Level 3 — ProductionSystems Biology & Frontiers

Systems Biology & Frontiers

⏱ 45 minutes60 marksprintable — key stays hidden on paper

Chapter: 6.5 Systems Biology & Frontiers Level: 3 (Production — derivations, code-from-memory, explain-out-loud) Time limit: 45 minutes Total marks: 60

Instructions: Answer all questions. Show full reasoning. Where code is asked, write it from memory — pseudocode is acceptable if logic is correct. Where math is asked, derive from first principles.

Question 1 — Define & Contrast (8 marks)

(a) Define systems biology and explain what "holistic modeling" means, contrasting it explicitly with the reductionist approach. (4)

(b) State two distinct emergent properties that arise in biological systems and explain, for one of them, why it cannot be predicted from the individual components alone. (4)

Question 2 — Gene Regulatory Network Modeling (12 marks)

Consider a single gene whose product $p$ represses its own transcription (a negative autoregulation motif).

(a) Write down, from memory, an ordinary differential equation for the rate of change of protein concentration $p$ using a Hill function for repression, defining every symbol. (5)

(b) Derive the steady-state expression by setting $\frac{dp}{dt}=0$ , for the special case of Hill coefficient $n=1$ . Give $p_{ss}$ explicitly. (4)

(c) Explain in one or two sentences the functional advantage negative autoregulation confers on the network's dynamics. (3)

Question 3 — Metabolic Network / Flux Balance (12 marks)

(a) State the steady-state mass-balance assumption used in Flux Balance Analysis (FBA) and write it in matrix form, defining the stoichiometric matrix $S$ and flux vector $v$ . (4)

(b) For the toy network below, write the stoichiometric matrix for internal metabolites $A$ and $B$ :

$v_1:\ \varnothing \to A, \qquad v_2:\ A \to B, \qquad v_3:\ B \to \varnothing$

Then write the steady-state constraints and solve for the relationship between $v_1, v_2, v_3$ . (5)

(c) FBA requires an objective function in addition to constraints. Explain why, and give one biologically common choice. (3)

Question 4 — Single-Cell & Spatial Methods (10 marks)

(a) Describe, in ordered steps, the core workflow of droplet-based single-cell RNA sequencing (e.g. barcoding of individual cells). Name what the cell barcode and the UMI each accomplish. (6)

(b) State one biological question answerable by spatial transcriptomics but not by dissociated single-cell RNA-seq, and explain why. (4)

Question 5 — Multi-omics Integration & Emergent Analysis (10 marks)

(a) Name three distinct omics layers and, for each, state the molecular class it measures. (6)

(b) Explain one key statistical/computational challenge in integrating multiple omics datasets and one strategy to address it. (4)

Question 6 — Synthetic Genomes, Microbiome & Ethics (8 marks)

(a) Define a minimal cell and state one insight the JCVI-syn3.0 synthetic minimal genome project provided about gene essentiality. (4)

(b) Describe one systemic effect of the human gut microbiome on the host, then name one ethical or societal challenge raised by frontier biology (e.g. synthetic genomes or genome editing). (4)

Answer keyMark scheme & solutions

Question 1 (8 marks)

(a) [4]

Systems biology = the study of biological systems as integrated networks of interacting components (genes, proteins, metabolites), aiming to understand system-level behaviour rather than isolated parts. (2)
Holistic modeling = representing the whole system and its interactions/feedbacks simultaneously (e.g. via networks, ODEs), so properties emerging from interactions are captured. (1)
Contrast: reductionism studies parts in isolation and assumes the whole = sum of parts; holistic modeling recognizes interactions produce behaviour absent from any single part. (1)

(b) [4]

Two emergent properties (any two, 1 each): oscillations (e.g. circadian rhythm), homeostasis/robustness, bistability/switch behaviour, pattern formation, multicellular differentiation. (2)
Explanation for one (2): e.g. oscillations require feedback loops with delay between multiple components; a single molecule has no dynamic loop, so period/amplitude cannot be inferred from components alone — they arise only from the topology of interaction.

Question 2 (12 marks)

(a) [5] $\frac{dp}{dt} = \frac{\beta \, K^n}{K^n + p^n} - \gamma p$

$\beta$ = maximal production rate. (1)
$K$ = repression threshold (concentration giving half-max production). (1)
$n$ = Hill coefficient (cooperativity). (1)
$\gamma$ = degradation/dilution rate constant. (1)
Correct repressive Hill form (decreasing in $p$ ) + linear degradation term. (1)

(b) [4] Set $n=1$ and $\frac{dp}{dt}=0$ : $\frac{\beta K}{K + p_{ss}} = \gamma p_{ss}$ $\beta K = \gamma p_{ss}(K + p_{ss}) = \gamma K p_{ss} + \gamma p_{ss}^2$ $\gamma p_{ss}^2 + \gamma K p_{ss} - \beta K = 0$ Solve quadratic, take positive root: (2 for setup, 1 for algebra) $p_{ss} = \frac{-\gamma K + \sqrt{\gamma^2 K^2 + 4\gamma\beta K}}{2\gamma} = \frac{K}{2}\left(-1 + \sqrt{1 + \tfrac{4\beta}{\gamma K}}\right)$ (1 for correct positive root)

(c) [3] Negative autoregulation speeds up the response time to steady state and reduces cell-to-cell variability (noise)/increases robustness to fluctuations in production rate. (Any valid: faster response, noise reduction, robustness — 3 marks for a correct clearly-stated advantage with reason.)

