$$ (5)

with $C_{s,\mathrm{RTX}}$, $C_{\mathrm{ly},\mathrm{RTX}}$, and $C_{\mathrm{bm},\mathrm{RTX}}$ as the serum, lymph and BM concentrations of RTX in $V_s$ (serum volume), $V_{\mathrm{ly}}$ (total lymph volume), and $V_{\mathrm{bm}}$ (BM volume). $C_{\mathrm{ti},\mathrm{RTX}}$ and $C_{\mathrm{le},\mathrm{RTX}}$ represent interstitial fluid concentrations of RTX in tissues with continuous endothelium ($V_{\mathrm{ti}}$) and fenestrated or discontinuous endothelium ($V_{\mathrm{le}}$). ${\sigma }_{1,\mathrm{RTX}}$ and ${\sigma }_{2,\mathrm{RTX}}$ are vascular reflection coefficients for leaky and tight tissues of RTX, and ${\sigma }_L$ is the lymphatic capillary reflection coefficient. $L_{\mathrm{tot}}$ is the total lymph flow and equals the sum of $L_1$ and $L_2$, which are one‐third and two‐thirds of $L_{\mathrm{tot}}$. ${\mathit{CL}}_{\mathrm{RTX}}$ is the linear clearance of RTX. $Q_{\mathrm{bm}}$ is the blood flow in the BM. $\text{In}{\left(t\right)}_{\mathrm{RTX}}$ is the zero‐order intravenous (i.v.) infusion rate, which is fixed for the duration of the infusion of RTX and then set to zero thereafter. Superscript zero represents initial (baseline) status of each concentration of RTX. Physiological parameters for the PK models are reported in Table S1.

2.3. Sub‐Model for CD20–RTX Binding and Elimination

To characterize CD20 binding with RTX and the elimination of the CD20–RTX complex via FcγR‐mediated degradation and internalization, a sub‐model was developed to determine a second‐order binding rate constant for surface CD20 and RTX ($k_{\mathrm{on},\mathrm{RTX}}$) and a first‐order dissociation rate constant for the CD20–RTX complex ($k_{\mathrm{off},\mathrm{RTX}}$) (Step‐3, Figures 1 and S2). As shown in Figure S2, $K_{\mathrm{ss},\mathrm{CD}20-\mathrm{RTX}}$, the equilibrium dissociation constant for surface CD20 and RTX, is defined as:

$$\begin{array}{c}{K}_{\mathrm{ss},\mathrm{CD}20-\mathrm{RTX}}=\frac{B_{s,t}·C_{t,\mathrm{RTX}}}{{\mathrm{RC}}_{\mathrm{RTX}}}=\frac{k_{\mathrm{off},\mathrm{RTX}}+k_{\mathrm{elm},\mathrm{CD}20-\mathrm{RTX}}}{k_{\mathrm{on},\mathrm{RTX}}}\end{array}$$ (6)

where $B_{s,t}$, ${\mathrm{RC}}_{\mathrm{RTX}}$, and $k_{\mathrm{elm},\mathrm{CD}20-\mathrm{RTX}}$, represent CD20‐expressing B cell subset in the BM, peripheral blood, and SLOs, concentration of CD20–RTX complex, and FcγR‐mediated degradation and internalization rate constant of CD20–RTX. Free concentration of CD20 surface receptor, $R_{f,\mathrm{CD}20}$, can be expressed by the $B_{s,t}$ as:

$$\begin{array}{c}{R}_{f,\mathrm{CD}20}=\frac{{\mathit{RD}}_{20}·B_{\mathrm{CD}20,s,t}}{N_A}\left(s=\mathrm{pre}B,\mathit{IB},\mathit{TB},\mathit{NB},\mathit{MB};t=\mathrm{bm},s,\mathrm{slo}\right)\end{array}$$ (7)

with $N_A$ and ${\mathrm{RD}}_{20}$ as Avogadro's constant and surface receptor density of CD20.

