Analysis of Subpopulation Emergence in Bacterial Cultures, a case Study for Model Based Clustering or Finite Mixture Models

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Analysis of Subpopulation Emergence in Bacterial Cultures, a case Study for Model Based Clustering or Finite Mixture Models Francisco J. Romero Campero http://www.cs.us.es/~fran fran@us.

1 Analysis of Subpopulation Emergence in Bacterial Cultures, a case Study for Model Based Clustering or Finite Mixture Models Francisco J. Romero Campero fran@us.es Dept. Computer Science Artificial Intelligence Universidad de Sevilla Pablo I. Nikel, Víctor de Lorenzo System Biology Program National Center for Biotechnology

2 Outline Relevance of Bacterial Systems. Pseudomonas putidas in the Biological Processing of Glycerol. Identification of Growth Patterns in Bacterial Cultures using Expectation-maximization algorithms Regulation of the Glycerol Metabolism in Pseudomonas putidas. 1/58

3 Outline Relevance of Bacterial Systems. Pseudomonas putidas in the Biological Processing of Glycerol. Identification of Growth Patterns in Bacterial Cultures using Expectation-maximization algorithms Regulation of the Glycerol Metabolism in Pseudomonas putidas. 2/58

4 Relevance of Bacteria in Biodiversity Microbian genomes are the biggest collection of genes in the biosphere. Microbian enzymatic pathways constitute the main set of enzymatic reactions on Earth. Microbian communities are essential in the maintenance and recycling of the living matter on Earth. 3/58

Relevance of Bacteria in Molecular Systems Biology Bacterial genomes are relatively small and easy to sequence. Bacterial gene regulation is relatively simple.

5 Relevance of Bacteria in Molecular Systems Biology Bacterial genomes are relatively small and easy to sequence. Bacterial gene regulation is relatively simple. Bacterial systems are the most studied systems constituting model organisms for the systems in higher order organisms. Bacterial gene regulation and enzymatic networks are well characterized. 4/58

6 Relevance of Bacteria in Biotechnology Biotechnology is the use of living organisms to develop products useful to human beings. Widely used in agriculture, farming, food production and medicine. Bacteria have a wide range of applications into biotechnology: Fermentation processes: brewing, baking, cheese, butter 5/58

7 Relevance of Bacteria in Biotechnology Biotechnology is the use of living organisms to develop products useful to human beings. Widely used in agriculture, farming, food production and medicine. Bacteria have a wide range of applications into biotechnology: Bioremediation: remove pollutants such as oil spills by biostimulation (facilitating the proliferation of bacteria). 6/58

8 Relevance of Bacteria in Biotechnology Biotechnology is the use of living organisms to develop products useful to human beings. Widely used in agriculture, farming, food production and medicine. Bacteria have a wide range of applications into biotechnology: Chemical manufacturing: 7/58

9 Biodiesel Production Biodiesel production uses the chemical reaction transesterification to convert vegetable fats and oils (triglycerides, esters containing three fatty acids) into biodisel and the byproduct glycerol. 8/58

vegetable fats and oils (triglycerides, esters

10 Biodiesel Production Biodiesel production uses the chemical reaction transesterification to convert vegetable fats and oils (triglycerides, esters containing three fatty acids) into biodisel and the byproduct glycerol. 9/58

11 Outline Relevance of Bacterial Systems. Pseudomonas putidas in the Biological Processing of Glycerol. Identification of Growth Patterns in Bacterial Cultures using Expectation-maximization algorithms Regulation of the Glycerol Metabolism in Pseudomonas putidas. 10/58

12 Pseudomonas putidas in Industrial Biotechnology Pseudomonas putidas are gram-negative bacteria discovered decades ago. They are well known to be metabolic versatile well-performing xenobiotic degraders. 11/58

13 Pseudomonas putida in industrial Biotechnology P. putidas show features that make them specially suitable for industrial biotechnology: genetically accessible, fast growth with simple nutrient demand, high biomass yield its genome was fully sequenced in 2002 and genome-wide pathway modelling is available since 2008 a very high robustness against extreme environmental conditions such as high temperature, extreme ph or the presence of toxins or inhibiting solvents succesfully used for the production of bio-based polymers and a broad range of chemicals 12/58

14 Pseudomonas putida in industrial Biotechnology The use of P. putida in industrial biotechnology is strongly driven by systems biotechnology, integrating systems metabolic engineering approaches with novel concepts from bioprocess engineering, including novel reactor designs and renewable feedstocks 13/58

putidas, intermediates of the tricarboxylic acid (TCA) cycle, such as

15 Glycerol Metabolism in P. putidas Glucose is not the preferred carbon substrate for P. putidas, intermediates of the tricarboxylic acid (TCA) cycle, such as succinate, are preferred. P. putidas are capable to use raw glycerol, a technical by-product from the biodiesel industry 14/58

