AbstractABL602 2 + 1, a bispecific antibody with two distinct domains binding to CLL-1 on leukemias and CD3 on T cells, exhibits superior T cell activation and tumour lysing activity. Treatment outcomes of bispecific antibody rely on acute myeloid leukemia cell replication and antibody induced tumour lysing, but their quantitative relationship was unknown.

摘要ABL602 2+ 1是一种双特异性抗体，具有两个不同的结构域，与白血病上的CLL-1和T细胞上的CD3结合，具有优异的T细胞活化和肿瘤溶解活性。双特异性抗体的治疗结果依赖于急性髓细胞白血病细胞复制和抗体诱导的肿瘤溶解，但它们的定量关系尚不清楚。

Mathematical models are employed to quantitatively investigate HL-60 cell kinetics determined by bispecific antibody and tumour burden. First, we analysed cytotoxicity assay data testing HL-60 cell against bispecific antibody and T cells, and found efficiency of bispecific antibody induced tumour lysing increases but saturates with increase of HL-60 cell, T cell and bispecific antibody concentration.

数学模型用于定量研究由双特异性抗体和肿瘤负荷确定的HL-60细胞动力学。首先，我们分析了针对双特异性抗体和T细胞测试HL-60细胞的细胞毒性测定数据，发现双特异性抗体诱导的肿瘤裂解效率增加，但随着HL-60细胞，T细胞和双特异性抗体浓度的增加而饱和。

As a result, their interaction leads to bistable HL-60 cell kinetics; namely, at a given bispecific antibody and T cell concentration interval, HL-60 cell kinetics with small tumour burdens are inhibited but refractory to large tumour burdens. T cell concentration is strong negatively correlated with HL-60 cell concentration.

结果，它们的相互作用导致双稳态HL-60细胞动力学；即，在给定的双特异性抗体和T细胞浓度区间，具有小肿瘤负荷的HL-60细胞动力学被抑制，但对大肿瘤负荷是难治的。T细胞浓度与HL-60细胞浓度呈强负相关。

With bispecific antibody clearance, observed bistable HL-60 cell kinetics still exists. Our finding explains observed phenomenon that bispecific antibody was less efficacious at high tumour burden even with enough activated cytotoxic CD8 + T cells. Maintaining high antibody concentration and preventing T-cell exhaustion are equivalently important to sustain long-term control..

在双特异性抗体清除的情况下，观察到的双稳态HL-60细胞动力学仍然存在。我们的发现解释了观察到的现象，即即使有足够活化的细胞毒性CD8+T细胞，双特异性抗体在高肿瘤负荷下也不太有效。维持高抗体浓度和防止T细胞衰竭对于维持长期控制同样重要。。

IntroductionAcute myeloid leukemia (AML) is one of the most common and fatal haematological malignancies in adults, with most of them having a poor prognosis1,2. Chemotherapy, radiation therapy and stem cell transplant are used to treat AML, but relapse rate likely is still very high, for example approximately 60–70% for patients older than sixty years old3,4.

。化疗，放射治疗和干细胞移植被用于治疗AML，但复发率可能仍然很高，例如60岁以上患者的复发率约为60-70%3,4。

In hematologic malignancies, immunotherapies aim to lyse tumour cells using cytolytic T lymphocytes, for example, such as chimeric antigen receptor (CAR) T cells5,6, bispecific T-cell engager (BiTE)7,8 and bispecific antibody (BiAb)9,10. Bispecific antibodies have two distinct binding domains that can bind to leukemia surface proteins (including CD33 and CLL-1) on AML cells and CD3 subunits on T cells simultaneously, and trigger T-cell activation and target cell lysis11,12.

在血液系统恶性肿瘤中，免疫疗法旨在使用溶细胞性T淋巴细胞裂解肿瘤细胞，例如嵌合抗原受体（CAR）T细胞5,6，双特异性T细胞接合剂（BiTE）7,8和双特异性抗体（BiAb）9,10。双特异性抗体具有两个不同的结合结构域，可以同时与AML细胞上的白血病表面蛋白（包括CD33和CLL-1）和T细胞上的CD3亚基结合，并触发T细胞活化和靶细胞裂解11,12。

C-type lectin-like molecule-1 (CLL-1) has high expression on the whole blast compartment in the majority of AML cell and becomes one of the target for immunotherapy, including CAR-T cell and bispecific antibody13. CD33 is a cell surface antigen that is present in more than 80% of patients with AML but is absent from pluripotent hematopoietic stem cells14.