For this sub‐model, in vivo data from human CD20 transgenic and FcγR^−/− (CD20 Tg × FcγR^−/−) mice were used, in which CD20 expression on the cell surface can be measured by preventing the B cell depletion from the antibody owing to the lack of FcγR [27]. An RTX‐like monoclonal antibody (Rit‐m2a), where hIgG1 was exchanged for mIgG2a, was used instead of RTX in this experiment, and Rit‐m2a maintains the binding function of RTX. The time‐course of CD20 expression on the surface was described in Equation (8).

$$\begin{array}{c}\begin{array}{c}\%\mathrm{CD}{20}_{\text{surface}}=100·\left\{1-\frac{I_{\max ,\mathrm{CD}20-\mathrm{RTX}}·C_{s,\mathrm{RTX}}}{K_{\mathrm{ss},\mathrm{CD}20-\mathrm{RTX}}+C_{s,\mathrm{RTX}}}\right\};\\ {\%\mathrm{CD}20}_{\text{surface}}^0=100,C_{s,\mathrm{RTX}}^0=0\hfill \end{array}\hfill \end{array}$$ (8)

with $I_{\max ,\mathrm{CD}20-\mathrm{RTX}}$ as the maximum inhibitory effect of RTX on surface CD20. Defining proportion of the surface CD20‐RTX complex as $f_{\mathrm{CD}20-\mathrm{RTX}}$, %CD20_surface can be rearranged based on Equation (6) as:

$$\begin{array}{c}\begin{array}{c}\%\mathrm{CD}{20}_{\text{surface}}=100·\left\{1-\frac{\left(1-f_{\mathrm{CD}20-\mathrm{RTX}}\right)·{\mathrm{RC}}_{\mathrm{RTX}}}{R_{f,\mathrm{CD}20}+{\mathrm{RC}}_{\mathrm{RTX}}}\right\}\hfill \\ =100·\left\{1-\frac{\left(1-f_{\mathrm{CD}20-\mathrm{RTX}}\right)·C_{s,\mathrm{RTX}}}{K_{\mathrm{ss},\mathrm{CD}20-\mathrm{RTX}}+C_{s,\mathrm{RTX}}}\right\};\hfill \\ f_{\mathrm{CD}20-\mathrm{RTX}}=\frac{k_{\mathrm{off},\mathrm{RTX}}}{k_{\mathrm{off},\mathrm{RTX}}+k_{\mathrm{elm},\mathrm{CD}20-\mathrm{RTX}}}\end{array}\hfill \end{array}$$ (9)

From Equations (8) and (9), $I_{\max ,\mathrm{CD}20-\mathrm{RTX}}$ can be defined as:

$$\begin{array}{c}{I}_{\max ,\mathrm{CD}20-\mathrm{RTX}}=1-f_{\mathrm{CD}20-\mathrm{RTX}}\end{array}$$ (10)

By using optimized parameters of $I_{\max ,\mathrm{CD}20-\mathrm{RTX}}$ and $K_{\mathrm{ss},\mathrm{CD}20-\mathrm{RTX}}$, $k_{\mathrm{on},\mathrm{RTX}}$ and $k_{\mathrm{off},\mathrm{RTX}}$ were derived from Equations (6), (8), and (9):

$$\begin{array}{c}{k}_{\mathrm{on},\mathrm{RTX}}=\frac{k_{\mathrm{off},\mathrm{RTX}}+k_{\mathrm{elm},\mathrm{CD}20-\mathrm{RTX}}}{K_{\mathrm{ss},\mathrm{CD}20-\mathrm{RTX}}}\end{array}$$ (11)

$$\begin{array}{c}{k}_{\mathrm{off},\mathrm{RTX}}=\frac{1-I_{\max ,\mathrm{CD}20-\mathrm{RTX}}}{I_{\max ,\mathrm{CD}20-\mathrm{RTX}}}·k_{\mathrm{elm},\mathrm{CD}20-\mathrm{RTX}}\end{array}$$ (12)

Full ODEs including the sub‐model are provided in Supporting Information S2.