16 Glycerol Metabolism in P. putidas Glycerol Media Cytosol Cell Membrane 15/58

17 Glycerol Metabolism in P. putidas Glycerol Media Glycolysis Cytosol Cell Membrane 16/58

18 Glycerol Metabolism in P. putidas Glycerol Glycerol GlpF Media Glycolysis Cytosol Cell Membrane 17/58

19 Glycerol Metabolism in P. putidas ATP Glycerol ADP Glycerol Glycerol-3P GlpF GlpK Media Glycolysis Cytosol Cell Membrane 18/58

20 Glycerol Metabolism in P. putidas ATP Glycerol ADP Glycerol NAD+ NADH Dihydroacetone phosphate Glycerol-3P GlpF GlpK Media GlpD Glycolysis Cytosol Cell Membrane 19/58

21 Glycerol Metabolism in P. putidas ATP Glycerol ADP Glycerol NAD+ NADH Dihydroacetone phosphate Glycerol-3P Glyceraldehyde-3P GlpF GlpK Media GlpD Tpi Glycolysis Cytosol Cell Membrane 20/58

22 Glycerol Metabolism in P. putidas ATP Glycerol ADP Glycerol NAD+ NADH Dihydroacetone phosphate Glycerol-3P Glyceraldehyde-3P GlpF GlpK Media GlpD Tpi Glycolysis Cytosol Cell Membrane 21/58

23 Growth Patterns of P. putida Single Cell Cultures in Glycerol Media Multi-well plates were inoculated with a highly diluted culture (roughly corresponding to 1 cell per well). We inoculated 1000 wells. 10ul 5 x x 108 cells/ml =142 cells / ml cells / ml 0.01=1.42 cells 22/58

24 Growth Patterns of P. putida Single Cell Cultures in Glycerol Media The time associated with the onset of the exponential phase was recorded as an indication of the metabolic state of cells Similar to the case of sensory transcriptional networks, we define the metabolic response time of a cell population growing in a well as the time necessary to reach the mid-exponential phase. 23/58

25 The characteristic time to attain mid-exponential phase depends on the culture medium 24/58

26 Growth Patterns of P. putida Single Cell Cultures in Glycerol Media If we assume that: the number of cells per well is proportional to its volume, the probability of having two cells in an infinitesimal volume is negligible the probability of inoculating a given number of cells is independent from the particular well The distribution of cells per well follows a Poisson probability distribution. 25/58

27 Growth Patterns of P. putida Single Cell Cultures in Glycerol Media 26/58

28 The apparent multi-modality in glycerol cultures is not due to the stochastic number of cells in each well Using the Poisson probability distribution we generated 1000 random numbers representing a common scenario in the distribution of cells over the 1000 wells used in our analysis. For each well containing at least one cell we modeled the population growth, number of cell per generation Nt, using the stochastic discrete logistic equation (Fulford et al., 1997) assuming the same average growth rate, rt, in every well: { N0 initial number of cells Nt N t +1= N t + r t 1 K ( ) with r t U [ 0.6,1 ] K = /58

The apparent multi-modality in glycerol cultures is not due to the stochastic number of cells in each well In spite of the variation of the number of cells inoculated in each well the modeled

29 The apparent multi-modality in glycerol cultures is not due to the stochastic number of cells in each well In spite of the variation of the number of cells inoculated in each well the modeled distribution of the metabolic response time follows a unimodal normal distribution. Therefore, our statistical analysis provides evidence against the possibility that the bimodal behaviour of our cell culture is due to the variation in the number of cells per well. 28/58

30 The apparent multi-modality in glycerol cultures is not due to the stochastic number of cells in each well The distribution of the metabolic response time in an isogenic culture of cells was studied when grown with different carbon sources. When grown in LB or glucose the distribution of the metabolic response time was clearly unimodal. Nevertheless, as it can be seen to the right when grown in glycerol a multimodal distribution is apparent. 29/58

31 The characteristic time to attain mid-exponential phase depends on the culture medium 30/58

32 Outline Relevance of Bacterial Systems. Pseudomonas putidas in the Biological Processing of Glycerol. Identification of Growth Patterns in Bacterial Cultures using Expectationmaximization algorithms Regulation of the Glycerol Metabolism in Pseudomonas putidas. 31/58