Question 3 (12 marks)

(a) [4]

Steady-state assumption: internal metabolite concentrations do not change over the timescale considered, so net production = net consumption for each. (2)
Matrix form: $S \cdot v = 0$ , where $S$ (m×n) is the stoichiometric matrix (rows = metabolites, columns = reactions) and $v$ is the flux vector. (2)

(b) [5] Rows = metabolites {A, B}; columns = {v₁, v₂, v₃}: $S = \begin{pmatrix} +1 & -1 & 0 \\ 0 & +1 & -1 \end{pmatrix}$ (2 for correct signs) Constraints $Sv=0$ :

A: $v_1 - v_2 = 0$
B: $v_2 - v_3 = 0$ (2) Therefore $v_1 = v_2 = v_3$ (flux is equal through the linear pathway). (1)

(c) [3]

Constraints alone define a solution space (many feasible flux distributions), not a unique solution. (1.5)
An objective function is optimized (linear programming) to select one biologically meaningful solution; common choice: maximize biomass production rate (or ATP yield). (1.5)

Question 4 (10 marks)

(a) [6] Ordered workflow (≈1 each, up to 4):

Dissociate tissue into a single-cell suspension.
Encapsulate individual cells with barcoded beads in droplets (microfluidics).
Lyse cell; mRNA captured on bead oligos carrying barcodes.
Reverse-transcribe, pool, amplify, and sequence. (4)

Cell barcode: identical for all reads from one cell → assigns each transcript to its cell of origin. (1)
UMI (Unique Molecular Identifier): unique tag per original mRNA molecule → removes PCR amplification bias, enables true molecule counting. (1)

(b) [4]

Question: where within the tissue a cell type/gene is expressed / spatial neighbourhood relationships (e.g. tumour margin vs core, cortical layers). (2)
Why: single-cell RNA-seq requires dissociation, which destroys spatial/positional information; spatial transcriptomics preserves the tissue coordinates of each expression measurement. (2)

Question 5 (10 marks)

(a) [6] (2 each — layer + molecular class)

Genomics → DNA sequence/variants.
Transcriptomics → RNA / gene expression (mRNA).
Proteomics → proteins.
(Also acceptable) Metabolomics → metabolites; Epigenomics → DNA methylation/chromatin marks.

(b) [4]

Challenge (2): differing scales/units, heterogeneous noise, dimensionality (many features, few samples), missing data, or aligning features across layers (e.g. batch effects).
Strategy (2): dimensionality reduction / joint latent-factor models (e.g. MOFA), network-based integration, normalization + batch correction, or multi-view machine learning.

Question 6 (8 marks)

(a) [4]

Minimal cell = a cell containing only the smallest set of genes essential for self-replication/viability under defined lab conditions. (2)
JCVI-syn3.0 insight: ~473 genes; a substantial fraction (~30%) had unknown function yet were essential, showing our knowledge of core life processes is incomplete. (2)

(b) [4]

Systemic microbiome effect (2): e.g. training/modulating the immune system, producing short-chain fatty acids affecting metabolism, gut-brain axis signalling, or synthesizing vitamins.
Ethical/societal challenge (2): e.g. biosecurity/dual-use of synthetic genomes, germline genome editing consent/equity, data privacy of genomic data, or "playing God"/ecological release concerns.

[
  {"claim":"Q2b steady state p_ss for n=1 satisfies gamma*p^2 + gamma*K*p - beta*K = 0 and positive root equals (K/2)(-1+sqrt(1+4b/(gK)))",
   "code":"beta,gamma,K,p=symbols('beta gamma K p',positive=True); eq=Eq(beta*K/(K+p)-gamma*p,0); sols=solve(eq,p); pos=[s for s in sols if s.subs({beta:1,gamma:1,K:1})>0][0]; formula=(K/2)*(-1+sqrt(1+4*beta/(gamma*K))); result=simplify(pos-formula)==0"},
  {"claim":"Q3b steady state S*v=0 forces v1=v2=v3",
   "code":"v1,v2,v3=symbols('v1 v2 v3'); S=Matrix([[1,-1,0],[0,1,-1]]); v=Matrix([v1,v2,v3]); sol=solve(list(S*v),[v1,v2]); result=(sol[v1]==v3 and sol[v2]==v3)"},
  {"claim":"Q2b quadratic derivation: beta*K/(K+p)=gamma*p expands to gamma*p^2+gamma*K*p-beta*K=0",
   "code":"beta,gamma,K,p=symbols('beta gamma K p'); lhs=(beta*K/(K+p)-gamma*p)*(K+p); result=expand(lhs-(-(gamma*p**2+gamma*K*p-beta*K)))==0"}
]