2.4. Model Development of the B Cell Differentiation (BCD) Model

Based on published data for each B cell subset from human BM and peripheral blood samples [18], the B cell differentiation process in the BM was defined as originating from CD19⁺ B progenitor (pro‐B) cells, which differentiate to pre‐B cells, immature B cells, transitional B cells, and naïve B cells. Among these subsets in the BM, transitional and naïve B cells were set to migrate into the systemic periphery. Transit compartment models are commonplace for hematopoietic precursors [28], and the basic ODE for pre‐B cells in the BM is defined as:

$$\begin{array}{c}\frac{{\mathit{dB}}_{\mathrm{pre}B,\mathrm{bm}}}{\mathit{dt}}=c{k}_{\mathit{df}}·\frac{B_{\mathrm{pro}B,\mathrm{bm}}}{K_{\mathrm{bm},B}}·{\beta }_1-\left(c{k}_{\mathit{df}}+k_{\mathrm{ap},B}·E_{\mathrm{RTX},\mathrm{bm}}\right)·\frac{B_{\mathrm{pre}B,\mathrm{bm}}}{K_{\mathrm{bm},B}}\mathrm{;}\\ \\ {\beta }_1=\frac{B_{\mathrm{pre}B,\mathrm{bm}}}{B_{\mathrm{pro}B,\mathrm{bm}}}·\left(1+\frac{k_{\mathrm{ap},B}}{c{k}_{\mathit{df}}}\right)\mathrm{;}\\ \\ c{k}_{\mathrm{df}}=k_{\mathrm{df}}·E_{\mathrm{IL}6,\mathit{df}}\mathrm{;}\\ \\ E_{\mathrm{RTX},\mathrm{bm}}=1+\frac{k_{\text{kill},\mathrm{RTX}}·C_{\mathrm{bm},\mathrm{RTX}}}{{\mathit{KC}}_{50,\mathrm{RTX}}+C_{\mathrm{bm},\mathrm{RTX}}}\end{array}$$ (13)

with a differentiation rate constant ($k_{\mathit{df}}$), an apoptotic rate constant ($k_{\mathrm{ap},B}$), and a B cell partition coefficient in BM ($K_{\mathrm{bm},B}$). $E_{\mathrm{IL}6,\mathit{df}}$ and $E_{\mathrm{RTX},\mathrm{bm}}$ represent the IL‐6 effect on B cell differentiation and the cytotoxic effect of RTX on B cells in BM. $k_{\text{kill},\mathrm{RTX}}$ and ${\mathrm{KC}}_{50,\mathrm{RTX}}$ represent the maximum cytotoxic effect of RTX and the RTX concentration producing 50% of $k_{\text{kill},\mathrm{RTX}}$.

Plasmablasts (short‐lived) are differentiated from naïve B cells in the periphery, whereas memory B cells and plasma cells are differentiated from germinal center B cells in lymphoid organs [5, 29]. To reflect such tissue localization of each B cell, partition coefficients of B cells and PCs in the BM ($K_{\mathrm{bm},B}$, $K_{\mathrm{bm},\mathrm{PC}}$) and SLOs ($K_{\mathrm{slo},B}$, $K_{\mathrm{slo},\mathrm{PC}}$) were set in the model (Table S2). A simplified schematic of the BCD model structure is shown in Figure 2. Full structural representation of the BCD model incorporating the sub‐model for RTX‐mediated CD20 internalization and effects by the study drugs is shown in Figure S2 and the ODEs are provided in Supporting Information S2.

FIGURE 2.

Schematic diagram of the B cell differentiation model. White and gray compartments show B cell counts and normalized signals. Effects of glucocorticoids (black) on CD19⁺ cells and RTX (red) on CD20⁺ cells are represented. Compartments for each B cell location are denoted by subscripts: bone marrow (bm), systemic periphery (s), and secondary lymphoid organs (slo). GCB, germinal center B cells; IB, immature B cells; MB, memory B cells; NB, naïve B cells; PB, plasmablasts; PC, plasma cells; TB, transitional B cells.

