Introduction

The production of recombinant proteins has been increasingly dominated by mammalian cell expression, which is especially due to favorable posttranslational modification patterns and human protein-like molecular structure assembly (Zhu 2012). Productivity improvements of mammalian cell culture processes have mainly focused on cell physiology and metabolism, cell line development, and process control strategy. However, influences of population-dependent variations on cellular physiology and kinetics and subsequently on the dynamics of culture productivity under bioproduction conditions have not yet been much in the focus of research. Since central cellular processes, like transfection efficiency (Brunner et al. 2000; Männistö et al. 2007), vary over the cell cycle, a systematic way to study populations of cell lines growing with synchrony under otherwise unperturbed conditions is needed. The consideration of inherent population inhomogeneity of mammalian cell cultures has, thus, become increasingly important for systems biology study and for developing more stable and efficient processes.

The interaction of cell cycle-specific variations of the cell behavior with large-scale process conditions can be optimally determined by means of (partially) synchronized cultivation under otherwise physiological conditions and subsequent population-resolved model adaptation. Both aspects are addressed in the following. The first aspect drives the need of a suitable method to synchronize a cell culture under widely undisturbed physiologic conditions and at a reasonable bioreactor scale for extensive study of effects of cell population variation.

The mammalian cell cycle

During the cell cycle (see Fig. 1), the cell genome, organelles, and macromolecules double their quantity to create two genetically identical daughter cells. These steps involve the two most important phases of the cell cycle, the S phase and the M phase. In the S phase (synthesis), the chromosomes replicate. In the M phase (mitosis), chromosome material is distributed to the new formed nuclei. Afterwards, the cytoplasm is divided (cytokinesis), resulting in the formation of two daughter cells. For the time needed by the cell for synthesis of precursors, organelle division, cell growth etc., there are two Gap phases: the first one (G 1) between the mitosis and the S phase, and the second one (G 2) between the S phase and the mitosis phase.

Fig. 1
figure 1

The four main phases of the cell cycle. In most of the cells, the Gap phases G 1 and G 2 separate the S and M phases from each other. If environmental growth conditions are not appropriate, cells may enter into a quiescent condition. This state is usually referred to as the G 0 phase, but the existence of such a state within the cell cycle has been discarded by Cooper (2003a). He argued that the so-called G 0 phase does not exist at all and has no biological meaning

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If the environmental growth conditions are not appropriate, cells in the G 1 phase will not move into the S phase, but may enter into a quiescent state, where they can remain for a long time. This state is often referred to as the G 0 phase, but the existence of such a state within the cell cycle has been discarded by Cooper (2003a). He argued that the so-called G 0 phase does not exist at all and has no biological meaning. Only at appropriate growth conditions, cells will reach a point at the end of the G 1 phase (commitment point or start), at which they will commit into DNA synthesis and division, even if growth and division signals cease to exist (Alberts et al. 2004).

Cell culture synchronization

For several decades, numerous cell synchronization methods have been proposed and also applied (see, e.g.,Campbell 1957; Zeuthen 1964), for example to study molecular interactions in cell cycle-related metabolic pathways. However, not all strategies are suitable for research on cell-cycle-dependent metabolism. An optimal strategy should be able to generate a homogeneous cell population within the same cell cycle phase, with similar cell size, and with the capability of further unperturbed growth.

In literature, a number of criteria defining the quality of synchronization can be found that are partially correlated (Keyomarsi et al. 1991; Cooper and Shedden 2003). Based on these, we summarize our criteria list as follows:

  1. 1.

    In synchronized culture, every cell parameter should have similar value as cells in the corresponding cell cycle phase in an unsynchronized culture.

  2. 2.

    Further unaffected cell growth after synchronization. Average kinetics should behave similarly in both nonsynchronized and synchronized cultivations after integration over integer multiples of the cell cycle duration.

  3. 3.

    Minimal increase in cell number during the interdivision time. This corresponds to a short fraction of time for division, compared to the duration of the cell cycle.

  4. 4.