C型凝集素样分子-1（CLL-1）在大多数AML细胞的整个胚细胞区室中具有高表达，并成为免疫治疗的靶标之一，包括CAR-T细胞和双特异性抗体13。CD33是一种细胞表面抗原，存在于80%以上的AML患者中，但多能造血干细胞中不存在14。

HL-60 cell line was isolated from a AML patient and used a model to study AML treatment and diagnosis since 197715, because it has a high expression of CLL-116 and CD3317. Bispecific antibody redirects T cells to lyse HL-60 cells by bringing them into physical contact and activating secretion of cytotoxic molecules18.ABL602 2 + 1, a bispecific antibody developed by ABL Bio Inc to treat patients with AML, has anti-CD3 Fab binding to T cells in one arm, and anti-CLL-1 Fab binding to tumour cell in each arm18.

自197715年以来，HL-60细胞系从AML患者中分离出来，并使用模型研究AML的治疗和诊断，因为它具有CLL-116和CD3317的高表达。双特异性抗体通过使T细胞与HL-60细胞发生物理接触并激活细胞毒性分子的分泌来重定向T细胞以裂解HL-60细胞18.ABL602 2 + 1是由ABL Bio Inc开发用于治疗AML患者的双特异性抗体，具有抗CD3 Fab与一只手臂中的T细胞结合，以及抗CLL-1 Fab与每只手臂中的肿瘤细胞结合18。

ABL602 2 + 1 exhibits strong tumour cytolytic activity against HL-60 cell, and lack of .

ABL602 2+ 1对HL-60细胞表现出强烈的肿瘤细胞溶解活性，并且缺乏。

(1)

(1)

\(T\left(t\right)\) represents tumour cell with respect to time \(t\). Parameter \(\rho\) represents per capita growth rate; \(\beta\) controls natural saturation of tumour cell replication at high tumour cell concentration.To establish quantitative relationship between bispecific antibody concentration and days post infusion, we fit cynomolgus monkey pharmacokinetic study assay data to clearance model Eq. (2) (shown in Fig.

\（T左（T右）代表肿瘤细胞相对于时间（T）。参数\（\ rho \）表示人均增长率\（\β\）在高肿瘤细胞浓度下控制肿瘤细胞复制的自然饱和。为了建立双特异性抗体浓度与输注后天数之间的定量关系，我们将食蟹猴药代动力学研究测定数据拟合到清除模型方程（2）（如图2所示）。

S2, Sect. 1.2, Supplementary Material). Clearance model is described as the one-dimensional ODE model43$$\frac{dA\left(t\right)}{dt}={-C}_{1}A\left(t\right){+C}_{0}$$.

。1.2，补充材料）。清除模型被描述为一维ODE模型43$$\frac{dA \ left（t \ right）}{dt}={-C}_{1}A\左（t \右）{+C}{0}$$。

(2)

(2)

\(A(t)\) represents bispecific antibody concentration with respect to time t. Parameter \({C}_{1}\) represent the clearance rate and parameter \({C}_{0}\) represent mass generation rate.To establish quantitative relationship among HL-60 cell concentration, bispecific antibody concentration and T cell concentration, we developed following five models, including unsaturated lysing efficiency (modelled by law of mass action)$$\left\{ {\begin{array}{*{20}c} {\frac{dT}{{dt}} = rT\left( {1 - \frac{T}{\beta }} \right) - \kappa ATE} \\ {\frac{dA}{{dt}} = - \varphi ATE} \\ {\frac{dE}{{dt}} = - \sigma E} \\ \end{array} } \right.$$.