2.5. Sobol Global Sensitivity Analyses

As a variance‐based GSA method [30], Sobol GSA was performed for changes in CD19⁺, CD20⁺, and ASCs from respective baselines at 8, 24, and 48 weeks after the initial dose. Following administration of 1000 mg RTX at Days 1 and 15, the variance of CD19⁺ and ASCs from respective baselines was evaluated. By varying within plausible ranges of each system parameter, first‐order and total‐order indices were visualized as the variance by a given single parameter and all interactions with other parameters.

2.6. Model Validation With External Data

Following RTX and glucocorticoid treatment, model‐simulated B cell dynamics were compared with observed values (e.g., CD19⁺ cells, related subsets) extracted from the literature from an external dataset under the same dosing regimen (Table 1). Relevant model parameters were defined with covariate relationships assuming plausible variabilities of each parameter.

2.7. Data and Statistical Analysis

Drug and B cell PK/PD data for RTX and concomitant glucocorticoids (i.e., MP, PNS, PNL) are summarized in Table 1, and their input and reference data were used for model development and validation. The model was developed using MATLAB SimBiology (MathWorks, Natick, MA). All simulations utilized validated ODE solvers such as the SUNDIALs suite and ode15s. The precision of parameter estimates was evaluated using relative standard errors (RSEs, %CV) calculated from the model variance–covariance matrix. Graphical visualization for goodness‐of‐fit plots, sensitivity analyses, and simulations for the model validation was achieved using the gglot2 package (version 3.5.1) in the R programming language.

3. Results

3.1. PK Modeling

Extracted plasma concentration–time profiles after intravenous administration of MP and PNL and oral administration of PNS (Table 1) were used to construct drug‐specific PK models. The PK model for RTX was built based on a simple mPBPK format for a monoclonal antibody including compartments for BM and SLOs (Figure S1). For all study drugs, model fitted plasma concentrations were within 2‐fold of observed values and optimized parameters were estimated with good precision (Figure 3A and Table S3). As an example, the mPBPK model for RTX well captured the serum concentration–time course (Figure 3B), and the fitted PK profiles for the glucocorticoids are shown in Figure S3.

FIGURE 3.

Goodness‐of‐fit plots and fitted time–courses of PK and B cells for the study drugs. (A) Goodness‐of‐fit plots of PK models. (B) Fitted and extracted serum concentration time–course of RTX (500 and 1000 mg, week 0, 2). (C) Goodness‐of‐fit plots for B cells. (D) Fitted time–course of blood CD20⁺ cells to baseline (%) following 1000 mg RTX doses (week 0, 2). Solid and dashed lines represent unity and 2‐fold boundaries (A, C). Graph with logarithmic y scale is included (D). Solid lines represent fitted curves and sources of extracted data (symbols) are provided in Table 1 (B, D). MP, methylprednisolone; PB, plasmablasts; PNL, prednisolone; PNS, prednisone; RTX, rituximab.

3.2. Sub‐Model for CD20–RTX Binding and Elimination

In RA and SLE patients, the CD20–RTX complex following RTX binding undergoes internalization, leading to the removal of CD20 from the cell surface and tolerance of RTX‐mediated CD20⁺ cell depletion effects [9]. A sub‐model was developed (Step‐3, Figure 1) to characterize the CD20–RTX degradation and internalization process using published in vivo data of human CD20 transgenic and FcγR^−/− mice (CD20 Tg × FcγR^−/−), in which CD20 expression on the cell surface can be readily measured [27]. The sub‐model well fitted the temporal patterns of CD20 expression on the cell surface, and its relevant parameters (I _max,CD20 and K _ss,CD20) were estimated with good precision (Table S3 and Figure S4A).