    Narrower DNA distribution and narrower size distribution compared to nonsynchronized culture. The progress of both distributions must be coherent with the cell growth and the doubling times.

The points 1 and 2 are crucial to assess if the culture has actually been synchronized or if it has been distorted in a way that the obtained populations are not representative any more to any subpopulation of the untreated culture. Failing criterion 1 means that the culture is not synchronized, although cells might be aligned with respect to one or several common properties (e.g., DNA content). This has been predicted and observed for whole culture methods, as summarized below.

The points 3–4 refer to the quality, or “sharpness,” of synchronization. Therefore, they may be subject to a tradeoff between the number of obtained cells and the quality of synchronization.

Another condition that we will stress from a bioprocess engineering point of view is that synchronized cultivation should be performed at reactor scales of, e.g., ≈1 L to obtain scalable results for production relevant processes. To achieve this goal, the number of viable synchronized cells must reach a magnitude of 5·108 cells per liter in a time scale that is short compared to the cell cycle duration, i.e., in maximum ≈1 h.

Several known methods have been categorized and evaluated according to their ability to fulfill the needs mentioned above, which is summarized in the following.

Methods frequently used for synchronization attempts

For many decades, there have been numerous attempts to synchronize cells and cell populations. The known methods can be divided into two main groups:physical and chemical methods. These two groups practically correspond to selection methods and whole-culture methods. All those methods are summarized in Fig. 2.

Fig. 2
figure 2

Summary of methods used in literature for cell culture synchronization attempts. Note that accuracy and yield of physical methods vary drastically. Chemical methods (i.e., whole-culture methods) are frequently used, but have been shown to not produce actual synchrony. 1 FA fluorescence activated, MA magnetic activated

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Chemical methods—or whole-culture methods—are believed to result mostly in a reversible blocking of cells at a certain growth phase by means of deprivation of a medium component or addition of chemicals (Krishan et al. 1976; Enninga et al. 1984; Keyomarsi et al. 1991; Knehr et al. 1995; Moore et al. 1997; Fiore et al. 2002). Some of these have focused on arresting cell growth in a determined cell cycle phase and studying the consequences of growth arrest. Colcemid or nocodazole have been used for trying to block cells in the M phase (Knehr et al. 1995; Boxberger 2007; Lindl and Gstraunthaler 2008); aphidicolin, hydroxyurea, mimosine, and thymidine excess, for trying to block cells in the S phase (Knehr et al. 1995; Matherly 1989); and serum or amino acid starvation, DMSO, and lovastatin, for trying to block cells in the G 1/G 0 phase (Fiore et al. 2002; Boxberger 2007). A variant is the periodic stimulation of the cell culture by nutrient deprivation (Dawson 1972; Fritsch et al. 2005) or modulation (Tian et al. 2012), also referred to as “phased feeding.” Also, temperature reduction methods have been applied frequently (Enninga et al. 1984; Moore et al. 1997; Boxberger 2007; Lindl and Gstraunthaler 2008).

It has been argued (Cooper 1998, 2003b) and shown that those whole-culture, or chemical, methods are not able to synchronize cells. They include lovastatin (Cooper 2002b), (double) thymidine block (Cooper et al. 2008), serum starvation (Cooper and Gonzalez-Hernandez 2009), and nocadozole (Cooper 2006). The primary problem with all those whole-culture methods is that criterion 1 is not fulfilled, i.e., for example the cell size distributions of the “synchronized” population show a different pattern than those of any subpopulation in the unsynchronized culture, proving that the culture physiology has been disturbed. Consequently, all other criteria are also not fulfilled because the starting point is invalid with respect to synchronization. Cooper has even proposed that it is generally impossible, by any whole-culture method, to produce a synchronized culture because these methods cannot produce a population of cells that reflect the composition, size, chemistry, or anything else of cells of a particular age during an unperturbed cell cycle. It should be noted that, despite the mentioned synchronization criteria are not fulfilled, and even though size and age distributions are admittedly altered, those methods are still regarded as valid by some authors (Spellman and Sherlock 2004). Therefore, it must be made clear that if the synchronization criteria are not fulfilled, the cells might be regarded as aligned with respect to one or several properties (e.g., DNA content), but this is not the same as synchronized. In other words, observations made on such cultivations whose synchrony is not proven cannot directly provide reliable information about cell cycle-specific processes in the cells.