\（A（t）\）表示相对于时间t的双特异性抗体浓度。参数\({C}_{1} \）表示清除率和参数\({C}_{0}\）表示质量生成率。为了建立HL-60细胞浓度，双特异性抗体浓度和T细胞浓度之间的定量关系，我们开发了以下五个模型，包括不饱和裂解效率（由质量作用定律建模）$$左{开始{阵列}{*{20}c}{\frac{dT}{dT}}=rT\left（{1-\frac{T}{\beta}}\ right）-\kappa-ATE}\\\{\frac{dA}{dT}=-\varphi-ATE}\\\ \frac{dE}{dT}=-\sigma E}\\ \ end{array}}\ right.$$。

(3)

(3)

semi-saturated lysing efficiency (modelled by Hill function)$$\left\{\begin{array}{c}\frac{dT}{dt}=rT\left(1-\frac{T}{\beta }\right)-\frac{\kappa }{1+aA}\frac{1}{1+\eta T}ATE\\ \frac{dA}{dt}=-\frac{\varphi }{1+aA}\frac{1}{1+\eta T}ATE\\ \frac{dE}{dt}=-\sigma E\end{array}\right.$$

半饱和裂解效率frac{1}{1+\eta T}ATE \\\frac{dE}{dT}=-\sigma E \ end{array}\右$$

(4)

(4)

saturated lysing efficiency$$\left\{\begin{array}{c}\frac{dT}{dt}=rT\left(1-\frac{T}{\beta }\right)-\frac{\kappa }{1+aA}\frac{1}{1+\gamma E+\eta T}ATE\\ \frac{dA}{dt}=-\frac{\varphi }{1+aA}\frac{1}{1+\gamma E+\eta T}ATE\\ \frac{dE}{dt}=-\sigma E\end{array}\right.$$

饱和裂解效率1}{1+\gamma E+\eta T}ATE\\ frac{dE}{dT}=-\sigma E \ end{array}\右$$

(5)

(5)

saturated lysing efficiency with experiential function,$$\ \left\{ \begin{gathered} \frac{{dT}}{{dt}} = \left( {1 - \frac{T}{\beta }} \right) - \frac{k}{{1 + e^{{aA}} }}\frac{1}{{\gamma + E + \eta T}}ATE \hfill \\ \frac{{dA}}{{dt}} = - \frac{\varphi }{{1 + e^{{ aA}} }}\frac{1}{{1 + \gamma \,E + \eta A}}ATE \hfill \\ \frac{{dE}}{{dt}} = - \sigma E \hfill \\ \end{gathered} \right.$$.

具有经验函数的饱和裂解效率，$$$\\左{\开始{聚集}\分数{dT}}{dT}=\左（{1-\分数{T}{\ beta}}\右）\ \分数{k}{{1+e ^{aA}}}\分数{1}{\γ+e+\ eta T}}ATE \ hfill分数{{dA}}{{dT}}=-\frac{\varphi}{{1+e^{aA}}}}\frac{1+\gamma，e+\eta A}}ATE\hfill \\ frac{{dE}}}{dT}=-\sigma e\hfill \\ end{collected}\ right.$$。

(6)

(6)

\(E\left(t\right)\) represents T cell concentration with respect to time \(t\). Parameter \(\kappa\) represents lysing rate by bispecific antibody binding and T cell; \(\varphi\) represents bispecific antibody consumption rate by binding to T cell and tumour cell; \(\eta\) controls the saturation in lysing rate as tumour cell concentration increases; \(\gamma\) controls the saturation in lysing rate as antibody-T-cell complex concentration increases; \(a\) controls the saturation in lysing rate as antibody concentration increases.

\（E \ left（t \ right）\）表示t细胞浓度相对于时间\（t \）。参数\（\ kappa \）表示双特异性抗体结合和T细胞的裂解率\（\ varphi \）通过与T细胞和肿瘤细胞结合代表双特异性抗体消耗率\随着肿瘤细胞浓度的增加，（\ eta \）控制裂解率的饱和度\随着抗体-T细胞复合物浓度的增加，（\γ\）控制裂解率的饱和度\（a）随着抗体浓度的增加，控制裂解率的饱和度。