3.3. Modeling Effects of Glucocorticoids and RTX on B Cells

Glucocorticoids have been used in placebo groups in clinical trials for RTX [21, 23]. Following glucocorticoid administration, CD19⁺ cells initially decreased but rapidly increased beyond pre‐treatment levels. The effects of glucocorticoids were incorporated into the BCD model (Step‐4, Figure 1), which well described the rebound of CD19⁺ cells post‐glucocorticoid administration (Figure S4B). Using extracted CD20⁺ cells and PBs following RTX monotherapy, the effect of RTX was incorporated into the BCD model along with the sub‐model of CD20–RTX binding and elimination (Step‐5, Figure 1). Almost all of the model‐fitted values for CD20⁺ cells and PBs as a percent of their respective baselines were within twice the observed data, and the model predicted small levels of cells (i.e., less than 1%) following drug administration (Figure 3C). The model captured the temporal dynamics of CD20⁺ cells and PBs following RTX administration (Figures 3D and S4C). All relevant parameters were well estimated to characterize the effects of the study drugs (Table S3).

3.4. Sensitivity Analysis and Validation of the BCD Model

Sobol GSA for changes in CD19⁺ cells and PBs from respective baselines post‐RTX at weeks 8, 24, and 48 were performed to evaluate sensitivities of the model to system parameters in a comprehensive manner. Model parameters were simultaneously varied within their plausible ranges (Table S4). Throughout the RTX treatment period over 48 weeks, k _{elm,CD20‐RTX}, K _{ss,CD20‐RTX}, and specific baseline B cell subsets (peripheral NBs and MBs) were identified as key parameters for the response of CD19⁺ cells among the relevant model parameters (Figure 4). In contrast to sensitivity of the model for CD19⁺ cells, ASCs primarily responded to baseline levels of PBs and PCs at 8 and 48 weeks, whereas k _{elm,CD20‐RTX} and K _{ss,CD20‐RTX} were most sensitive at 24 weeks, with a minor contribution of k _df, k _ap,B, and baseline IL‐6. For both CD19⁺ cells and ASCs, k _df and k _ap,B were also suggested as sensitive terms as their increasing contributions are shown later in the treatment period (Figure 4).

FIGURE 4.

Global sensitivity analysis for changes in CD19⁺ cells and antibody‐secreting cells (ASCs) by rituximab (RTX). The total/first sensitivity indices for percent changes in CD19⁺ cells and ASCs in peripheral blood from respective baselines 8, 24, and 48 weeks after initial dose of RTX. Sensitivities were calculated by providing a variance within plausible ranges of each parameter (Table S4).

For model validation, simulated changes in B cells after drug administration were compared to two extracted profiles, which were not used in model development and were combinatorial treatments of RTX with various glucocorticoids (Table 1). Model validation was performed using plausible ranges of model parameters (Table S4), which were selected among the obvious contributing parameters as revealed by the GSA evaluations (Figure 4). Model‐simulations well covered the variability of CD19⁺ cell profiles, particularly in the later phase of treatment (Figures 5A and S5). The model also informed temporal patterns of ASCs, which were different from the CD19⁺, with large variability (Figure 5B). These simulations suggest that the extent and duration of the CD20‐depletion effect on ASCs was less than that on CD19⁺ cells.

FIGURE 5.

Model‐based simulations of time–courses of CD19⁺ cells and antibody‐secreting cells (ASCs) by rituximab (RTX) and prednisolone (PNL). Simulated time–courses of peripheral blood CD19⁺ cells (A) and ASCs (B) are shown after combination treatment of 1000 mg RTX and 12.5 mg PNL at week 0 and 2 (arrows). Symbols and bars represent mean and standard deviation (SD) of extracted data [23]. Solid lines and shades represent mean and ranges (red: SD, purple: 5th–95th percentile) of simulated values.