33 Identification of Growth Patterns in Glycerol Cultures of P. putidas Clustering techniques. Population of individuals may often be divided into groups. Unsupervised clustering: data analysis to discern and describe subgroups of individuals when there is no observable variable that directly classifies them. 32/58

34 Identification of Growth Patterns in Glycerol Cultures of P. putidas Model based clustering or finite mixture models: inference of descriptive models in terms of probability distributions of the different subgroups in the population of individuals. This clustering technique provides a description of the structure of the population rather than simply assigning individuals to subgroups. 33/58

35 Finite Mixture Models Main assumption: the subgroups or subpopulations are distributed according to a particular parametric distribution (often univariate or multi-variate normal distribution) Assume we have a random sample of size n : x 1, x 2,..., x n from a finite mixture of m > 1 normal distributions (components or clusters). The density function of this distribution is then: m g θ ( x i )= j =1 λ j ϕ j ( x i ;μ j, σ j ) 2 θ=( λ 1,..., λ m,μ 1, σ 1,..., μ m,σ m ) 34/58

36 Finite Mixture Models Main assumption: the subgroups or subpopulations are distributed according to a particular parametric distribution (often univariate or multi-variate normal distribution) Assume we have a random sample of size n : x 1, x 2,..., x n from a finite mixture of m > 1 normal distributions (components or clusters). The density function of this distribution is then: m g θ ( x i )= j =1 λ j ϕ j ( x i ;μ j, σ ) 2 j θ=( λ 1,..., λ m,μ 1, σ 1,..., μ m,σ m ) [ 1 x μ j exp σj 2 2 ϕ j ( x ; μ j, σ j)= σ j 2 π ( )] 2 35/58

37 Expectation-Maximization Algorithm for Finite Mixture Models The problem can be reduced to the estimation of the parameters m and λ1,...,λm,μ1,, μm, σ1,, σm. The Expectation-Maximization (EM) Algorithm represents this problem as a maximum likelihood estimation (MLE) assuming independence and identically distributed (iid) observations: x 1, x 2,..., x n n i =1 g θ ( x i ) L( x joint probability of observing x 1,..., x n n 1,..., x n ) (λ 1,..., λ m,μ 1,...μ m, σ1,..., σ m )= i=1 log g θ ( x i ) n ( λ 1,..., λ m, μ 1,... μ m, σ 1,..., σ m )= argmax i =1 log g θ ( x i ) 36/58

38 Expectation-Maximization Algorithm for Finite Mixture Models Considering x1,, xn as incomplete data facilitates the calculation of λ1,...,λm, μ1,, μm, σ1,, σm The associated hidden data that makes xi, for i=1,...,n complete consists of zi1,, zim where: z ij = { 1 0 if x i component j else The density function of this complete data is then: m h θ ( x i, z i1,..., z ℑ )= j=1 z ij λ j ϕ j ( x i ;μ j, σ 2j ) θ=(λ 1,..., λ m,μ 1, σ1,...,μ m, σ m) 37/58

39 Expectation-Maximization Algorithm for Finite Mixture Models EM algorithm seeks to solve this problem or at least find a local optimum by iteratively applying two steps called E-step and Mstep. Initialization: Given the sample x1,, xn assign initial values to the parameters: λ1 =λ λ m =λ m μ1 =μ μ n =μ n σ1 =σ σ n =σ n 38/58

40 Expectation-Maximization Algorithm for Finite Mixture Models Iterative process until convergence or for a given number of steps: E-step: Given the sample x1,, xn and estimates compute the following expectation that in the case of normal distributions can be determined analytically: t E [ log (h θ ( X, Z )) ; X,θ ] M-step: Using the expectation computed in the E-step associated to the hidden data Z perform a MLE to determine new estimates for the paramters θ: θ t+ 1 =argmax θ log (h θ ( X, Z )) 39/58

41 Two or Three Subpopulations are Apparent 40/58

42 Two or Three Subpopulations are Apparent 41/58

43 Two or Three Subpopulations are Apparent 42/58

44 Three Subpopulations In this case, the EM algorithm partitions the population of cells into three different subpopulations exhibiting distinctive metabolic response times: Subpopulation 1 (red) comprises 6% of the entire population and exhibits an averagemetabolic response time of 19.1 hours with a standard deviation of 0.3 hours. Supopulation 2 (green) comprise 81% of the entire population and exhibits a metabolic response time of 24 hours with a standard deviation of 1.8 hours. Subpopulation 3 (blue) comprises 13% of the entire population and exhibits a metabolic response time of 29.7 hours with a standard deviation of 0.8 hours. 43/58