Parameter σ represents natural death rate of T cells.To establish quantitative relationship among HL-60 cell concentration, bispecific antibody concentration and T cell concentration in presence of antibody clearance, we proposed a three-dimension ODE model$$\left\{ {\begin{array}{*{20}c} {\frac{{dT}}{{dt}} = rT\left( {1 - \frac{T}{\beta }} \right) - \frac{\kappa }{{1 + aA}}\frac{1}{{1 + \gamma E + \eta T}}ATE} \\ {\frac{{dA}}{{dt}} = - \frac{\varphi }{{1 + aA}}\frac{1}{{1 + \gamma E + \eta A}}ATE - C_{1} A\left( t \right) - C_{0} } \\ {\frac{{dE}}{{dt}} = - \sigma E} \\ \end{array} } \right.$$.

参数σ表示T细胞的自然死亡率。为了建立抗体清除存在时HL-60细胞浓度、双特异性抗体浓度和T细胞浓度之间的定量关系，我们提出了一个三维ODE模型{*{20}c}{\frac{{dT}}{dT}}=rT\left（{1-\frac{T}{\beta}}\right）-\frac{\kappa}{{1+aA}}\frac{1}{{1+\gamma E+\eta T}}}ATE}\\\ frac{{dA}}{dT}}=-\frac{\varphi}{1+aA}}\frac{1}{1+\ gamma E+\ eta A}}ATE-C{1}A \左（T \右）-C{0}}\ \ frac{dE}{dT}=-\ sigma E}\ \ end{array}\ right.$$。

(7)

(7)

Parameter estimationTo estimate HL-60 cell parameters, the sum of squared error (SSE) is defined as \({SSE}_{1}={\sum }_{i=1}^{n}{\left({log}_{10}\left({T}_{A}\right)-{log}_{10}F\left({T}_{A}\right)\right)}^{2}\)φ, \({T}_{A}\) and \(F\left({T}_{A}\right)\) represent experiment tumour cell concentration at time (\(t\)) and estimated tumour cell concentration at time (\(t\)).

\({SSE}_{1} ={\总和}{i=1}^{n}{\左({log}_{10} \左({T}_{A} \正确）-{log}_{10}F\左({T}_{A} \右\右）}^{2}\）φ\({T}_{A} \）和\（左）({T}_{A} \右）\）代表时间（\（t）\）的实验肿瘤细胞浓度和时间（\（t）\）的估计肿瘤细胞浓度。

Initial guesses used for parameter estimation are \({\rho }_{0}={10}^{-1}\) and \({\beta }_{0}={10}^{5}\).To estimation of bispecific antibody clearance, all concentration data with microgram per milliliter units (μg/mL) were converted to equivalent nanomolar concentrations (nM) dividing concentrations in μg/mL by 1.5 × 105, because molecular weight of a typical antibody 150 kDa.

用于参数估计的初始猜测是\（{\ rho}u0}={10}^{-1}\）和\（{\ beta}u0}={10}^{5}\）。为了估计双特异性抗体清除率，将所有微克/毫升单位（μg/mL）的浓度数据转换为等效纳摩尔浓度（nM），将μg/mL的浓度除以1.5×105，因为典型抗体的分子量为150 kDa。

The sum of squared error (SSE) is defined as \({SSE}_{2}={\sum }_{i=1}^{n}{\left({log}_{10}\left(A(t)\right)-{log}_{10}G\left(A(t)\right)\right)}^{2}\), \(A(t)\) and \(G\left(A(t)\right)\) represent experiment bispecific antibody concentration at time (\(t\)) and estimated bispecific antibody concentration at time (\(t\)).

平方误差之和（SSE）定义为\({SSE}_{2} ={\总和}{i=1}^{n}{\左({log}_{10} \左（A（t）\右）-{log}_{10}G\左（A（t）\右）\ ^{2}\），\（A（t）\）和\（G \左（A（t）\右）\）表示时间（\（t）\）的实验双特异性抗体浓度和时间（\（t）\）的估计双特异性抗体浓度。

Initial guesses used for parameter estimation are \({C}_{{0}_{0}}={10}^{-1}\) and \({C}_{{1}_{0}}={10}^{-1}\).To estimation bispecific antibody induced lysing parameters, target tumour cell concentration is calculated using the formula, tumour cell = 5 × TN cells/mL, where TN represented the number of tumour cell in each well; T cell concentration is calculated using the formula, T cell = 5 × MN/mL, where TN represented the number of T cell in each well; Antibody concentration is calculated using the formula, antibody concentration = 5 × AN nm /mL, where AN represented antibody concentration the in each well.