4. Discussion

A BCD model was developed to characterize the process of B cell differentiation leading to ASCs utilizing published clinical data from RA patients treated with RTX and/or glucocorticoids (Figure 2). This study sought to gain quantitative insights into factors driving variability in RTX‐mediated therapeutic responses based on the BCD model. Early B cells are present only in the bone marrow (BM) and appear in peripheral blood after differentiating into TBs and NBs [18]. Following further differentiation, MBs, PBs, and PCs appear in SLOs (e.g., lymph nodes, spleen, and tonsils) and the BM [11, 29, 31, 32]. To reflect such tissue localization of each B cell, the cellular distribution of B cells and PCs was considered in the model [19]. In addition, the model incorporates the influence of interleukin (IL)‐6 on B cells, which plays a pivotal role in RA pathology. IL‐6 is known to be a B cell differentiation factor and has been reported to support PC survival [33, 34, 35]. Tocilizumab, a monoclonal antibody directed against the IL‐6 receptor, reduced the number of IgA/IgG‐secreting cells while maintaining stable PB levels [36]. Other cytokines such as IL‐4 and BAFF could also influence B cell differentiation and survival, and these elements could be incorporated into a future version of the model to enhance this mechanistic framework for identifying key determinants of therapeutic responses.

Relevant parameters of PK and pharmacodynamics for RTX and glucocorticoids were calibrated to reproduce the extracted data [21, 23]. Unlike cancer patients in whom RTX exhibits nonlinear target‐mediated drug disposition (TMDD), patients with RA show linear RTX PK profiles (500–1000 mg) (Figure 3B). Accordingly, RTX was modeled using a linear PK framework in this study. All parameters were estimated with low RSEs (%CV), suggesting practical identifiability based on the available calibration data (Table S3). After glucocorticoid administration, B cell counts initially decreased but then increased beyond baseline levels. Glucocorticoids induce apoptosis of CD19⁺ cells in human bone marrow‐derived B cells [37]. Glucocorticoid‐stimulatory effects on B cell differentiation were incorporated based on in vitro evidence showing stage‐dependent B cell sensitivity: early activation/proliferation was suppressed, whereas later differentiation to immunoglobulin‐secreting states was enhanced [38]. Several potential mechanisms have been suggested for the rebound effect following glucocorticoid withdrawal: (i) enhancement of B cell differentiation alongside T cell repopulation [39]; (ii) glucocorticoid‐induced stimulation via IL‐4‐induced B cell differentiation [40]; and (iii) redistribution of lymphocytes from peripheral blood to BM and SLOs during glucocorticoid exposure followed by subsequent remobilization following systemic clearance [41]. Although the stimulation effect of glucocorticoids on B cell differentiation in the bone marrow was set in this model, this process could be further updated once more details of this phenomenon is elucidated. As illustrated in Figure S4B, the model accurately followed the temporal changes in CD19⁺ cells post‐glucocorticoid administration. Similarly, the model accurately captured the dynamics of CD20⁺ cells and PBs following RTX administration (Figures 3D and S4C). Residual error from the actual values were observed, but this may be attributed to several patient‐specific factors, such as B cell subset counts at baseline that may be unavailable in clinical studies. Previous studies have reported significant inter‐individual variability in post‐RTX dynamics of B cells [23], with various factors such as baseline values of specific B cell subsets, FcγR polymorphisms, and residual B cells in tissues being implicated [8, 10, 42, 43]. For CD20⁺ cells–time course, k _{elm,CD20‐RTX} was estimated with good precision (Table S3), and used to calculate k _on,RTX (0.277 1/nM/h) and k _off,RTX (0.243 1/h) from Equations (11) and (12). Although any experimental data of k _{elm,CD20‐RTX} are not available currently, the values of k _on,RTX and k _off,RTX were comparable with previous experimental data by a real‐time measurement on living cells: k _on,RTX and k _off,RTX determined as 0.032–0.13 (1/nM/h) and 0.011–1.0 (1/h) [44]. Hence, this finding supports our model setting and parameter values.