Physical methods—or selection methods—comprise approaches such as mitotic shake-off (Zwanenburg 1983), gradient centrifugation (Rola-Pleszczynski and Churchill 1978; Holley 1988), membrane elution, also referred to as “eukaryotic baby machine” (Helmstetter and Cummings 1963; Cooper2002a; Helmstetter et al. 2003), fluorescent-activated cell sorting (FACS) (Rieseberg et al. 2001; Jorgensen and Tyers 2004), magnetic-activated cell sorting (MACS) (Miltenyi et al. 1990), centrifugal elutriation (Banfalvi 2008), microfluidic sorting according to size (Migita et al. 2011; Lee et al. 2011), deformability, electric or optical properties, by means of hydrodynamics (Moon et al. 2011; Choi et al. 2009), or acoustophoresis (Thévoz et al. 2010) (reviewed in Autebert et al. (2012)), and more.

In contrast to chemical methods, the physical selection methods are assumed to not principally interfere with cell cycle control and central metabolism. Depending on scalability or parallelization, physical selection methods like cell sorting, centrifugation, and elutriation have the potential to perform fast in relation to the cell cycle duration, principally allowing for relatively high synchronization yields while minimally influencing other cultivation conditions.

In our lab, the physical selection methods countercurrent centrifugal elutriation, gradient centrifugation, an alginate-bead based variant of the membrane elution method, and FACS have been applied and evaluated (Platas Barradas 2011, 2013). The only whole-culture method applied in our lab, temperature reduction, led to enrichment of cells with G1 amount of DNA, but not to synchronized cultures. Since temperature reduction presumably has many side effects on cell metabolism, it has not been further considered.

Gradient centrifugation as well as centrifugation of cells in solutions of higher density (no gradient) were carried out to separate cells into subpopulations using the cell size as the main separation variable (cell density variation through the cell cycle being neglectable). Separation performed in sucrose solutions points to a successful separation of cells. However, the necessary sucrose concentrations expose the cells to osmotic shocks, which can only be avoided by the use of other molecules/polymers. A combination of sucrose and Ficoll 400™, a sucrose-epichlorohydrin polymer, reduced the osmolarity of the solution by keeping the solution’s density constant but has not yielded better separation results. The choice of a polymer for the preparation of higher density solutions should consider the density and viscosity of both solutions to avoid phase formation during separation. Furthermore, low yields are obtained from this method, since the centrifugation of high cell numbers led to pelleting inside the tubes during spinning.

In our experiments, the best results combining yields of up to ≈ 8·108 usable cells, high reproducibility and cell cycle phase discrimination could be achieved with the countercurrent centrifugal elutriation method. This method has been adapted from Banfalvi (2008) and applied to both animal and human cell lines (Platas Barradas et al. 2014), i.e., AGE1.HNFootnote 1, an industrial human cell line, Chinese Hamster Ovary (CHO) cells and HEK293. It allows to select cell populations according to their size in a funnel-shaped countercurrent flow chamber under the influence of the opposing forces of sedimentation and a washing flow (Fig. 3). Variation of the flow rate allows for selection of different populations representing a specific diameter range each. Since cell cycle position is highly correlated with cell size, this corresponds to a scanning along a cell cycle phase plot, represented by G1 and S contributions, with increasing population count (1–8) representing increasing flow rates and thus cell diameters (Fig. 4, blue line). The separation efficiency is moderate, i.e., not exactly at the corners of Fig. 4, however, sufficient to achieve clear oscillation during subsequent cultivation (Figs. 4 and 5a–c). Furthermore, the throughput is very high, allowing for elutriation of an unsynchronized starter population of 350–500 million cells per run, with a total yield of approx. 60 %. Since one elutriation run only takes a few minutes, the subpopulations of multiple runs can be individually pooled and used for inoculation of a bioreactor with relatively high cell density.