用于参数估计的初始猜测是\({C}_（笑声）{{0}_{0}}={10}^{-1}\）和\({C}_（笑声）{{1}_{0}}={10}^{-1}\）。为了估计双特异性抗体诱导的裂解参数，使用以下公式计算靶肿瘤细胞浓度：肿瘤细胞=5×TN细胞/mL，其中TN代表每个孔中肿瘤细胞的数量；；使用以下公式计算抗体浓度：抗体浓度=5 nm/mL，其中每个孔中代表的抗体浓度。

The SSE is defined as \({SSE}_{3}={\sum }_{i=1}^{n}{\left({log}_{10}\left({T}_{B}\.

SSE定义为\({SSE}_{3} ={\总和}{i=1}^{n}{\左({log}_{10} \左({T}_{B} \。

Data availability

数据可用性

All data analysed in this manuscript is deposited in https://github.com/ShlomoBergg/Bispecific-antibody-ABL602-2–1-induced-bistable-acute-myeloid-leukemia-kinetics.

本手稿中分析的所有数据均保存在https://github.com/ShlomoBergg/Bispecific-antibody-ABL602-2–1诱导的双稳态急性髓系白血病动力学。

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Download referencesAcknowledgementsWe thank Dr. Eunhee Lee and Dr. Jonghwa Won from ABL Bio Inc, Seongnam, Korea (the Republic of) for cytotoxicity assay data testing HL-60 cells against ABL602 2+1 bispecific antibody and purified human T cell. Without Dr. Eunhee Lee and Dr. Jonghwa Won’s kindly help, we count not perform any analysis on bispecific antibody (ABL602 2+1).Author informationAuthors and AffiliationsDepartment of Environment and Genetics, School of Agriculture, Biomedicine and Environment, La Trobe University, Bundoora, AustraliaShilian XuDepartment of Mathematical and Physical Science, La Trobe University, Bundoora, AustraliaShilian XuAuthorsShilian XuView author publicationsYou can also search for this author in.

下载参考文献致谢我们感谢韩国城南ABL Bio Inc.的Eunhee Lee博士和Jonghwa Won博士针对ABL602 2+1双特异性抗体和纯化的人T细胞测试HL-60细胞的细胞毒性测定数据。如果没有Eunhee Lee博士和Jonghwa博士的善意帮助，我们将不会对双特异性抗体（ABL602 2+1）进行任何分析。作者信息作者和附属机构拉筹伯大学农业、生物医学与环境学院环境与遗传学系，澳大利亚，澳大利亚，拉筹伯大学数学与物理科学系，澳大利亚，澳大利亚，澳大利亚，澳大利亚，澳大利亚，澳大利亚，澳大利亚，澳大利亚，澳大利亚，澳大利亚。

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Reprints and permissionsAbout this articleCite this articleXu, S. Bispecific antibody (ABL602 2 + 1) induced bistable acute myeloid leukemia kinetics.

转载和许可本文引用本文，S.双特异性抗体（ABL602 2 + 1）诱导双稳态急性髓细胞白血病动力学。

Sci Rep 14, 25557 (2024). https://doi.org/10.1038/s41598-024-75971-4Download citationReceived: 15 May 2024Accepted: 09 October 2024Published: 26 October 2024DOI: https://doi.org/10.1038/s41598-024-75971-4Share this articleAnyone you share the following link with will be able to read this content:Get shareable linkSorry, a shareable link is not currently available for this article.Copy to clipboard.

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KeywordsBispecific antibodyABL602 2 + 1BistabilityAcute myeloid leukemiaImmunotherapyTumour burden

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Applied mathematicsCancerCancer immunotherapyComputational biology and bioinformaticsHaematological cancerImmunologyMathematics and computing

应用数学癌症免疫治疗计算生物学和生物信息学血液学癌症免疫数学和计算