In this study, the factors affecting the responses of CD19⁺ cells and ASCs to RTX treatment within the BCD model were evaluated simultaneously. GSA demonstrated that drug‐related parameters, k _{elm,CD20‐RTX} and K _{ss,CD20‐RTX}, were key drivers for not only CD19⁺ cells but also ASC responses to RTX (Figure 4). k _{elm,CD20‐RTX} reflects not only the internalization rate constant of the CD20–RTX complex but also the FcγR‐mediated degradation by antibody‐dependent cell‐mediated cytotoxicity (ADCC); a mechanism of action of RTX. RTX‐mediated B cell depletion varies significantly among SLE patients owing to FCGR3A‐158V/F variant [45]. Meta‐analyses have indicated that this variant is a major determinant of not only the extent of RTX‐mediated CD20 depletion but also clinical outcomes like DAS28CRP in patients with RA. This highlights ADCC effects mediated by NK cells, which express FCGR3A, as the primary mechanism of action of RTX [11]. Although the BCD model does not include the dynamics of NK cells, these findings are consistent with the importance of k _{elm,CD20‐RTX} as identified by the GSA (Figure 4). Additionally, the model was sensitive to baseline NBs and MBs in peripheral blood for CD19⁺ cells and PBs and PCs for ASCs (Figure 4), which is consistent with previous reports [10, 46]. The identified parameters offer mechanistic explanations for therapeutic variability: RTX‐responders might possibly exhibit favorable baseline B cell profiles and efficient FcγR‐mediated ADCC, whereas non‐responders might show contrasting B cell status and reduced ADCC efficiency. Interestingly, the differentiation rate parameter k_df was particularly sensitive for the behavior of both CD19⁺ cells and ASCs at the later stage of the treatment period (week 48) (Figure 4). IL‐6 was somewhat sensitive in the later stage (i.e., 24 and 48W) for ASCs (Figure 4), which is generally consistent with a previous report on an IL‐6 (−174 G/C) variant associated with responses to RTX [47]. In addition to IL‐6, other factors such as IL‐4, BAFF, and Pax5 are involved in B cell differentiation and plasma cell survival, likely contributing to the later stage variability captured by the k _df [48]. These non‐modeled biological inputs represent limitations of the current model. The incorporation of such additional regulators into future versions of the model is warranted to better predict inter‐patient variability under sustained B cell depletion.

Model validation was conducted by considering the inter‐individual variability of several major parameters identified through GSA. The extracted external dataset used for model validation (Table 1) lacked individual patient data and detailed background information necessitating assumptions about potential inter‐individual variability of model parameters (Table S4). Model simulations for validation purposes were used to assess the combined effects of RTX and glucocorticoids and demonstrated that the model accurately captured the variability and trends in CD19⁺ cells and their subsets despite different trial conditions and dosing regimens (Figures 5 and S5). This was achieved without the use of a traditional empirical drug–drug interaction parameter [49] after individual drug effects were combined in a mechanistic manner. As expected, although RTX and glucocorticoids produce contrasting temporal patterns of B cells on their own, the effect of RTX was predominant under combination treatment [34, 35]. The BCD model provides a mechanistic framework to inform such treatment effects of B cell subsets in BM and SLOs; however, it remains to be confirmed whether B cells in such tissues could be recapitulated like those in peripheral blood. To achieve a more rigorous version and validation of this model, the incorporation of additional data from relevant tissues is warranted along with system perturbations by other pertinent drugs.

In conclusion, a BCD model that characterizes the relevant process of B cell differentiation including BM and SLOs was developed using data for RTX and glucocorticoids in RA patients. The model recapitulated various temporal patterns of B cells according to respective dose regimens of the study drugs. The model identified RTX‐mediated binding with CD20 and its elimination process as key drivers determining the responses of ASCs to RTX, confirming a potential impact of FCGR polymorphisms on the mechanisms of action for RTX and therapeutic outcomes. Furthermore, baseline B cell profiles were also confirmed to be important to cellular responses. Although the model was validated against B cell dynamics rather than direct clinical endpoints, it leverages established correlations between cellular depletion and therapeutic outcomes [5, 6, 19]. Future incorporation of longitudinal clinical data would enhance the translational potential of the model for guiding dosing strategies and mechanism‐based evaluations of other relevant drugs, alone or in combination, that alter B cell differentiation in autoimmune diseases.