Fig. 3
figure 3

Centrifugal elutriation process: cell separation according to their size. Modified from Dorin (1994) and Banfalvi (2008)

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Fig. 4
figure 4

Damped oscillation during synchronized cultivation of human AGE1.HN cells: visualization of stable (red) and oscillating (yellow, green) cultivations, depending on the G1/S phase distributions when starting the cultivation of human AGE1.HN cells under otherwise same process conditions, according to simulation. Blue typical achievable subpopulations during the elutriation process, dot sizes indicate cell counts. Black damped oscillation, spiralizing towards the working point

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Fig. 5
figure 5

Example of process data development during synchronized cultivation, here for the industrial human cell line AGE1.HN in a dialysis bioreactor (Platas Barradas et al. 2014). a–c Distribution of cells among the G1, S, or G2/M phases during cultivations, dots and lines experimental results, blue lines simulation results. d Increase of viable cell density X v (t), dots experimental results, line simulation result. e Time-dependent mitotic growth rate (black), derived from (d) after low-pass filtering (see text for details). The approximate average cell volume (in μm3) as derived from at-line microscopy data is depicted in green. Note the phase shift: peak volumes are reached just before the subsequent peak in mitotic rate. f Example for the production of a metabolite, here lactate, during the cultivation. No clear oscillation can be seen directly from raw data. g Cell volume-specific turnover (production) rate of lactate after low-pass filtering. Oscillations can be observed and are aligned to the progress of the cell cycle, as indicated by the overlayed relative S-phase amount of cells (green, same data as in subfigure b). Note that in the dialysis process, the medium volume is ≈ 5 times larger than the cultivation volume, therefore the apparent turnover rates are reduced by a factor of ≈ 5

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A typical example of synchronized cultivation, in this case of a industrial human cell line (AGE1.HN) in a dialysis bioreactor (Pörtner and Märkl 1998), is summarized in Fig. 5. The increase of cell counts on a logarithmic scale (Fig. 5d, black dots) exhibits a smoothed staircase-like pattern, however, not necessarily distinct enough to clearly judge the quality of synchrony (Platas Barradas et al. 2014). However, derived from that data and after an additional low-pass filter step (Jandt et al. 2014), clear oscillations of the time-dependent mitotic growth rate μ sync(t) can be obtained (Fig. 5e, black line). Similarly, time-dependent metabolic production or consumption rates can be derived from analysis of medium components, like, e.g., for lactate (Fig. 5g), potentially exhibiting an oscillation as well. With the combined data of Fig. 5 and subsequent population-balanced model adaptation (next section), specific parameters can be assigned to single subpopulation, corresponding to single cell cycle phases.

A further promising way to reliably obtain synchronized cells for further analysis and cultivation is the application of microfluidic separation techniques as reviewed in Autebert et al. (2012), and shown to reach throughputs of more than 107 cells/h (Lee et al. 2011), combined with potentially very high selectivity (e.g., up to 95 %, Choi et al. 2009). The yield is very high for microfluidic systems, though not yet quite sufficient for cultivations at bioreactor scale, which might be partly mitigated by parallelization. Their special potential lies in the possibility to directly connect the sorted cells for further manipulation and incubation (Mu et al. 2013; Bahnemann et al. 2013), cultivation, or analytics sections on-chip (Mir et al. 2011; Wurm and Zeng 2012).

Model description of population dynamics

The described synchronization methods along with synchronized cultivation provide us with the opportunity to systematically determine how cell cycle-specific behavior of cells in cell cultures interacts with large-scale process conditions. Because there is practically no method available for perfectly synchronizing a cell culture suitable for a bioreactor scale study, mathematical modeling of population dynamics may help to answer some of unclear and disputed issues like possible variations of physiological parameters during the cell cycle.