45 Two Subpopulations In this case, the EM algorithm partitions the population of cells into two different subpopulations exhibiting distinctive metabolic response times: Subpopulation 1 (red) comprises 89% of the entire population and exhibits an average metabolic response time of 23.7 hours with a standard deviation of 2.2 hours. Supopulation 2 (green) comprise 11% of the entire population and exhibits a metabolic response time of 29.8 hours with a standard deviation of 0.7 hours. 44/58

46 Model Selection In order to discriminate between these scenarios we performed several model selection methods, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Integrated Completed Likelihood (ICL) and Consistent Akaike Information Criterion (CAIC). The most plausible scenario is the one with two subpopulations. All methods gave a very poor score to the scenario with one single population. Only BIC, ICL were not able to discriminate between two and three subpopulations. 45/58

47 Outline Relevance of Bacterial Systems. Pseudomonas putidas in the Biological Processing of Glycerol. Identification of Growth Patterns in Bacterial Cultures using Expectation-maximization algorithms Regulation of the Glycerol Metabolism in Pseudomonas putidas. 46/58

48 Glycerol Metabolism Regulation in P. putidas ATP Glycerol ADP Glycerol NAD+ NADH Dihydroacetone phosphate Glycerol-3P Glyceraldehyde-3P GlpF GlpD GlpK Tpi Glycolysis Media glpd Cell Membrane glpr glpk glpf Cytosol 47/58

49 Glycerol Metabolism Regulation in P. putidas: No Glycerol GlpF GlpK Media Tpi GlpR glpd Cell Membrane GlpD glpr glpk glpf Cytosol 48/58

50 Glycerol Metabolism Regulation in P. putidas: No Glycerol GlpF Tpi GlpK Media GlpR glpd Cell Membrane glpr glpk glpf Cytosol 49/58

51 Glycerol Metabolism Regulation in P. putidas: No Glycerol GlpF Tpi GlpK Media GlpR glpd Cell Membrane glpr glpk glpf Cytosol 50/58

52 Glycerol Metabolism Regulation in P. putidas: With Glycerol GlpF Tpi GlpK Media GlpR glpd Cell Membrane glpr glpk glpf Cytosol 51/58

53 Glycerol Metabolism Regulation in P. putidas: With Glycerol ATP ADP Glycerol Glycerol-3P GlpF Tpi GlpK Media GlpR glpd Cell Membrane glpr glpk glpf Cytosol 52/58

54 Glycerol Metabolism Regulation in P. putidas: With Glycerol ATP ADP Glycerol Glycerol-3P GlpF Tpi GlpK Media GlpR glpd Cell Membrane glpr glpk glpf Cytosol 53/58

55 Glycerol Metabolism Regulation in P. putidas: With Glycerol ATP ADP Glycerol Glycerol-3P GlpF Tpi GlpK Media GlpR glpd Cell Membrane glpr glpk glpf Cytosol 54/58

56 Glycerol Metabolism Regulation in P. putidas: With Glycerol ATP ADP Glycerol Glycerol-3P GlpF Tpi GlpK Media GlpR glpd Cell Membrane glpr glpk glpf Cytosol 55/58

57 Glycerol Metabolism Regulation in P. putidas: With Glycerol ATP ADP Glycerol Glycerol-3P GlpF Tpi GlpK Media GlpD GlpR glpd Cell Membrane glpr glpk glpf Cytosol 56/58

58 Glycerol Metabolism Regulation in P. putidas: With Glycerol ATP ADP Glycerol NADH Dihydroacetone phosphate Glycerol-3P Glyceraldehyde-3P GlpF GlpK Media GlpD Tpi Glycolysis GlpD GlpR glpd Cell Membrane glpr glpk glpf Cytosol 57/58

59 Conclusions Glycerol is a problematic byproduct in the production of biodiesel from triglycerides. Pseudomonas putidas are good candidates to produce biomass from glycerol being a good example of the relevance of bacterial systems in industrial biotechnology. Expectation-maximization algorithms together with model selection techniques show that wild type Pseudomonas putidas grow suboptimally in glycerol forming different subpopulations. Genetic engineering is necessary to optimise the use of Pseudomonas putidas (possibly developing glpr mutants). 58/58

NOTES: Ch 9, part & Fermentation & Regulation of Cellular Respiration

NOTES: Ch 9, part & Fermentation & Regulation of Cellular Respiration NOTES: Ch 9, part 4-9.5 & 9.6 - Fermentation & Regulation of Cellular Respiration 9.5 - Fermentation enables some cells to produce ATP without the use of oxygen Cellular respiration requires O 2 to produce