Author Contributions

T.N. and D.E.M. wrote the manuscript. T.N. and D.E.M. designed the research. T.N. performed the research. T.N. analyzed the data.

Conflicts of Interest

T.N. is an employee of Mitsubishi Tanabe Pharma Corporation. D.E.M. is a Simcyp Scientific Advisory Board Member and President and CEO of Enhanced Pharmacodynamics LLC.

Supporting information

Data S1: psp470151‐sup‐0001‐DataS1.pdf.

Figure S1: Schematic diagram of PK models for the study drugs. (A) Methylprednisolone (MP), free prednisolone (fPNL), and prednisone CLRTX (PNS), (B) Rituximab (RTX). Double‐lined compartments represent clinical measurement sites. #, Dosing compartment; C, drug concentration; Le, leaky tissue (fenestrated/discontinuous endothelium); Ly, total lymph; S, serum; Ti, tight tissue (continuous endothelium); X, drug amount. Each parameter is listed in Table S1.

Figure S2: Detailed structure of the B cell differentiation model. White and gray compartments show B cell counts and normalized signals. Black and red bars represent glucocorticoid‐and rituximab (RTX)‐mediated effects on CD19+ and CD20+ cells. Each parameter is listed in Table S2. AF: auto‐feedback. BM: bone marrow. GCB, germinal center B cells. IB, immature B cells. MB, memory B cells. NB, naïve B cells. PB, plasmablasts. PC, plasma cells. SLO, secondary lymphoid organs. TB, transitional B cells. The top‐left corner represents the sub‐model for CD20–RTX binding and elimination. B_s,t and RC_RTX represent a CD20‐expressing B cellsubset (s = PreB, IB, TB, NB, and MB; t = bm, s, slo) and CD20 RTX complex. *, The same value was assigned in both directions.

Figure S3: Fitted plasma concentration time–course of glucocorticoids. (A) Methylprednisolone (MP) after an intravenous administration of 100 mg MP prodrug. (B) Free prednisolone (fPNL) after an intravenous administration of 16.4 (blue) and 49.2 mg (red) PNL. (C) Prednisone (PNS) after an oral administration of 20 (blue) and 50 mg (red) PNS. Solid lines and symbols represent fitted curves and extracted data (Table 1).

Figure S4: Fitted time–courses of surface CD20, CD19+ cells, and PBs. (A) Percentage of surface CD20 expression relative to the baseline after an intravenous administration of an RTX‐like monoclonal antibody (Rit‐m2a). (B) Fitted time–course of blood CD19+ cells to baseline (%) following glucocorticoids whose administration timings are given in Table 1. (C) Fitted time–course of blood PBs to baseline (%) following 1000 mg RTX doses (week 0, 2). Solid lines and symbols represent fitted curves and extracted data (Table 1).

Figure S5: Model‐based simulations of CD19+ cells changes by RTX and MP. Simulated time–courses of CD19+ cells after combination treatment of 1000 mg RTX and 100 mg MP at week 0 and 2 (arrows). Symbols and bars represent median and 25th–75th percentile of the extracted data [19]. Solid line and shades represent median and ranges (red: 25th–75th percentile, purple: 5th–95th percentile) of simulated values.

Data S2: psp470151‐sup‐0007‐DataS2.7z.

Nakada T. and Mager D. E., “B Cell Differentiation Model for Identifying Predictors of Responses to Rituximab‐Mediated B Cell Depletion in Rheumatic Diseases,” CPT: Pharmacometrics & Systems Pharmacology 15, no. 1 (2026): e70151, 10.1002/psp4.70151.