Bioprocess parameters allow predictive adaptation to other cell lines. Survival was assessed after twenty-four hours in growth medium in 20-cell HES2 clusters (**A**; 0.60 +/− 0.16, N=6). For H9, viable cell numbers were too low to count after clustering of 20 cells, while approximately 40% survival was attained with clusters of 40, 60 and 100 cells, with highest coefficient of variance at the 40-cell size (**A**; N=4, CV = 0.21, 0.14, 0.18 respectively). Differentiation of H9 cells from 60-cell clusters was successful, with expansion and yield of approximately 5.65-fold and 3.75-fold respectively, and similar results from IPS and H1 lines (**B**; N=11, 22 and 6 respectively). In our model (**C**), optimal aggregate size is a function of trajectory through the “optimal envelope”. Efficiency of cell production is maximal when aggregates approach the upper size limit, beyond which viability and / or purity are adversely impacted, immediately prior to harvest. The trajectory followed from a given starting point then depends on the amount of cell loss experienced after aggregate formation, and the rate at which real expansion of cell numbers occurs. Aggregate size may be reset by dissociation and re-aggregation to allow for repeated cycles of expansion (left side) or subsequent differentiation steps (right side).

**Supplementary Table S1.** Antibodies and supplier information.

**Supplementary Table S2.** Primer sequences employed for quantitative real-time polymerase chain reaction quantification of transcript levels.

**Supplementary Figure S3.** In the course of this differentiation process, CFSE peak spreading precluded assessment of population doublings via peak counting. We therefore obtained expansion data from the population fluorescence profile by treating the measured profile on a given day as a linear combination of contributions from a reference population shifted by different numbers of cell divisions, after compensating for a CFSE half-life of 72 hours. Population doubling history was obtained by minimizing the squares of the residuals (**A-F**: hatched – measured profile; white – reference profile; red line – best fit line; bar plot – fitted relative contributions).

**Supplementary Figure S4.** Differentiation competence cannot be isolated prospectively on the basis of SSEA3 or TG30 expression levels. In order to test the selective differentiation hypothesis, equal numbers of cells were differentiated after flow sorting the input population (**A,B**) into low (**C,D** - bottom 15th percentile), medium (**E,F** - middle 70%) and high (**G,H** - top 15th percentile) on the basis of expression levels of SSEA3 or TG30. Neither marker permitted prospective isolation of the competent population of cells (**I,J**), although the population with the lowest SSEA3 expression did exhibit a statistically significant reduction in yield (**I** - Low vs Medium / High, Mann-Whitney U, P=0.026 and 0.0022 respectively, N=6), consistent with the expected presence of contaminating differentiated cells in this fraction. These results are consistent with non-specific cell loss in an instructive-differentiation model.

**Supplementary Figure S5**. Mann-Whitney U tests were used to compare all combinations of cell yields from 60-, 100-, and 200-cell aggregates expanded during 10 serial passages (**A**). Our analysis demonstrates that there is no consistent pattern of significant differences such as would be observed should changes in proliferation or self-renewal rates accumulate over successive passages (for example, an increase in proliferation rates with time would lead to a consistent pattern of black squares [significant differences] when comparing later to earlier passage results – see inset for hypothetical dataset showing this property). This data supports the notation that fundamental cell properties (single cell survival, cell proliferation rate) do not change during the study. Representative FACS plots of the expression of the pluripotency markers OCT4 and SSEA3 do not alter appreciably during serial passaging (**B**), suggesting that cells do not lose their pluripotent state during the 35 day culture period.

**Supplementary Figure S6.** Expansion of H9 hPSC through 5 serial passages results in a unimodal distribution with aggregate size, consistent with observations made using HES2 hPSC. Mean expansion was maximal with an initial aggregates size of 60 cells, and not significantly different from expansion of H9 cells cultured on MEF (*P* > 0.2). H9 cells were expanded under the same conditions as HES2, other than minor differences in medium composition noted in the Materials and Methods section under Cell culture (aggregate suspension expansion).

**Supplementary Figure S7.** Karyotype analysis demonstrates the genetic stability of hPSCs cultured serially in the microwell system. HES2 (top row) and H9 cells were cultured over 6 serial passages either on MEF or in microwells, and processed for karyotype analysis (0.05 mg / mL Colcemid for one hour; hypotonic KCl solution for 30 minutes, desiccated overnight at room temperature, then at 90^{o}C for 90 minutes, and treated with 0.4x Pancreatin for 3 minutes 15 seconds). Representative karyotypes from each condition are as indicated.

**Supplementary Figure S8.** Teratoma analysis of HES2 cells serially passaged in the microwell system. Tumours (**A**) resulting from the injection of HES2 cells serially passaged using conventional passaging on MEF (**B**), as 40-cell aggregates (**C**), as 100-cell aggregates (**D**), or as 200-cell aggregates (**E**) contain cells from all germ layers, contrasting with a growth arising from the injection of proliferating MEF cells (**F**). Tumours 1-5 in (**A**) correspond to panels (**B-F**) respectively.

**Supplementary Figure S9.** Differentiation is not controlled by a simple cell-division counting mechanism. Cells on the 5^{th} day of differentiation (S5) were assessed flow cytometrically for CFSE intensity (FITC channel) and CXCR4 staining (APC channel). A control (CFSE alone) sample indicated that CFSE signal did not have a substantial effect on APC fluorescence intensity (not shown), and no substantial correlation between cell division history and differentiation status that might have indicated a division-counting mechanism active in fate decisions was observed.

**Supplementary Figure S10.** Aggregate dimensions remain consistent after 6 days of differentiation. Particle analysis was performed using ImageJ (1.44i) on images captured at 10x magnification, which were calibrated, thresholded automatically, subjected to the binary Close function (iterations = 10, count = 4) to close internal holes, and segmented using the Watershed algorithm. An example image (**A**) shows close correspondence between input image and best-fit ellipses (red). Aggregates remain highly uniform (Feret’s diameter 73.8 +/− 13.7 μm) and symmetrical (Circularity 0.79 +/− 0.08) (N=351 for both measurements) (**B**). Approximating aggregates as uniform spheres of radius r, we can calculate the minimum free path (MFP) between aggregates, defined as the shortest path connecting the surfaces of two adjacent aggregates that does not pass through the microwell substrate (**C**). We first calculate the height (H) of the aggregate centre above the base of the microwell, and then determine MFP for a given well depth (WD) and pitch (P) trigonometrically. Using the calculated Feret’s diameter (**C, upper panel, middle sphere**) gives MFP_{200} = 179 μm in a 200 μm microwell, or MFP_{400} = 519 μm in a 400 μm microwell (**C, lower panel**). Repeating this calculation with aggregates one standard deviation below (**C, upper panel, left sphere**) or above (**C, upper panel, right sphere**) the average gives MFP_{200} = 152 μm and 208 μm and MFP_{400} = 488 μm and 551 μm respectively.

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