As soon as reasonable computation power became affordable, the first population heterogeneity-based modeling algorithms were implemented in the late 1960s (Tsuchiya et al. 1966). Two main directions are common to implement population models: conventionally, as a system of partial differential equations (population balance system, PBE), or as a stochastic cell ensemble model (CEM) (Henson 2003). The first is limited with respect to internal variables and states but generally allows for sophisticated analysis like, e.g., bifurcation analysis. The latter method facilitates a direct implementation of single-cell models or model parts, but it is more computationally intensive and prone to noise and numerical artifacts. The analytical adaptation of kinetic model parameters on experimental data can, however, become very challenging and even close to impossible due to the high number of degrees of freedom and the impossibility to solve the inverse functions (Groh et al. 2011). Improvements can be achieved by sophisticated numerical adaptation, like free boundary finite element algorithms (Kavousanakis et al. 2009) or, more generally, Downhill Simplex (Singer and Singer 2004) or genetic optimization algorithms.

Recent studies based on PBEs focused on the impact of extrinsic heterogeneity caused by uneven distribution of intracellular content between daughter cells (Kavousanakis et al. 2009), description of the cell cycle of myeloma (Liu et al. 2007) or hybridoma cells (Faraday et al. 2001), or feedback loop expression dynamics exhibiting bistability (Mantzaris 2005). Apart from cell culture, ensemble models have been popularly used to describe for example protein folding heterogeneities (Bernadó et al. 2010; Fenwick and Salvatella 2011), or dynamics of neuronal networks (Solinas et al. 2013; Marreiros et al. 2010).

In our lab, a stochastic cell ensemble model has been implemented and adapted to synchronized cultivations of mammalian cell lines (Jandt et al. 2013, 2014). The resulting simulated data trajectories adapted to a synchronized cultivation of human AGE1.HN cell line are depicted in each of the plots of Fig. 5a–g, as indicated. The adaptation has been performed by means of multiple randomly initialized Downhill Simplex adaptations in order to evaluate the accuracy of the adaptation with respect to noise and multiplicity. Growth-related phase-specific kinetics can be estimated with an accuracy of ≈ 5−10 %, while metabolic rates usually exhibit reduced accuracy, i.e., up to ≈40 %. The main cause is that in oscillating systems, phase-shifting artifacts (jitter) can often occur due to irregular or too long sampling intervals. It shows that for a stable parameter estimation of oscillating cultures, a dense sampling is necessary. The sample rate must at least be twice the frequency of the oscillation according to the Nyquist-Shannon theorem. Generally, it should resemble an integer multiple of twice the oscillation frequency to also avoid phase-shifting artifacts. High computational stability can be achieved by low-pass filtering with a cutoff relative to the cell cycle period time T p (using a Gaussian filter with σ=0.2T p ) and subsequent resampling at equidistant time intervals before calculation of derivatives. A straightforward practical way to avoid sampling artifacts is to increase sampling frequency or otherwise adapt the sampling timing to the (predicted) state of the culture. Both approaches may be achieved based on (semi-)automated sampling and analysis methods (Bahnemann et al. 2013) with improved controlling and adapted sampling timing.

Despite these limitations, the numerical adaptation to metabolic processing rates, i.e., the time-resolved and potentially oscillating consumption or production rate of metabolites (Fig. 5g), allows to deduce the behavior and contribution of subpopulations (Jandt et al. 2013, 2014) and to which extent any cell cycle-specific variation can be observed. That contribution can be given as volumetric growth yield (Y, with the unit μm3·fmol−1), providing a measure of how much cell volume (regarded equivalent to cell mass) is synthesized along with a certain consumed or produced amount of a metabolite. If Y is held constant for all phases, no oscillations like depicted in Fig. 5g are obtained by simulation. By numerically adapting Y in a phase-specific manner and minimizing the mean squared deviation compared to the experimental data, oscillations can be reproduced in many cases. Multiple adaptations with differently randomized start conditions allow for an estimation of the remaining uncertainty of the fit. In case of the data plotted in Fig. 5g, it shows that the volumetric growth yield in AGE1.HN cells with respect to lactate apparently exhibits cell cycle-related behavior with Y Lac,G1 < Y Lac,S,Y Lac,G2/M. Similar variations also occur in CHO cells.

