### 3D clinostat development

The 3D clinostat hardware was designed and manufactured according to a conventional 3D clinostat structure described in previous studies (Fig. 1). The clinostat used in this study consists of two perpendicular frames that can rotate independently. The structure of the 3D clinostat was designed using the CAD program (SolidWorks, Dassault Systemes, France, using Seoul National University Academic License) and manufactured using a milling machine with aluminum plates. Two motors (MX-64T, ROBOTIS, Seoul, Republic of Korea) were used to actuate the two frames of the clinostat. Electrical wires for power supply and communication were connected via slip ring, which enables electrical connection between external and rotating frames. The dimensions of the clinostat were limited to 300 × 310 × 350 mm (length × width × height) as the hardware was to be operated within an incubator for cell proliferation. A mechanical stage, which fixes 25 cm^{2} flasks (SPL Life Sciences Co, Korea) for cell cultivation and is capable of accommodating a maximum of eight flasks simultaneously, was affixed at the center of the clinostat (Fig. 1). The quantitative dimensions of the mechanical stage relative to its center of rotation are provided in Fig. 2. The clinostat was controlled by a control algorithm embedded in an external personal computer. The control algorithm provided constant angular velocities for two actuators; the angular velocities were determined by considering the symmetric distribution of the acceleration vector, which consists of the gravitational acceleration and non-gravitational acceleration. The optimal angular velocities were determined according to simulation based on the kinematic model. A graphical user interface was implemented using LabVIEW 2009 (National Instruments, Austin, TX, USA, using Seoul National University Academic License) for convenient and stable operation (Fig. 3).

### Clinostat simulation

Prior to the cell proliferation experiment, the 3D clinostat should be simulated to guarantee taSMG. One of the most important features of a 3D clinostat is the angular velocities of the two actuators. In order to determine the optimal angular velocity, that enables symmetric acceleration distribution and reduces the effect of non-gravitational acceleration (centrifugal and tangential accelerations), kinematics of the clinostat were modeled, as shown in Eqs. (1)–(9) below (see “List of symbols” at the end of the manuscript). The coordinates are defined as shown in Fig. 4. The global frame indicates the external inertial frame (external observer), the local 1 frame indicates a coordinate used by the outer frame, and the local 2 frame indicates a coordinate used by the inner frame and stage.

$$w_{1}^{T} = [{\dot{\theta }}_{1} ,0,0]{w^{\prime}}_{2}^{T} = [0,{\dot{\theta }}_{2} ,0]$$

(1)

$$ w_{2} = R_{x} \left( {\theta_{1} } \right)w^{\prime}_{2} = \left[ {\begin{array}{ccc} 1 & 0 & 0 \\ 0 & {\cos \theta_{1} } & { - \sin \theta_{1} } \\ 0 & {\sin \theta_{1} } & {\cos \theta_{1} } \\ \end{array} } \right]\left[ {\begin{array}{c} 0 \\ {\dot{\theta }_{2} } \\ 0 \\ \end{array} } \right] = \left[ {\begin{array}{c} 0 \\ {\dot{\theta }_{2} \cos \theta_{1} } \\ {\dot{\theta }_{2} \sin \theta_{1} } \\ \end{array} } \right] $$

(2)

$$ w = w_{1} + w_{2} = \left[ {\begin{array}{*{20}c} {\dot{\theta }_{1} } \\ {\dot{\theta }_{2} \cos \theta_{1} } \\ {\dot{\theta }_{2} \sin \theta_{1} } \\ \end{array} } \right]\;\left( \text{{Summation\;of\;angular\;velocity}} \right) $$

(3)

$$ \dot{w} = \left[ {\begin{array}{*{20}c} 0 \\ { - \dot{\theta }_{1} \dot{\theta }_{2} \sin \theta_{1} } \\ {\dot{\theta }_{1} \dot{\theta }_{2} \cos \theta_{1} } \\ \end{array} } \right] $$

(4)

$$ r = R_{x} (\theta_{1} )R_{y} (\theta_{2} ) \left[ {\begin{array}{*{20}c} {\Delta x} \\ {\Delta y} \\ {\Delta z} \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} {\Delta x\cos \theta_{2} + \Delta z\sin \theta_{2} } \\ {\Delta y\cos \theta_{1} + \Delta x\sin \theta_{1} \sin \theta_{2} - \Delta z\sin \theta_{1} \cos \theta_{2} } \\ {\Delta y\sin \theta_{1} - \Delta x\cos \theta_{1} \sin \theta_{2} + \Delta z\cos \theta_{1} \cos \theta_{2} } \\ \end{array} } \right] $$