During a cultivation, the status of the synchronization of cells can optimally be determined according to the relative contribution of cells exhibiting a certain phase compared to the whole population. Analysis of the cell cycle phases as determined by flow cytometric analysis (FACS) of propodium iodide (PI) stained cells shows that the contribution of cells of all phases in a synchronized batch bioreactor experiment of a industrial human cell line (AGE1.HN, Fig. 5a–c) exhibits a damped oscillation with a trend to a stable level. This corresponds to a spiralization in a G 1/S diagram (Jandt et al. 2014) toward a working point (Fig. 4).

An important question is to estimate the remaining distortion of the synchronization procedure on the physiology of the cells, which is to be kept as low as possible. Good indicators are bulk kinetics that should behave similarly in both nonsynchronized and synchronized cultivations after integration over integer multiples of the cell cycle duration. This holds true for example for average mitotic growth rates (\(\overline \mu _{\text {AGE}}^{\text {sync}}=0.401~{\mathrm {d}^{-1}}\) vs. \(\overline \mu _{\text {AGE}}^{\text {nsync}}=0.431~{\mathrm {d}^{-1}} \pm 1.6~{\%}\), n= 6 ), and roughly for average metabolite throughput rates, e.g., for lactate production at the beginning (\({\overline \mu_{\text{AGE}}^{\text{sync}}}\) \(\overline c^{\prime \text {sync}}_{\mathrm {Lac,AGE}} \approx ~0.16~{\text {fmol} (\mu \mathrm {m}^{3} \cdot \mathrm {h} )^{-1}}\) according to Fig. 5g vs. \(\overline c^{\prime \text {nsync}}_{\mathrm {Lac,AGE}} = 0.15~{\text {fmol} (\mu \mathrm {m}^{3} \cdot \mathrm {h} )^{-1}}\), which decreases to \(\overline c^{\prime \text {sync}}_{\mathrm {Lac,AGE}} \approx ~0.08~{\text {fmol} (\mu \mathrm {m}^{3} \cdot \mathrm {h} )^{-1}}\) and \(\overline c^{\prime \text {nsync}}_{\mathrm {Lac,AGE}} = 0.05~\text {fmol} (\mu \mathrm {m}^{3} \cdot \mathrm {h})^{-1}\), respectively, after approx 96 h.) The same applies also to CHO-K1 cells (Jandt et al. 2014).

Based on simulations, the expected long-term oscillation behavior depending on start conditions can be predicted, especially with respect to the composition of cell cycle phases. This is depicted in the colored plot 4, indicating low (red) versus high sustained oscillation (green). The blue curve indicates achievable subpopulations yielded from one elutration run with dot sizes indicating the relative number of cells. Combining that data, optimal conditions to set up the cultivation can be obtained (Jandt et al. 2013).

Conclusions

Physical synchronization methods with high yields and minimal distortion of cultivation conditions, subsequent synchronized cultivation, combined with population resolved analysis and modeling provide a promising workflow to elucidate cell cycle-related regulation effects under physiological conditions in bioreactor cultivations. Several synchronization and modeling methods established by other groups and in our labs have been introduced and compared in this overview. It is noted that frequently used whole-culture, or chemical, methods are not able to synchronize cells correctly, rather they are only able to align cells with respect to single parameters. Selection, or physical, methods vary strongly with respect to cell yield and synchronization efficiency. For the desired purpose, which aims at liter-scale cultivations with principally arbitrary population composition and with respect to overall synchronization efficiency, yield and reproducibility, a modified countercurrent centrifugal elutriation method turned out to be superior to other potential methods such as gradient centrifugation, microfluidic cell separation, and chemical methods. This can be optimally combined with population ensemble modeling for the extraction of corresponding cell cycle-related parameters and simulation of dynamic interaction of subpopulations. For smaller cultivation volumes, i.e., at milliliter scales, microfluidic spiral separation may be a very good alternative with high synchronization accuracy.