(5)

$$ a\left( t \right) = - \left\{ {\dot{w} \times r + w \times (w \times r)} \right\} $$

(6)

$$ a(t)^{\prime\prime} = R_{2}^{1} R_{1}^{0} a\left( t \right) = R_{y}^{ - 1} (\theta_{1} )R_{x}^{ - 1} (\theta_{2} )a\left( t \right) = R_{y}^{T} (\theta_{1} )R_{x}^{T} (\theta_{2} )a\left( t \right) $$

(7)

$$ g(t)^{\prime\prime} = R_{y}^{ - 1} \left( {\theta_{1} } \right)R_{x}^{ - 1} \left( {\theta_{2} } \right)g = R_{y}^{T} \left( {\theta_{1} } \right)R_{x}^{T} \left( {\theta_{2} } \right)g \left( {\because g = \left[ { \begin{array}{*{20}c} 0 & { - 9.8} & 0 \\ \end{array} } \right]^{T} } \right) $$

(8)

$$ a(t)^{\prime\prime}_{tot} = a(t)^{\prime\prime} + g(t)^{\prime\prime} $$

(9)

Among the acceleration experienced by non-inertial frame, local 2, external (gravitational acceleration), centrifugal, and tangential acceleration were considered and Coriolis and radial accelerations were excluded from the analysis. When magnitudes of angular velocities, \( \dot{\theta }_{1} \) and \( \dot{\theta }_{2} \), are sufficiently small, fluidic movement inside flasks can be negligible. Thus, mechanical condition inside the flasks can be assumed as quasi-static state, and the relative movement inside the flasks is neglected. Therefore, three types of acceleration, centrifugal, tangential and gravitational acceleration, were analyzed in this study.

In order to ensure symmetrical distribution of acceleration, the trajectory of the acceleration vector must avoid asymmetrically distributed path. 3D clinostats with asymmetric acceleration trajectory do not cover all orientations. Therefore, simulation based on the kinematics model was performed using MATLAB R2014b (Mathworks Inc., Natick, MA, USA, using Seoul National University Academic License). Using the Taguchi method [29], which is a well-known optimization approach in mechanical engineering, a combination of two angular velocities was determined from the initial state (1 rpm for angular velocities of outer frame and inner frame). The objective function was diversity of the orientation of the acceleration vectors (including gravitational and non-gravitational acceleration vectors). The magnitude of residual acceleration after 24 h was estimated to guarantee taSMG.

### Cell lines and culture conditions

The human Hodgkin’s lymphoma cell lines L-540 and HDLM-2 were obtained from the German Collection of Microorganisms and Cell Cultures (DSMZ, Braunschweig, Germany) [30]. The human dermal fibroblast (HDF) cells were purchased from the American Type Culture Collection (ATCC, Manassas, VA, USA). L-540 and HDLM-2 cells were maintained in RPMI 1640 (Life Technologies, Gaithersburg, MD, USA) supplemented with 10% fetal bovine serum (FBS, Life Technologies) and 1% penicillin/streptomycin solution (Life Technologies) at 37 °C in 5% CO_{2}. HDF cells were maintained in Dulbecco’s Modified Eagle’s Medium (DMEM, HyClone, South Logan, Utah, US) supplemented with 10% FBS and 1% penicillin/streptomycin solution at 37 °C in 5% CO_{2}.

### Operating 3D clinostat

Cells were seeded in 25 cm^{2} flasks with the total 5 × 10^{6} cells. Before being placed in the clinostat, the flasks were carefully filled with medium (approximately 80 ml) without air bubbles in order to avoid shearing of the fluid [31]. After the flasks were fixed on the stage of the clinostat, the clinostat was operated for 1, 2, and 3 days in a commercially available incubator set at 37 °C and supplied with 5% CO_{2}. The same cells were grown in parallel at 1 G comprised the control culture, which was kept statically in the same incubator as the clinostat. The same procedure was repeated for four times.

### Cell proliferation assay

Cell counting was performed manually with a hemocytometer (Biosystems, Nunningen, Switzerland) on trypan blue (Life Technologies) treated cells to assess cell concentration and viability, according to the dye exclusion method. The counts were carried out in triplicate per independent sample.

### Statistical analysis

Cell counting data were represented as means with standard error of the mean (SEM). Statistical significance was determined via a two-tailed Student’s t test and analyzed using Graph Pad Prism 6 (Graph Pad Software, Inc., San Diego, CA, USA). Differences were considered to be significant at *p* < 0.05.